52.289 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.145 * * * [progress]: [2/2] Setting up program.
0.149 * [progress]: [Phase 2 of 3] Improving.
0.149 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.149 * * [simplify]: iteration 0: 13 enodes
0.152 * * [simplify]: iteration 1: 29 enodes
0.156 * * [simplify]: iteration 2: 59 enodes
0.166 * * [simplify]: iteration 3: 120 enodes
0.245 * * [simplify]: iteration 4: 328 enodes
0.415 * * [simplify]: iteration 5: 1541 enodes
0.956 * * [simplify]: iteration complete: 5000 enodes
0.956 * * [simplify]: Extracting #0: cost 1 inf + 0
0.956 * * [simplify]: Extracting #1: cost 169 inf + 0
0.960 * * [simplify]: Extracting #2: cost 1666 inf + 1
0.965 * * [simplify]: Extracting #3: cost 2154 inf + 127
0.978 * * [simplify]: Extracting #4: cost 2277 inf + 3690
1.020 * * [simplify]: Extracting #5: cost 1696 inf + 217499
1.162 * * [simplify]: Extracting #6: cost 193 inf + 1045012
1.385 * * [simplify]: Extracting #7: cost 0 inf + 1202666
1.672 * * [simplify]: Extracting #8: cost 0 inf + 1202415
1.910 * [simplify]: Simplified to:
  (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
1.911 * * [progress]: iteration 1 / 4
1.911 * * * [progress]: picking best candidate
1.919 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
1.919 * * * [progress]: localizing error
1.953 * * * [progress]: generating rewritten candidates
1.953 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
1.958 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
1.975 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
2.034 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
2.078 * * * [progress]: generating series expansions
2.078 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
2.078 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
2.078 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
2.078 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
2.078 * [taylor]: Taking taylor expansion of 1.0 in k
2.078 * [backup-simplify]: Simplify 1.0 into 1.0
2.078 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.078 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.078 * [taylor]: Taking taylor expansion of k in k
2.078 * [backup-simplify]: Simplify 0 into 0
2.078 * [backup-simplify]: Simplify 1 into 1
2.079 * [backup-simplify]: Simplify (/ 1 1) into 1
2.079 * [backup-simplify]: Simplify (sqrt 0) into 0
2.081 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.081 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
2.081 * [taylor]: Taking taylor expansion of 1.0 in k
2.081 * [backup-simplify]: Simplify 1.0 into 1.0
2.081 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.081 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.081 * [taylor]: Taking taylor expansion of k in k
2.081 * [backup-simplify]: Simplify 0 into 0
2.082 * [backup-simplify]: Simplify 1 into 1
2.082 * [backup-simplify]: Simplify (/ 1 1) into 1
2.082 * [backup-simplify]: Simplify (sqrt 0) into 0
2.084 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.084 * [backup-simplify]: Simplify (* 1.0 0) into 0
2.084 * [backup-simplify]: Simplify 0 into 0
2.086 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
2.086 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.087 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.091 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.093 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
2.093 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.094 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.098 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.101 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
2.101 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.107 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
2.107 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
2.108 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
2.108 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
2.108 * [taylor]: Taking taylor expansion of 1.0 in k
2.108 * [backup-simplify]: Simplify 1.0 into 1.0
2.108 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.108 * [taylor]: Taking taylor expansion of k in k
2.108 * [backup-simplify]: Simplify 0 into 0
2.108 * [backup-simplify]: Simplify 1 into 1
2.108 * [backup-simplify]: Simplify (sqrt 0) into 0
2.110 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.110 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
2.110 * [taylor]: Taking taylor expansion of 1.0 in k
2.110 * [backup-simplify]: Simplify 1.0 into 1.0
2.110 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.110 * [taylor]: Taking taylor expansion of k in k
2.110 * [backup-simplify]: Simplify 0 into 0
2.110 * [backup-simplify]: Simplify 1 into 1
2.110 * [backup-simplify]: Simplify (sqrt 0) into 0
2.112 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.112 * [backup-simplify]: Simplify (* 1.0 0) into 0
2.112 * [backup-simplify]: Simplify 0 into 0
2.114 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
2.114 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.118 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.120 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
2.120 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.125 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.127 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
2.127 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.129 * [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))))))))
2.129 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
2.129 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
2.129 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
2.129 * [taylor]: Taking taylor expansion of 1.0 in k
2.129 * [backup-simplify]: Simplify 1.0 into 1.0
2.129 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.129 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.129 * [taylor]: Taking taylor expansion of -1 in k
2.129 * [backup-simplify]: Simplify -1 into -1
2.129 * [taylor]: Taking taylor expansion of k in k
2.130 * [backup-simplify]: Simplify 0 into 0
2.130 * [backup-simplify]: Simplify 1 into 1
2.130 * [backup-simplify]: Simplify (/ -1 1) into -1
2.130 * [backup-simplify]: Simplify (sqrt 0) into 0
2.132 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.133 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
2.133 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
2.133 * [taylor]: Taking taylor expansion of 1.0 in k
2.133 * [backup-simplify]: Simplify 1.0 into 1.0
2.133 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.133 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.133 * [taylor]: Taking taylor expansion of -1 in k
2.133 * [backup-simplify]: Simplify -1 into -1
2.133 * [taylor]: Taking taylor expansion of k in k
2.133 * [backup-simplify]: Simplify 0 into 0
2.133 * [backup-simplify]: Simplify 1 into 1
2.133 * [backup-simplify]: Simplify (/ -1 1) into -1
2.134 * [backup-simplify]: Simplify (sqrt 0) into 0
2.135 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.136 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
2.136 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.140 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.142 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
2.143 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.148 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.153 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
2.153 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
2.154 * [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)))))
2.154 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
2.155 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
2.155 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
2.155 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.155 * [taylor]: Taking taylor expansion of 2.0 in n
2.155 * [backup-simplify]: Simplify 2.0 into 2.0
2.155 * [taylor]: Taking taylor expansion of (* n PI) in n
2.155 * [taylor]: Taking taylor expansion of n in n
2.155 * [backup-simplify]: Simplify 0 into 0
2.155 * [backup-simplify]: Simplify 1 into 1
2.155 * [taylor]: Taking taylor expansion of PI in n
2.155 * [backup-simplify]: Simplify PI into PI
2.155 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.155 * [taylor]: Taking taylor expansion of 2.0 in n
2.155 * [backup-simplify]: Simplify 2.0 into 2.0
2.155 * [taylor]: Taking taylor expansion of (* n PI) in n
2.155 * [taylor]: Taking taylor expansion of n in n
2.156 * [backup-simplify]: Simplify 0 into 0
2.156 * [backup-simplify]: Simplify 1 into 1
2.156 * [taylor]: Taking taylor expansion of PI in n
2.156 * [backup-simplify]: Simplify PI into PI
2.156 * [backup-simplify]: Simplify (* 0 PI) into 0
2.157 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.157 * [backup-simplify]: Simplify 0 into 0
2.159 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.160 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.161 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.162 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.163 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
2.163 * [backup-simplify]: Simplify 0 into 0
2.164 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.166 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.166 * [backup-simplify]: Simplify 0 into 0
2.167 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.169 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.169 * [backup-simplify]: Simplify 0 into 0
2.171 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.173 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
2.173 * [backup-simplify]: Simplify 0 into 0
2.175 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.177 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
2.177 * [backup-simplify]: Simplify 0 into 0
2.179 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
2.181 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
2.181 * [backup-simplify]: Simplify 0 into 0
2.182 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
2.182 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
2.182 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
2.182 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.182 * [taylor]: Taking taylor expansion of 2.0 in n
2.183 * [backup-simplify]: Simplify 2.0 into 2.0
2.183 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.183 * [taylor]: Taking taylor expansion of PI in n
2.183 * [backup-simplify]: Simplify PI into PI
2.183 * [taylor]: Taking taylor expansion of n in n
2.183 * [backup-simplify]: Simplify 0 into 0
2.183 * [backup-simplify]: Simplify 1 into 1
2.183 * [backup-simplify]: Simplify (/ PI 1) into PI
2.183 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.183 * [taylor]: Taking taylor expansion of 2.0 in n
2.183 * [backup-simplify]: Simplify 2.0 into 2.0
2.183 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.183 * [taylor]: Taking taylor expansion of PI in n
2.183 * [backup-simplify]: Simplify PI into PI
2.183 * [taylor]: Taking taylor expansion of n in n
2.183 * [backup-simplify]: Simplify 0 into 0
2.183 * [backup-simplify]: Simplify 1 into 1
2.184 * [backup-simplify]: Simplify (/ PI 1) into PI
2.184 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.185 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.186 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.187 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.187 * [backup-simplify]: Simplify 0 into 0
2.188 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.189 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.189 * [backup-simplify]: Simplify 0 into 0
2.190 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.191 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.191 * [backup-simplify]: Simplify 0 into 0
2.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.194 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.194 * [backup-simplify]: Simplify 0 into 0
2.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.197 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.197 * [backup-simplify]: Simplify 0 into 0
2.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.200 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.200 * [backup-simplify]: Simplify 0 into 0
2.201 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
2.201 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
2.201 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
2.201 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.201 * [taylor]: Taking taylor expansion of -2.0 in n
2.201 * [backup-simplify]: Simplify -2.0 into -2.0
2.201 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.201 * [taylor]: Taking taylor expansion of PI in n
2.201 * [backup-simplify]: Simplify PI into PI
2.201 * [taylor]: Taking taylor expansion of n in n
2.202 * [backup-simplify]: Simplify 0 into 0
2.202 * [backup-simplify]: Simplify 1 into 1
2.202 * [backup-simplify]: Simplify (/ PI 1) into PI
2.202 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.202 * [taylor]: Taking taylor expansion of -2.0 in n
2.202 * [backup-simplify]: Simplify -2.0 into -2.0
2.202 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.202 * [taylor]: Taking taylor expansion of PI in n
2.202 * [backup-simplify]: Simplify PI into PI
2.202 * [taylor]: Taking taylor expansion of n in n
2.202 * [backup-simplify]: Simplify 0 into 0
2.202 * [backup-simplify]: Simplify 1 into 1
2.203 * [backup-simplify]: Simplify (/ PI 1) into PI
2.203 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.204 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.206 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
2.206 * [backup-simplify]: Simplify 0 into 0
2.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.208 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.208 * [backup-simplify]: Simplify 0 into 0
2.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.210 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.210 * [backup-simplify]: Simplify 0 into 0
2.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.213 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.213 * [backup-simplify]: Simplify 0 into 0
2.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.216 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.216 * [backup-simplify]: Simplify 0 into 0
2.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.219 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.219 * [backup-simplify]: Simplify 0 into 0
2.220 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
2.220 * * * * [progress]: [ 3 / 4 ] generating series at (2)
2.221 * [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))))
2.221 * [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
2.221 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
2.221 * [taylor]: Taking taylor expansion of 1.0 in n
2.221 * [backup-simplify]: Simplify 1.0 into 1.0
2.221 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
2.221 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
2.221 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
2.221 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
2.221 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
2.221 * [taylor]: Taking taylor expansion of 0.5 in n
2.221 * [backup-simplify]: Simplify 0.5 into 0.5
2.221 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
2.221 * [taylor]: Taking taylor expansion of 1.0 in n
2.221 * [backup-simplify]: Simplify 1.0 into 1.0
2.221 * [taylor]: Taking taylor expansion of k in n
2.221 * [backup-simplify]: Simplify k into k
2.221 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.222 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.222 * [taylor]: Taking taylor expansion of 2.0 in n
2.222 * [backup-simplify]: Simplify 2.0 into 2.0
2.222 * [taylor]: Taking taylor expansion of (* n PI) in n
2.222 * [taylor]: Taking taylor expansion of n in n
2.222 * [backup-simplify]: Simplify 0 into 0
2.222 * [backup-simplify]: Simplify 1 into 1
2.222 * [taylor]: Taking taylor expansion of PI in n
2.222 * [backup-simplify]: Simplify PI into PI
2.222 * [backup-simplify]: Simplify (* 0 PI) into 0
2.223 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.224 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.226 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.228 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.228 * [backup-simplify]: Simplify (- k) into (- k)
2.228 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
2.228 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
2.229 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.231 * [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))))
2.232 * [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)))))
2.232 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.232 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.232 * [taylor]: Taking taylor expansion of k in n
2.232 * [backup-simplify]: Simplify k into k
2.232 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.232 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.233 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.233 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
2.233 * [taylor]: Taking taylor expansion of 1.0 in k
2.233 * [backup-simplify]: Simplify 1.0 into 1.0
2.233 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
2.233 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
2.233 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
2.233 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
2.233 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
2.233 * [taylor]: Taking taylor expansion of 0.5 in k
2.233 * [backup-simplify]: Simplify 0.5 into 0.5
2.233 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
2.233 * [taylor]: Taking taylor expansion of 1.0 in k
2.233 * [backup-simplify]: Simplify 1.0 into 1.0
2.233 * [taylor]: Taking taylor expansion of k in k
2.233 * [backup-simplify]: Simplify 0 into 0
2.233 * [backup-simplify]: Simplify 1 into 1
2.233 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
2.233 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
2.233 * [taylor]: Taking taylor expansion of 2.0 in k
2.233 * [backup-simplify]: Simplify 2.0 into 2.0
2.233 * [taylor]: Taking taylor expansion of (* n PI) in k
2.233 * [taylor]: Taking taylor expansion of n in k
2.233 * [backup-simplify]: Simplify n into n
2.233 * [taylor]: Taking taylor expansion of PI in k
2.233 * [backup-simplify]: Simplify PI into PI
2.233 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.234 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
2.234 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
2.234 * [backup-simplify]: Simplify (- 0) into 0
2.235 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
2.235 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
2.235 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
2.235 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
2.235 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.235 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.235 * [taylor]: Taking taylor expansion of k in k
2.235 * [backup-simplify]: Simplify 0 into 0
2.236 * [backup-simplify]: Simplify 1 into 1
2.236 * [backup-simplify]: Simplify (/ 1 1) into 1
2.236 * [backup-simplify]: Simplify (sqrt 0) into 0
2.238 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.238 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
2.238 * [taylor]: Taking taylor expansion of 1.0 in k
2.238 * [backup-simplify]: Simplify 1.0 into 1.0
2.238 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
2.238 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
2.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
2.238 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
2.238 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
2.238 * [taylor]: Taking taylor expansion of 0.5 in k
2.238 * [backup-simplify]: Simplify 0.5 into 0.5
2.238 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
2.238 * [taylor]: Taking taylor expansion of 1.0 in k
2.238 * [backup-simplify]: Simplify 1.0 into 1.0
2.238 * [taylor]: Taking taylor expansion of k in k
2.238 * [backup-simplify]: Simplify 0 into 0
2.238 * [backup-simplify]: Simplify 1 into 1
2.238 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
2.238 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
2.238 * [taylor]: Taking taylor expansion of 2.0 in k
2.238 * [backup-simplify]: Simplify 2.0 into 2.0
2.238 * [taylor]: Taking taylor expansion of (* n PI) in k
2.239 * [taylor]: Taking taylor expansion of n in k
2.239 * [backup-simplify]: Simplify n into n
2.239 * [taylor]: Taking taylor expansion of PI in k
2.239 * [backup-simplify]: Simplify PI into PI
2.239 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.239 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
2.239 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
2.239 * [backup-simplify]: Simplify (- 0) into 0
2.240 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
2.240 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
2.240 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
2.241 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
2.241 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.241 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.241 * [taylor]: Taking taylor expansion of k in k
2.241 * [backup-simplify]: Simplify 0 into 0
2.241 * [backup-simplify]: Simplify 1 into 1
2.241 * [backup-simplify]: Simplify (/ 1 1) into 1
2.241 * [backup-simplify]: Simplify (sqrt 0) into 0
2.243 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.243 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0
2.244 * [backup-simplify]: Simplify (* 1.0 0) into 0
2.244 * [taylor]: Taking taylor expansion of 0 in n
2.244 * [backup-simplify]: Simplify 0 into 0
2.244 * [backup-simplify]: Simplify 0 into 0
2.244 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
2.245 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
2.246 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
2.246 * [backup-simplify]: Simplify (- 1) into -1
2.247 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.248 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
2.249 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
2.250 * [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)))))
2.252 * [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)))
2.254 * [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)))
2.254 * [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
2.254 * [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
2.254 * [taylor]: Taking taylor expansion of +nan.0 in n
2.254 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.254 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.254 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.254 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.254 * [taylor]: Taking taylor expansion of 0.5 in n
2.254 * [backup-simplify]: Simplify 0.5 into 0.5
2.254 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.254 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.254 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.254 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.254 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.254 * [taylor]: Taking taylor expansion of 1.0 in n
2.254 * [backup-simplify]: Simplify 1.0 into 1.0
2.254 * [taylor]: Taking taylor expansion of (log PI) in n
2.254 * [taylor]: Taking taylor expansion of PI in n
2.254 * [backup-simplify]: Simplify PI into PI
2.255 * [backup-simplify]: Simplify (log PI) into (log PI)
2.256 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.257 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.257 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.257 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.257 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.257 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.257 * [taylor]: Taking taylor expansion of 1.0 in n
2.257 * [backup-simplify]: Simplify 1.0 into 1.0
2.257 * [taylor]: Taking taylor expansion of (log n) in n
2.257 * [taylor]: Taking taylor expansion of n in n
2.257 * [backup-simplify]: Simplify 0 into 0
2.257 * [backup-simplify]: Simplify 1 into 1
2.257 * [backup-simplify]: Simplify (log 1) into 0
2.258 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.258 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.258 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.258 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.258 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.258 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.258 * [taylor]: Taking taylor expansion of 1.0 in n
2.258 * [backup-simplify]: Simplify 1.0 into 1.0
2.258 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.258 * [taylor]: Taking taylor expansion of 2.0 in n
2.258 * [backup-simplify]: Simplify 2.0 into 2.0
2.258 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.259 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.262 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.263 * [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)
2.264 * [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)
2.264 * [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))
2.266 * [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)))
2.267 * [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)
2.268 * [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))
2.268 * [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)))
2.269 * [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)))
2.269 * [backup-simplify]: Simplify 0 into 0
2.270 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.272 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.272 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
2.273 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
2.274 * [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
2.274 * [backup-simplify]: Simplify (- 0) into 0
2.275 * [backup-simplify]: Simplify (+ 0 0) into 0
2.275 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
2.276 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
2.277 * [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)))
2.279 * [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)))))
2.282 * [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)))))
2.282 * [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
2.282 * [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
2.282 * [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
2.282 * [taylor]: Taking taylor expansion of +nan.0 in n
2.282 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.282 * [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
2.282 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.282 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.282 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.282 * [taylor]: Taking taylor expansion of 0.5 in n
2.282 * [backup-simplify]: Simplify 0.5 into 0.5
2.282 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.282 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.282 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.282 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.282 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.282 * [taylor]: Taking taylor expansion of 1.0 in n
2.282 * [backup-simplify]: Simplify 1.0 into 1.0
2.282 * [taylor]: Taking taylor expansion of (log PI) in n
2.282 * [taylor]: Taking taylor expansion of PI in n
2.282 * [backup-simplify]: Simplify PI into PI
2.283 * [backup-simplify]: Simplify (log PI) into (log PI)
2.283 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.285 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.285 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.285 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.285 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.285 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.285 * [taylor]: Taking taylor expansion of 1.0 in n
2.285 * [backup-simplify]: Simplify 1.0 into 1.0
2.285 * [taylor]: Taking taylor expansion of (log n) in n
2.285 * [taylor]: Taking taylor expansion of n in n
2.285 * [backup-simplify]: Simplify 0 into 0
2.285 * [backup-simplify]: Simplify 1 into 1
2.286 * [backup-simplify]: Simplify (log 1) into 0
2.286 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.286 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.286 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.286 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.286 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.286 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.286 * [taylor]: Taking taylor expansion of 1.0 in n
2.286 * [backup-simplify]: Simplify 1.0 into 1.0
2.286 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.286 * [taylor]: Taking taylor expansion of 2.0 in n
2.287 * [backup-simplify]: Simplify 2.0 into 2.0
2.287 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.288 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.289 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.290 * [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)
2.291 * [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)
2.292 * [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))
2.293 * [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)))
2.294 * [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)
2.294 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.294 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.294 * [taylor]: Taking taylor expansion of 2.0 in n
2.294 * [backup-simplify]: Simplify 2.0 into 2.0
2.294 * [taylor]: Taking taylor expansion of (* n PI) in n
2.294 * [taylor]: Taking taylor expansion of n in n
2.294 * [backup-simplify]: Simplify 0 into 0
2.294 * [backup-simplify]: Simplify 1 into 1
2.294 * [taylor]: Taking taylor expansion of PI in n
2.294 * [backup-simplify]: Simplify PI into PI
2.294 * [backup-simplify]: Simplify (* 0 PI) into 0
2.295 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.296 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.297 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.297 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.297 * [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
2.297 * [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
2.297 * [taylor]: Taking taylor expansion of +nan.0 in n
2.297 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.297 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.297 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.297 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.297 * [taylor]: Taking taylor expansion of 0.5 in n
2.297 * [backup-simplify]: Simplify 0.5 into 0.5
2.297 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.297 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.297 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.297 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.297 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.297 * [taylor]: Taking taylor expansion of 1.0 in n
2.298 * [backup-simplify]: Simplify 1.0 into 1.0
2.298 * [taylor]: Taking taylor expansion of (log PI) in n
2.298 * [taylor]: Taking taylor expansion of PI in n
2.298 * [backup-simplify]: Simplify PI into PI
2.298 * [backup-simplify]: Simplify (log PI) into (log PI)
2.298 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.299 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.299 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.300 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.300 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.300 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.300 * [taylor]: Taking taylor expansion of 1.0 in n
2.300 * [backup-simplify]: Simplify 1.0 into 1.0
2.300 * [taylor]: Taking taylor expansion of (log n) in n
2.300 * [taylor]: Taking taylor expansion of n in n
2.300 * [backup-simplify]: Simplify 0 into 0
2.300 * [backup-simplify]: Simplify 1 into 1
2.300 * [backup-simplify]: Simplify (log 1) into 0
2.300 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.300 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.300 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.300 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.300 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.300 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.300 * [taylor]: Taking taylor expansion of 1.0 in n
2.300 * [backup-simplify]: Simplify 1.0 into 1.0
2.300 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.300 * [taylor]: Taking taylor expansion of 2.0 in n
2.300 * [backup-simplify]: Simplify 2.0 into 2.0
2.301 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.301 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.302 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.303 * [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)
2.303 * [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)
2.304 * [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))
2.305 * [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)))
2.306 * [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)
2.307 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.308 * [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)))
2.310 * [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))))
2.311 * [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))
2.312 * [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)))
2.314 * [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)))))))
2.318 * [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)))))))))
2.324 * [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)))))))
2.326 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
2.326 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
2.328 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
2.329 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
2.330 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.330 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
2.331 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
2.332 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
2.334 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
2.335 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
2.336 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
2.338 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
2.340 * [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
2.341 * [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
2.342 * [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
2.343 * [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
2.344 * [backup-simplify]: Simplify (- 0) into 0
2.344 * [backup-simplify]: Simplify 0 into 0
2.344 * [backup-simplify]: Simplify 0 into 0
2.344 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.347 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.347 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.348 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
2.350 * [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
2.350 * [backup-simplify]: Simplify (- 0) into 0
2.350 * [backup-simplify]: Simplify (+ 0 0) into 0
2.351 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
2.352 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
2.353 * [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)))
2.357 * [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))))))))
2.363 * [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))))))))
2.364 * [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
2.364 * [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
2.364 * [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
2.364 * [taylor]: Taking taylor expansion of +nan.0 in n
2.364 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.364 * [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
2.364 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.364 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.364 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.364 * [taylor]: Taking taylor expansion of 0.5 in n
2.364 * [backup-simplify]: Simplify 0.5 into 0.5
2.364 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.364 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.364 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.364 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.364 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.364 * [taylor]: Taking taylor expansion of 1.0 in n
2.364 * [backup-simplify]: Simplify 1.0 into 1.0
2.364 * [taylor]: Taking taylor expansion of (log PI) in n
2.364 * [taylor]: Taking taylor expansion of PI in n
2.364 * [backup-simplify]: Simplify PI into PI
2.364 * [backup-simplify]: Simplify (log PI) into (log PI)
2.367 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.369 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.369 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.369 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.369 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.369 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.369 * [taylor]: Taking taylor expansion of 1.0 in n
2.369 * [backup-simplify]: Simplify 1.0 into 1.0
2.369 * [taylor]: Taking taylor expansion of (log n) in n
2.369 * [taylor]: Taking taylor expansion of n in n
2.369 * [backup-simplify]: Simplify 0 into 0
2.369 * [backup-simplify]: Simplify 1 into 1
2.369 * [backup-simplify]: Simplify (log 1) into 0
2.369 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.370 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.370 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.370 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.370 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.370 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.370 * [taylor]: Taking taylor expansion of 1.0 in n
2.370 * [backup-simplify]: Simplify 1.0 into 1.0
2.370 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.370 * [taylor]: Taking taylor expansion of 2.0 in n
2.370 * [backup-simplify]: Simplify 2.0 into 2.0
2.370 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.371 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.371 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.372 * [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)
2.373 * [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)
2.373 * [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))
2.374 * [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)))
2.375 * [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)
2.375 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.375 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.375 * [taylor]: Taking taylor expansion of 2.0 in n
2.375 * [backup-simplify]: Simplify 2.0 into 2.0
2.375 * [taylor]: Taking taylor expansion of (* n PI) in n
2.375 * [taylor]: Taking taylor expansion of n in n
2.375 * [backup-simplify]: Simplify 0 into 0
2.375 * [backup-simplify]: Simplify 1 into 1
2.375 * [taylor]: Taking taylor expansion of PI in n
2.375 * [backup-simplify]: Simplify PI into PI
2.376 * [backup-simplify]: Simplify (* 0 PI) into 0
2.376 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.377 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.378 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.379 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.379 * [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
2.379 * [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
2.379 * [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
2.379 * [taylor]: Taking taylor expansion of +nan.0 in n
2.379 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.379 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
2.379 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
2.379 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
2.379 * [taylor]: Taking taylor expansion of 0.5 in n
2.379 * [backup-simplify]: Simplify 0.5 into 0.5
2.379 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
2.379 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
2.379 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.379 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.379 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.379 * [taylor]: Taking taylor expansion of 1.0 in n
2.379 * [backup-simplify]: Simplify 1.0 into 1.0
2.379 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.379 * [taylor]: Taking taylor expansion of 2.0 in n
2.379 * [backup-simplify]: Simplify 2.0 into 2.0
2.379 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.380 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.381 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.381 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
2.381 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.381 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.381 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.381 * [taylor]: Taking taylor expansion of 1.0 in n
2.381 * [backup-simplify]: Simplify 1.0 into 1.0
2.381 * [taylor]: Taking taylor expansion of (log n) in n
2.381 * [taylor]: Taking taylor expansion of n in n
2.381 * [backup-simplify]: Simplify 0 into 0
2.381 * [backup-simplify]: Simplify 1 into 1
2.381 * [backup-simplify]: Simplify (log 1) into 0
2.382 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.382 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.382 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.382 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.382 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.382 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.382 * [taylor]: Taking taylor expansion of 1.0 in n
2.382 * [backup-simplify]: Simplify 1.0 into 1.0
2.382 * [taylor]: Taking taylor expansion of (log PI) in n
2.382 * [taylor]: Taking taylor expansion of PI in n
2.382 * [backup-simplify]: Simplify PI into PI
2.382 * [backup-simplify]: Simplify (log PI) into (log PI)
2.383 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.384 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.385 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
2.385 * [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)
2.386 * [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))
2.387 * [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)))
2.388 * [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)
2.388 * [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
2.388 * [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
2.388 * [taylor]: Taking taylor expansion of +nan.0 in n
2.388 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.388 * [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
2.388 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.388 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.388 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.388 * [taylor]: Taking taylor expansion of 0.5 in n
2.388 * [backup-simplify]: Simplify 0.5 into 0.5
2.388 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.388 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.388 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.388 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.388 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.388 * [taylor]: Taking taylor expansion of 1.0 in n
2.388 * [backup-simplify]: Simplify 1.0 into 1.0
2.388 * [taylor]: Taking taylor expansion of (log PI) in n
2.388 * [taylor]: Taking taylor expansion of PI in n
2.388 * [backup-simplify]: Simplify PI into PI
2.389 * [backup-simplify]: Simplify (log PI) into (log PI)
2.389 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.390 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.390 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.390 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.390 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.390 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.390 * [taylor]: Taking taylor expansion of 1.0 in n
2.390 * [backup-simplify]: Simplify 1.0 into 1.0
2.390 * [taylor]: Taking taylor expansion of (log n) in n
2.390 * [taylor]: Taking taylor expansion of n in n
2.390 * [backup-simplify]: Simplify 0 into 0
2.390 * [backup-simplify]: Simplify 1 into 1
2.391 * [backup-simplify]: Simplify (log 1) into 0
2.391 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.391 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.391 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.391 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.391 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.391 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.391 * [taylor]: Taking taylor expansion of 1.0 in n
2.391 * [backup-simplify]: Simplify 1.0 into 1.0
2.391 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.391 * [taylor]: Taking taylor expansion of 2.0 in n
2.391 * [backup-simplify]: Simplify 2.0 into 2.0
2.391 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.392 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.393 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.393 * [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)
2.394 * [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)
2.395 * [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))
2.396 * [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)))
2.397 * [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)
2.397 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
2.397 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.397 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.397 * [taylor]: Taking taylor expansion of 2.0 in n
2.397 * [backup-simplify]: Simplify 2.0 into 2.0
2.397 * [taylor]: Taking taylor expansion of (* n PI) in n
2.397 * [taylor]: Taking taylor expansion of n in n
2.397 * [backup-simplify]: Simplify 0 into 0
2.397 * [backup-simplify]: Simplify 1 into 1
2.397 * [taylor]: Taking taylor expansion of PI in n
2.397 * [backup-simplify]: Simplify PI into PI
2.397 * [backup-simplify]: Simplify (* 0 PI) into 0
2.397 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.398 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.399 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.400 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.402 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.404 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.406 * [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)))
2.409 * [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))))
2.410 * [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))
2.412 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.413 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.416 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
2.418 * [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))
2.421 * [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)))
2.424 * [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))))))))
2.435 * [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)))))))))
2.446 * [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))))))))))
2.460 * [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)))))))))))))
2.478 * [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)))))))))))))
2.495 * [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)))))))))))))))
2.518 * [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)))))))))))))))))))))))
2.519 * [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)))
2.519 * [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
2.519 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
2.519 * [taylor]: Taking taylor expansion of 1.0 in n
2.519 * [backup-simplify]: Simplify 1.0 into 1.0
2.519 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
2.519 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
2.519 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
2.519 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
2.519 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
2.519 * [taylor]: Taking taylor expansion of 0.5 in n
2.519 * [backup-simplify]: Simplify 0.5 into 0.5
2.519 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.519 * [taylor]: Taking taylor expansion of 1.0 in n
2.520 * [backup-simplify]: Simplify 1.0 into 1.0
2.520 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.520 * [taylor]: Taking taylor expansion of k in n
2.520 * [backup-simplify]: Simplify k into k
2.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.520 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.520 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.520 * [taylor]: Taking taylor expansion of 2.0 in n
2.520 * [backup-simplify]: Simplify 2.0 into 2.0
2.520 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.520 * [taylor]: Taking taylor expansion of PI in n
2.520 * [backup-simplify]: Simplify PI into PI
2.520 * [taylor]: Taking taylor expansion of n in n
2.520 * [backup-simplify]: Simplify 0 into 0
2.520 * [backup-simplify]: Simplify 1 into 1
2.520 * [backup-simplify]: Simplify (/ PI 1) into PI
2.521 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.521 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.521 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.522 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.522 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
2.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.523 * [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))))
2.524 * [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)))))
2.524 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.524 * [taylor]: Taking taylor expansion of k in n
2.524 * [backup-simplify]: Simplify k into k
2.524 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.524 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.524 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
2.524 * [taylor]: Taking taylor expansion of 1.0 in k
2.524 * [backup-simplify]: Simplify 1.0 into 1.0
2.524 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
2.524 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
2.524 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
2.525 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
2.525 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
2.525 * [taylor]: Taking taylor expansion of 0.5 in k
2.525 * [backup-simplify]: Simplify 0.5 into 0.5
2.525 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.525 * [taylor]: Taking taylor expansion of 1.0 in k
2.525 * [backup-simplify]: Simplify 1.0 into 1.0
2.525 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.525 * [taylor]: Taking taylor expansion of k in k
2.525 * [backup-simplify]: Simplify 0 into 0
2.525 * [backup-simplify]: Simplify 1 into 1
2.525 * [backup-simplify]: Simplify (/ 1 1) into 1
2.525 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
2.525 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
2.525 * [taylor]: Taking taylor expansion of 2.0 in k
2.525 * [backup-simplify]: Simplify 2.0 into 2.0
2.525 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.525 * [taylor]: Taking taylor expansion of PI in k
2.525 * [backup-simplify]: Simplify PI into PI
2.525 * [taylor]: Taking taylor expansion of n in k
2.525 * [backup-simplify]: Simplify n into n
2.525 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.525 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
2.525 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
2.525 * [backup-simplify]: Simplify (- 1) into -1
2.526 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.526 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
2.526 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
2.526 * [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))))))
2.526 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.526 * [taylor]: Taking taylor expansion of k in k
2.526 * [backup-simplify]: Simplify 0 into 0
2.526 * [backup-simplify]: Simplify 1 into 1
2.527 * [backup-simplify]: Simplify (sqrt 0) into 0
2.528 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.528 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
2.528 * [taylor]: Taking taylor expansion of 1.0 in k
2.528 * [backup-simplify]: Simplify 1.0 into 1.0
2.528 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
2.528 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
2.528 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
2.528 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
2.528 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
2.528 * [taylor]: Taking taylor expansion of 0.5 in k
2.528 * [backup-simplify]: Simplify 0.5 into 0.5
2.528 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.528 * [taylor]: Taking taylor expansion of 1.0 in k
2.528 * [backup-simplify]: Simplify 1.0 into 1.0
2.528 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.528 * [taylor]: Taking taylor expansion of k in k
2.528 * [backup-simplify]: Simplify 0 into 0
2.528 * [backup-simplify]: Simplify 1 into 1
2.528 * [backup-simplify]: Simplify (/ 1 1) into 1
2.528 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
2.528 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
2.528 * [taylor]: Taking taylor expansion of 2.0 in k
2.528 * [backup-simplify]: Simplify 2.0 into 2.0
2.529 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.529 * [taylor]: Taking taylor expansion of PI in k
2.529 * [backup-simplify]: Simplify PI into PI
2.529 * [taylor]: Taking taylor expansion of n in k
2.529 * [backup-simplify]: Simplify n into n
2.529 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.529 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
2.529 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
2.529 * [backup-simplify]: Simplify (- 1) into -1
2.529 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.530 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
2.530 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
2.530 * [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))))))
2.530 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.530 * [taylor]: Taking taylor expansion of k in k
2.530 * [backup-simplify]: Simplify 0 into 0
2.530 * [backup-simplify]: Simplify 1 into 1
2.530 * [backup-simplify]: Simplify (sqrt 0) into 0
2.531 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.531 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0
2.532 * [backup-simplify]: Simplify (* 1.0 0) into 0
2.532 * [taylor]: Taking taylor expansion of 0 in n
2.532 * [backup-simplify]: Simplify 0 into 0
2.532 * [backup-simplify]: Simplify 0 into 0
2.532 * [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))))))))
2.533 * [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))))))))
2.533 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
2.533 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
2.533 * [taylor]: Taking taylor expansion of +nan.0 in n
2.533 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.533 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
2.533 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
2.533 * [taylor]: Taking taylor expansion of 0.5 in n
2.533 * [backup-simplify]: Simplify 0.5 into 0.5
2.533 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
2.533 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.533 * [taylor]: Taking taylor expansion of 1.0 in n
2.533 * [backup-simplify]: Simplify 1.0 into 1.0
2.533 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.533 * [taylor]: Taking taylor expansion of k in n
2.533 * [backup-simplify]: Simplify k into k
2.533 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.533 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.533 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.533 * [taylor]: Taking taylor expansion of 2.0 in n
2.533 * [backup-simplify]: Simplify 2.0 into 2.0
2.533 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.533 * [taylor]: Taking taylor expansion of PI in n
2.533 * [backup-simplify]: Simplify PI into PI
2.533 * [taylor]: Taking taylor expansion of n in n
2.533 * [backup-simplify]: Simplify 0 into 0
2.533 * [backup-simplify]: Simplify 1 into 1
2.533 * [backup-simplify]: Simplify (/ PI 1) into PI
2.534 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.535 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.535 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.535 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.537 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
2.537 * [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))))
2.538 * [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)))))
2.539 * [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))))))
2.540 * [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)))))))
2.541 * [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)))))))
2.542 * [backup-simplify]: Simplify 0 into 0
2.545 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.546 * [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))))))))
2.547 * [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))))))))
2.547 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
2.547 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
2.547 * [taylor]: Taking taylor expansion of +nan.0 in n
2.547 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.547 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
2.547 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
2.547 * [taylor]: Taking taylor expansion of 0.5 in n
2.547 * [backup-simplify]: Simplify 0.5 into 0.5
2.547 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
2.547 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.547 * [taylor]: Taking taylor expansion of 1.0 in n
2.548 * [backup-simplify]: Simplify 1.0 into 1.0
2.548 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.548 * [taylor]: Taking taylor expansion of k in n
2.548 * [backup-simplify]: Simplify k into k
2.548 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.548 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.548 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.548 * [taylor]: Taking taylor expansion of 2.0 in n
2.548 * [backup-simplify]: Simplify 2.0 into 2.0
2.548 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.548 * [taylor]: Taking taylor expansion of PI in n
2.548 * [backup-simplify]: Simplify PI into PI
2.548 * [taylor]: Taking taylor expansion of n in n
2.548 * [backup-simplify]: Simplify 0 into 0
2.548 * [backup-simplify]: Simplify 1 into 1
2.548 * [backup-simplify]: Simplify (/ PI 1) into PI
2.549 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.550 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.550 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.550 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.553 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
2.554 * [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))))
2.555 * [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)))))
2.557 * [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))))))
2.558 * [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)))))))
2.559 * [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)))))))
2.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.561 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.563 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.563 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.564 * [backup-simplify]: Simplify (- 0) into 0
2.564 * [backup-simplify]: Simplify (+ 0 0) into 0
2.565 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.567 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
2.568 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0
2.570 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.572 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
2.572 * [backup-simplify]: Simplify (- 0) into 0
2.572 * [backup-simplify]: Simplify 0 into 0
2.573 * [backup-simplify]: Simplify 0 into 0
2.576 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.578 * [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))))))))
2.579 * [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))))))))
2.579 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
2.579 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
2.579 * [taylor]: Taking taylor expansion of +nan.0 in n
2.579 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.579 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
2.579 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
2.579 * [taylor]: Taking taylor expansion of 0.5 in n
2.579 * [backup-simplify]: Simplify 0.5 into 0.5
2.579 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
2.580 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.580 * [taylor]: Taking taylor expansion of 1.0 in n
2.580 * [backup-simplify]: Simplify 1.0 into 1.0
2.580 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.580 * [taylor]: Taking taylor expansion of k in n
2.580 * [backup-simplify]: Simplify k into k
2.580 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.580 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.580 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.580 * [taylor]: Taking taylor expansion of 2.0 in n
2.580 * [backup-simplify]: Simplify 2.0 into 2.0
2.580 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.580 * [taylor]: Taking taylor expansion of PI in n
2.580 * [backup-simplify]: Simplify PI into PI
2.580 * [taylor]: Taking taylor expansion of n in n
2.580 * [backup-simplify]: Simplify 0 into 0
2.580 * [backup-simplify]: Simplify 1 into 1
2.580 * [backup-simplify]: Simplify (/ PI 1) into PI
2.581 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.582 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.582 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.582 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.585 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
2.586 * [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))))
2.587 * [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)))))
2.589 * [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))))))
2.590 * [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)))))))
2.592 * [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)))))))
2.596 * [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))))))))
2.597 * [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))))
2.597 * [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
2.597 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
2.597 * [taylor]: Taking taylor expansion of 1.0 in n
2.597 * [backup-simplify]: Simplify 1.0 into 1.0
2.597 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
2.597 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
2.597 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
2.597 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
2.597 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
2.597 * [taylor]: Taking taylor expansion of 0.5 in n
2.597 * [backup-simplify]: Simplify 0.5 into 0.5
2.597 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.597 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.598 * [taylor]: Taking taylor expansion of k in n
2.598 * [backup-simplify]: Simplify k into k
2.598 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.598 * [taylor]: Taking taylor expansion of 1.0 in n
2.598 * [backup-simplify]: Simplify 1.0 into 1.0
2.598 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.598 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.598 * [taylor]: Taking taylor expansion of -2.0 in n
2.598 * [backup-simplify]: Simplify -2.0 into -2.0
2.598 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.598 * [taylor]: Taking taylor expansion of PI in n
2.598 * [backup-simplify]: Simplify PI into PI
2.598 * [taylor]: Taking taylor expansion of n in n
2.598 * [backup-simplify]: Simplify 0 into 0
2.598 * [backup-simplify]: Simplify 1 into 1
2.599 * [backup-simplify]: Simplify (/ PI 1) into PI
2.599 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.600 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.600 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.600 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
2.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.603 * [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)))
2.604 * [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))))
2.604 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.604 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.604 * [taylor]: Taking taylor expansion of -1 in n
2.604 * [backup-simplify]: Simplify -1 into -1
2.604 * [taylor]: Taking taylor expansion of k in n
2.604 * [backup-simplify]: Simplify k into k
2.604 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.605 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.605 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.605 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.606 * [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)))
2.606 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
2.606 * [taylor]: Taking taylor expansion of 1.0 in k
2.606 * [backup-simplify]: Simplify 1.0 into 1.0
2.606 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
2.607 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
2.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
2.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
2.607 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
2.607 * [taylor]: Taking taylor expansion of 0.5 in k
2.607 * [backup-simplify]: Simplify 0.5 into 0.5
2.607 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.607 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.607 * [taylor]: Taking taylor expansion of k in k
2.607 * [backup-simplify]: Simplify 0 into 0
2.607 * [backup-simplify]: Simplify 1 into 1
2.607 * [backup-simplify]: Simplify (/ 1 1) into 1
2.607 * [taylor]: Taking taylor expansion of 1.0 in k
2.607 * [backup-simplify]: Simplify 1.0 into 1.0
2.607 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
2.607 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
2.607 * [taylor]: Taking taylor expansion of -2.0 in k
2.607 * [backup-simplify]: Simplify -2.0 into -2.0
2.607 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.608 * [taylor]: Taking taylor expansion of PI in k
2.608 * [backup-simplify]: Simplify PI into PI
2.608 * [taylor]: Taking taylor expansion of n in k
2.608 * [backup-simplify]: Simplify n into n
2.608 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.608 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
2.608 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
2.608 * [backup-simplify]: Simplify (+ 1 0) into 1
2.609 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
2.609 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
2.609 * [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))))
2.609 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.609 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.609 * [taylor]: Taking taylor expansion of -1 in k
2.609 * [backup-simplify]: Simplify -1 into -1
2.609 * [taylor]: Taking taylor expansion of k in k
2.609 * [backup-simplify]: Simplify 0 into 0
2.610 * [backup-simplify]: Simplify 1 into 1
2.610 * [backup-simplify]: Simplify (/ -1 1) into -1
2.610 * [backup-simplify]: Simplify (sqrt 0) into 0
2.612 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.612 * [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)))))
2.612 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
2.612 * [taylor]: Taking taylor expansion of 1.0 in k
2.612 * [backup-simplify]: Simplify 1.0 into 1.0
2.612 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
2.612 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
2.612 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
2.612 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
2.612 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
2.613 * [taylor]: Taking taylor expansion of 0.5 in k
2.613 * [backup-simplify]: Simplify 0.5 into 0.5
2.613 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.613 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.613 * [taylor]: Taking taylor expansion of k in k
2.613 * [backup-simplify]: Simplify 0 into 0
2.613 * [backup-simplify]: Simplify 1 into 1
2.613 * [backup-simplify]: Simplify (/ 1 1) into 1
2.613 * [taylor]: Taking taylor expansion of 1.0 in k
2.613 * [backup-simplify]: Simplify 1.0 into 1.0
2.613 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
2.613 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
2.613 * [taylor]: Taking taylor expansion of -2.0 in k
2.613 * [backup-simplify]: Simplify -2.0 into -2.0
2.613 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.613 * [taylor]: Taking taylor expansion of PI in k
2.613 * [backup-simplify]: Simplify PI into PI
2.613 * [taylor]: Taking taylor expansion of n in k
2.613 * [backup-simplify]: Simplify n into n
2.614 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.614 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
2.614 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
2.614 * [backup-simplify]: Simplify (+ 1 0) into 1
2.615 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
2.615 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
2.615 * [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))))
2.615 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.615 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.615 * [taylor]: Taking taylor expansion of -1 in k
2.615 * [backup-simplify]: Simplify -1 into -1
2.615 * [taylor]: Taking taylor expansion of k in k
2.615 * [backup-simplify]: Simplify 0 into 0
2.615 * [backup-simplify]: Simplify 1 into 1
2.616 * [backup-simplify]: Simplify (/ -1 1) into -1
2.616 * [backup-simplify]: Simplify (sqrt 0) into 0
2.617 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.618 * [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)))))
2.618 * [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)))))
2.618 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
2.618 * [taylor]: Taking taylor expansion of +nan.0 in n
2.618 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.618 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
2.618 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
2.618 * [taylor]: Taking taylor expansion of 0.5 in n
2.618 * [backup-simplify]: Simplify 0.5 into 0.5
2.618 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
2.619 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.619 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.619 * [taylor]: Taking taylor expansion of -2.0 in n
2.619 * [backup-simplify]: Simplify -2.0 into -2.0
2.619 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.619 * [taylor]: Taking taylor expansion of PI in n
2.619 * [backup-simplify]: Simplify PI into PI
2.619 * [taylor]: Taking taylor expansion of n in n
2.619 * [backup-simplify]: Simplify 0 into 0
2.619 * [backup-simplify]: Simplify 1 into 1
2.619 * [backup-simplify]: Simplify (/ PI 1) into PI
2.620 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.621 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.621 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.621 * [taylor]: Taking taylor expansion of k in n
2.621 * [backup-simplify]: Simplify k into k
2.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.621 * [taylor]: Taking taylor expansion of 1.0 in n
2.621 * [backup-simplify]: Simplify 1.0 into 1.0
2.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.623 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.624 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
2.625 * [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)))
2.627 * [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))))
2.628 * [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)))))
2.630 * [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)))))
2.631 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.634 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.635 * [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))))))
2.636 * [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))))))
2.636 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
2.636 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
2.636 * [taylor]: Taking taylor expansion of +nan.0 in n
2.636 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.636 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
2.636 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
2.636 * [taylor]: Taking taylor expansion of 0.5 in n
2.636 * [backup-simplify]: Simplify 0.5 into 0.5
2.636 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
2.636 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.636 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.636 * [taylor]: Taking taylor expansion of -2.0 in n
2.636 * [backup-simplify]: Simplify -2.0 into -2.0
2.636 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.636 * [taylor]: Taking taylor expansion of PI in n
2.636 * [backup-simplify]: Simplify PI into PI
2.636 * [taylor]: Taking taylor expansion of n in n
2.636 * [backup-simplify]: Simplify 0 into 0
2.636 * [backup-simplify]: Simplify 1 into 1
2.640 * [backup-simplify]: Simplify (/ PI 1) into PI
2.641 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.642 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.642 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.642 * [taylor]: Taking taylor expansion of k in n
2.642 * [backup-simplify]: Simplify k into k
2.642 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.642 * [taylor]: Taking taylor expansion of 1.0 in n
2.643 * [backup-simplify]: Simplify 1.0 into 1.0
2.644 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.644 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.645 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
2.647 * [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)))
2.648 * [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))))
2.649 * [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)))))
2.651 * [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))))))
2.652 * [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))))))
2.654 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.654 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.654 * [backup-simplify]: Simplify (+ 0 0) into 0
2.655 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.656 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
2.658 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
2.660 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0
2.661 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0
2.663 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.665 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
2.665 * [backup-simplify]: Simplify 0 into 0
2.666 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.670 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.672 * [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))))))
2.673 * [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))))))
2.673 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
2.673 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
2.673 * [taylor]: Taking taylor expansion of +nan.0 in n
2.673 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.674 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
2.674 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
2.674 * [taylor]: Taking taylor expansion of 0.5 in n
2.674 * [backup-simplify]: Simplify 0.5 into 0.5
2.674 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
2.674 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.674 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.674 * [taylor]: Taking taylor expansion of -2.0 in n
2.674 * [backup-simplify]: Simplify -2.0 into -2.0
2.674 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.674 * [taylor]: Taking taylor expansion of PI in n
2.674 * [backup-simplify]: Simplify PI into PI
2.674 * [taylor]: Taking taylor expansion of n in n
2.674 * [backup-simplify]: Simplify 0 into 0
2.674 * [backup-simplify]: Simplify 1 into 1
2.675 * [backup-simplify]: Simplify (/ PI 1) into PI
2.675 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.676 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.676 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.676 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.676 * [taylor]: Taking taylor expansion of k in n
2.676 * [backup-simplify]: Simplify k into k
2.676 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.676 * [taylor]: Taking taylor expansion of 1.0 in n
2.676 * [backup-simplify]: Simplify 1.0 into 1.0
2.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.679 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.680 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
2.681 * [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)))
2.682 * [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))))
2.684 * [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)))))
2.684 * [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))))))
2.685 * [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))))))
2.688 * [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))))))))
2.688 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
2.689 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
2.689 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
2.689 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
2.689 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
2.689 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
2.689 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
2.689 * [taylor]: Taking taylor expansion of 0.5 in k
2.689 * [backup-simplify]: Simplify 0.5 into 0.5
2.689 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
2.689 * [taylor]: Taking taylor expansion of 1.0 in k
2.689 * [backup-simplify]: Simplify 1.0 into 1.0
2.689 * [taylor]: Taking taylor expansion of k in k
2.689 * [backup-simplify]: Simplify 0 into 0
2.689 * [backup-simplify]: Simplify 1 into 1
2.689 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
2.689 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
2.689 * [taylor]: Taking taylor expansion of 2.0 in k
2.689 * [backup-simplify]: Simplify 2.0 into 2.0
2.689 * [taylor]: Taking taylor expansion of (* n PI) in k
2.689 * [taylor]: Taking taylor expansion of n in k
2.689 * [backup-simplify]: Simplify n into n
2.689 * [taylor]: Taking taylor expansion of PI in k
2.689 * [backup-simplify]: Simplify PI into PI
2.689 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.689 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
2.689 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
2.689 * [backup-simplify]: Simplify (- 0) into 0
2.690 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
2.690 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
2.690 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
2.690 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
2.690 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
2.690 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
2.690 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
2.690 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
2.690 * [taylor]: Taking taylor expansion of 0.5 in n
2.690 * [backup-simplify]: Simplify 0.5 into 0.5
2.690 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
2.690 * [taylor]: Taking taylor expansion of 1.0 in n
2.690 * [backup-simplify]: Simplify 1.0 into 1.0
2.690 * [taylor]: Taking taylor expansion of k in n
2.690 * [backup-simplify]: Simplify k into k
2.690 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.690 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.690 * [taylor]: Taking taylor expansion of 2.0 in n
2.690 * [backup-simplify]: Simplify 2.0 into 2.0
2.690 * [taylor]: Taking taylor expansion of (* n PI) in n
2.690 * [taylor]: Taking taylor expansion of n in n
2.690 * [backup-simplify]: Simplify 0 into 0
2.690 * [backup-simplify]: Simplify 1 into 1
2.690 * [taylor]: Taking taylor expansion of PI in n
2.690 * [backup-simplify]: Simplify PI into PI
2.691 * [backup-simplify]: Simplify (* 0 PI) into 0
2.691 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.692 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.693 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.694 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.694 * [backup-simplify]: Simplify (- k) into (- k)
2.694 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
2.694 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
2.695 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.695 * [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))))
2.696 * [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)))))
2.696 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
2.696 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
2.696 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
2.696 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
2.696 * [taylor]: Taking taylor expansion of 0.5 in n
2.696 * [backup-simplify]: Simplify 0.5 into 0.5
2.696 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
2.696 * [taylor]: Taking taylor expansion of 1.0 in n
2.696 * [backup-simplify]: Simplify 1.0 into 1.0
2.696 * [taylor]: Taking taylor expansion of k in n
2.696 * [backup-simplify]: Simplify k into k
2.696 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.696 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.697 * [taylor]: Taking taylor expansion of 2.0 in n
2.697 * [backup-simplify]: Simplify 2.0 into 2.0
2.697 * [taylor]: Taking taylor expansion of (* n PI) in n
2.697 * [taylor]: Taking taylor expansion of n in n
2.697 * [backup-simplify]: Simplify 0 into 0
2.697 * [backup-simplify]: Simplify 1 into 1
2.697 * [taylor]: Taking taylor expansion of PI in n
2.697 * [backup-simplify]: Simplify PI into PI
2.697 * [backup-simplify]: Simplify (* 0 PI) into 0
2.697 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.698 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.699 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.700 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.700 * [backup-simplify]: Simplify (- k) into (- k)
2.700 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
2.700 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
2.701 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.702 * [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))))
2.702 * [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)))))
2.702 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
2.703 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
2.703 * [taylor]: Taking taylor expansion of 0.5 in k
2.703 * [backup-simplify]: Simplify 0.5 into 0.5
2.703 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
2.703 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
2.703 * [taylor]: Taking taylor expansion of 1.0 in k
2.703 * [backup-simplify]: Simplify 1.0 into 1.0
2.703 * [taylor]: Taking taylor expansion of k in k
2.703 * [backup-simplify]: Simplify 0 into 0
2.703 * [backup-simplify]: Simplify 1 into 1
2.703 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
2.703 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
2.703 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
2.703 * [taylor]: Taking taylor expansion of 2.0 in k
2.703 * [backup-simplify]: Simplify 2.0 into 2.0
2.703 * [taylor]: Taking taylor expansion of PI in k
2.703 * [backup-simplify]: Simplify PI into PI
2.703 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.704 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.704 * [taylor]: Taking taylor expansion of (log n) in k
2.704 * [taylor]: Taking taylor expansion of n in k
2.704 * [backup-simplify]: Simplify n into n
2.704 * [backup-simplify]: Simplify (log n) into (log n)
2.704 * [backup-simplify]: Simplify (- 0) into 0
2.704 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
2.705 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
2.706 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
2.706 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
2.707 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
2.708 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
2.709 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.709 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
2.710 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.710 * [backup-simplify]: Simplify (- 0) into 0
2.711 * [backup-simplify]: Simplify (+ 0 0) into 0
2.711 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
2.712 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.714 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
2.716 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.716 * [taylor]: Taking taylor expansion of 0 in k
2.716 * [backup-simplify]: Simplify 0 into 0
2.716 * [backup-simplify]: Simplify 0 into 0
2.717 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.718 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.719 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.720 * [backup-simplify]: Simplify (+ 0 0) into 0
2.720 * [backup-simplify]: Simplify (- 1) into -1
2.721 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.722 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
2.725 * [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))))
2.728 * [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))))))
2.732 * [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))))))
2.733 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.738 * [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
2.739 * [backup-simplify]: Simplify (- 0) into 0
2.739 * [backup-simplify]: Simplify (+ 0 0) into 0
2.740 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
2.742 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.743 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
2.745 * [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
2.745 * [taylor]: Taking taylor expansion of 0 in k
2.745 * [backup-simplify]: Simplify 0 into 0
2.745 * [backup-simplify]: Simplify 0 into 0
2.745 * [backup-simplify]: Simplify 0 into 0
2.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.747 * [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
2.749 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.749 * [backup-simplify]: Simplify (+ 0 0) into 0
2.749 * [backup-simplify]: Simplify (- 0) into 0
2.750 * [backup-simplify]: Simplify (+ 0 0) into 0
2.751 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
2.753 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
2.755 * [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))))))
2.759 * [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))))))
2.768 * [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)))))
2.768 * [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))))
2.768 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
2.768 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
2.768 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
2.769 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
2.769 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
2.769 * [taylor]: Taking taylor expansion of 0.5 in k
2.769 * [backup-simplify]: Simplify 0.5 into 0.5
2.769 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.769 * [taylor]: Taking taylor expansion of 1.0 in k
2.769 * [backup-simplify]: Simplify 1.0 into 1.0
2.769 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.769 * [taylor]: Taking taylor expansion of k in k
2.769 * [backup-simplify]: Simplify 0 into 0
2.769 * [backup-simplify]: Simplify 1 into 1
2.769 * [backup-simplify]: Simplify (/ 1 1) into 1
2.769 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
2.769 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
2.769 * [taylor]: Taking taylor expansion of 2.0 in k
2.769 * [backup-simplify]: Simplify 2.0 into 2.0
2.769 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.769 * [taylor]: Taking taylor expansion of PI in k
2.769 * [backup-simplify]: Simplify PI into PI
2.769 * [taylor]: Taking taylor expansion of n in k
2.769 * [backup-simplify]: Simplify n into n
2.769 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.769 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
2.769 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
2.769 * [backup-simplify]: Simplify (- 1) into -1
2.770 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.770 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
2.770 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
2.770 * [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))))))
2.770 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
2.770 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
2.770 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
2.770 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
2.770 * [taylor]: Taking taylor expansion of 0.5 in n
2.770 * [backup-simplify]: Simplify 0.5 into 0.5
2.770 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.770 * [taylor]: Taking taylor expansion of 1.0 in n
2.770 * [backup-simplify]: Simplify 1.0 into 1.0
2.770 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.770 * [taylor]: Taking taylor expansion of k in n
2.770 * [backup-simplify]: Simplify k into k
2.770 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.770 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.771 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.771 * [taylor]: Taking taylor expansion of 2.0 in n
2.771 * [backup-simplify]: Simplify 2.0 into 2.0
2.771 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.771 * [taylor]: Taking taylor expansion of PI in n
2.771 * [backup-simplify]: Simplify PI into PI
2.771 * [taylor]: Taking taylor expansion of n in n
2.771 * [backup-simplify]: Simplify 0 into 0
2.771 * [backup-simplify]: Simplify 1 into 1
2.771 * [backup-simplify]: Simplify (/ PI 1) into PI
2.771 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.772 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.772 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.772 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.773 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
2.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.775 * [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))))
2.777 * [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)))))
2.777 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
2.777 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
2.777 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
2.777 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
2.777 * [taylor]: Taking taylor expansion of 0.5 in n
2.777 * [backup-simplify]: Simplify 0.5 into 0.5
2.777 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.777 * [taylor]: Taking taylor expansion of 1.0 in n
2.777 * [backup-simplify]: Simplify 1.0 into 1.0
2.777 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.777 * [taylor]: Taking taylor expansion of k in n
2.777 * [backup-simplify]: Simplify k into k
2.777 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.777 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.777 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.777 * [taylor]: Taking taylor expansion of 2.0 in n
2.777 * [backup-simplify]: Simplify 2.0 into 2.0
2.777 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.777 * [taylor]: Taking taylor expansion of PI in n
2.777 * [backup-simplify]: Simplify PI into PI
2.777 * [taylor]: Taking taylor expansion of n in n
2.777 * [backup-simplify]: Simplify 0 into 0
2.777 * [backup-simplify]: Simplify 1 into 1
2.778 * [backup-simplify]: Simplify (/ PI 1) into PI
2.779 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.780 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.780 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.780 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.780 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
2.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.783 * [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))))
2.784 * [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)))))
2.784 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
2.784 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
2.784 * [taylor]: Taking taylor expansion of 0.5 in k
2.784 * [backup-simplify]: Simplify 0.5 into 0.5
2.784 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
2.784 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.784 * [taylor]: Taking taylor expansion of 1.0 in k
2.784 * [backup-simplify]: Simplify 1.0 into 1.0
2.784 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.784 * [taylor]: Taking taylor expansion of k in k
2.784 * [backup-simplify]: Simplify 0 into 0
2.785 * [backup-simplify]: Simplify 1 into 1
2.785 * [backup-simplify]: Simplify (/ 1 1) into 1
2.785 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
2.785 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
2.785 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
2.785 * [taylor]: Taking taylor expansion of 2.0 in k
2.785 * [backup-simplify]: Simplify 2.0 into 2.0
2.785 * [taylor]: Taking taylor expansion of PI in k
2.785 * [backup-simplify]: Simplify PI into PI
2.786 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.787 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.787 * [taylor]: Taking taylor expansion of (log n) in k
2.787 * [taylor]: Taking taylor expansion of n in k
2.787 * [backup-simplify]: Simplify n into n
2.787 * [backup-simplify]: Simplify (log n) into (log n)
2.787 * [backup-simplify]: Simplify (- 1) into -1
2.788 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.788 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.789 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
2.790 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
2.792 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
2.793 * [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)))))
2.794 * [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)))))
2.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.798 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.798 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.799 * [backup-simplify]: Simplify (- 0) into 0
2.799 * [backup-simplify]: Simplify (+ 0 0) into 0
2.800 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
2.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.803 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
2.805 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.805 * [taylor]: Taking taylor expansion of 0 in k
2.805 * [backup-simplify]: Simplify 0 into 0
2.805 * [backup-simplify]: Simplify 0 into 0
2.805 * [backup-simplify]: Simplify 0 into 0
2.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.807 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.810 * [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
2.811 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.811 * [backup-simplify]: Simplify (- 0) into 0
2.812 * [backup-simplify]: Simplify (+ 0 0) into 0
2.813 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
2.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.816 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
2.818 * [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
2.818 * [taylor]: Taking taylor expansion of 0 in k
2.818 * [backup-simplify]: Simplify 0 into 0
2.818 * [backup-simplify]: Simplify 0 into 0
2.819 * [backup-simplify]: Simplify 0 into 0
2.819 * [backup-simplify]: Simplify 0 into 0
2.820 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.821 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.827 * [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
2.827 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.828 * [backup-simplify]: Simplify (- 0) into 0
2.828 * [backup-simplify]: Simplify (+ 0 0) into 0
2.830 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
2.831 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.834 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
2.836 * [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
2.837 * [taylor]: Taking taylor expansion of 0 in k
2.837 * [backup-simplify]: Simplify 0 into 0
2.837 * [backup-simplify]: Simplify 0 into 0
2.838 * [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))))))
2.839 * [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)))
2.839 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
2.839 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
2.839 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
2.839 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
2.839 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
2.839 * [taylor]: Taking taylor expansion of 0.5 in k
2.839 * [backup-simplify]: Simplify 0.5 into 0.5
2.839 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.839 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.839 * [taylor]: Taking taylor expansion of k in k
2.839 * [backup-simplify]: Simplify 0 into 0
2.839 * [backup-simplify]: Simplify 1 into 1
2.840 * [backup-simplify]: Simplify (/ 1 1) into 1
2.840 * [taylor]: Taking taylor expansion of 1.0 in k
2.840 * [backup-simplify]: Simplify 1.0 into 1.0
2.840 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
2.840 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
2.840 * [taylor]: Taking taylor expansion of -2.0 in k
2.840 * [backup-simplify]: Simplify -2.0 into -2.0
2.840 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.840 * [taylor]: Taking taylor expansion of PI in k
2.840 * [backup-simplify]: Simplify PI into PI
2.840 * [taylor]: Taking taylor expansion of n in k
2.840 * [backup-simplify]: Simplify n into n
2.840 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.840 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
2.840 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
2.841 * [backup-simplify]: Simplify (+ 1 0) into 1
2.841 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
2.841 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
2.842 * [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))))
2.842 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
2.842 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
2.842 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
2.842 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
2.842 * [taylor]: Taking taylor expansion of 0.5 in n
2.842 * [backup-simplify]: Simplify 0.5 into 0.5
2.842 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.842 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.842 * [taylor]: Taking taylor expansion of k in n
2.842 * [backup-simplify]: Simplify k into k
2.842 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.842 * [taylor]: Taking taylor expansion of 1.0 in n
2.842 * [backup-simplify]: Simplify 1.0 into 1.0
2.842 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.842 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.842 * [taylor]: Taking taylor expansion of -2.0 in n
2.842 * [backup-simplify]: Simplify -2.0 into -2.0
2.842 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.842 * [taylor]: Taking taylor expansion of PI in n
2.842 * [backup-simplify]: Simplify PI into PI
2.842 * [taylor]: Taking taylor expansion of n in n
2.842 * [backup-simplify]: Simplify 0 into 0
2.842 * [backup-simplify]: Simplify 1 into 1
2.843 * [backup-simplify]: Simplify (/ PI 1) into PI
2.843 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.844 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.845 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.845 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
2.846 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.847 * [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)))
2.849 * [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))))
2.849 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
2.849 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
2.849 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
2.849 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
2.849 * [taylor]: Taking taylor expansion of 0.5 in n
2.849 * [backup-simplify]: Simplify 0.5 into 0.5
2.849 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.849 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.849 * [taylor]: Taking taylor expansion of k in n
2.849 * [backup-simplify]: Simplify k into k
2.849 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.849 * [taylor]: Taking taylor expansion of 1.0 in n
2.849 * [backup-simplify]: Simplify 1.0 into 1.0
2.849 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.849 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.849 * [taylor]: Taking taylor expansion of -2.0 in n
2.849 * [backup-simplify]: Simplify -2.0 into -2.0
2.849 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.849 * [taylor]: Taking taylor expansion of PI in n
2.849 * [backup-simplify]: Simplify PI into PI
2.849 * [taylor]: Taking taylor expansion of n in n
2.849 * [backup-simplify]: Simplify 0 into 0
2.849 * [backup-simplify]: Simplify 1 into 1
2.850 * [backup-simplify]: Simplify (/ PI 1) into PI
2.850 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.852 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.852 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.852 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
2.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.855 * [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)))
2.856 * [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))))
2.856 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
2.856 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
2.856 * [taylor]: Taking taylor expansion of 0.5 in k
2.856 * [backup-simplify]: Simplify 0.5 into 0.5
2.856 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
2.856 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
2.856 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
2.856 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
2.856 * [taylor]: Taking taylor expansion of -2.0 in k
2.856 * [backup-simplify]: Simplify -2.0 into -2.0
2.856 * [taylor]: Taking taylor expansion of PI in k
2.856 * [backup-simplify]: Simplify PI into PI
2.857 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.858 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.858 * [taylor]: Taking taylor expansion of (log n) in k
2.858 * [taylor]: Taking taylor expansion of n in k
2.858 * [backup-simplify]: Simplify n into n
2.858 * [backup-simplify]: Simplify (log n) into (log n)
2.858 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.858 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.858 * [taylor]: Taking taylor expansion of k in k
2.858 * [backup-simplify]: Simplify 0 into 0
2.858 * [backup-simplify]: Simplify 1 into 1
2.859 * [backup-simplify]: Simplify (/ 1 1) into 1
2.859 * [taylor]: Taking taylor expansion of 1.0 in k
2.859 * [backup-simplify]: Simplify 1.0 into 1.0
2.859 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.860 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
2.860 * [backup-simplify]: Simplify (+ 1 0) into 1
2.861 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
2.863 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
2.864 * [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))))
2.865 * [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))))
2.866 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.867 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
2.869 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
2.869 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.870 * [backup-simplify]: Simplify (+ 0 0) into 0
2.870 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
2.872 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.873 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
2.875 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.875 * [taylor]: Taking taylor expansion of 0 in k
2.875 * [backup-simplify]: Simplify 0 into 0
2.875 * [backup-simplify]: Simplify 0 into 0
2.875 * [backup-simplify]: Simplify 0 into 0
2.876 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.877 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.881 * [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
2.881 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.882 * [backup-simplify]: Simplify (+ 0 0) into 0
2.883 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
2.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.886 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
2.888 * [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
2.888 * [taylor]: Taking taylor expansion of 0 in k
2.888 * [backup-simplify]: Simplify 0 into 0
2.889 * [backup-simplify]: Simplify 0 into 0
2.889 * [backup-simplify]: Simplify 0 into 0
2.889 * [backup-simplify]: Simplify 0 into 0
2.890 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.891 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.898 * [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
2.898 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.899 * [backup-simplify]: Simplify (+ 0 0) into 0
2.900 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
2.901 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.903 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
2.906 * [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
2.906 * [taylor]: Taking taylor expansion of 0 in k
2.906 * [backup-simplify]: Simplify 0 into 0
2.906 * [backup-simplify]: Simplify 0 into 0
2.908 * [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))))))
2.908 * * * [progress]: simplifying candidates
2.915 * [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))))))
2.922 * * [simplify]: iteration 0: 353 enodes
3.025 * * [simplify]: iteration 1: 987 enodes
3.753 * * [simplify]: iteration 2: 4803 enodes
4.908 * * [simplify]: iteration complete: 5000 enodes
4.909 * * [simplify]: Extracting #0: cost 120 inf + 0
4.912 * * [simplify]: Extracting #1: cost 792 inf + 84
4.921 * * [simplify]: Extracting #2: cost 1285 inf + 7308
4.944 * * [simplify]: Extracting #3: cost 1106 inf + 95528
5.003 * * [simplify]: Extracting #4: cost 533 inf + 311248
5.097 * * [simplify]: Extracting #5: cost 322 inf + 426872
5.235 * * [simplify]: Extracting #6: cost 351 inf + 459535
5.352 * * [simplify]: Extracting #7: cost 306 inf + 481293
5.459 * * [simplify]: Extracting #8: cost 140 inf + 632028
5.607 * * [simplify]: Extracting #9: cost 34 inf + 739280
5.766 * * [simplify]: Extracting #10: cost 6 inf + 791010
5.930 * * [simplify]: Extracting #11: cost 0 inf + 804212
6.092 * [simplify]: Simplified to:
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (/ (* 1.0 1.0) (* (sqrt k) k)) 1.0)
  (* (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) (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)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (exp (* (* n PI) 2.0))
  (* (* (* (* 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 (* (* n PI) 2.0)) (cbrt (* (* n PI) 2.0)))
  (cbrt (* (* n PI) 2.0))
  (* (* (* (* n PI) 2.0) (* (* n PI) 2.0)) (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (* (* (* (cbrt n) (cbrt n)) PI) 2.0)
  (* (* (sqrt n) PI) 2.0)
  (* PI 2.0)
  (* n PI)
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (log (/ 1.0 (sqrt k))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (* (/ (* 1.0 1.0) (* (sqrt k) k)) 1.0) (* (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (* (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (pow (* (* n PI) 2.0) (/ 1.0 2.0)) 1.0)
  (* (sqrt k) (pow (* (* n PI) 2.0) (/ k 2.0)))
  (* (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))))
  (/ (* 1.0 (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (/ 1.0 (sqrt k))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt k))
  (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))
  (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* (sqrt 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (/ (sqrt k) (pow (* (* n PI) 2.0) (/ 1.0 2.0))))
  (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0)
  (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0)
  (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0)
  (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* (* n PI) 2.0) (/ 1.0 2.0))
  (pow (* (* n PI) 2.0) (/ k 2.0))
  (pow (* (* n PI) 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* n PI) 2.0) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* n PI) 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* n PI) 2.0) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* (* n PI) 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* n PI) 2.0) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n PI) 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* n PI) 2.0) (sqrt (- 1.0 k)))
  (pow (* (* n PI) 2.0) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n PI) 2.0) (/ 1 (sqrt 2.0)))
  (* (* n PI) 2.0)
  (pow (* (* n PI) 2.0) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n PI) 2.0) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* n PI) 2.0) (+ (sqrt 1.0) (sqrt k)))
  (pow (* (* n PI) 2.0) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n PI) 2.0) (/ 1 (sqrt 2.0)))
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (exp (* (log (* (* n PI) 2.0)) (- 1.0 k)))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0)
  (exp (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2.0) 2))
  (+ (- +nan.0 (* k +nan.0)) (* (* k k) (- +nan.0)))
  (+ (- (/ +nan.0 k) (/ (/ +nan.0 k) (* k k))) (/ (- +nan.0) (* k k)))
  (- (+ (- (/ (/ +nan.0 k) k) (/ +nan.0 k)) +nan.0))
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (- (- (* k (* +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)) (* k k)) (+ (- (* (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5) (* +nan.0 (* (* k k) (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 (* PI 2.0)) k) (* (log (* PI 2.0)) k)))) (* (* +nan.0 (* (* (* k k) (log (* PI 2.0))) (log n))) (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)) (* k (log (* PI 2.0)))) (- (* +nan.0 (* (log n) (* k (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5)))) (* +nan.0 (- (* (* (* k k) (log (* PI 2.0))) (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5)) (* (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5) (* (* (log n) k) (* (log n) k))))))))))))
  (- (+ (- (/ +nan.0 (/ (* k k) (exp (* (* (log (* (* n PI) 2.0)) (- 1.0 k)) 0.5)))) (/ (* (exp (* (* (log (* (* n PI) 2.0)) (- 1.0 k)) 0.5)) +nan.0) k)) (/ (* (exp (* (* (log (* (* n PI) 2.0)) (- 1.0 k)) 0.5)) +nan.0) (* (* 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)))))
  (+ (+ (* (* (* (log (* PI 2.0)) 0.25) (exp (* (log (* (* n PI) 2.0)) 0.5))) (* (* k k) (log n))) (* (exp (* (log (* (* n PI) 2.0)) 0.5)) (* (* (* k k) (* (log n) (log n))) 0.125))) (- (+ (exp (* (log (* (* n PI) 2.0)) 0.5)) (* (* (log (* PI 2.0)) (log (* PI 2.0))) (* (* (exp (* (log (* (* n PI) 2.0)) 0.5)) (* k k)) 0.125))) (* (* k (+ (* (log n) (exp (* (log (* (* n PI) 2.0)) 0.5))) (* (log (* PI 2.0)) (exp (* (log (* (* n PI) 2.0)) 0.5))))) 0.5)))
  (exp (* (* (log (* (* n PI) 2.0)) (- 1.0 k)) 0.5))
  (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ -1 n))) (- 1.0 k))))
6.103 * * * [progress]: adding candidates to table
7.003 * * [progress]: iteration 2 / 4
7.003 * * * [progress]: picking best candidate
7.083 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
7.083 * * * [progress]: localizing error
7.125 * * * [progress]: generating rewritten candidates
7.125 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2 1)
7.155 * * * * [progress]: [ 2 / 3 ] rewriting at (2)
7.186 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1 2)
7.209 * * * [progress]: generating series expansions
7.209 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2 1)
7.209 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
7.210 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
7.210 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.210 * [taylor]: Taking taylor expansion of 2.0 in n
7.210 * [backup-simplify]: Simplify 2.0 into 2.0
7.210 * [taylor]: Taking taylor expansion of (* n PI) in n
7.210 * [taylor]: Taking taylor expansion of n in n
7.210 * [backup-simplify]: Simplify 0 into 0
7.210 * [backup-simplify]: Simplify 1 into 1
7.210 * [taylor]: Taking taylor expansion of PI in n
7.210 * [backup-simplify]: Simplify PI into PI
7.210 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.210 * [taylor]: Taking taylor expansion of 2.0 in n
7.210 * [backup-simplify]: Simplify 2.0 into 2.0
7.210 * [taylor]: Taking taylor expansion of (* n PI) in n
7.210 * [taylor]: Taking taylor expansion of n in n
7.210 * [backup-simplify]: Simplify 0 into 0
7.210 * [backup-simplify]: Simplify 1 into 1
7.210 * [taylor]: Taking taylor expansion of PI in n
7.210 * [backup-simplify]: Simplify PI into PI
7.210 * [backup-simplify]: Simplify (* 0 PI) into 0
7.211 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.211 * [backup-simplify]: Simplify 0 into 0
7.212 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.213 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.213 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.214 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.214 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.214 * [backup-simplify]: Simplify 0 into 0
7.215 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.216 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.216 * [backup-simplify]: Simplify 0 into 0
7.217 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.218 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.218 * [backup-simplify]: Simplify 0 into 0
7.219 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.220 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
7.220 * [backup-simplify]: Simplify 0 into 0
7.221 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.222 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
7.222 * [backup-simplify]: Simplify 0 into 0
7.223 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
7.225 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
7.226 * [backup-simplify]: Simplify 0 into 0
7.226 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
7.227 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
7.227 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
7.227 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.227 * [taylor]: Taking taylor expansion of 2.0 in n
7.227 * [backup-simplify]: Simplify 2.0 into 2.0
7.227 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.227 * [taylor]: Taking taylor expansion of PI in n
7.227 * [backup-simplify]: Simplify PI into PI
7.227 * [taylor]: Taking taylor expansion of n in n
7.227 * [backup-simplify]: Simplify 0 into 0
7.227 * [backup-simplify]: Simplify 1 into 1
7.228 * [backup-simplify]: Simplify (/ PI 1) into PI
7.228 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.228 * [taylor]: Taking taylor expansion of 2.0 in n
7.228 * [backup-simplify]: Simplify 2.0 into 2.0
7.228 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.228 * [taylor]: Taking taylor expansion of PI in n
7.228 * [backup-simplify]: Simplify PI into PI
7.228 * [taylor]: Taking taylor expansion of n in n
7.228 * [backup-simplify]: Simplify 0 into 0
7.228 * [backup-simplify]: Simplify 1 into 1
7.228 * [backup-simplify]: Simplify (/ PI 1) into PI
7.229 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.229 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.231 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.231 * [backup-simplify]: Simplify 0 into 0
7.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.233 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.233 * [backup-simplify]: Simplify 0 into 0
7.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.236 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.236 * [backup-simplify]: Simplify 0 into 0
7.237 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.239 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.239 * [backup-simplify]: Simplify 0 into 0
7.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.242 * [backup-simplify]: Simplify 0 into 0
7.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.245 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.245 * [backup-simplify]: Simplify 0 into 0
7.245 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
7.246 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
7.246 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
7.246 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.246 * [taylor]: Taking taylor expansion of -2.0 in n
7.246 * [backup-simplify]: Simplify -2.0 into -2.0
7.246 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.246 * [taylor]: Taking taylor expansion of PI in n
7.246 * [backup-simplify]: Simplify PI into PI
7.246 * [taylor]: Taking taylor expansion of n in n
7.246 * [backup-simplify]: Simplify 0 into 0
7.246 * [backup-simplify]: Simplify 1 into 1
7.247 * [backup-simplify]: Simplify (/ PI 1) into PI
7.247 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.247 * [taylor]: Taking taylor expansion of -2.0 in n
7.247 * [backup-simplify]: Simplify -2.0 into -2.0
7.247 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.247 * [taylor]: Taking taylor expansion of PI in n
7.247 * [backup-simplify]: Simplify PI into PI
7.247 * [taylor]: Taking taylor expansion of n in n
7.247 * [backup-simplify]: Simplify 0 into 0
7.247 * [backup-simplify]: Simplify 1 into 1
7.248 * [backup-simplify]: Simplify (/ PI 1) into PI
7.248 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.249 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.250 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.251 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.251 * [backup-simplify]: Simplify 0 into 0
7.252 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.253 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.253 * [backup-simplify]: Simplify 0 into 0
7.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.256 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.256 * [backup-simplify]: Simplify 0 into 0
7.256 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.257 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.257 * [backup-simplify]: Simplify 0 into 0
7.258 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.259 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
7.259 * [backup-simplify]: Simplify 0 into 0
7.259 * [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
7.260 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
7.260 * [backup-simplify]: Simplify 0 into 0
7.261 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
7.261 * * * * [progress]: [ 2 / 3 ] generating series at (2)
7.264 * [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))))
7.264 * [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
7.264 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
7.264 * [taylor]: Taking taylor expansion of 1.0 in k
7.264 * [backup-simplify]: Simplify 1.0 into 1.0
7.265 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
7.265 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
7.265 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
7.265 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
7.265 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
7.265 * [taylor]: Taking taylor expansion of 0.5 in k
7.265 * [backup-simplify]: Simplify 0.5 into 0.5
7.265 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.265 * [taylor]: Taking taylor expansion of 1.0 in k
7.265 * [backup-simplify]: Simplify 1.0 into 1.0
7.265 * [taylor]: Taking taylor expansion of k in k
7.265 * [backup-simplify]: Simplify 0 into 0
7.265 * [backup-simplify]: Simplify 1 into 1
7.265 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
7.265 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
7.265 * [taylor]: Taking taylor expansion of 2.0 in k
7.265 * [backup-simplify]: Simplify 2.0 into 2.0
7.265 * [taylor]: Taking taylor expansion of (* n PI) in k
7.265 * [taylor]: Taking taylor expansion of n in k
7.265 * [backup-simplify]: Simplify n into n
7.265 * [taylor]: Taking taylor expansion of PI in k
7.265 * [backup-simplify]: Simplify PI into PI
7.265 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.265 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
7.265 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
7.265 * [backup-simplify]: Simplify (- 0) into 0
7.266 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.266 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
7.266 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
7.266 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
7.266 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.266 * [taylor]: Taking taylor expansion of k in k
7.266 * [backup-simplify]: Simplify 0 into 0
7.266 * [backup-simplify]: Simplify 1 into 1
7.266 * [backup-simplify]: Simplify (/ 1 1) into 1
7.267 * [backup-simplify]: Simplify (sqrt 0) into 0
7.268 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.268 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
7.268 * [taylor]: Taking taylor expansion of 1.0 in n
7.268 * [backup-simplify]: Simplify 1.0 into 1.0
7.268 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
7.268 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.268 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.268 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.268 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.268 * [taylor]: Taking taylor expansion of 0.5 in n
7.268 * [backup-simplify]: Simplify 0.5 into 0.5
7.268 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.268 * [taylor]: Taking taylor expansion of 1.0 in n
7.268 * [backup-simplify]: Simplify 1.0 into 1.0
7.268 * [taylor]: Taking taylor expansion of k in n
7.268 * [backup-simplify]: Simplify k into k
7.268 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.268 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.268 * [taylor]: Taking taylor expansion of 2.0 in n
7.268 * [backup-simplify]: Simplify 2.0 into 2.0
7.268 * [taylor]: Taking taylor expansion of (* n PI) in n
7.268 * [taylor]: Taking taylor expansion of n in n
7.268 * [backup-simplify]: Simplify 0 into 0
7.268 * [backup-simplify]: Simplify 1 into 1
7.268 * [taylor]: Taking taylor expansion of PI in n
7.268 * [backup-simplify]: Simplify PI into PI
7.269 * [backup-simplify]: Simplify (* 0 PI) into 0
7.269 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.270 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.271 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.272 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.272 * [backup-simplify]: Simplify (- k) into (- k)
7.272 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.272 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.273 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.273 * [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))))
7.274 * [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)))))
7.274 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.274 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.274 * [taylor]: Taking taylor expansion of k in n
7.274 * [backup-simplify]: Simplify k into k
7.274 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.274 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.274 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.274 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
7.274 * [taylor]: Taking taylor expansion of 1.0 in n
7.275 * [backup-simplify]: Simplify 1.0 into 1.0
7.275 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
7.275 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.275 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.275 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.275 * [taylor]: Taking taylor expansion of 0.5 in n
7.275 * [backup-simplify]: Simplify 0.5 into 0.5
7.275 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.275 * [taylor]: Taking taylor expansion of 1.0 in n
7.275 * [backup-simplify]: Simplify 1.0 into 1.0
7.275 * [taylor]: Taking taylor expansion of k in n
7.275 * [backup-simplify]: Simplify k into k
7.275 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.275 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.275 * [taylor]: Taking taylor expansion of 2.0 in n
7.275 * [backup-simplify]: Simplify 2.0 into 2.0
7.275 * [taylor]: Taking taylor expansion of (* n PI) in n
7.275 * [taylor]: Taking taylor expansion of n in n
7.275 * [backup-simplify]: Simplify 0 into 0
7.275 * [backup-simplify]: Simplify 1 into 1
7.275 * [taylor]: Taking taylor expansion of PI in n
7.275 * [backup-simplify]: Simplify PI into PI
7.275 * [backup-simplify]: Simplify (* 0 PI) into 0
7.276 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.276 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.277 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.278 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.278 * [backup-simplify]: Simplify (- k) into (- k)
7.278 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.278 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.279 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.280 * [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))))
7.281 * [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)))))
7.281 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.281 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.281 * [taylor]: Taking taylor expansion of k in n
7.281 * [backup-simplify]: Simplify k into k
7.281 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.281 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.281 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.281 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.282 * [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)))
7.283 * [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))))
7.283 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
7.283 * [taylor]: Taking taylor expansion of 1.0 in k
7.283 * [backup-simplify]: Simplify 1.0 into 1.0
7.283 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
7.283 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
7.283 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
7.283 * [taylor]: Taking taylor expansion of 0.5 in k
7.283 * [backup-simplify]: Simplify 0.5 into 0.5
7.283 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
7.283 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.283 * [taylor]: Taking taylor expansion of 1.0 in k
7.283 * [backup-simplify]: Simplify 1.0 into 1.0
7.283 * [taylor]: Taking taylor expansion of k in k
7.283 * [backup-simplify]: Simplify 0 into 0
7.283 * [backup-simplify]: Simplify 1 into 1
7.283 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
7.283 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.283 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.283 * [taylor]: Taking taylor expansion of 2.0 in k
7.283 * [backup-simplify]: Simplify 2.0 into 2.0
7.283 * [taylor]: Taking taylor expansion of PI in k
7.283 * [backup-simplify]: Simplify PI into PI
7.283 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.284 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.285 * [taylor]: Taking taylor expansion of (log n) in k
7.285 * [taylor]: Taking taylor expansion of n in k
7.285 * [backup-simplify]: Simplify n into n
7.285 * [backup-simplify]: Simplify (log n) into (log n)
7.285 * [backup-simplify]: Simplify (- 0) into 0
7.285 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.287 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
7.288 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
7.289 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
7.290 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.290 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.290 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.290 * [taylor]: Taking taylor expansion of k in k
7.290 * [backup-simplify]: Simplify 0 into 0
7.290 * [backup-simplify]: Simplify 1 into 1
7.291 * [backup-simplify]: Simplify (/ 1 1) into 1
7.291 * [backup-simplify]: Simplify (sqrt 0) into 0
7.293 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.294 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
7.295 * [backup-simplify]: Simplify (* 1.0 0) into 0
7.295 * [backup-simplify]: Simplify 0 into 0
7.296 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.297 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.299 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.299 * [backup-simplify]: Simplify (- 0) into 0
7.300 * [backup-simplify]: Simplify (+ 0 0) into 0
7.300 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
7.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.303 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
7.305 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.306 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
7.308 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
7.308 * [taylor]: Taking taylor expansion of 0 in k
7.308 * [backup-simplify]: Simplify 0 into 0
7.309 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.311 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.312 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.312 * [backup-simplify]: Simplify (+ 0 0) into 0
7.313 * [backup-simplify]: Simplify (- 1) into -1
7.313 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.315 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
7.317 * [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))))
7.319 * [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))))))
7.322 * [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))))))
7.323 * [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))))))
7.323 * [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))))))
7.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.324 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
7.325 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.326 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.328 * [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
7.328 * [backup-simplify]: Simplify (- 0) into 0
7.328 * [backup-simplify]: Simplify (+ 0 0) into 0
7.329 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
7.330 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.331 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.332 * [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
7.333 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
7.335 * [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
7.335 * [taylor]: Taking taylor expansion of 0 in k
7.335 * [backup-simplify]: Simplify 0 into 0
7.335 * [backup-simplify]: Simplify 0 into 0
7.335 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
7.337 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.338 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.340 * [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
7.341 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.341 * [backup-simplify]: Simplify (+ 0 0) into 0
7.342 * [backup-simplify]: Simplify (- 0) into 0
7.342 * [backup-simplify]: Simplify (+ 0 0) into 0
7.343 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.345 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.347 * [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))))))
7.358 * [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)))))))))))
7.365 * [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)))))))))))
7.370 * [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)))))))))))
7.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.371 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
7.373 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.374 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.380 * [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
7.384 * [backup-simplify]: Simplify (- 0) into 0
7.384 * [backup-simplify]: Simplify (+ 0 0) into 0
7.386 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
7.387 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.389 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.392 * [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
7.395 * [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
7.397 * [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
7.397 * [taylor]: Taking taylor expansion of 0 in k
7.397 * [backup-simplify]: Simplify 0 into 0
7.397 * [backup-simplify]: Simplify 0 into 0
7.397 * [backup-simplify]: Simplify 0 into 0
7.398 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.403 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.409 * [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
7.411 * [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
7.411 * [backup-simplify]: Simplify (+ 0 0) into 0
7.411 * [backup-simplify]: Simplify (- 0) into 0
7.411 * [backup-simplify]: Simplify (+ 0 0) into 0
7.413 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.415 * [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
7.420 * [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))))))
7.431 * [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)))))))))))))))))
7.444 * [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)))))))))))))))))
7.458 * [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)))))))))))))))))
7.480 * [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)))))))))))))))))))))
7.482 * [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)))
7.482 * [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
7.482 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
7.482 * [taylor]: Taking taylor expansion of 1.0 in k
7.482 * [backup-simplify]: Simplify 1.0 into 1.0
7.482 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
7.482 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
7.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
7.482 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
7.482 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
7.482 * [taylor]: Taking taylor expansion of 0.5 in k
7.482 * [backup-simplify]: Simplify 0.5 into 0.5
7.482 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.482 * [taylor]: Taking taylor expansion of 1.0 in k
7.482 * [backup-simplify]: Simplify 1.0 into 1.0
7.482 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.482 * [taylor]: Taking taylor expansion of k in k
7.482 * [backup-simplify]: Simplify 0 into 0
7.482 * [backup-simplify]: Simplify 1 into 1
7.483 * [backup-simplify]: Simplify (/ 1 1) into 1
7.483 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
7.483 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
7.483 * [taylor]: Taking taylor expansion of 2.0 in k
7.483 * [backup-simplify]: Simplify 2.0 into 2.0
7.483 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.483 * [taylor]: Taking taylor expansion of PI in k
7.483 * [backup-simplify]: Simplify PI into PI
7.483 * [taylor]: Taking taylor expansion of n in k
7.483 * [backup-simplify]: Simplify n into n
7.483 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.483 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
7.483 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
7.484 * [backup-simplify]: Simplify (- 1) into -1
7.484 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.484 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
7.485 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
7.485 * [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))))))
7.485 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.485 * [taylor]: Taking taylor expansion of k in k
7.485 * [backup-simplify]: Simplify 0 into 0
7.485 * [backup-simplify]: Simplify 1 into 1
7.485 * [backup-simplify]: Simplify (sqrt 0) into 0
7.487 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.487 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
7.487 * [taylor]: Taking taylor expansion of 1.0 in n
7.487 * [backup-simplify]: Simplify 1.0 into 1.0
7.487 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
7.487 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.487 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.487 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.487 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.487 * [taylor]: Taking taylor expansion of 0.5 in n
7.487 * [backup-simplify]: Simplify 0.5 into 0.5
7.487 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.487 * [taylor]: Taking taylor expansion of 1.0 in n
7.487 * [backup-simplify]: Simplify 1.0 into 1.0
7.487 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.487 * [taylor]: Taking taylor expansion of k in n
7.487 * [backup-simplify]: Simplify k into k
7.487 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.487 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.487 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.487 * [taylor]: Taking taylor expansion of 2.0 in n
7.487 * [backup-simplify]: Simplify 2.0 into 2.0
7.488 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.488 * [taylor]: Taking taylor expansion of PI in n
7.488 * [backup-simplify]: Simplify PI into PI
7.488 * [taylor]: Taking taylor expansion of n in n
7.488 * [backup-simplify]: Simplify 0 into 0
7.488 * [backup-simplify]: Simplify 1 into 1
7.488 * [backup-simplify]: Simplify (/ PI 1) into PI
7.489 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.490 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.490 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.490 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.490 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.492 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.493 * [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))))
7.495 * [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)))))
7.495 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.495 * [taylor]: Taking taylor expansion of k in n
7.495 * [backup-simplify]: Simplify k into k
7.495 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.495 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.495 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
7.495 * [taylor]: Taking taylor expansion of 1.0 in n
7.495 * [backup-simplify]: Simplify 1.0 into 1.0
7.495 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
7.495 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.495 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.495 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.495 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.495 * [taylor]: Taking taylor expansion of 0.5 in n
7.495 * [backup-simplify]: Simplify 0.5 into 0.5
7.495 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.495 * [taylor]: Taking taylor expansion of 1.0 in n
7.495 * [backup-simplify]: Simplify 1.0 into 1.0
7.495 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.495 * [taylor]: Taking taylor expansion of k in n
7.495 * [backup-simplify]: Simplify k into k
7.495 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.495 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.495 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.496 * [taylor]: Taking taylor expansion of 2.0 in n
7.496 * [backup-simplify]: Simplify 2.0 into 2.0
7.496 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.496 * [taylor]: Taking taylor expansion of PI in n
7.496 * [backup-simplify]: Simplify PI into PI
7.496 * [taylor]: Taking taylor expansion of n in n
7.496 * [backup-simplify]: Simplify 0 into 0
7.496 * [backup-simplify]: Simplify 1 into 1
7.496 * [backup-simplify]: Simplify (/ PI 1) into PI
7.497 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.498 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.498 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.498 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.498 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.501 * [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))))
7.502 * [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)))))
7.502 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.502 * [taylor]: Taking taylor expansion of k in n
7.502 * [backup-simplify]: Simplify k into k
7.503 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.503 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.504 * [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))
7.505 * [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)))
7.505 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
7.506 * [taylor]: Taking taylor expansion of 1.0 in k
7.506 * [backup-simplify]: Simplify 1.0 into 1.0
7.506 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
7.506 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
7.506 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
7.506 * [taylor]: Taking taylor expansion of 0.5 in k
7.506 * [backup-simplify]: Simplify 0.5 into 0.5
7.506 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
7.506 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.506 * [taylor]: Taking taylor expansion of 1.0 in k
7.506 * [backup-simplify]: Simplify 1.0 into 1.0
7.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.506 * [taylor]: Taking taylor expansion of k in k
7.506 * [backup-simplify]: Simplify 0 into 0
7.506 * [backup-simplify]: Simplify 1 into 1
7.506 * [backup-simplify]: Simplify (/ 1 1) into 1
7.506 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
7.506 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.506 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.506 * [taylor]: Taking taylor expansion of 2.0 in k
7.507 * [backup-simplify]: Simplify 2.0 into 2.0
7.507 * [taylor]: Taking taylor expansion of PI in k
7.507 * [backup-simplify]: Simplify PI into PI
7.507 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.511 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.511 * [taylor]: Taking taylor expansion of (log n) in k
7.511 * [taylor]: Taking taylor expansion of n in k
7.511 * [backup-simplify]: Simplify n into n
7.512 * [backup-simplify]: Simplify (log n) into (log n)
7.512 * [backup-simplify]: Simplify (- 1) into -1
7.512 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.512 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.514 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
7.515 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
7.516 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
7.517 * [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)))))
7.517 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.517 * [taylor]: Taking taylor expansion of k in k
7.517 * [backup-simplify]: Simplify 0 into 0
7.517 * [backup-simplify]: Simplify 1 into 1
7.518 * [backup-simplify]: Simplify (sqrt 0) into 0
7.519 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.521 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
7.521 * [backup-simplify]: Simplify (* 1.0 0) into 0
7.521 * [backup-simplify]: Simplify 0 into 0
7.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.525 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.525 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.525 * [backup-simplify]: Simplify (- 0) into 0
7.526 * [backup-simplify]: Simplify (+ 0 0) into 0
7.526 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
7.528 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.529 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
7.532 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.533 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
7.535 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
7.535 * [taylor]: Taking taylor expansion of 0 in k
7.535 * [backup-simplify]: Simplify 0 into 0
7.535 * [backup-simplify]: Simplify 0 into 0
7.537 * [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)))))))
7.538 * [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)))))))
7.540 * [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)))))))
7.541 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
7.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.547 * [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
7.547 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.548 * [backup-simplify]: Simplify (- 0) into 0
7.548 * [backup-simplify]: Simplify (+ 0 0) into 0
7.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
7.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.552 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
7.555 * [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
7.556 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
7.557 * [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
7.557 * [taylor]: Taking taylor expansion of 0 in k
7.558 * [backup-simplify]: Simplify 0 into 0
7.558 * [backup-simplify]: Simplify 0 into 0
7.558 * [backup-simplify]: Simplify 0 into 0
7.560 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.561 * [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)))))))
7.563 * [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)))))))
7.564 * [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)))))))
7.564 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
7.565 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.566 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.569 * [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
7.569 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.569 * [backup-simplify]: Simplify (- 0) into 0
7.570 * [backup-simplify]: Simplify (+ 0 0) into 0
7.570 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
7.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.572 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
7.574 * [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
7.575 * [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
7.577 * [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
7.577 * [taylor]: Taking taylor expansion of 0 in k
7.577 * [backup-simplify]: Simplify 0 into 0
7.577 * [backup-simplify]: Simplify 0 into 0
7.577 * [backup-simplify]: Simplify 0 into 0
7.577 * [backup-simplify]: Simplify 0 into 0
7.579 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.581 * [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)))))))
7.583 * [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)))))))
7.584 * [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)))))))
7.590 * [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))))))))
7.591 * [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))))
7.591 * [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
7.591 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 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 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
7.591 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
7.591 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
7.591 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
7.591 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) 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 k) 1.0) in k
7.591 * [taylor]: Taking taylor expansion of (/ 1 k) in k
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 * [backup-simplify]: Simplify (/ 1 1) into 1
7.592 * [taylor]: Taking taylor expansion of 1.0 in k
7.592 * [backup-simplify]: Simplify 1.0 into 1.0
7.592 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
7.592 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
7.592 * [taylor]: Taking taylor expansion of -2.0 in k
7.592 * [backup-simplify]: Simplify -2.0 into -2.0
7.592 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.592 * [taylor]: Taking taylor expansion of PI in k
7.592 * [backup-simplify]: Simplify PI into PI
7.592 * [taylor]: Taking taylor expansion of n in k
7.592 * [backup-simplify]: Simplify n into n
7.592 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.592 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
7.592 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
7.593 * [backup-simplify]: Simplify (+ 1 0) into 1
7.593 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
7.593 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
7.594 * [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))))
7.594 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.594 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.594 * [taylor]: Taking taylor expansion of -1 in k
7.594 * [backup-simplify]: Simplify -1 into -1
7.594 * [taylor]: Taking taylor expansion of k in k
7.594 * [backup-simplify]: Simplify 0 into 0
7.594 * [backup-simplify]: Simplify 1 into 1
7.594 * [backup-simplify]: Simplify (/ -1 1) into -1
7.595 * [backup-simplify]: Simplify (sqrt 0) into 0
7.596 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.596 * [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)))))
7.596 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
7.597 * [taylor]: Taking taylor expansion of 1.0 in n
7.597 * [backup-simplify]: Simplify 1.0 into 1.0
7.597 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
7.597 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.597 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.597 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.597 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.597 * [taylor]: Taking taylor expansion of 0.5 in n
7.597 * [backup-simplify]: Simplify 0.5 into 0.5
7.597 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.597 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.597 * [taylor]: Taking taylor expansion of k in n
7.597 * [backup-simplify]: Simplify k into k
7.597 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.597 * [taylor]: Taking taylor expansion of 1.0 in n
7.597 * [backup-simplify]: Simplify 1.0 into 1.0
7.597 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.597 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.597 * [taylor]: Taking taylor expansion of -2.0 in n
7.597 * [backup-simplify]: Simplify -2.0 into -2.0
7.597 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.597 * [taylor]: Taking taylor expansion of PI in n
7.597 * [backup-simplify]: Simplify PI into PI
7.597 * [taylor]: Taking taylor expansion of n in n
7.597 * [backup-simplify]: Simplify 0 into 0
7.597 * [backup-simplify]: Simplify 1 into 1
7.598 * [backup-simplify]: Simplify (/ PI 1) into PI
7.598 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.599 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.600 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.600 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.601 * [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)))
7.602 * [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))))
7.602 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.602 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.602 * [taylor]: Taking taylor expansion of -1 in n
7.602 * [backup-simplify]: Simplify -1 into -1
7.602 * [taylor]: Taking taylor expansion of k in n
7.602 * [backup-simplify]: Simplify k into k
7.602 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.602 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.602 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.602 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.603 * [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)))
7.603 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
7.603 * [taylor]: Taking taylor expansion of 1.0 in n
7.603 * [backup-simplify]: Simplify 1.0 into 1.0
7.603 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
7.603 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.603 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.603 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.603 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.603 * [taylor]: Taking taylor expansion of 0.5 in n
7.603 * [backup-simplify]: Simplify 0.5 into 0.5
7.603 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.603 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.603 * [taylor]: Taking taylor expansion of k in n
7.603 * [backup-simplify]: Simplify k into k
7.604 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.604 * [taylor]: Taking taylor expansion of 1.0 in n
7.604 * [backup-simplify]: Simplify 1.0 into 1.0
7.604 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.604 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.604 * [taylor]: Taking taylor expansion of -2.0 in n
7.604 * [backup-simplify]: Simplify -2.0 into -2.0
7.604 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.604 * [taylor]: Taking taylor expansion of PI in n
7.604 * [backup-simplify]: Simplify PI into PI
7.604 * [taylor]: Taking taylor expansion of n in n
7.604 * [backup-simplify]: Simplify 0 into 0
7.604 * [backup-simplify]: Simplify 1 into 1
7.604 * [backup-simplify]: Simplify (/ PI 1) into PI
7.604 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.605 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.605 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.605 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.607 * [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)))
7.608 * [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))))
7.608 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.608 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.608 * [taylor]: Taking taylor expansion of -1 in n
7.608 * [backup-simplify]: Simplify -1 into -1
7.608 * [taylor]: Taking taylor expansion of k in n
7.608 * [backup-simplify]: Simplify k into k
7.608 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.608 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.608 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.608 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.609 * [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)))
7.610 * [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))))
7.610 * [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
7.610 * [taylor]: Taking taylor expansion of 1.0 in k
7.610 * [backup-simplify]: Simplify 1.0 into 1.0
7.610 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
7.610 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
7.610 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
7.610 * [taylor]: Taking taylor expansion of 0.5 in k
7.610 * [backup-simplify]: Simplify 0.5 into 0.5
7.610 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
7.610 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
7.610 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
7.610 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
7.610 * [taylor]: Taking taylor expansion of -2.0 in k
7.610 * [backup-simplify]: Simplify -2.0 into -2.0
7.610 * [taylor]: Taking taylor expansion of PI in k
7.610 * [backup-simplify]: Simplify PI into PI
7.610 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.611 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.611 * [taylor]: Taking taylor expansion of (log n) in k
7.611 * [taylor]: Taking taylor expansion of n in k
7.611 * [backup-simplify]: Simplify n into n
7.611 * [backup-simplify]: Simplify (log n) into (log n)
7.611 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.611 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.611 * [taylor]: Taking taylor expansion of k in k
7.611 * [backup-simplify]: Simplify 0 into 0
7.611 * [backup-simplify]: Simplify 1 into 1
7.611 * [backup-simplify]: Simplify (/ 1 1) into 1
7.611 * [taylor]: Taking taylor expansion of 1.0 in k
7.611 * [backup-simplify]: Simplify 1.0 into 1.0
7.611 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.612 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
7.612 * [backup-simplify]: Simplify (+ 1 0) into 1
7.613 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
7.614 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
7.615 * [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))))
7.615 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.615 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.615 * [taylor]: Taking taylor expansion of -1 in k
7.615 * [backup-simplify]: Simplify -1 into -1
7.615 * [taylor]: Taking taylor expansion of k in k
7.615 * [backup-simplify]: Simplify 0 into 0
7.615 * [backup-simplify]: Simplify 1 into 1
7.615 * [backup-simplify]: Simplify (/ -1 1) into -1
7.615 * [backup-simplify]: Simplify (sqrt 0) into 0
7.616 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.617 * [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)))))
7.618 * [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)))))
7.619 * [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)))))
7.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.620 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.621 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
7.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.621 * [backup-simplify]: Simplify (+ 0 0) into 0
7.621 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
7.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.623 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
7.624 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.628 * [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
7.629 * [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
7.629 * [taylor]: Taking taylor expansion of 0 in k
7.629 * [backup-simplify]: Simplify 0 into 0
7.629 * [backup-simplify]: Simplify 0 into 0
7.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
7.631 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.633 * [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))))))
7.636 * [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))))))
7.637 * [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))))))
7.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.640 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.644 * [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
7.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.644 * [backup-simplify]: Simplify (+ 0 0) into 0
7.645 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
7.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.648 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
7.651 * [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
7.651 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.652 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
7.653 * [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
7.656 * [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
7.656 * [taylor]: Taking taylor expansion of 0 in k
7.656 * [backup-simplify]: Simplify 0 into 0
7.656 * [backup-simplify]: Simplify 0 into 0
7.656 * [backup-simplify]: Simplify 0 into 0
7.657 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.661 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.664 * [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))))))
7.667 * [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))))))
7.668 * [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))))))
7.671 * [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))))))))
7.671 * * * * [progress]: [ 3 / 3 ] generating series at (2 1 2)
7.671 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
7.671 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
7.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
7.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
7.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
7.671 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
7.671 * [taylor]: Taking taylor expansion of 0.5 in k
7.671 * [backup-simplify]: Simplify 0.5 into 0.5
7.671 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.671 * [taylor]: Taking taylor expansion of 1.0 in k
7.671 * [backup-simplify]: Simplify 1.0 into 1.0
7.671 * [taylor]: Taking taylor expansion of k in k
7.671 * [backup-simplify]: Simplify 0 into 0
7.671 * [backup-simplify]: Simplify 1 into 1
7.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
7.671 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
7.671 * [taylor]: Taking taylor expansion of 2.0 in k
7.671 * [backup-simplify]: Simplify 2.0 into 2.0
7.671 * [taylor]: Taking taylor expansion of (* n PI) in k
7.671 * [taylor]: Taking taylor expansion of n in k
7.671 * [backup-simplify]: Simplify n into n
7.671 * [taylor]: Taking taylor expansion of PI in k
7.671 * [backup-simplify]: Simplify PI into PI
7.672 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.672 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
7.672 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
7.672 * [backup-simplify]: Simplify (- 0) into 0
7.672 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.672 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
7.673 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
7.673 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
7.673 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.673 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.673 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.673 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.673 * [taylor]: Taking taylor expansion of 0.5 in n
7.673 * [backup-simplify]: Simplify 0.5 into 0.5
7.673 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.673 * [taylor]: Taking taylor expansion of 1.0 in n
7.673 * [backup-simplify]: Simplify 1.0 into 1.0
7.673 * [taylor]: Taking taylor expansion of k in n
7.673 * [backup-simplify]: Simplify k into k
7.673 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.673 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.673 * [taylor]: Taking taylor expansion of 2.0 in n
7.673 * [backup-simplify]: Simplify 2.0 into 2.0
7.673 * [taylor]: Taking taylor expansion of (* n PI) in n
7.673 * [taylor]: Taking taylor expansion of n in n
7.673 * [backup-simplify]: Simplify 0 into 0
7.673 * [backup-simplify]: Simplify 1 into 1
7.673 * [taylor]: Taking taylor expansion of PI in n
7.673 * [backup-simplify]: Simplify PI into PI
7.673 * [backup-simplify]: Simplify (* 0 PI) into 0
7.674 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.675 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.675 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.676 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.676 * [backup-simplify]: Simplify (- k) into (- k)
7.676 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.676 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.677 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.678 * [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))))
7.679 * [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)))))
7.679 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.679 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.679 * [taylor]: Taking taylor expansion of 0.5 in n
7.679 * [backup-simplify]: Simplify 0.5 into 0.5
7.679 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.679 * [taylor]: Taking taylor expansion of 1.0 in n
7.679 * [backup-simplify]: Simplify 1.0 into 1.0
7.679 * [taylor]: Taking taylor expansion of k in n
7.679 * [backup-simplify]: Simplify k into k
7.679 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.679 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.679 * [taylor]: Taking taylor expansion of 2.0 in n
7.679 * [backup-simplify]: Simplify 2.0 into 2.0
7.679 * [taylor]: Taking taylor expansion of (* n PI) in n
7.679 * [taylor]: Taking taylor expansion of n in n
7.679 * [backup-simplify]: Simplify 0 into 0
7.679 * [backup-simplify]: Simplify 1 into 1
7.679 * [taylor]: Taking taylor expansion of PI in n
7.679 * [backup-simplify]: Simplify PI into PI
7.679 * [backup-simplify]: Simplify (* 0 PI) into 0
7.680 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.681 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.682 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.682 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.682 * [backup-simplify]: Simplify (- k) into (- k)
7.682 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.683 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.683 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.684 * [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))))
7.685 * [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)))))
7.685 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
7.685 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
7.685 * [taylor]: Taking taylor expansion of 0.5 in k
7.685 * [backup-simplify]: Simplify 0.5 into 0.5
7.685 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
7.685 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.685 * [taylor]: Taking taylor expansion of 1.0 in k
7.685 * [backup-simplify]: Simplify 1.0 into 1.0
7.685 * [taylor]: Taking taylor expansion of k in k
7.685 * [backup-simplify]: Simplify 0 into 0
7.685 * [backup-simplify]: Simplify 1 into 1
7.685 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
7.685 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.685 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.685 * [taylor]: Taking taylor expansion of 2.0 in k
7.685 * [backup-simplify]: Simplify 2.0 into 2.0
7.685 * [taylor]: Taking taylor expansion of PI in k
7.685 * [backup-simplify]: Simplify PI into PI
7.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.686 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.686 * [taylor]: Taking taylor expansion of (log n) in k
7.686 * [taylor]: Taking taylor expansion of n in k
7.686 * [backup-simplify]: Simplify n into n
7.686 * [backup-simplify]: Simplify (log n) into (log n)
7.687 * [backup-simplify]: Simplify (- 0) into 0
7.687 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.688 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
7.688 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
7.689 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
7.690 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.691 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.691 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.692 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.693 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.693 * [backup-simplify]: Simplify (- 0) into 0
7.693 * [backup-simplify]: Simplify (+ 0 0) into 0
7.694 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
7.695 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.695 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
7.697 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.697 * [taylor]: Taking taylor expansion of 0 in k
7.697 * [backup-simplify]: Simplify 0 into 0
7.697 * [backup-simplify]: Simplify 0 into 0
7.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.700 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.701 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.702 * [backup-simplify]: Simplify (+ 0 0) into 0
7.702 * [backup-simplify]: Simplify (- 1) into -1
7.702 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.704 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
7.706 * [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))))
7.710 * [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))))))
7.713 * [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))))))
7.714 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.719 * [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
7.720 * [backup-simplify]: Simplify (- 0) into 0
7.720 * [backup-simplify]: Simplify (+ 0 0) into 0
7.721 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
7.722 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.724 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.726 * [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
7.726 * [taylor]: Taking taylor expansion of 0 in k
7.727 * [backup-simplify]: Simplify 0 into 0
7.727 * [backup-simplify]: Simplify 0 into 0
7.727 * [backup-simplify]: Simplify 0 into 0
7.728 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.731 * [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
7.733 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.734 * [backup-simplify]: Simplify (+ 0 0) into 0
7.734 * [backup-simplify]: Simplify (- 0) into 0
7.735 * [backup-simplify]: Simplify (+ 0 0) into 0
7.737 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.739 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.743 * [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))))))
7.749 * [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))))))
7.763 * [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)))))
7.764 * [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))))
7.764 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
7.764 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
7.764 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
7.764 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
7.764 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
7.764 * [taylor]: Taking taylor expansion of 0.5 in k
7.764 * [backup-simplify]: Simplify 0.5 into 0.5
7.764 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.764 * [taylor]: Taking taylor expansion of 1.0 in k
7.764 * [backup-simplify]: Simplify 1.0 into 1.0
7.764 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.764 * [taylor]: Taking taylor expansion of k in k
7.764 * [backup-simplify]: Simplify 0 into 0
7.765 * [backup-simplify]: Simplify 1 into 1
7.765 * [backup-simplify]: Simplify (/ 1 1) into 1
7.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
7.765 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
7.765 * [taylor]: Taking taylor expansion of 2.0 in k
7.765 * [backup-simplify]: Simplify 2.0 into 2.0
7.765 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.765 * [taylor]: Taking taylor expansion of PI in k
7.765 * [backup-simplify]: Simplify PI into PI
7.765 * [taylor]: Taking taylor expansion of n in k
7.765 * [backup-simplify]: Simplify n into n
7.765 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.765 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
7.765 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
7.766 * [backup-simplify]: Simplify (- 1) into -1
7.766 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.767 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
7.767 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
7.767 * [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))))))
7.767 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.767 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.767 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.767 * [taylor]: Taking taylor expansion of 0.5 in n
7.767 * [backup-simplify]: Simplify 0.5 into 0.5
7.767 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.767 * [taylor]: Taking taylor expansion of 1.0 in n
7.767 * [backup-simplify]: Simplify 1.0 into 1.0
7.767 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.767 * [taylor]: Taking taylor expansion of k in n
7.767 * [backup-simplify]: Simplify k into k
7.768 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.768 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.768 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.768 * [taylor]: Taking taylor expansion of 2.0 in n
7.768 * [backup-simplify]: Simplify 2.0 into 2.0
7.768 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.768 * [taylor]: Taking taylor expansion of PI in n
7.768 * [backup-simplify]: Simplify PI into PI
7.768 * [taylor]: Taking taylor expansion of n in n
7.768 * [backup-simplify]: Simplify 0 into 0
7.768 * [backup-simplify]: Simplify 1 into 1
7.768 * [backup-simplify]: Simplify (/ PI 1) into PI
7.769 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.770 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.770 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.770 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.770 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.773 * [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))))
7.774 * [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)))))
7.774 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.774 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.774 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.774 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.774 * [taylor]: Taking taylor expansion of 0.5 in n
7.774 * [backup-simplify]: Simplify 0.5 into 0.5
7.774 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.774 * [taylor]: Taking taylor expansion of 1.0 in n
7.774 * [backup-simplify]: Simplify 1.0 into 1.0
7.774 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.774 * [taylor]: Taking taylor expansion of k in n
7.774 * [backup-simplify]: Simplify k into k
7.775 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.775 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.775 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.775 * [taylor]: Taking taylor expansion of 2.0 in n
7.775 * [backup-simplify]: Simplify 2.0 into 2.0
7.775 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.775 * [taylor]: Taking taylor expansion of PI in n
7.775 * [backup-simplify]: Simplify PI into PI
7.775 * [taylor]: Taking taylor expansion of n in n
7.775 * [backup-simplify]: Simplify 0 into 0
7.775 * [backup-simplify]: Simplify 1 into 1
7.775 * [backup-simplify]: Simplify (/ PI 1) into PI
7.776 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.777 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.777 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.777 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.777 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.779 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.780 * [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))))
7.782 * [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)))))
7.782 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
7.782 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
7.782 * [taylor]: Taking taylor expansion of 0.5 in k
7.782 * [backup-simplify]: Simplify 0.5 into 0.5
7.782 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
7.782 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.782 * [taylor]: Taking taylor expansion of 1.0 in k
7.782 * [backup-simplify]: Simplify 1.0 into 1.0
7.782 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.782 * [taylor]: Taking taylor expansion of k in k
7.782 * [backup-simplify]: Simplify 0 into 0
7.782 * [backup-simplify]: Simplify 1 into 1
7.782 * [backup-simplify]: Simplify (/ 1 1) into 1
7.782 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
7.783 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.783 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.783 * [taylor]: Taking taylor expansion of 2.0 in k
7.783 * [backup-simplify]: Simplify 2.0 into 2.0
7.783 * [taylor]: Taking taylor expansion of PI in k
7.783 * [backup-simplify]: Simplify PI into PI
7.783 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.784 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.784 * [taylor]: Taking taylor expansion of (log n) in k
7.784 * [taylor]: Taking taylor expansion of n in k
7.784 * [backup-simplify]: Simplify n into n
7.785 * [backup-simplify]: Simplify (log n) into (log n)
7.785 * [backup-simplify]: Simplify (- 1) into -1
7.785 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.785 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.787 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
7.788 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
7.789 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
7.790 * [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)))))
7.792 * [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)))))
7.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.794 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.796 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.796 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.796 * [backup-simplify]: Simplify (- 0) into 0
7.797 * [backup-simplify]: Simplify (+ 0 0) into 0
7.797 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
7.799 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.800 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
7.803 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.803 * [taylor]: Taking taylor expansion of 0 in k
7.803 * [backup-simplify]: Simplify 0 into 0
7.803 * [backup-simplify]: Simplify 0 into 0
7.803 * [backup-simplify]: Simplify 0 into 0
7.804 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.806 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.809 * [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
7.810 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.810 * [backup-simplify]: Simplify (- 0) into 0
7.811 * [backup-simplify]: Simplify (+ 0 0) into 0
7.812 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
7.813 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.814 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
7.815 * [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
7.815 * [taylor]: Taking taylor expansion of 0 in k
7.815 * [backup-simplify]: Simplify 0 into 0
7.815 * [backup-simplify]: Simplify 0 into 0
7.815 * [backup-simplify]: Simplify 0 into 0
7.815 * [backup-simplify]: Simplify 0 into 0
7.816 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.817 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.820 * [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
7.820 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.821 * [backup-simplify]: Simplify (- 0) into 0
7.821 * [backup-simplify]: Simplify (+ 0 0) into 0
7.822 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
7.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.824 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
7.826 * [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
7.826 * [taylor]: Taking taylor expansion of 0 in k
7.826 * [backup-simplify]: Simplify 0 into 0
7.826 * [backup-simplify]: Simplify 0 into 0
7.827 * [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))))))
7.827 * [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)))
7.827 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
7.827 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
7.827 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
7.827 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
7.827 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
7.827 * [taylor]: Taking taylor expansion of 0.5 in k
7.827 * [backup-simplify]: Simplify 0.5 into 0.5
7.827 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.827 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.827 * [taylor]: Taking taylor expansion of k in k
7.827 * [backup-simplify]: Simplify 0 into 0
7.827 * [backup-simplify]: Simplify 1 into 1
7.828 * [backup-simplify]: Simplify (/ 1 1) into 1
7.828 * [taylor]: Taking taylor expansion of 1.0 in k
7.828 * [backup-simplify]: Simplify 1.0 into 1.0
7.828 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
7.828 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
7.828 * [taylor]: Taking taylor expansion of -2.0 in k
7.828 * [backup-simplify]: Simplify -2.0 into -2.0
7.828 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.828 * [taylor]: Taking taylor expansion of PI in k
7.828 * [backup-simplify]: Simplify PI into PI
7.828 * [taylor]: Taking taylor expansion of n in k
7.828 * [backup-simplify]: Simplify n into n
7.828 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.828 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
7.828 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
7.828 * [backup-simplify]: Simplify (+ 1 0) into 1
7.829 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
7.829 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
7.829 * [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))))
7.829 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.829 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.829 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.829 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.829 * [taylor]: Taking taylor expansion of 0.5 in n
7.829 * [backup-simplify]: Simplify 0.5 into 0.5
7.829 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.829 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.829 * [taylor]: Taking taylor expansion of k in n
7.829 * [backup-simplify]: Simplify k into k
7.829 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.829 * [taylor]: Taking taylor expansion of 1.0 in n
7.829 * [backup-simplify]: Simplify 1.0 into 1.0
7.829 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.829 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.829 * [taylor]: Taking taylor expansion of -2.0 in n
7.829 * [backup-simplify]: Simplify -2.0 into -2.0
7.829 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.829 * [taylor]: Taking taylor expansion of PI in n
7.829 * [backup-simplify]: Simplify PI into PI
7.829 * [taylor]: Taking taylor expansion of n in n
7.829 * [backup-simplify]: Simplify 0 into 0
7.829 * [backup-simplify]: Simplify 1 into 1
7.830 * [backup-simplify]: Simplify (/ PI 1) into PI
7.830 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.831 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.831 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.831 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.832 * [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)))
7.833 * [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))))
7.833 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.833 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.833 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.833 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.833 * [taylor]: Taking taylor expansion of 0.5 in n
7.833 * [backup-simplify]: Simplify 0.5 into 0.5
7.833 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.833 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.833 * [taylor]: Taking taylor expansion of k in n
7.833 * [backup-simplify]: Simplify k into k
7.834 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.834 * [taylor]: Taking taylor expansion of 1.0 in n
7.834 * [backup-simplify]: Simplify 1.0 into 1.0
7.834 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.834 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.834 * [taylor]: Taking taylor expansion of -2.0 in n
7.834 * [backup-simplify]: Simplify -2.0 into -2.0
7.834 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.834 * [taylor]: Taking taylor expansion of PI in n
7.834 * [backup-simplify]: Simplify PI into PI
7.834 * [taylor]: Taking taylor expansion of n in n
7.834 * [backup-simplify]: Simplify 0 into 0
7.834 * [backup-simplify]: Simplify 1 into 1
7.834 * [backup-simplify]: Simplify (/ PI 1) into PI
7.834 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.835 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.835 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.835 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.836 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.837 * [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)))
7.838 * [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))))
7.838 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
7.838 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
7.838 * [taylor]: Taking taylor expansion of 0.5 in k
7.838 * [backup-simplify]: Simplify 0.5 into 0.5
7.838 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
7.838 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
7.838 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
7.838 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
7.838 * [taylor]: Taking taylor expansion of -2.0 in k
7.838 * [backup-simplify]: Simplify -2.0 into -2.0
7.838 * [taylor]: Taking taylor expansion of PI in k
7.838 * [backup-simplify]: Simplify PI into PI
7.838 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.839 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.839 * [taylor]: Taking taylor expansion of (log n) in k
7.839 * [taylor]: Taking taylor expansion of n in k
7.839 * [backup-simplify]: Simplify n into n
7.839 * [backup-simplify]: Simplify (log n) into (log n)
7.839 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.839 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.839 * [taylor]: Taking taylor expansion of k in k
7.839 * [backup-simplify]: Simplify 0 into 0
7.839 * [backup-simplify]: Simplify 1 into 1
7.839 * [backup-simplify]: Simplify (/ 1 1) into 1
7.839 * [taylor]: Taking taylor expansion of 1.0 in k
7.839 * [backup-simplify]: Simplify 1.0 into 1.0
7.840 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.841 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
7.841 * [backup-simplify]: Simplify (+ 1 0) into 1
7.842 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
7.844 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
7.845 * [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))))
7.846 * [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))))
7.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.848 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.850 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
7.850 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.850 * [backup-simplify]: Simplify (+ 0 0) into 0
7.851 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
7.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.854 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
7.856 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.856 * [taylor]: Taking taylor expansion of 0 in k
7.856 * [backup-simplify]: Simplify 0 into 0
7.856 * [backup-simplify]: Simplify 0 into 0
7.856 * [backup-simplify]: Simplify 0 into 0
7.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.859 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.863 * [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
7.863 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.863 * [backup-simplify]: Simplify (+ 0 0) into 0
7.864 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
7.866 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.867 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
7.870 * [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
7.870 * [taylor]: Taking taylor expansion of 0 in k
7.870 * [backup-simplify]: Simplify 0 into 0
7.870 * [backup-simplify]: Simplify 0 into 0
7.870 * [backup-simplify]: Simplify 0 into 0
7.870 * [backup-simplify]: Simplify 0 into 0
7.872 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.873 * [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
7.877 * [backup-simplify]: Simplify (+ 0 0) into 0
7.877 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
7.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.880 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
7.881 * [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
7.881 * [taylor]: Taking taylor expansion of 0 in k
7.881 * [backup-simplify]: Simplify 0 into 0
7.881 * [backup-simplify]: Simplify 0 into 0
7.882 * [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))))))
7.882 * * * [progress]: simplifying candidates
7.886 * [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))))))
7.888 * * [simplify]: iteration 0: 262 enodes
7.955 * * [simplify]: iteration 1: 740 enodes
8.280 * * [simplify]: iteration 2: 3467 enodes
9.204 * * [simplify]: iteration complete: 5000 enodes
9.204 * * [simplify]: Extracting #0: cost 68 inf + 0
9.207 * * [simplify]: Extracting #1: cost 768 inf + 1
9.216 * * [simplify]: Extracting #2: cost 1663 inf + 5836
9.232 * * [simplify]: Extracting #3: cost 1366 inf + 88585
9.299 * * [simplify]: Extracting #4: cost 552 inf + 429061
9.405 * * [simplify]: Extracting #5: cost 200 inf + 605311
9.539 * * [simplify]: Extracting #6: cost 137 inf + 659564
9.716 * * [simplify]: Extracting #7: cost 77 inf + 699714
9.895 * * [simplify]: Extracting #8: cost 29 inf + 732349
10.054 * * [simplify]: Extracting #9: cost 0 inf + 749067
10.241 * * [simplify]: Extracting #10: cost 0 inf + 745447
10.373 * * [simplify]: Extracting #11: cost 0 inf + 745407
10.507 * [simplify]: Simplified to:
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (exp (* (* n PI) 2.0))
  (* (* (* (* 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 (* (* n PI) 2.0)) (cbrt (* (* n PI) 2.0)))
  (cbrt (* (* n PI) 2.0))
  (* (* (* (* n PI) 2.0) (* (* n PI) 2.0)) (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (* (* (cbrt n) (cbrt n)) (* 2.0 PI))
  (* (* 2.0 PI) (sqrt n))
  (* 2.0 PI)
  (* n PI)
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (- (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0))) (log (/ (sqrt k) 1.0)))
  (exp (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (/ (* (sqrt k) k) (* (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (/ (* (sqrt k) k) (* (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))))
  (* (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (* (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (- 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (- (sqrt k))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (/ (sqrt k) 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (fabs (cbrt k)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* n PI) 2.0) (/ k 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* (* n PI) 2.0)))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* (* n PI) 2.0) (/ 1.0 2.0))
  (pow (* (* n PI) 2.0) (/ k 2.0))
  (pow (* (* n PI) 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* n PI) 2.0) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* n PI) 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* n PI) 2.0) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* n PI) 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* n PI) 2.0) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n PI) 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* n PI) 2.0) (sqrt (- 1.0 k)))
  (pow (* (* n PI) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n PI) 2.0) (/ 1 (sqrt 2.0)))
  (* (* n PI) 2.0)
  (pow (* (* n PI) 2.0) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n PI) 2.0) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* (* n PI) 2.0) (+ (sqrt k) (sqrt 1.0)))
  (pow (* (* n PI) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n PI) 2.0) (/ 1 (sqrt 2.0)))
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (exp (* (log (* (* n PI) 2.0)) (- 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 (* (* n PI) 2.0)))
  (exp (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (* (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2) 2.0))
  (pow (* (* n PI) 2.0) (/ (/ (- 1.0 k) 2) 2.0))
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (+ (- (* +nan.0 (exp (* (log (* (* n PI) 2.0)) 0.5))) (- (* (* (log (* 2.0 PI)) (* (log (* 2.0 PI)) (exp (* (log (* (* n PI) 2.0)) 0.5)))) (* (* k k) +nan.0)) (+ (- (* (exp (* (log (* (* n PI) 2.0)) 0.5)) (* (* k k) +nan.0)) (* (* (* (log n) (log n)) (* (exp (* (log (* (* n PI) 2.0)) 0.5)) (* k k))) +nan.0)) (- (* (exp (* (log (* (* n PI) 2.0)) 0.5)) (* (* (log n) (* k k)) +nan.0)) (+ (- (* +nan.0 (* (* (exp (* (log (* (* n PI) 2.0)) 0.5)) (* k k)) (log (* 2.0 PI)))) (* (* +nan.0 (exp (* (log (* (* n PI) 2.0)) 0.5))) (* k (log n)))) (* (* k (exp (* (log (* (* n PI) 2.0)) 0.5))) (- (* +nan.0 (log (* 2.0 PI))) +nan.0))))))) (- (* (* (* +nan.0 (log (* 2.0 PI))) (exp (* (log (* (* n PI) 2.0)) 0.5))) (* (log n) (* k k)))))
  (+ (* (/ (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* n PI) 2.0)))) k) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* n PI) 2.0)))) k) (/ (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* n PI) 2.0)))) k) (* k k)))))
  (+ (* (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n))))) (- +nan.0)) (* +nan.0 (- (/ (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n))))) k) (/ (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n))))) (* k k)))))
  (- (+ (+ (* (* 0.25 (* (log (* 2.0 PI)) (exp (* (log (* (* n PI) 2.0)) 0.5)))) (* (log n) (* k k))) (+ (exp (* (log (* (* n PI) 2.0)) 0.5)) (* (* (* k k) (* (log n) (log n))) (* (exp (* (log (* (* n PI) 2.0)) 0.5)) 0.125)))) (* (* (log (* 2.0 PI)) (* (log (* 2.0 PI)) (exp (* (log (* (* n PI) 2.0)) 0.5)))) (* (* k k) 0.125))) (* 0.5 (* k (+ (* (log n) (exp (* (log (* (* n PI) 2.0)) 0.5))) (* (log (* 2.0 PI)) (exp (* (log (* (* n PI) 2.0)) 0.5)))))))
  (exp (* (* 0.5 (- 1.0 k)) (log (* (* n PI) 2.0))))
  (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n)))))
10.514 * * * [progress]: adding candidates to table
11.090 * * [progress]: iteration 3 / 4
11.090 * * * [progress]: picking best candidate
11.143 * * * * [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)))))>
11.143 * * * [progress]: localizing error
11.201 * * * [progress]: generating rewritten candidates
11.201 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 2 1)
11.215 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
11.240 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
11.280 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
11.300 * * * [progress]: generating series expansions
11.300 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 2 1)
11.301 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.301 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
11.301 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.301 * [taylor]: Taking taylor expansion of 2.0 in n
11.301 * [backup-simplify]: Simplify 2.0 into 2.0
11.301 * [taylor]: Taking taylor expansion of (* n PI) in n
11.301 * [taylor]: Taking taylor expansion of n in n
11.301 * [backup-simplify]: Simplify 0 into 0
11.301 * [backup-simplify]: Simplify 1 into 1
11.301 * [taylor]: Taking taylor expansion of PI in n
11.301 * [backup-simplify]: Simplify PI into PI
11.301 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.301 * [taylor]: Taking taylor expansion of 2.0 in n
11.301 * [backup-simplify]: Simplify 2.0 into 2.0
11.301 * [taylor]: Taking taylor expansion of (* n PI) in n
11.301 * [taylor]: Taking taylor expansion of n in n
11.301 * [backup-simplify]: Simplify 0 into 0
11.301 * [backup-simplify]: Simplify 1 into 1
11.301 * [taylor]: Taking taylor expansion of PI in n
11.301 * [backup-simplify]: Simplify PI into PI
11.302 * [backup-simplify]: Simplify (* 0 PI) into 0
11.302 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.302 * [backup-simplify]: Simplify 0 into 0
11.303 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.305 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.306 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.307 * [backup-simplify]: Simplify 0 into 0
11.308 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.309 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.309 * [backup-simplify]: Simplify 0 into 0
11.311 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.312 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.312 * [backup-simplify]: Simplify 0 into 0
11.314 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
11.315 * [backup-simplify]: Simplify 0 into 0
11.316 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
11.317 * [backup-simplify]: Simplify 0 into 0
11.318 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.320 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
11.320 * [backup-simplify]: Simplify 0 into 0
11.320 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.321 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
11.321 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
11.321 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.321 * [taylor]: Taking taylor expansion of 2.0 in n
11.321 * [backup-simplify]: Simplify 2.0 into 2.0
11.321 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.321 * [taylor]: Taking taylor expansion of PI in n
11.321 * [backup-simplify]: Simplify PI into PI
11.321 * [taylor]: Taking taylor expansion of n in n
11.321 * [backup-simplify]: Simplify 0 into 0
11.321 * [backup-simplify]: Simplify 1 into 1
11.322 * [backup-simplify]: Simplify (/ PI 1) into PI
11.322 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.322 * [taylor]: Taking taylor expansion of 2.0 in n
11.322 * [backup-simplify]: Simplify 2.0 into 2.0
11.322 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.322 * [taylor]: Taking taylor expansion of PI in n
11.322 * [backup-simplify]: Simplify PI into PI
11.322 * [taylor]: Taking taylor expansion of n in n
11.322 * [backup-simplify]: Simplify 0 into 0
11.322 * [backup-simplify]: Simplify 1 into 1
11.322 * [backup-simplify]: Simplify (/ PI 1) into PI
11.323 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.323 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.325 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.325 * [backup-simplify]: Simplify 0 into 0
11.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.327 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.327 * [backup-simplify]: Simplify 0 into 0
11.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.330 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.330 * [backup-simplify]: Simplify 0 into 0
11.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.333 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.333 * [backup-simplify]: Simplify 0 into 0
11.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.336 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.336 * [backup-simplify]: Simplify 0 into 0
11.337 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.338 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.338 * [backup-simplify]: Simplify 0 into 0
11.338 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
11.338 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
11.338 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
11.339 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.339 * [taylor]: Taking taylor expansion of -2.0 in n
11.339 * [backup-simplify]: Simplify -2.0 into -2.0
11.339 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.339 * [taylor]: Taking taylor expansion of PI in n
11.339 * [backup-simplify]: Simplify PI into PI
11.339 * [taylor]: Taking taylor expansion of n in n
11.339 * [backup-simplify]: Simplify 0 into 0
11.339 * [backup-simplify]: Simplify 1 into 1
11.339 * [backup-simplify]: Simplify (/ PI 1) into PI
11.339 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.339 * [taylor]: Taking taylor expansion of -2.0 in n
11.339 * [backup-simplify]: Simplify -2.0 into -2.0
11.339 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.339 * [taylor]: Taking taylor expansion of PI in n
11.339 * [backup-simplify]: Simplify PI into PI
11.339 * [taylor]: Taking taylor expansion of n in n
11.339 * [backup-simplify]: Simplify 0 into 0
11.339 * [backup-simplify]: Simplify 1 into 1
11.339 * [backup-simplify]: Simplify (/ PI 1) into PI
11.340 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.340 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.341 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.341 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.341 * [backup-simplify]: Simplify 0 into 0
11.342 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.343 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.343 * [backup-simplify]: Simplify 0 into 0
11.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.344 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.344 * [backup-simplify]: Simplify 0 into 0
11.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.346 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.346 * [backup-simplify]: Simplify 0 into 0
11.347 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.348 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.348 * [backup-simplify]: Simplify 0 into 0
11.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.350 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.350 * [backup-simplify]: Simplify 0 into 0
11.350 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
11.350 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
11.351 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.351 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
11.351 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.351 * [taylor]: Taking taylor expansion of 2.0 in n
11.351 * [backup-simplify]: Simplify 2.0 into 2.0
11.351 * [taylor]: Taking taylor expansion of (* n PI) in n
11.351 * [taylor]: Taking taylor expansion of n in n
11.351 * [backup-simplify]: Simplify 0 into 0
11.351 * [backup-simplify]: Simplify 1 into 1
11.351 * [taylor]: Taking taylor expansion of PI in n
11.351 * [backup-simplify]: Simplify PI into PI
11.351 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.351 * [taylor]: Taking taylor expansion of 2.0 in n
11.351 * [backup-simplify]: Simplify 2.0 into 2.0
11.351 * [taylor]: Taking taylor expansion of (* n PI) in n
11.351 * [taylor]: Taking taylor expansion of n in n
11.351 * [backup-simplify]: Simplify 0 into 0
11.351 * [backup-simplify]: Simplify 1 into 1
11.351 * [taylor]: Taking taylor expansion of PI in n
11.351 * [backup-simplify]: Simplify PI into PI
11.351 * [backup-simplify]: Simplify (* 0 PI) into 0
11.351 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.352 * [backup-simplify]: Simplify 0 into 0
11.353 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.354 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.354 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.355 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.359 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.359 * [backup-simplify]: Simplify 0 into 0
11.360 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.361 * [backup-simplify]: Simplify 0 into 0
11.362 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.362 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.363 * [backup-simplify]: Simplify 0 into 0
11.363 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.364 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
11.364 * [backup-simplify]: Simplify 0 into 0
11.365 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.366 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
11.366 * [backup-simplify]: Simplify 0 into 0
11.368 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.369 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
11.369 * [backup-simplify]: Simplify 0 into 0
11.369 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.370 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
11.370 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
11.370 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.370 * [taylor]: Taking taylor expansion of 2.0 in n
11.370 * [backup-simplify]: Simplify 2.0 into 2.0
11.370 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.370 * [taylor]: Taking taylor expansion of PI in n
11.370 * [backup-simplify]: Simplify PI into PI
11.370 * [taylor]: Taking taylor expansion of n in n
11.370 * [backup-simplify]: Simplify 0 into 0
11.370 * [backup-simplify]: Simplify 1 into 1
11.370 * [backup-simplify]: Simplify (/ PI 1) into PI
11.370 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.370 * [taylor]: Taking taylor expansion of 2.0 in n
11.370 * [backup-simplify]: Simplify 2.0 into 2.0
11.370 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.370 * [taylor]: Taking taylor expansion of PI in n
11.370 * [backup-simplify]: Simplify PI into PI
11.370 * [taylor]: Taking taylor expansion of n in n
11.370 * [backup-simplify]: Simplify 0 into 0
11.370 * [backup-simplify]: Simplify 1 into 1
11.370 * [backup-simplify]: Simplify (/ PI 1) into PI
11.371 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.371 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.372 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.372 * [backup-simplify]: Simplify 0 into 0
11.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.374 * [backup-simplify]: Simplify 0 into 0
11.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.375 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.375 * [backup-simplify]: Simplify 0 into 0
11.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.376 * [backup-simplify]: Simplify 0 into 0
11.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.378 * [backup-simplify]: Simplify 0 into 0
11.379 * [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
11.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.380 * [backup-simplify]: Simplify 0 into 0
11.380 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
11.381 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
11.381 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
11.381 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.381 * [taylor]: Taking taylor expansion of -2.0 in n
11.381 * [backup-simplify]: Simplify -2.0 into -2.0
11.381 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.381 * [taylor]: Taking taylor expansion of PI in n
11.381 * [backup-simplify]: Simplify PI into PI
11.381 * [taylor]: Taking taylor expansion of n in n
11.381 * [backup-simplify]: Simplify 0 into 0
11.381 * [backup-simplify]: Simplify 1 into 1
11.381 * [backup-simplify]: Simplify (/ PI 1) into PI
11.381 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.381 * [taylor]: Taking taylor expansion of -2.0 in n
11.381 * [backup-simplify]: Simplify -2.0 into -2.0
11.381 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.381 * [taylor]: Taking taylor expansion of PI in n
11.381 * [backup-simplify]: Simplify PI into PI
11.381 * [taylor]: Taking taylor expansion of n in n
11.381 * [backup-simplify]: Simplify 0 into 0
11.381 * [backup-simplify]: Simplify 1 into 1
11.382 * [backup-simplify]: Simplify (/ PI 1) into PI
11.382 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.382 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.383 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.384 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.384 * [backup-simplify]: Simplify 0 into 0
11.384 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.385 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.385 * [backup-simplify]: Simplify 0 into 0
11.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.386 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.386 * [backup-simplify]: Simplify 0 into 0
11.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.388 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.388 * [backup-simplify]: Simplify 0 into 0
11.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.389 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.389 * [backup-simplify]: Simplify 0 into 0
11.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.391 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.391 * [backup-simplify]: Simplify 0 into 0
11.391 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
11.391 * * * * [progress]: [ 3 / 4 ] generating series at (2)
11.393 * [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)))
11.393 * [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
11.393 * [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
11.393 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k
11.393 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
11.393 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
11.393 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
11.393 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
11.393 * [taylor]: Taking taylor expansion of 0.5 in k
11.393 * [backup-simplify]: Simplify 0.5 into 0.5
11.393 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.393 * [taylor]: Taking taylor expansion of 1.0 in k
11.393 * [backup-simplify]: Simplify 1.0 into 1.0
11.393 * [taylor]: Taking taylor expansion of k in k
11.393 * [backup-simplify]: Simplify 0 into 0
11.393 * [backup-simplify]: Simplify 1 into 1
11.393 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
11.393 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
11.393 * [taylor]: Taking taylor expansion of 2.0 in k
11.393 * [backup-simplify]: Simplify 2.0 into 2.0
11.393 * [taylor]: Taking taylor expansion of (* n PI) in k
11.393 * [taylor]: Taking taylor expansion of n in k
11.393 * [backup-simplify]: Simplify n into n
11.393 * [taylor]: Taking taylor expansion of PI in k
11.393 * [backup-simplify]: Simplify PI into PI
11.393 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.393 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
11.393 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
11.393 * [backup-simplify]: Simplify (- 0) into 0
11.394 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.394 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
11.394 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
11.394 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
11.394 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.394 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.394 * [taylor]: Taking taylor expansion of 1.0 in k
11.394 * [backup-simplify]: Simplify 1.0 into 1.0
11.395 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.395 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.395 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.395 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.395 * [taylor]: Taking taylor expansion of k in k
11.395 * [backup-simplify]: Simplify 0 into 0
11.395 * [backup-simplify]: Simplify 1 into 1
11.395 * [backup-simplify]: Simplify (/ 1 1) into 1
11.396 * [backup-simplify]: Simplify (sqrt 0) into 0
11.396 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.396 * [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
11.397 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
11.397 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.397 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.397 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.397 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.397 * [taylor]: Taking taylor expansion of 0.5 in n
11.397 * [backup-simplify]: Simplify 0.5 into 0.5
11.397 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.397 * [taylor]: Taking taylor expansion of 1.0 in n
11.397 * [backup-simplify]: Simplify 1.0 into 1.0
11.397 * [taylor]: Taking taylor expansion of k in n
11.397 * [backup-simplify]: Simplify k into k
11.397 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.397 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.397 * [taylor]: Taking taylor expansion of 2.0 in n
11.397 * [backup-simplify]: Simplify 2.0 into 2.0
11.397 * [taylor]: Taking taylor expansion of (* n PI) in n
11.397 * [taylor]: Taking taylor expansion of n in n
11.397 * [backup-simplify]: Simplify 0 into 0
11.397 * [backup-simplify]: Simplify 1 into 1
11.397 * [taylor]: Taking taylor expansion of PI in n
11.397 * [backup-simplify]: Simplify PI into PI
11.397 * [backup-simplify]: Simplify (* 0 PI) into 0
11.397 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.398 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.399 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.400 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.400 * [backup-simplify]: Simplify (- k) into (- k)
11.400 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.400 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.401 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.402 * [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))))
11.403 * [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)))))
11.403 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.403 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.403 * [taylor]: Taking taylor expansion of 1.0 in n
11.403 * [backup-simplify]: Simplify 1.0 into 1.0
11.403 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.403 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.403 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.403 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.404 * [taylor]: Taking taylor expansion of k in n
11.404 * [backup-simplify]: Simplify k into k
11.404 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.404 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.404 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.404 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.404 * [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
11.404 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
11.404 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.404 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.404 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.404 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.404 * [taylor]: Taking taylor expansion of 0.5 in n
11.404 * [backup-simplify]: Simplify 0.5 into 0.5
11.404 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.404 * [taylor]: Taking taylor expansion of 1.0 in n
11.404 * [backup-simplify]: Simplify 1.0 into 1.0
11.404 * [taylor]: Taking taylor expansion of k in n
11.404 * [backup-simplify]: Simplify k into k
11.404 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.404 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.404 * [taylor]: Taking taylor expansion of 2.0 in n
11.404 * [backup-simplify]: Simplify 2.0 into 2.0
11.404 * [taylor]: Taking taylor expansion of (* n PI) in n
11.404 * [taylor]: Taking taylor expansion of n in n
11.404 * [backup-simplify]: Simplify 0 into 0
11.404 * [backup-simplify]: Simplify 1 into 1
11.404 * [taylor]: Taking taylor expansion of PI in n
11.404 * [backup-simplify]: Simplify PI into PI
11.404 * [backup-simplify]: Simplify (* 0 PI) into 0
11.405 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.406 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.407 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.407 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.407 * [backup-simplify]: Simplify (- k) into (- k)
11.407 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.408 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.409 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.411 * [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))))
11.412 * [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)))))
11.412 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.412 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.412 * [taylor]: Taking taylor expansion of 1.0 in n
11.412 * [backup-simplify]: Simplify 1.0 into 1.0
11.412 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.413 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.413 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.413 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.413 * [taylor]: Taking taylor expansion of k in n
11.413 * [backup-simplify]: Simplify k into k
11.413 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.413 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.414 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.414 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.415 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.417 * [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))))))
11.420 * [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)))
11.420 * [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
11.420 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
11.420 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.420 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.420 * [taylor]: Taking taylor expansion of 1.0 in k
11.420 * [backup-simplify]: Simplify 1.0 into 1.0
11.420 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.421 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.421 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
11.421 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
11.421 * [taylor]: Taking taylor expansion of 0.5 in k
11.421 * [backup-simplify]: Simplify 0.5 into 0.5
11.421 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
11.421 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.421 * [taylor]: Taking taylor expansion of 1.0 in k
11.421 * [backup-simplify]: Simplify 1.0 into 1.0
11.421 * [taylor]: Taking taylor expansion of k in k
11.421 * [backup-simplify]: Simplify 0 into 0
11.421 * [backup-simplify]: Simplify 1 into 1
11.422 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
11.422 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
11.422 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
11.422 * [taylor]: Taking taylor expansion of 2.0 in k
11.422 * [backup-simplify]: Simplify 2.0 into 2.0
11.422 * [taylor]: Taking taylor expansion of PI in k
11.422 * [backup-simplify]: Simplify PI into PI
11.422 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.423 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.423 * [taylor]: Taking taylor expansion of (log n) in k
11.423 * [taylor]: Taking taylor expansion of n in k
11.423 * [backup-simplify]: Simplify n into n
11.424 * [backup-simplify]: Simplify (log n) into (log n)
11.424 * [backup-simplify]: Simplify (- 0) into 0
11.424 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.425 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
11.427 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
11.428 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
11.429 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
11.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.429 * [taylor]: Taking taylor expansion of k in k
11.429 * [backup-simplify]: Simplify 0 into 0
11.429 * [backup-simplify]: Simplify 1 into 1
11.430 * [backup-simplify]: Simplify (/ 1 1) into 1
11.430 * [backup-simplify]: Simplify (sqrt 0) into 0
11.431 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.433 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.435 * [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)))))
11.438 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) 0) into 0
11.438 * [backup-simplify]: Simplify 0 into 0
11.439 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.440 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.443 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.443 * [backup-simplify]: Simplify (- 0) into 0
11.444 * [backup-simplify]: Simplify (+ 0 0) into 0
11.444 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
11.446 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.447 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
11.449 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.451 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0
11.453 * [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
11.453 * [taylor]: Taking taylor expansion of 0 in k
11.453 * [backup-simplify]: Simplify 0 into 0
11.453 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.454 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.455 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.455 * [backup-simplify]: Simplify (+ 0 0) into 0
11.455 * [backup-simplify]: Simplify (- 1) into -1
11.456 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.457 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
11.458 * [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))))
11.460 * [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))))))
11.461 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.464 * [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)))))))))
11.474 * [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)))))))
11.475 * [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)))))))
11.475 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.476 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
11.477 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.477 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.478 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.479 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.481 * [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
11.481 * [backup-simplify]: Simplify (- 0) into 0
11.481 * [backup-simplify]: Simplify (+ 0 0) into 0
11.482 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
11.483 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.484 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
11.486 * [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
11.489 * [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
11.492 * [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
11.492 * [taylor]: Taking taylor expansion of 0 in k
11.492 * [backup-simplify]: Simplify 0 into 0
11.492 * [backup-simplify]: Simplify 0 into 0
11.493 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
11.496 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.497 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.501 * [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
11.503 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.503 * [backup-simplify]: Simplify (+ 0 0) into 0
11.504 * [backup-simplify]: Simplify (- 0) into 0
11.504 * [backup-simplify]: Simplify (+ 0 0) into 0
11.506 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
11.509 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.513 * [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))))))
11.514 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.515 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.527 * [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))))))
11.547 * [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)))))))))))
11.556 * [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)))))))))))
11.556 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.557 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
11.558 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
11.559 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
11.561 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.562 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.568 * [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
11.569 * [backup-simplify]: Simplify (- 0) into 0
11.569 * [backup-simplify]: Simplify (+ 0 0) into 0
11.570 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
11.572 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.574 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.577 * [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
11.579 * [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
11.583 * [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
11.583 * [taylor]: Taking taylor expansion of 0 in k
11.583 * [backup-simplify]: Simplify 0 into 0
11.583 * [backup-simplify]: Simplify 0 into 0
11.583 * [backup-simplify]: Simplify 0 into 0
11.584 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.587 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.587 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.591 * [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
11.593 * [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
11.593 * [backup-simplify]: Simplify (+ 0 0) into 0
11.593 * [backup-simplify]: Simplify (- 0) into 0
11.593 * [backup-simplify]: Simplify (+ 0 0) into 0
11.595 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.597 * [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
11.606 * [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))))))
11.606 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
11.607 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
11.621 * [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)))))))))))
11.659 * [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)))))))))))))))
11.681 * [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)))))))))))))))
11.702 * [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))))))))))))))))))))))))
11.703 * [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))
11.703 * [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
11.703 * [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
11.703 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
11.703 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.704 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.704 * [taylor]: Taking taylor expansion of 1.0 in k
11.704 * [backup-simplify]: Simplify 1.0 into 1.0
11.704 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.704 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.704 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
11.704 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
11.704 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
11.704 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
11.704 * [taylor]: Taking taylor expansion of 0.5 in k
11.704 * [backup-simplify]: Simplify 0.5 into 0.5
11.704 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
11.704 * [taylor]: Taking taylor expansion of 1.0 in k
11.704 * [backup-simplify]: Simplify 1.0 into 1.0
11.704 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.704 * [taylor]: Taking taylor expansion of k in k
11.704 * [backup-simplify]: Simplify 0 into 0
11.704 * [backup-simplify]: Simplify 1 into 1
11.705 * [backup-simplify]: Simplify (/ 1 1) into 1
11.705 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
11.705 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
11.705 * [taylor]: Taking taylor expansion of 2.0 in k
11.705 * [backup-simplify]: Simplify 2.0 into 2.0
11.705 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.705 * [taylor]: Taking taylor expansion of PI in k
11.705 * [backup-simplify]: Simplify PI into PI
11.705 * [taylor]: Taking taylor expansion of n in k
11.705 * [backup-simplify]: Simplify n into n
11.705 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.705 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
11.705 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
11.705 * [backup-simplify]: Simplify (- 1) into -1
11.706 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.706 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
11.706 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
11.706 * [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))))))
11.706 * [taylor]: Taking taylor expansion of (sqrt k) in k
11.706 * [taylor]: Taking taylor expansion of k in k
11.706 * [backup-simplify]: Simplify 0 into 0
11.706 * [backup-simplify]: Simplify 1 into 1
11.707 * [backup-simplify]: Simplify (sqrt 0) into 0
11.708 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.708 * [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
11.708 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
11.708 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.708 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.708 * [taylor]: Taking taylor expansion of 1.0 in n
11.708 * [backup-simplify]: Simplify 1.0 into 1.0
11.708 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.709 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.709 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
11.709 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
11.709 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
11.709 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
11.709 * [taylor]: Taking taylor expansion of 0.5 in n
11.709 * [backup-simplify]: Simplify 0.5 into 0.5
11.709 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
11.709 * [taylor]: Taking taylor expansion of 1.0 in n
11.709 * [backup-simplify]: Simplify 1.0 into 1.0
11.709 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.709 * [taylor]: Taking taylor expansion of k in n
11.709 * [backup-simplify]: Simplify k into k
11.709 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.709 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
11.709 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.709 * [taylor]: Taking taylor expansion of 2.0 in n
11.709 * [backup-simplify]: Simplify 2.0 into 2.0
11.709 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.709 * [taylor]: Taking taylor expansion of PI in n
11.709 * [backup-simplify]: Simplify PI into PI
11.709 * [taylor]: Taking taylor expansion of n in n
11.709 * [backup-simplify]: Simplify 0 into 0
11.709 * [backup-simplify]: Simplify 1 into 1
11.710 * [backup-simplify]: Simplify (/ PI 1) into PI
11.710 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.711 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.711 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.711 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
11.711 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
11.712 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.712 * [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))))
11.713 * [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)))))
11.713 * [taylor]: Taking taylor expansion of (sqrt k) in n
11.713 * [taylor]: Taking taylor expansion of k in n
11.713 * [backup-simplify]: Simplify k into k
11.713 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
11.713 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
11.713 * [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
11.714 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
11.714 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.714 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.714 * [taylor]: Taking taylor expansion of 1.0 in n
11.714 * [backup-simplify]: Simplify 1.0 into 1.0
11.714 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.714 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.714 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
11.714 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
11.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
11.714 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
11.714 * [taylor]: Taking taylor expansion of 0.5 in n
11.714 * [backup-simplify]: Simplify 0.5 into 0.5
11.714 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
11.714 * [taylor]: Taking taylor expansion of 1.0 in n
11.714 * [backup-simplify]: Simplify 1.0 into 1.0
11.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.715 * [taylor]: Taking taylor expansion of k in n
11.715 * [backup-simplify]: Simplify k into k
11.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
11.715 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.715 * [taylor]: Taking taylor expansion of 2.0 in n
11.715 * [backup-simplify]: Simplify 2.0 into 2.0
11.715 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.715 * [taylor]: Taking taylor expansion of PI in n
11.715 * [backup-simplify]: Simplify PI into PI
11.715 * [taylor]: Taking taylor expansion of n in n
11.715 * [backup-simplify]: Simplify 0 into 0
11.715 * [backup-simplify]: Simplify 1 into 1
11.715 * [backup-simplify]: Simplify (/ PI 1) into PI
11.715 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.716 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.716 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.716 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
11.716 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
11.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.718 * [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))))
11.723 * [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)))))
11.723 * [taylor]: Taking taylor expansion of (sqrt k) in n
11.723 * [taylor]: Taking taylor expansion of k in n
11.723 * [backup-simplify]: Simplify k into k
11.723 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
11.723 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
11.724 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.725 * [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))))))
11.727 * [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))
11.727 * [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
11.727 * [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
11.727 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.727 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.727 * [taylor]: Taking taylor expansion of 1.0 in k
11.727 * [backup-simplify]: Simplify 1.0 into 1.0
11.727 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.727 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.727 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
11.728 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
11.728 * [taylor]: Taking taylor expansion of 0.5 in k
11.728 * [backup-simplify]: Simplify 0.5 into 0.5
11.728 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
11.728 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
11.728 * [taylor]: Taking taylor expansion of 1.0 in k
11.728 * [backup-simplify]: Simplify 1.0 into 1.0
11.728 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.728 * [taylor]: Taking taylor expansion of k in k
11.728 * [backup-simplify]: Simplify 0 into 0
11.728 * [backup-simplify]: Simplify 1 into 1
11.728 * [backup-simplify]: Simplify (/ 1 1) into 1
11.728 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
11.728 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
11.728 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
11.728 * [taylor]: Taking taylor expansion of 2.0 in k
11.728 * [backup-simplify]: Simplify 2.0 into 2.0
11.728 * [taylor]: Taking taylor expansion of PI in k
11.728 * [backup-simplify]: Simplify PI into PI
11.728 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.729 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.729 * [taylor]: Taking taylor expansion of (log n) in k
11.729 * [taylor]: Taking taylor expansion of n in k
11.729 * [backup-simplify]: Simplify n into n
11.729 * [backup-simplify]: Simplify (log n) into (log n)
11.729 * [backup-simplify]: Simplify (- 1) into -1
11.730 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.730 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.730 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
11.731 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
11.732 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
11.733 * [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)))))
11.733 * [taylor]: Taking taylor expansion of (sqrt k) in k
11.733 * [taylor]: Taking taylor expansion of k in k
11.733 * [backup-simplify]: Simplify 0 into 0
11.733 * [backup-simplify]: Simplify 1 into 1
11.733 * [backup-simplify]: Simplify (sqrt 0) into 0
11.734 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.735 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.736 * [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))))))
11.738 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) into 0
11.738 * [backup-simplify]: Simplify 0 into 0
11.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.739 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.740 * [backup-simplify]: Simplify (- 0) into 0
11.740 * [backup-simplify]: Simplify (+ 0 0) into 0
11.741 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
11.742 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.742 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
11.744 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.744 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.746 * [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
11.747 * [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
11.747 * [taylor]: Taking taylor expansion of 0 in k
11.747 * [backup-simplify]: Simplify 0 into 0
11.747 * [backup-simplify]: Simplify 0 into 0
11.748 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.749 * [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
11.751 * [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))))))))
11.752 * [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))))))))
11.753 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
11.753 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.754 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.756 * [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
11.756 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.756 * [backup-simplify]: Simplify (- 0) into 0
11.757 * [backup-simplify]: Simplify (+ 0 0) into 0
11.757 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
11.758 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.759 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
11.761 * [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
11.761 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.762 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.764 * [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
11.765 * [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 (sqrt k)))) into 0
11.766 * [taylor]: Taking taylor expansion of 0 in k
11.766 * [backup-simplify]: Simplify 0 into 0
11.766 * [backup-simplify]: Simplify 0 into 0
11.766 * [backup-simplify]: Simplify 0 into 0
11.768 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.769 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.770 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.772 * [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
11.776 * [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))))))))
11.778 * [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))))))))
11.779 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
11.780 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.782 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.788 * [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
11.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.788 * [backup-simplify]: Simplify (- 0) into 0
11.789 * [backup-simplify]: Simplify (+ 0 0) into 0
11.790 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
11.792 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.794 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
11.797 * [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
11.798 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
11.800 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
11.802 * [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
11.806 * [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
11.806 * [taylor]: Taking taylor expansion of 0 in k
11.806 * [backup-simplify]: Simplify 0 into 0
11.806 * [backup-simplify]: Simplify 0 into 0
11.806 * [backup-simplify]: Simplify 0 into 0
11.806 * [backup-simplify]: Simplify 0 into 0
11.810 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.812 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
11.813 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
11.816 * [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
11.819 * [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))))))))
11.822 * [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))))))))
11.828 * [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))))))))
11.829 * [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)))
11.829 * [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
11.829 * [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
11.829 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
11.829 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.829 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.829 * [taylor]: Taking taylor expansion of 1.0 in k
11.829 * [backup-simplify]: Simplify 1.0 into 1.0
11.830 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.830 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.830 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
11.830 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
11.830 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
11.830 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
11.830 * [taylor]: Taking taylor expansion of 0.5 in k
11.830 * [backup-simplify]: Simplify 0.5 into 0.5
11.830 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
11.830 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.830 * [taylor]: Taking taylor expansion of k in k
11.830 * [backup-simplify]: Simplify 0 into 0
11.831 * [backup-simplify]: Simplify 1 into 1
11.831 * [backup-simplify]: Simplify (/ 1 1) into 1
11.831 * [taylor]: Taking taylor expansion of 1.0 in k
11.831 * [backup-simplify]: Simplify 1.0 into 1.0
11.831 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
11.831 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
11.831 * [taylor]: Taking taylor expansion of -2.0 in k
11.831 * [backup-simplify]: Simplify -2.0 into -2.0
11.831 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.831 * [taylor]: Taking taylor expansion of PI in k
11.831 * [backup-simplify]: Simplify PI into PI
11.831 * [taylor]: Taking taylor expansion of n in k
11.831 * [backup-simplify]: Simplify n into n
11.831 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.831 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
11.831 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
11.831 * [backup-simplify]: Simplify (+ 1 0) into 1
11.832 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
11.832 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
11.832 * [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))))
11.832 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
11.832 * [taylor]: Taking taylor expansion of (/ -1 k) in k
11.832 * [taylor]: Taking taylor expansion of -1 in k
11.832 * [backup-simplify]: Simplify -1 into -1
11.832 * [taylor]: Taking taylor expansion of k in k
11.832 * [backup-simplify]: Simplify 0 into 0
11.832 * [backup-simplify]: Simplify 1 into 1
11.832 * [backup-simplify]: Simplify (/ -1 1) into -1
11.833 * [backup-simplify]: Simplify (sqrt 0) into 0
11.833 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
11.834 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.835 * [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)))))
11.836 * [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))))))
11.836 * [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
11.836 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
11.836 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.836 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.836 * [taylor]: Taking taylor expansion of 1.0 in n
11.836 * [backup-simplify]: Simplify 1.0 into 1.0
11.836 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.843 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.843 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
11.843 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
11.843 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
11.843 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
11.843 * [taylor]: Taking taylor expansion of 0.5 in n
11.843 * [backup-simplify]: Simplify 0.5 into 0.5
11.843 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
11.843 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.843 * [taylor]: Taking taylor expansion of k in n
11.843 * [backup-simplify]: Simplify k into k
11.843 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.843 * [taylor]: Taking taylor expansion of 1.0 in n
11.843 * [backup-simplify]: Simplify 1.0 into 1.0
11.843 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
11.843 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.843 * [taylor]: Taking taylor expansion of -2.0 in n
11.843 * [backup-simplify]: Simplify -2.0 into -2.0
11.843 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.843 * [taylor]: Taking taylor expansion of PI in n
11.843 * [backup-simplify]: Simplify PI into PI
11.843 * [taylor]: Taking taylor expansion of n in n
11.843 * [backup-simplify]: Simplify 0 into 0
11.843 * [backup-simplify]: Simplify 1 into 1
11.844 * [backup-simplify]: Simplify (/ PI 1) into PI
11.844 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.845 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
11.845 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
11.845 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
11.846 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.847 * [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)))
11.848 * [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))))
11.848 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
11.848 * [taylor]: Taking taylor expansion of (/ -1 k) in n
11.848 * [taylor]: Taking taylor expansion of -1 in n
11.848 * [backup-simplify]: Simplify -1 into -1
11.848 * [taylor]: Taking taylor expansion of k in n
11.848 * [backup-simplify]: Simplify k into k
11.848 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
11.848 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
11.848 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
11.848 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
11.849 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.851 * [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)))))
11.852 * [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)))
11.852 * [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
11.853 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
11.853 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.853 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.853 * [taylor]: Taking taylor expansion of 1.0 in n
11.853 * [backup-simplify]: Simplify 1.0 into 1.0
11.853 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.854 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.854 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
11.854 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
11.854 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
11.854 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
11.854 * [taylor]: Taking taylor expansion of 0.5 in n
11.854 * [backup-simplify]: Simplify 0.5 into 0.5
11.854 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
11.854 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.854 * [taylor]: Taking taylor expansion of k in n
11.854 * [backup-simplify]: Simplify k into k
11.854 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.854 * [taylor]: Taking taylor expansion of 1.0 in n
11.854 * [backup-simplify]: Simplify 1.0 into 1.0
11.854 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
11.854 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.854 * [taylor]: Taking taylor expansion of -2.0 in n
11.854 * [backup-simplify]: Simplify -2.0 into -2.0
11.854 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.854 * [taylor]: Taking taylor expansion of PI in n
11.855 * [backup-simplify]: Simplify PI into PI
11.855 * [taylor]: Taking taylor expansion of n in n
11.855 * [backup-simplify]: Simplify 0 into 0
11.855 * [backup-simplify]: Simplify 1 into 1
11.855 * [backup-simplify]: Simplify (/ PI 1) into PI
11.856 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.857 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
11.857 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
11.857 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
11.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.860 * [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)))
11.861 * [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))))
11.861 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
11.861 * [taylor]: Taking taylor expansion of (/ -1 k) in n
11.861 * [taylor]: Taking taylor expansion of -1 in n
11.861 * [backup-simplify]: Simplify -1 into -1
11.861 * [taylor]: Taking taylor expansion of k in n
11.861 * [backup-simplify]: Simplify k into k
11.862 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
11.862 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
11.862 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
11.862 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
11.863 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.866 * [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)))))
11.868 * [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)))
11.868 * [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
11.868 * [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
11.869 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.869 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.869 * [taylor]: Taking taylor expansion of 1.0 in k
11.869 * [backup-simplify]: Simplify 1.0 into 1.0
11.869 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.870 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.870 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
11.870 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
11.870 * [taylor]: Taking taylor expansion of 0.5 in k
11.870 * [backup-simplify]: Simplify 0.5 into 0.5
11.870 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
11.870 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
11.870 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
11.870 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
11.870 * [taylor]: Taking taylor expansion of -2.0 in k
11.870 * [backup-simplify]: Simplify -2.0 into -2.0
11.870 * [taylor]: Taking taylor expansion of PI in k
11.870 * [backup-simplify]: Simplify PI into PI
11.871 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.872 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
11.872 * [taylor]: Taking taylor expansion of (log n) in k
11.872 * [taylor]: Taking taylor expansion of n in k
11.872 * [backup-simplify]: Simplify n into n
11.872 * [backup-simplify]: Simplify (log n) into (log n)
11.872 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
11.872 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.872 * [taylor]: Taking taylor expansion of k in k
11.873 * [backup-simplify]: Simplify 0 into 0
11.873 * [backup-simplify]: Simplify 1 into 1
11.873 * [backup-simplify]: Simplify (/ 1 1) into 1
11.873 * [taylor]: Taking taylor expansion of 1.0 in k
11.873 * [backup-simplify]: Simplify 1.0 into 1.0
11.873 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.874 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
11.875 * [backup-simplify]: Simplify (+ 1 0) into 1
11.876 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
11.878 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
11.879 * [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))))
11.879 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
11.879 * [taylor]: Taking taylor expansion of (/ -1 k) in k
11.879 * [taylor]: Taking taylor expansion of -1 in k
11.879 * [backup-simplify]: Simplify -1 into -1
11.879 * [taylor]: Taking taylor expansion of k in k
11.879 * [backup-simplify]: Simplify 0 into 0
11.879 * [backup-simplify]: Simplify 1 into 1
11.880 * [backup-simplify]: Simplify (/ -1 1) into -1
11.880 * [backup-simplify]: Simplify (sqrt 0) into 0
11.882 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
11.883 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.886 * [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)))))
11.888 * [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))))))
11.891 * [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))))))
11.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.893 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.894 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
11.895 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.895 * [backup-simplify]: Simplify (+ 0 0) into 0
11.896 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
11.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.899 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
11.901 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
11.902 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.904 * [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
11.906 * [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
11.906 * [taylor]: Taking taylor expansion of 0 in k
11.907 * [backup-simplify]: Simplify 0 into 0
11.907 * [backup-simplify]: Simplify 0 into 0
11.907 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.910 * [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
11.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
11.914 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.917 * [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)))))))
11.920 * [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)))))))
11.921 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.922 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.926 * [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
11.926 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.926 * [backup-simplify]: Simplify (+ 0 0) into 0
11.927 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
11.929 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.930 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
11.933 * [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
11.934 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.935 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.938 * [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
11.938 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.939 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
11.942 * [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
11.942 * [taylor]: Taking taylor expansion of 0 in k
11.942 * [backup-simplify]: Simplify 0 into 0
11.942 * [backup-simplify]: Simplify 0 into 0
11.942 * [backup-simplify]: Simplify 0 into 0
11.943 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.944 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.947 * [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
11.948 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.952 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.958 * [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)))))))
11.960 * [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)))))))
11.968 * [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))))))))
11.969 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
11.969 * [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))))
11.969 * [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
11.969 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
11.969 * [taylor]: Taking taylor expansion of 1.0 in k
11.970 * [backup-simplify]: Simplify 1.0 into 1.0
11.970 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
11.970 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
11.970 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
11.970 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
11.970 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
11.970 * [taylor]: Taking taylor expansion of 0.5 in k
11.970 * [backup-simplify]: Simplify 0.5 into 0.5
11.970 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.970 * [taylor]: Taking taylor expansion of 1.0 in k
11.970 * [backup-simplify]: Simplify 1.0 into 1.0
11.970 * [taylor]: Taking taylor expansion of k in k
11.970 * [backup-simplify]: Simplify 0 into 0
11.970 * [backup-simplify]: Simplify 1 into 1
11.970 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
11.970 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
11.970 * [taylor]: Taking taylor expansion of 2.0 in k
11.970 * [backup-simplify]: Simplify 2.0 into 2.0
11.970 * [taylor]: Taking taylor expansion of (* n PI) in k
11.970 * [taylor]: Taking taylor expansion of n in k
11.970 * [backup-simplify]: Simplify n into n
11.970 * [taylor]: Taking taylor expansion of PI in k
11.970 * [backup-simplify]: Simplify PI into PI
11.970 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.970 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
11.970 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
11.971 * [backup-simplify]: Simplify (- 0) into 0
11.971 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.972 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
11.972 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
11.972 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
11.972 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.972 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.972 * [taylor]: Taking taylor expansion of k in k
11.972 * [backup-simplify]: Simplify 0 into 0
11.972 * [backup-simplify]: Simplify 1 into 1
11.972 * [backup-simplify]: Simplify (/ 1 1) into 1
11.973 * [backup-simplify]: Simplify (sqrt 0) into 0
11.974 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.974 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
11.974 * [taylor]: Taking taylor expansion of 1.0 in n
11.974 * [backup-simplify]: Simplify 1.0 into 1.0
11.974 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
11.974 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.974 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.974 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.974 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.974 * [taylor]: Taking taylor expansion of 0.5 in n
11.974 * [backup-simplify]: Simplify 0.5 into 0.5
11.974 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.974 * [taylor]: Taking taylor expansion of 1.0 in n
11.975 * [backup-simplify]: Simplify 1.0 into 1.0
11.975 * [taylor]: Taking taylor expansion of k in n
11.975 * [backup-simplify]: Simplify k into k
11.975 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.975 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.975 * [taylor]: Taking taylor expansion of 2.0 in n
11.975 * [backup-simplify]: Simplify 2.0 into 2.0
11.975 * [taylor]: Taking taylor expansion of (* n PI) in n
11.975 * [taylor]: Taking taylor expansion of n in n
11.975 * [backup-simplify]: Simplify 0 into 0
11.975 * [backup-simplify]: Simplify 1 into 1
11.975 * [taylor]: Taking taylor expansion of PI in n
11.975 * [backup-simplify]: Simplify PI into PI
11.975 * [backup-simplify]: Simplify (* 0 PI) into 0
11.976 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.977 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.979 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.980 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.980 * [backup-simplify]: Simplify (- k) into (- k)
11.980 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.980 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.983 * [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))))
11.985 * [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)))))
11.985 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.985 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.985 * [taylor]: Taking taylor expansion of k in n
11.985 * [backup-simplify]: Simplify k into k
11.985 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.985 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.985 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.985 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.985 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
11.985 * [taylor]: Taking taylor expansion of 1.0 in n
11.985 * [backup-simplify]: Simplify 1.0 into 1.0
11.985 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
11.985 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.986 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.986 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.986 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.986 * [taylor]: Taking taylor expansion of 0.5 in n
11.986 * [backup-simplify]: Simplify 0.5 into 0.5
11.986 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.986 * [taylor]: Taking taylor expansion of 1.0 in n
11.986 * [backup-simplify]: Simplify 1.0 into 1.0
11.986 * [taylor]: Taking taylor expansion of k in n
11.986 * [backup-simplify]: Simplify k into k
11.986 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.986 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.986 * [taylor]: Taking taylor expansion of 2.0 in n
11.986 * [backup-simplify]: Simplify 2.0 into 2.0
11.986 * [taylor]: Taking taylor expansion of (* n PI) in n
11.986 * [taylor]: Taking taylor expansion of n in n
11.986 * [backup-simplify]: Simplify 0 into 0
11.986 * [backup-simplify]: Simplify 1 into 1
11.986 * [taylor]: Taking taylor expansion of PI in n
11.986 * [backup-simplify]: Simplify PI into PI
11.987 * [backup-simplify]: Simplify (* 0 PI) into 0
11.987 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.989 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.990 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.991 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.991 * [backup-simplify]: Simplify (- k) into (- k)
11.991 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.992 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.999 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.000 * [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))))
12.002 * [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)))))
12.002 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.002 * [taylor]: Taking taylor expansion of k in n
12.002 * [backup-simplify]: Simplify k into k
12.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.002 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.002 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.002 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.003 * [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)))
12.005 * [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))))
12.005 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
12.005 * [taylor]: Taking taylor expansion of 1.0 in k
12.005 * [backup-simplify]: Simplify 1.0 into 1.0
12.005 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
12.005 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
12.005 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
12.005 * [taylor]: Taking taylor expansion of 0.5 in k
12.005 * [backup-simplify]: Simplify 0.5 into 0.5
12.005 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
12.005 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.005 * [taylor]: Taking taylor expansion of 1.0 in k
12.005 * [backup-simplify]: Simplify 1.0 into 1.0
12.005 * [taylor]: Taking taylor expansion of k in k
12.005 * [backup-simplify]: Simplify 0 into 0
12.005 * [backup-simplify]: Simplify 1 into 1
12.005 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
12.005 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.005 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.005 * [taylor]: Taking taylor expansion of 2.0 in k
12.005 * [backup-simplify]: Simplify 2.0 into 2.0
12.005 * [taylor]: Taking taylor expansion of PI in k
12.005 * [backup-simplify]: Simplify PI into PI
12.006 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.007 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.007 * [taylor]: Taking taylor expansion of (log n) in k
12.007 * [taylor]: Taking taylor expansion of n in k
12.007 * [backup-simplify]: Simplify n into n
12.007 * [backup-simplify]: Simplify (log n) into (log n)
12.008 * [backup-simplify]: Simplify (- 0) into 0
12.008 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.009 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
12.010 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
12.011 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
12.013 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
12.013 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.013 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.013 * [taylor]: Taking taylor expansion of k in k
12.013 * [backup-simplify]: Simplify 0 into 0
12.013 * [backup-simplify]: Simplify 1 into 1
12.013 * [backup-simplify]: Simplify (/ 1 1) into 1
12.014 * [backup-simplify]: Simplify (sqrt 0) into 0
12.016 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.017 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
12.017 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.017 * [backup-simplify]: Simplify 0 into 0
12.018 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.019 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.021 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.022 * [backup-simplify]: Simplify (- 0) into 0
12.022 * [backup-simplify]: Simplify (+ 0 0) into 0
12.023 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
12.024 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.025 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
12.027 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.028 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
12.030 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
12.030 * [taylor]: Taking taylor expansion of 0 in k
12.030 * [backup-simplify]: Simplify 0 into 0
12.031 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.032 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.033 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.033 * [backup-simplify]: Simplify (+ 0 0) into 0
12.033 * [backup-simplify]: Simplify (- 1) into -1
12.034 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.035 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
12.036 * [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))))
12.038 * [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))))))
12.041 * [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))))))
12.042 * [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))))))
12.043 * [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))))))
12.043 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.043 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
12.044 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.045 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.047 * [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
12.047 * [backup-simplify]: Simplify (- 0) into 0
12.047 * [backup-simplify]: Simplify (+ 0 0) into 0
12.048 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
12.049 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.050 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.051 * [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
12.052 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
12.054 * [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
12.054 * [taylor]: Taking taylor expansion of 0 in k
12.054 * [backup-simplify]: Simplify 0 into 0
12.054 * [backup-simplify]: Simplify 0 into 0
12.054 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.056 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.057 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.059 * [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
12.060 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.060 * [backup-simplify]: Simplify (+ 0 0) into 0
12.061 * [backup-simplify]: Simplify (- 0) into 0
12.061 * [backup-simplify]: Simplify (+ 0 0) into 0
12.062 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.064 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.066 * [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))))))
12.076 * [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)))))))))))
12.081 * [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)))))))))))
12.085 * [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)))))))))))
12.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.085 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
12.086 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.087 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.090 * [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
12.091 * [backup-simplify]: Simplify (- 0) into 0
12.091 * [backup-simplify]: Simplify (+ 0 0) into 0
12.092 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
12.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.094 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.096 * [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
12.097 * [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
12.098 * [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
12.098 * [taylor]: Taking taylor expansion of 0 in k
12.099 * [backup-simplify]: Simplify 0 into 0
12.099 * [backup-simplify]: Simplify 0 into 0
12.099 * [backup-simplify]: Simplify 0 into 0
12.099 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.102 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.102 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.110 * [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
12.113 * [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
12.113 * [backup-simplify]: Simplify (+ 0 0) into 0
12.113 * [backup-simplify]: Simplify (- 0) into 0
12.113 * [backup-simplify]: Simplify (+ 0 0) into 0
12.115 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.117 * [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
12.122 * [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))))))
12.141 * [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)))))))))))))))))
12.163 * [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)))))))))))))))))
12.175 * [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)))))))))))))))))
12.188 * [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)))))))))))))))))))))
12.189 * [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)))
12.189 * [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
12.189 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
12.189 * [taylor]: Taking taylor expansion of 1.0 in k
12.189 * [backup-simplify]: Simplify 1.0 into 1.0
12.189 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
12.189 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
12.189 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
12.189 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
12.189 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
12.189 * [taylor]: Taking taylor expansion of 0.5 in k
12.189 * [backup-simplify]: Simplify 0.5 into 0.5
12.189 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.189 * [taylor]: Taking taylor expansion of 1.0 in k
12.189 * [backup-simplify]: Simplify 1.0 into 1.0
12.189 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.189 * [taylor]: Taking taylor expansion of k in k
12.189 * [backup-simplify]: Simplify 0 into 0
12.189 * [backup-simplify]: Simplify 1 into 1
12.190 * [backup-simplify]: Simplify (/ 1 1) into 1
12.190 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
12.190 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
12.190 * [taylor]: Taking taylor expansion of 2.0 in k
12.190 * [backup-simplify]: Simplify 2.0 into 2.0
12.190 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.190 * [taylor]: Taking taylor expansion of PI in k
12.190 * [backup-simplify]: Simplify PI into PI
12.190 * [taylor]: Taking taylor expansion of n in k
12.190 * [backup-simplify]: Simplify n into n
12.190 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.190 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
12.190 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
12.190 * [backup-simplify]: Simplify (- 1) into -1
12.190 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.191 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
12.191 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
12.191 * [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))))))
12.191 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.191 * [taylor]: Taking taylor expansion of k in k
12.191 * [backup-simplify]: Simplify 0 into 0
12.191 * [backup-simplify]: Simplify 1 into 1
12.191 * [backup-simplify]: Simplify (sqrt 0) into 0
12.192 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.192 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
12.192 * [taylor]: Taking taylor expansion of 1.0 in n
12.192 * [backup-simplify]: Simplify 1.0 into 1.0
12.192 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
12.192 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.192 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.192 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.192 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.192 * [taylor]: Taking taylor expansion of 0.5 in n
12.192 * [backup-simplify]: Simplify 0.5 into 0.5
12.192 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.192 * [taylor]: Taking taylor expansion of 1.0 in n
12.192 * [backup-simplify]: Simplify 1.0 into 1.0
12.192 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.192 * [taylor]: Taking taylor expansion of k in n
12.192 * [backup-simplify]: Simplify k into k
12.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.193 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.193 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.193 * [taylor]: Taking taylor expansion of 2.0 in n
12.193 * [backup-simplify]: Simplify 2.0 into 2.0
12.193 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.193 * [taylor]: Taking taylor expansion of PI in n
12.193 * [backup-simplify]: Simplify PI into PI
12.193 * [taylor]: Taking taylor expansion of n in n
12.193 * [backup-simplify]: Simplify 0 into 0
12.193 * [backup-simplify]: Simplify 1 into 1
12.193 * [backup-simplify]: Simplify (/ PI 1) into PI
12.193 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.194 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.194 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.194 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.194 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.195 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.196 * [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))))
12.197 * [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)))))
12.197 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.197 * [taylor]: Taking taylor expansion of k in n
12.197 * [backup-simplify]: Simplify k into k
12.197 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.197 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.197 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
12.197 * [taylor]: Taking taylor expansion of 1.0 in n
12.197 * [backup-simplify]: Simplify 1.0 into 1.0
12.197 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
12.197 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.197 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.197 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.197 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.197 * [taylor]: Taking taylor expansion of 0.5 in n
12.197 * [backup-simplify]: Simplify 0.5 into 0.5
12.197 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.197 * [taylor]: Taking taylor expansion of 1.0 in n
12.197 * [backup-simplify]: Simplify 1.0 into 1.0
12.197 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.197 * [taylor]: Taking taylor expansion of k in n
12.197 * [backup-simplify]: Simplify k into k
12.197 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.197 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.197 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.197 * [taylor]: Taking taylor expansion of 2.0 in n
12.197 * [backup-simplify]: Simplify 2.0 into 2.0
12.197 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.197 * [taylor]: Taking taylor expansion of PI in n
12.197 * [backup-simplify]: Simplify PI into PI
12.197 * [taylor]: Taking taylor expansion of n in n
12.197 * [backup-simplify]: Simplify 0 into 0
12.197 * [backup-simplify]: Simplify 1 into 1
12.198 * [backup-simplify]: Simplify (/ PI 1) into PI
12.198 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.199 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.199 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.199 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.199 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.201 * [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))))
12.201 * [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)))))
12.201 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.201 * [taylor]: Taking taylor expansion of k in n
12.201 * [backup-simplify]: Simplify k into k
12.201 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.201 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.202 * [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))
12.203 * [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)))
12.203 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
12.203 * [taylor]: Taking taylor expansion of 1.0 in k
12.203 * [backup-simplify]: Simplify 1.0 into 1.0
12.203 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
12.203 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
12.203 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
12.203 * [taylor]: Taking taylor expansion of 0.5 in k
12.203 * [backup-simplify]: Simplify 0.5 into 0.5
12.203 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
12.203 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.203 * [taylor]: Taking taylor expansion of 1.0 in k
12.203 * [backup-simplify]: Simplify 1.0 into 1.0
12.203 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.203 * [taylor]: Taking taylor expansion of k in k
12.203 * [backup-simplify]: Simplify 0 into 0
12.203 * [backup-simplify]: Simplify 1 into 1
12.204 * [backup-simplify]: Simplify (/ 1 1) into 1
12.204 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
12.204 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.204 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.204 * [taylor]: Taking taylor expansion of 2.0 in k
12.204 * [backup-simplify]: Simplify 2.0 into 2.0
12.204 * [taylor]: Taking taylor expansion of PI in k
12.204 * [backup-simplify]: Simplify PI into PI
12.205 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.206 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.206 * [taylor]: Taking taylor expansion of (log n) in k
12.206 * [taylor]: Taking taylor expansion of n in k
12.206 * [backup-simplify]: Simplify n into n
12.206 * [backup-simplify]: Simplify (log n) into (log n)
12.206 * [backup-simplify]: Simplify (- 1) into -1
12.207 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.207 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.208 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
12.209 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
12.210 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
12.212 * [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)))))
12.212 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.212 * [taylor]: Taking taylor expansion of k in k
12.212 * [backup-simplify]: Simplify 0 into 0
12.212 * [backup-simplify]: Simplify 1 into 1
12.212 * [backup-simplify]: Simplify (sqrt 0) into 0
12.213 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.215 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
12.215 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.215 * [backup-simplify]: Simplify 0 into 0
12.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.217 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.219 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.219 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.220 * [backup-simplify]: Simplify (- 0) into 0
12.220 * [backup-simplify]: Simplify (+ 0 0) into 0
12.221 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
12.222 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.224 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
12.226 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.227 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
12.229 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
12.229 * [taylor]: Taking taylor expansion of 0 in k
12.229 * [backup-simplify]: Simplify 0 into 0
12.229 * [backup-simplify]: Simplify 0 into 0
12.231 * [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)))))))
12.239 * [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)))))))
12.241 * [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)))))))
12.242 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
12.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.244 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.249 * [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
12.249 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.250 * [backup-simplify]: Simplify (- 0) into 0
12.250 * [backup-simplify]: Simplify (+ 0 0) into 0
12.252 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
12.253 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.255 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
12.258 * [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
12.260 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
12.262 * [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
12.262 * [taylor]: Taking taylor expansion of 0 in k
12.262 * [backup-simplify]: Simplify 0 into 0
12.262 * [backup-simplify]: Simplify 0 into 0
12.263 * [backup-simplify]: Simplify 0 into 0
12.266 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.269 * [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)))))))
12.272 * [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)))))))
12.274 * [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)))))))
12.275 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
12.276 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.283 * [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
12.283 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.284 * [backup-simplify]: Simplify (- 0) into 0
12.284 * [backup-simplify]: Simplify (+ 0 0) into 0
12.286 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
12.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.289 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
12.293 * [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
12.295 * [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
12.298 * [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
12.298 * [taylor]: Taking taylor expansion of 0 in k
12.298 * [backup-simplify]: Simplify 0 into 0
12.298 * [backup-simplify]: Simplify 0 into 0
12.298 * [backup-simplify]: Simplify 0 into 0
12.298 * [backup-simplify]: Simplify 0 into 0
12.302 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.304 * [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)))))))
12.309 * [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)))))))
12.310 * [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)))))))
12.315 * [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))))))))
12.316 * [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))))
12.316 * [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
12.316 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
12.316 * [taylor]: Taking taylor expansion of 1.0 in k
12.316 * [backup-simplify]: Simplify 1.0 into 1.0
12.317 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
12.317 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
12.317 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
12.317 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
12.317 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
12.317 * [taylor]: Taking taylor expansion of 0.5 in k
12.317 * [backup-simplify]: Simplify 0.5 into 0.5
12.317 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.317 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.317 * [taylor]: Taking taylor expansion of k in k
12.317 * [backup-simplify]: Simplify 0 into 0
12.317 * [backup-simplify]: Simplify 1 into 1
12.317 * [backup-simplify]: Simplify (/ 1 1) into 1
12.317 * [taylor]: Taking taylor expansion of 1.0 in k
12.317 * [backup-simplify]: Simplify 1.0 into 1.0
12.317 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
12.317 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
12.317 * [taylor]: Taking taylor expansion of -2.0 in k
12.317 * [backup-simplify]: Simplify -2.0 into -2.0
12.317 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.317 * [taylor]: Taking taylor expansion of PI in k
12.318 * [backup-simplify]: Simplify PI into PI
12.318 * [taylor]: Taking taylor expansion of n in k
12.318 * [backup-simplify]: Simplify n into n
12.318 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.318 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
12.318 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
12.318 * [backup-simplify]: Simplify (+ 1 0) into 1
12.319 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
12.319 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
12.319 * [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))))
12.319 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.319 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.319 * [taylor]: Taking taylor expansion of -1 in k
12.319 * [backup-simplify]: Simplify -1 into -1
12.319 * [taylor]: Taking taylor expansion of k in k
12.319 * [backup-simplify]: Simplify 0 into 0
12.319 * [backup-simplify]: Simplify 1 into 1
12.320 * [backup-simplify]: Simplify (/ -1 1) into -1
12.320 * [backup-simplify]: Simplify (sqrt 0) into 0
12.321 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.322 * [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)))))
12.322 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
12.322 * [taylor]: Taking taylor expansion of 1.0 in n
12.322 * [backup-simplify]: Simplify 1.0 into 1.0
12.322 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
12.322 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.322 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.322 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.322 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.322 * [taylor]: Taking taylor expansion of 0.5 in n
12.322 * [backup-simplify]: Simplify 0.5 into 0.5
12.322 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.322 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.322 * [taylor]: Taking taylor expansion of k in n
12.322 * [backup-simplify]: Simplify k into k
12.322 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.322 * [taylor]: Taking taylor expansion of 1.0 in n
12.322 * [backup-simplify]: Simplify 1.0 into 1.0
12.322 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.322 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.322 * [taylor]: Taking taylor expansion of -2.0 in n
12.323 * [backup-simplify]: Simplify -2.0 into -2.0
12.323 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.323 * [taylor]: Taking taylor expansion of PI in n
12.323 * [backup-simplify]: Simplify PI into PI
12.323 * [taylor]: Taking taylor expansion of n in n
12.323 * [backup-simplify]: Simplify 0 into 0
12.323 * [backup-simplify]: Simplify 1 into 1
12.323 * [backup-simplify]: Simplify (/ PI 1) into PI
12.324 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.324 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.324 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.324 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.325 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.326 * [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)))
12.327 * [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))))
12.327 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.327 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.327 * [taylor]: Taking taylor expansion of -1 in n
12.327 * [backup-simplify]: Simplify -1 into -1
12.327 * [taylor]: Taking taylor expansion of k in n
12.327 * [backup-simplify]: Simplify k into k
12.327 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.327 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.327 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.327 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.328 * [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)))
12.328 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
12.328 * [taylor]: Taking taylor expansion of 1.0 in n
12.328 * [backup-simplify]: Simplify 1.0 into 1.0
12.328 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
12.328 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.328 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.328 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.328 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.328 * [taylor]: Taking taylor expansion of 0.5 in n
12.328 * [backup-simplify]: Simplify 0.5 into 0.5
12.328 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.328 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.328 * [taylor]: Taking taylor expansion of k in n
12.329 * [backup-simplify]: Simplify k into k
12.329 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.329 * [taylor]: Taking taylor expansion of 1.0 in n
12.329 * [backup-simplify]: Simplify 1.0 into 1.0
12.329 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
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
12.329 * [backup-simplify]: Simplify (/ PI 1) into PI
12.329 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.330 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.330 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.330 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.331 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.332 * [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)))
12.333 * [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))))
12.333 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.333 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.333 * [taylor]: Taking taylor expansion of -1 in n
12.333 * [backup-simplify]: Simplify -1 into -1
12.333 * [taylor]: Taking taylor expansion of k in n
12.333 * [backup-simplify]: Simplify k into k
12.333 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.333 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.333 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.333 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.334 * [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)))
12.335 * [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))))
12.335 * [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
12.335 * [taylor]: Taking taylor expansion of 1.0 in k
12.335 * [backup-simplify]: Simplify 1.0 into 1.0
12.335 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
12.335 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
12.335 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
12.335 * [taylor]: Taking taylor expansion of 0.5 in k
12.335 * [backup-simplify]: Simplify 0.5 into 0.5
12.335 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
12.335 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
12.335 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
12.335 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
12.335 * [taylor]: Taking taylor expansion of -2.0 in k
12.335 * [backup-simplify]: Simplify -2.0 into -2.0
12.335 * [taylor]: Taking taylor expansion of PI in k
12.335 * [backup-simplify]: Simplify PI into PI
12.335 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.336 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.336 * [taylor]: Taking taylor expansion of (log n) in k
12.336 * [taylor]: Taking taylor expansion of n in k
12.336 * [backup-simplify]: Simplify n into n
12.336 * [backup-simplify]: Simplify (log n) into (log n)
12.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.336 * [taylor]: Taking taylor expansion of k in k
12.336 * [backup-simplify]: Simplify 0 into 0
12.336 * [backup-simplify]: Simplify 1 into 1
12.336 * [backup-simplify]: Simplify (/ 1 1) into 1
12.336 * [taylor]: Taking taylor expansion of 1.0 in k
12.336 * [backup-simplify]: Simplify 1.0 into 1.0
12.336 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.337 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
12.337 * [backup-simplify]: Simplify (+ 1 0) into 1
12.338 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
12.339 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
12.340 * [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))))
12.340 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.340 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.340 * [taylor]: Taking taylor expansion of -1 in k
12.340 * [backup-simplify]: Simplify -1 into -1
12.340 * [taylor]: Taking taylor expansion of k in k
12.340 * [backup-simplify]: Simplify 0 into 0
12.340 * [backup-simplify]: Simplify 1 into 1
12.340 * [backup-simplify]: Simplify (/ -1 1) into -1
12.340 * [backup-simplify]: Simplify (sqrt 0) into 0
12.341 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.342 * [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)))))
12.343 * [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)))))
12.344 * [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)))))
12.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.345 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.346 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
12.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.346 * [backup-simplify]: Simplify (+ 0 0) into 0
12.347 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
12.347 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.348 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
12.349 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.350 * [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
12.352 * [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
12.352 * [taylor]: Taking taylor expansion of 0 in k
12.352 * [backup-simplify]: Simplify 0 into 0
12.352 * [backup-simplify]: Simplify 0 into 0
12.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.354 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.355 * [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))))))
12.360 * [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))))))
12.361 * [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))))))
12.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.363 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.367 * [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
12.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.368 * [backup-simplify]: Simplify (+ 0 0) into 0
12.369 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
12.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.372 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
12.373 * [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
12.373 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.374 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
12.380 * [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
12.382 * [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
12.382 * [taylor]: Taking taylor expansion of 0 in k
12.382 * [backup-simplify]: Simplify 0 into 0
12.382 * [backup-simplify]: Simplify 0 into 0
12.382 * [backup-simplify]: Simplify 0 into 0
12.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.385 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.387 * [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))))))
12.390 * [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))))))
12.391 * [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))))))
12.394 * [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))))))))
12.394 * * * [progress]: simplifying candidates
12.396 * [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))))))))
12.401 * * [simplify]: iteration 0: 340 enodes
12.535 * * [simplify]: iteration 1: 921 enodes
12.924 * * [simplify]: iteration 2: 4729 enodes
14.087 * * [simplify]: iteration complete: 5000 enodes
14.087 * * [simplify]: Extracting #0: cost 65 inf + 0
14.090 * * [simplify]: Extracting #1: cost 612 inf + 3
14.096 * * [simplify]: Extracting #2: cost 1061 inf + 7790
14.105 * * [simplify]: Extracting #3: cost 1090 inf + 37680
14.119 * * [simplify]: Extracting #4: cost 1140 inf + 61406
14.162 * * [simplify]: Extracting #5: cost 1008 inf + 145695
14.240 * * [simplify]: Extracting #6: cost 519 inf + 415917
14.359 * * [simplify]: Extracting #7: cost 195 inf + 601079
14.539 * * [simplify]: Extracting #8: cost 82 inf + 689759
14.772 * * [simplify]: Extracting #9: cost 8 inf + 738951
14.954 * * [simplify]: Extracting #10: cost 0 inf + 741433
15.148 * * [simplify]: Extracting #11: cost 0 inf + 740073
15.380 * [simplify]: Simplified to:
  (* (* 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)
  (* (* 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
  1
  2
  1
  1
  (* (* (/ 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))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  2
  (+ (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)))
  (exp (* (/ 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))))
  (* (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))))
  (* (* (/ 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))))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)
  (sqrt k)
  (* (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))))
  (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 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)))))
  (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))))
  (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))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (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 (sqrt k)))
  (/ (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 k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (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 k))
  1
  (* (/ 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)
  (/ 1 (sqrt k))
  (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))))
  (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
  (* (/ 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))))
  (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))))
  (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))))
  (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
  2
  1
  (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (cbrt (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))))))
  (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (fabs (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (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)))))
  (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (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)))) (sqrt 1.0))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (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)))) (sqrt 1.0))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (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)))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (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)))))
  (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (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)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (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)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))))
  (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (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 k))) (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)))) (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 k))) (sqrt (* (/ 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 (sqrt k))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (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 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 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 (* (* 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 (* (* 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 (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 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 (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (* (sqrt k) k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) k) (/ (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt k)))
  (* (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))))
  (* (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (- (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 (fabs (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
  (/ (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
  (/ (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 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (fabs (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)))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)
  (* (/ 1.0 (sqrt (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 k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (+ (* (* (* +nan.0 1.0) k) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (- (* +nan.0 (log (* 2.0 PI)))) (* (* 1.0 k) (exp (* (log (* (* 2.0 PI) n)) 0.5))))) (- (* (* +nan.0 (* 1.0 (log (* 2.0 PI)))) (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* k k))) (+ (- (* (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* k k)) (* +nan.0 1.0)) (* (* (* +nan.0 (log (* 2.0 PI))) 1.0) (* (log n) (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* k k))))) (- (* (* (* +nan.0 1.0) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (* (* k (log n)) (* k (log n)))) (- (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* +nan.0 1.0)) (- (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* k k)) (* +nan.0 1.0))) (* 1.0 (* (* +nan.0 (* (* k k) (log n))) (exp (* (log (* (* 2.0 PI) n)) 0.5)))))))))) (* (- (* +nan.0 1.0)) (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* (log n) k))))
  (+ (- (/ (* (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) +nan.0) (/ (* k (* k k)) 1.0))) (* +nan.0 (- (/ 1.0 (/ k (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))))) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (/ (* k k) 1.0)))))
  (+ (- (* (/ (exp (* (- 1.0 k) (* (- (log (* -2.0 PI)) (log (/ -1 n))) 0.5))) (/ k 1.0)) +nan.0)) (* +nan.0 (- (* (exp (* (- 1.0 k) (* (- (log (* -2.0 PI)) (log (/ -1 n))) 0.5))) 1.0) (/ (exp (* (- 1.0 k) (* (- (log (* -2.0 PI)) (log (/ -1 n))) 0.5))) (/ (* k k) 1.0)))))
  (- (+ (- (* (* (* +nan.0 (* (* k k) (log n))) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (log (* 2.0 PI))) (* +nan.0 (exp (* (log (* (* 2.0 PI) n)) 0.5)))) (+ (- (* (* (* (* +nan.0 (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 k)) +nan.0)) (- (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* +nan.0 (* (* k (log n)) (* k (log n))))) (- (* (* +nan.0 (* (* k k) (log n))) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (+ (- (* (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* k k)) (* +nan.0 (log (* 2.0 PI)))) (* +nan.0 (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* (log n) k)))) (* (* k (exp (* (log (* (* 2.0 PI) n)) 0.5))) (- (* +nan.0 (log (* 2.0 PI))) +nan.0))))))))
  (+ (* (- +nan.0) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (* k k))) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (* k (* k k))))))
  (+ (* (- (exp (* (- 1.0 k) (* (- (log (* -2.0 PI)) (log (/ -1 n))) 0.5)))) +nan.0) (* +nan.0 (- (/ (exp (* (- 1.0 k) (* (- (log (* -2.0 PI)) (log (/ -1 n))) 0.5))) k) (/ (exp (* (- 1.0 k) (* (- (log (* -2.0 PI)) (log (/ -1 n))) 0.5))) (* k k)))))
15.395 * * * [progress]: adding candidates to table
16.304 * * [progress]: iteration 4 / 4
16.304 * * * [progress]: picking best candidate
16.370 * * * * [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 (sqrt k))) (sqrt (sqrt k))))))>
16.370 * * * [progress]: localizing error
16.442 * * * [progress]: generating rewritten candidates
16.442 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 1 2 1)
16.464 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
16.477 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
16.611 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
16.657 * * * [progress]: generating series expansions
16.657 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 1 2 1)
16.658 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
16.658 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
16.658 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
16.658 * [taylor]: Taking taylor expansion of 2.0 in n
16.658 * [backup-simplify]: Simplify 2.0 into 2.0
16.658 * [taylor]: Taking taylor expansion of (* n PI) in n
16.658 * [taylor]: Taking taylor expansion of n in n
16.658 * [backup-simplify]: Simplify 0 into 0
16.658 * [backup-simplify]: Simplify 1 into 1
16.658 * [taylor]: Taking taylor expansion of PI in n
16.658 * [backup-simplify]: Simplify PI into PI
16.658 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
16.658 * [taylor]: Taking taylor expansion of 2.0 in n
16.658 * [backup-simplify]: Simplify 2.0 into 2.0
16.658 * [taylor]: Taking taylor expansion of (* n PI) in n
16.658 * [taylor]: Taking taylor expansion of n in n
16.658 * [backup-simplify]: Simplify 0 into 0
16.659 * [backup-simplify]: Simplify 1 into 1
16.659 * [taylor]: Taking taylor expansion of PI in n
16.659 * [backup-simplify]: Simplify PI into PI
16.659 * [backup-simplify]: Simplify (* 0 PI) into 0
16.659 * [backup-simplify]: Simplify (* 2.0 0) into 0
16.659 * [backup-simplify]: Simplify 0 into 0
16.660 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.661 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
16.662 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
16.663 * [backup-simplify]: Simplify 0 into 0
16.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.665 * [backup-simplify]: Simplify 0 into 0
16.666 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.667 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
16.667 * [backup-simplify]: Simplify 0 into 0
16.668 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
16.669 * [backup-simplify]: Simplify 0 into 0
16.670 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.671 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
16.671 * [backup-simplify]: Simplify 0 into 0
16.672 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
16.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
16.673 * [backup-simplify]: Simplify 0 into 0
16.673 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
16.674 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
16.674 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
16.674 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
16.674 * [taylor]: Taking taylor expansion of 2.0 in n
16.674 * [backup-simplify]: Simplify 2.0 into 2.0
16.674 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.674 * [taylor]: Taking taylor expansion of PI in n
16.674 * [backup-simplify]: Simplify PI into PI
16.674 * [taylor]: Taking taylor expansion of n in n
16.674 * [backup-simplify]: Simplify 0 into 0
16.674 * [backup-simplify]: Simplify 1 into 1
16.674 * [backup-simplify]: Simplify (/ PI 1) into PI
16.674 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
16.674 * [taylor]: Taking taylor expansion of 2.0 in n
16.674 * [backup-simplify]: Simplify 2.0 into 2.0
16.674 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.674 * [taylor]: Taking taylor expansion of PI in n
16.674 * [backup-simplify]: Simplify PI into PI
16.674 * [taylor]: Taking taylor expansion of n in n
16.674 * [backup-simplify]: Simplify 0 into 0
16.674 * [backup-simplify]: Simplify 1 into 1
16.675 * [backup-simplify]: Simplify (/ PI 1) into PI
16.675 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.675 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
16.676 * [backup-simplify]: Simplify 0 into 0
16.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.678 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
16.678 * [backup-simplify]: Simplify 0 into 0
16.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.679 * [backup-simplify]: Simplify 0 into 0
16.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.681 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.681 * [backup-simplify]: Simplify 0 into 0
16.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.684 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.684 * [backup-simplify]: Simplify 0 into 0
16.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.688 * [backup-simplify]: Simplify 0 into 0
16.688 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
16.689 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
16.689 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
16.689 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
16.689 * [taylor]: Taking taylor expansion of -2.0 in n
16.689 * [backup-simplify]: Simplify -2.0 into -2.0
16.689 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.689 * [taylor]: Taking taylor expansion of PI in n
16.689 * [backup-simplify]: Simplify PI into PI
16.689 * [taylor]: Taking taylor expansion of n in n
16.689 * [backup-simplify]: Simplify 0 into 0
16.689 * [backup-simplify]: Simplify 1 into 1
16.690 * [backup-simplify]: Simplify (/ PI 1) into PI
16.690 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
16.690 * [taylor]: Taking taylor expansion of -2.0 in n
16.690 * [backup-simplify]: Simplify -2.0 into -2.0
16.690 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.690 * [taylor]: Taking taylor expansion of PI in n
16.690 * [backup-simplify]: Simplify PI into PI
16.690 * [taylor]: Taking taylor expansion of n in n
16.690 * [backup-simplify]: Simplify 0 into 0
16.690 * [backup-simplify]: Simplify 1 into 1
16.690 * [backup-simplify]: Simplify (/ PI 1) into PI
16.691 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
16.691 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
16.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.693 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
16.693 * [backup-simplify]: Simplify 0 into 0
16.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.696 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
16.696 * [backup-simplify]: Simplify 0 into 0
16.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.698 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.698 * [backup-simplify]: Simplify 0 into 0
16.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.701 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.701 * [backup-simplify]: Simplify 0 into 0
16.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.704 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.704 * [backup-simplify]: Simplify 0 into 0
16.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.707 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.707 * [backup-simplify]: Simplify 0 into 0
16.708 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
16.708 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
16.716 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
16.716 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
16.716 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
16.716 * [taylor]: Taking taylor expansion of 2.0 in n
16.716 * [backup-simplify]: Simplify 2.0 into 2.0
16.716 * [taylor]: Taking taylor expansion of (* n PI) in n
16.716 * [taylor]: Taking taylor expansion of n in n
16.716 * [backup-simplify]: Simplify 0 into 0
16.716 * [backup-simplify]: Simplify 1 into 1
16.716 * [taylor]: Taking taylor expansion of PI in n
16.716 * [backup-simplify]: Simplify PI into PI
16.716 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
16.716 * [taylor]: Taking taylor expansion of 2.0 in n
16.716 * [backup-simplify]: Simplify 2.0 into 2.0
16.716 * [taylor]: Taking taylor expansion of (* n PI) in n
16.716 * [taylor]: Taking taylor expansion of n in n
16.716 * [backup-simplify]: Simplify 0 into 0
16.716 * [backup-simplify]: Simplify 1 into 1
16.716 * [taylor]: Taking taylor expansion of PI in n
16.716 * [backup-simplify]: Simplify PI into PI
16.717 * [backup-simplify]: Simplify (* 0 PI) into 0
16.718 * [backup-simplify]: Simplify (* 2.0 0) into 0
16.718 * [backup-simplify]: Simplify 0 into 0
16.719 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.721 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
16.721 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.723 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
16.724 * [backup-simplify]: Simplify 0 into 0
16.725 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.727 * [backup-simplify]: Simplify 0 into 0
16.728 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
16.730 * [backup-simplify]: Simplify 0 into 0
16.731 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.733 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
16.733 * [backup-simplify]: Simplify 0 into 0
16.735 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.736 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
16.736 * [backup-simplify]: Simplify 0 into 0
16.737 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
16.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
16.738 * [backup-simplify]: Simplify 0 into 0
16.739 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
16.739 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
16.739 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
16.739 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
16.739 * [taylor]: Taking taylor expansion of 2.0 in n
16.739 * [backup-simplify]: Simplify 2.0 into 2.0
16.739 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.739 * [taylor]: Taking taylor expansion of PI in n
16.739 * [backup-simplify]: Simplify PI into PI
16.739 * [taylor]: Taking taylor expansion of n in n
16.739 * [backup-simplify]: Simplify 0 into 0
16.739 * [backup-simplify]: Simplify 1 into 1
16.740 * [backup-simplify]: Simplify (/ PI 1) into PI
16.740 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
16.740 * [taylor]: Taking taylor expansion of 2.0 in n
16.740 * [backup-simplify]: Simplify 2.0 into 2.0
16.740 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.740 * [taylor]: Taking taylor expansion of PI in n
16.740 * [backup-simplify]: Simplify PI into PI
16.740 * [taylor]: Taking taylor expansion of n in n
16.740 * [backup-simplify]: Simplify 0 into 0
16.740 * [backup-simplify]: Simplify 1 into 1
16.740 * [backup-simplify]: Simplify (/ PI 1) into PI
16.740 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.741 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.742 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
16.742 * [backup-simplify]: Simplify 0 into 0
16.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
16.743 * [backup-simplify]: Simplify 0 into 0
16.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.745 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.745 * [backup-simplify]: Simplify 0 into 0
16.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.746 * [backup-simplify]: Simplify 0 into 0
16.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.748 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.748 * [backup-simplify]: Simplify 0 into 0
16.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.750 * [backup-simplify]: Simplify 0 into 0
16.750 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
16.750 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
16.751 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
16.751 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
16.751 * [taylor]: Taking taylor expansion of -2.0 in n
16.751 * [backup-simplify]: Simplify -2.0 into -2.0
16.751 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.751 * [taylor]: Taking taylor expansion of PI in n
16.751 * [backup-simplify]: Simplify PI into PI
16.751 * [taylor]: Taking taylor expansion of n in n
16.751 * [backup-simplify]: Simplify 0 into 0
16.751 * [backup-simplify]: Simplify 1 into 1
16.751 * [backup-simplify]: Simplify (/ PI 1) into PI
16.751 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
16.751 * [taylor]: Taking taylor expansion of -2.0 in n
16.751 * [backup-simplify]: Simplify -2.0 into -2.0
16.751 * [taylor]: Taking taylor expansion of (/ PI n) in n
16.751 * [taylor]: Taking taylor expansion of PI in n
16.751 * [backup-simplify]: Simplify PI into PI
16.751 * [taylor]: Taking taylor expansion of n in n
16.751 * [backup-simplify]: Simplify 0 into 0
16.751 * [backup-simplify]: Simplify 1 into 1
16.751 * [backup-simplify]: Simplify (/ PI 1) into PI
16.752 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
16.752 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
16.753 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
16.753 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
16.753 * [backup-simplify]: Simplify 0 into 0
16.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
16.755 * [backup-simplify]: Simplify 0 into 0
16.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.757 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.757 * [backup-simplify]: Simplify 0 into 0
16.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.758 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.758 * [backup-simplify]: Simplify 0 into 0
16.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.760 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
16.760 * [backup-simplify]: Simplify 0 into 0
16.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
16.762 * [backup-simplify]: Simplify 0 into 0
16.762 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
16.762 * * * * [progress]: [ 3 / 4 ] generating series at (2)
16.763 * [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 (sqrt k))) (sqrt (sqrt k))))) into (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k)))
16.763 * [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
16.764 * [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
16.764 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k
16.764 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
16.764 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
16.764 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
16.764 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
16.764 * [taylor]: Taking taylor expansion of 0.5 in k
16.764 * [backup-simplify]: Simplify 0.5 into 0.5
16.764 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
16.764 * [taylor]: Taking taylor expansion of 1.0 in k
16.764 * [backup-simplify]: Simplify 1.0 into 1.0
16.764 * [taylor]: Taking taylor expansion of k in k
16.764 * [backup-simplify]: Simplify 0 into 0
16.764 * [backup-simplify]: Simplify 1 into 1
16.764 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
16.764 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
16.764 * [taylor]: Taking taylor expansion of 2.0 in k
16.764 * [backup-simplify]: Simplify 2.0 into 2.0
16.764 * [taylor]: Taking taylor expansion of (* n PI) in k
16.764 * [taylor]: Taking taylor expansion of n in k
16.764 * [backup-simplify]: Simplify n into n
16.764 * [taylor]: Taking taylor expansion of PI in k
16.764 * [backup-simplify]: Simplify PI into PI
16.764 * [backup-simplify]: Simplify (* n PI) into (* n PI)
16.764 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
16.764 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
16.764 * [backup-simplify]: Simplify (- 0) into 0
16.765 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
16.765 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
16.765 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
16.765 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
16.765 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
16.765 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
16.765 * [taylor]: Taking taylor expansion of 1.0 in k
16.765 * [backup-simplify]: Simplify 1.0 into 1.0
16.765 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
16.766 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
16.766 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
16.766 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.766 * [taylor]: Taking taylor expansion of k in k
16.766 * [backup-simplify]: Simplify 0 into 0
16.766 * [backup-simplify]: Simplify 1 into 1
16.766 * [backup-simplify]: Simplify (/ 1 1) into 1
16.766 * [backup-simplify]: Simplify (sqrt 0) into 0
16.767 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.767 * [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
16.767 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
16.767 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
16.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
16.767 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
16.767 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
16.768 * [taylor]: Taking taylor expansion of 0.5 in n
16.768 * [backup-simplify]: Simplify 0.5 into 0.5
16.768 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
16.768 * [taylor]: Taking taylor expansion of 1.0 in n
16.768 * [backup-simplify]: Simplify 1.0 into 1.0
16.768 * [taylor]: Taking taylor expansion of k in n
16.768 * [backup-simplify]: Simplify k into k
16.768 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
16.768 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
16.768 * [taylor]: Taking taylor expansion of 2.0 in n
16.768 * [backup-simplify]: Simplify 2.0 into 2.0
16.768 * [taylor]: Taking taylor expansion of (* n PI) in n
16.768 * [taylor]: Taking taylor expansion of n in n
16.768 * [backup-simplify]: Simplify 0 into 0
16.768 * [backup-simplify]: Simplify 1 into 1
16.768 * [taylor]: Taking taylor expansion of PI in n
16.768 * [backup-simplify]: Simplify PI into PI
16.768 * [backup-simplify]: Simplify (* 0 PI) into 0
16.768 * [backup-simplify]: Simplify (* 2.0 0) into 0
16.769 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.770 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
16.771 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
16.771 * [backup-simplify]: Simplify (- k) into (- k)
16.771 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
16.771 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
16.772 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
16.773 * [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))))
16.774 * [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)))))
16.774 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
16.774 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
16.774 * [taylor]: Taking taylor expansion of 1.0 in n
16.774 * [backup-simplify]: Simplify 1.0 into 1.0
16.774 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
16.775 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
16.775 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
16.775 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.775 * [taylor]: Taking taylor expansion of k in n
16.775 * [backup-simplify]: Simplify k into k
16.775 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.775 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
16.775 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.775 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
16.775 * [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
16.775 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
16.775 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
16.775 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
16.775 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
16.775 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
16.775 * [taylor]: Taking taylor expansion of 0.5 in n
16.775 * [backup-simplify]: Simplify 0.5 into 0.5
16.775 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
16.775 * [taylor]: Taking taylor expansion of 1.0 in n
16.775 * [backup-simplify]: Simplify 1.0 into 1.0
16.775 * [taylor]: Taking taylor expansion of k in n
16.775 * [backup-simplify]: Simplify k into k
16.775 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
16.775 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
16.775 * [taylor]: Taking taylor expansion of 2.0 in n
16.775 * [backup-simplify]: Simplify 2.0 into 2.0
16.775 * [taylor]: Taking taylor expansion of (* n PI) in n
16.775 * [taylor]: Taking taylor expansion of n in n
16.775 * [backup-simplify]: Simplify 0 into 0
16.775 * [backup-simplify]: Simplify 1 into 1
16.775 * [taylor]: Taking taylor expansion of PI in n
16.775 * [backup-simplify]: Simplify PI into PI
16.776 * [backup-simplify]: Simplify (* 0 PI) into 0
16.776 * [backup-simplify]: Simplify (* 2.0 0) into 0
16.778 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
16.779 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
16.780 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
16.780 * [backup-simplify]: Simplify (- k) into (- k)
16.781 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
16.781 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
16.782 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
16.783 * [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))))
16.785 * [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)))))
16.785 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
16.785 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
16.785 * [taylor]: Taking taylor expansion of 1.0 in n
16.785 * [backup-simplify]: Simplify 1.0 into 1.0
16.785 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
16.786 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
16.786 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
16.786 * [taylor]: Taking taylor expansion of (/ 1 k) in n
16.786 * [taylor]: Taking taylor expansion of k in n
16.786 * [backup-simplify]: Simplify k into k
16.786 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
16.786 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
16.786 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
16.786 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
16.788 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
16.790 * [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))))))
16.793 * [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)))
16.793 * [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
16.793 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
16.793 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
16.793 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
16.793 * [taylor]: Taking taylor expansion of 1.0 in k
16.793 * [backup-simplify]: Simplify 1.0 into 1.0
16.793 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
16.794 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
16.794 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
16.794 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
16.794 * [taylor]: Taking taylor expansion of 0.5 in k
16.794 * [backup-simplify]: Simplify 0.5 into 0.5
16.794 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
16.794 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
16.794 * [taylor]: Taking taylor expansion of 1.0 in k
16.794 * [backup-simplify]: Simplify 1.0 into 1.0
16.794 * [taylor]: Taking taylor expansion of k in k
16.794 * [backup-simplify]: Simplify 0 into 0
16.794 * [backup-simplify]: Simplify 1 into 1
16.794 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
16.794 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
16.794 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
16.794 * [taylor]: Taking taylor expansion of 2.0 in k
16.795 * [backup-simplify]: Simplify 2.0 into 2.0
16.795 * [taylor]: Taking taylor expansion of PI in k
16.795 * [backup-simplify]: Simplify PI into PI
16.795 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
16.796 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
16.796 * [taylor]: Taking taylor expansion of (log n) in k
16.796 * [taylor]: Taking taylor expansion of n in k
16.796 * [backup-simplify]: Simplify n into n
16.796 * [backup-simplify]: Simplify (log n) into (log n)
16.797 * [backup-simplify]: Simplify (- 0) into 0
16.797 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
16.798 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
16.800 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
16.801 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
16.802 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
16.802 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
16.802 * [taylor]: Taking taylor expansion of (/ 1 k) in k
16.802 * [taylor]: Taking taylor expansion of k in k
16.802 * [backup-simplify]: Simplify 0 into 0
16.802 * [backup-simplify]: Simplify 1 into 1
16.803 * [backup-simplify]: Simplify (/ 1 1) into 1
16.803 * [backup-simplify]: Simplify (sqrt 0) into 0
16.804 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
16.806 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
16.808 * [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)))))
16.811 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) 0) into 0
16.811 * [backup-simplify]: Simplify 0 into 0
16.812 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
16.813 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
16.814 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
16.816 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
16.816 * [backup-simplify]: Simplify (- 0) into 0
16.817 * [backup-simplify]: Simplify (+ 0 0) into 0
16.817 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
16.819 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
16.820 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
16.822 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
16.824 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0
16.827 * [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
16.827 * [taylor]: Taking taylor expansion of 0 in k
16.827 * [backup-simplify]: Simplify 0 into 0
16.828 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
16.830 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
16.831 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
16.831 * [backup-simplify]: Simplify (+ 0 0) into 0
16.831 * [backup-simplify]: Simplify (- 1) into -1
16.832 * [backup-simplify]: Simplify (+ 0 -1) into -1
16.833 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
16.836 * [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))))
16.839 * [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))))))
16.840 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
16.853 * [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)))))))))
16.859 * [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)))))))
16.861 * [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)))))))
16.861 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.861 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
16.862 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
16.863 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
16.864 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
16.864 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
16.866 * [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
16.867 * [backup-simplify]: Simplify (- 0) into 0
16.867 * [backup-simplify]: Simplify (+ 0 0) into 0
16.867 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
16.868 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
16.870 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
16.871 * [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
16.872 * [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
16.874 * [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
16.874 * [taylor]: Taking taylor expansion of 0 in k
16.874 * [backup-simplify]: Simplify 0 into 0
16.875 * [backup-simplify]: Simplify 0 into 0
16.875 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
16.877 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
16.878 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
16.880 * [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
16.881 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
16.881 * [backup-simplify]: Simplify (+ 0 0) into 0
16.881 * [backup-simplify]: Simplify (- 0) into 0
16.882 * [backup-simplify]: Simplify (+ 0 0) into 0
16.883 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
16.885 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
16.887 * [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))))))
16.888 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
16.890 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
16.901 * [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))))))
16.922 * [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)))))))))))
16.932 * [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)))))))))))
16.932 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
16.933 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
16.934 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
16.936 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
16.937 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
16.939 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
16.945 * [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
16.946 * [backup-simplify]: Simplify (- 0) into 0
16.946 * [backup-simplify]: Simplify (+ 0 0) into 0
16.947 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
16.948 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
16.950 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
16.951 * [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
16.953 * [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
16.955 * [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
16.955 * [taylor]: Taking taylor expansion of 0 in k
16.955 * [backup-simplify]: Simplify 0 into 0
16.955 * [backup-simplify]: Simplify 0 into 0
16.955 * [backup-simplify]: Simplify 0 into 0
16.955 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
16.958 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
16.959 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
16.962 * [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
16.964 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
16.964 * [backup-simplify]: Simplify (+ 0 0) into 0
16.964 * [backup-simplify]: Simplify (- 0) into 0
16.965 * [backup-simplify]: Simplify (+ 0 0) into 0
16.966 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
16.974 * [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
16.980 * [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))))))
16.981 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
16.983 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
17.002 * [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)))))))))))
17.028 * [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)))))))))))))))
17.043 * [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)))))))))))))))
17.078 * [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))))))))))))))))))))))))
17.081 * [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 (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k))
17.081 * [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
17.081 * [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
17.081 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
17.081 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.081 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.081 * [taylor]: Taking taylor expansion of 1.0 in k
17.081 * [backup-simplify]: Simplify 1.0 into 1.0
17.082 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.083 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.083 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
17.083 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
17.083 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
17.083 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
17.083 * [taylor]: Taking taylor expansion of 0.5 in k
17.083 * [backup-simplify]: Simplify 0.5 into 0.5
17.083 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
17.083 * [taylor]: Taking taylor expansion of 1.0 in k
17.083 * [backup-simplify]: Simplify 1.0 into 1.0
17.083 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.083 * [taylor]: Taking taylor expansion of k in k
17.083 * [backup-simplify]: Simplify 0 into 0
17.083 * [backup-simplify]: Simplify 1 into 1
17.083 * [backup-simplify]: Simplify (/ 1 1) into 1
17.083 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
17.083 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
17.083 * [taylor]: Taking taylor expansion of 2.0 in k
17.083 * [backup-simplify]: Simplify 2.0 into 2.0
17.084 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.084 * [taylor]: Taking taylor expansion of PI in k
17.084 * [backup-simplify]: Simplify PI into PI
17.084 * [taylor]: Taking taylor expansion of n in k
17.084 * [backup-simplify]: Simplify n into n
17.084 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.084 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
17.084 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
17.084 * [backup-simplify]: Simplify (- 1) into -1
17.085 * [backup-simplify]: Simplify (+ 0 -1) into -1
17.085 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
17.085 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
17.086 * [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))))))
17.086 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.086 * [taylor]: Taking taylor expansion of k in k
17.086 * [backup-simplify]: Simplify 0 into 0
17.086 * [backup-simplify]: Simplify 1 into 1
17.086 * [backup-simplify]: Simplify (sqrt 0) into 0
17.088 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.088 * [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
17.088 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
17.088 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
17.088 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
17.088 * [taylor]: Taking taylor expansion of 1.0 in n
17.088 * [backup-simplify]: Simplify 1.0 into 1.0
17.088 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.089 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.089 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
17.089 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
17.089 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
17.089 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
17.089 * [taylor]: Taking taylor expansion of 0.5 in n
17.089 * [backup-simplify]: Simplify 0.5 into 0.5
17.089 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
17.089 * [taylor]: Taking taylor expansion of 1.0 in n
17.089 * [backup-simplify]: Simplify 1.0 into 1.0
17.089 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.089 * [taylor]: Taking taylor expansion of k in n
17.089 * [backup-simplify]: Simplify k into k
17.089 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.089 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
17.089 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
17.090 * [taylor]: Taking taylor expansion of 2.0 in n
17.090 * [backup-simplify]: Simplify 2.0 into 2.0
17.090 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.090 * [taylor]: Taking taylor expansion of PI in n
17.090 * [backup-simplify]: Simplify PI into PI
17.090 * [taylor]: Taking taylor expansion of n in n
17.090 * [backup-simplify]: Simplify 0 into 0
17.090 * [backup-simplify]: Simplify 1 into 1
17.090 * [backup-simplify]: Simplify (/ PI 1) into PI
17.091 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.092 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.092 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
17.092 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
17.092 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
17.094 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.101 * [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))))
17.103 * [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)))))
17.103 * [taylor]: Taking taylor expansion of (sqrt k) in n
17.103 * [taylor]: Taking taylor expansion of k in n
17.103 * [backup-simplify]: Simplify k into k
17.103 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
17.103 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
17.103 * [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
17.103 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
17.103 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
17.103 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
17.103 * [taylor]: Taking taylor expansion of 1.0 in n
17.103 * [backup-simplify]: Simplify 1.0 into 1.0
17.104 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.104 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.104 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
17.104 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
17.104 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
17.105 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
17.105 * [taylor]: Taking taylor expansion of 0.5 in n
17.105 * [backup-simplify]: Simplify 0.5 into 0.5
17.105 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
17.105 * [taylor]: Taking taylor expansion of 1.0 in n
17.105 * [backup-simplify]: Simplify 1.0 into 1.0
17.105 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.105 * [taylor]: Taking taylor expansion of k in n
17.105 * [backup-simplify]: Simplify k into k
17.105 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.105 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
17.105 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
17.105 * [taylor]: Taking taylor expansion of 2.0 in n
17.105 * [backup-simplify]: Simplify 2.0 into 2.0
17.105 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.105 * [taylor]: Taking taylor expansion of PI in n
17.105 * [backup-simplify]: Simplify PI into PI
17.105 * [taylor]: Taking taylor expansion of n in n
17.105 * [backup-simplify]: Simplify 0 into 0
17.105 * [backup-simplify]: Simplify 1 into 1
17.106 * [backup-simplify]: Simplify (/ PI 1) into PI
17.106 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.107 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.107 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
17.107 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
17.107 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
17.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.110 * [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))))
17.111 * [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)))))
17.111 * [taylor]: Taking taylor expansion of (sqrt k) in n
17.111 * [taylor]: Taking taylor expansion of k in n
17.112 * [backup-simplify]: Simplify k into k
17.112 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
17.112 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
17.113 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.115 * [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))))))
17.118 * [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))
17.118 * [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
17.118 * [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
17.118 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.118 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.118 * [taylor]: Taking taylor expansion of 1.0 in k
17.118 * [backup-simplify]: Simplify 1.0 into 1.0
17.119 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.119 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.119 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
17.119 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
17.119 * [taylor]: Taking taylor expansion of 0.5 in k
17.119 * [backup-simplify]: Simplify 0.5 into 0.5
17.120 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
17.120 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
17.120 * [taylor]: Taking taylor expansion of 1.0 in k
17.120 * [backup-simplify]: Simplify 1.0 into 1.0
17.120 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.120 * [taylor]: Taking taylor expansion of k in k
17.120 * [backup-simplify]: Simplify 0 into 0
17.120 * [backup-simplify]: Simplify 1 into 1
17.120 * [backup-simplify]: Simplify (/ 1 1) into 1
17.120 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
17.120 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
17.120 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
17.120 * [taylor]: Taking taylor expansion of 2.0 in k
17.120 * [backup-simplify]: Simplify 2.0 into 2.0
17.120 * [taylor]: Taking taylor expansion of PI in k
17.120 * [backup-simplify]: Simplify PI into PI
17.121 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.122 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.122 * [taylor]: Taking taylor expansion of (log n) in k
17.122 * [taylor]: Taking taylor expansion of n in k
17.122 * [backup-simplify]: Simplify n into n
17.122 * [backup-simplify]: Simplify (log n) into (log n)
17.122 * [backup-simplify]: Simplify (- 1) into -1
17.123 * [backup-simplify]: Simplify (+ 0 -1) into -1
17.123 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.124 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
17.125 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
17.127 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
17.128 * [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)))))
17.128 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.128 * [taylor]: Taking taylor expansion of k in k
17.128 * [backup-simplify]: Simplify 0 into 0
17.128 * [backup-simplify]: Simplify 1 into 1
17.129 * [backup-simplify]: Simplify (sqrt 0) into 0
17.130 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.131 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.133 * [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))))))
17.136 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) into 0
17.136 * [backup-simplify]: Simplify 0 into 0
17.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.137 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
17.139 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
17.140 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.140 * [backup-simplify]: Simplify (- 0) into 0
17.141 * [backup-simplify]: Simplify (+ 0 0) into 0
17.141 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
17.143 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.144 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
17.146 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.147 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.149 * [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
17.152 * [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
17.152 * [taylor]: Taking taylor expansion of 0 in k
17.152 * [backup-simplify]: Simplify 0 into 0
17.152 * [backup-simplify]: Simplify 0 into 0
17.153 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.155 * [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
17.158 * [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))))))))
17.161 * [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))))))))
17.162 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
17.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.164 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
17.168 * [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
17.169 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.169 * [backup-simplify]: Simplify (- 0) into 0
17.170 * [backup-simplify]: Simplify (+ 0 0) into 0
17.170 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
17.172 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.174 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
17.177 * [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
17.178 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.179 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.182 * [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
17.184 * [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
17.184 * [taylor]: Taking taylor expansion of 0 in k
17.184 * [backup-simplify]: Simplify 0 into 0
17.184 * [backup-simplify]: Simplify 0 into 0
17.184 * [backup-simplify]: Simplify 0 into 0
17.186 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.187 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.188 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.189 * [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
17.191 * [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))))))))
17.193 * [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))))))))
17.193 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
17.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.195 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.198 * [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
17.198 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.199 * [backup-simplify]: Simplify (- 0) into 0
17.199 * [backup-simplify]: Simplify (+ 0 0) into 0
17.200 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
17.201 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.202 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
17.204 * [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
17.205 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
17.205 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
17.207 * [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
17.209 * [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
17.209 * [taylor]: Taking taylor expansion of 0 in k
17.209 * [backup-simplify]: Simplify 0 into 0
17.209 * [backup-simplify]: Simplify 0 into 0
17.209 * [backup-simplify]: Simplify 0 into 0
17.209 * [backup-simplify]: Simplify 0 into 0
17.212 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.213 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
17.213 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
17.215 * [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
17.218 * [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))))))))
17.221 * [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))))))))
17.230 * [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))))))))
17.233 * [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 (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))))) into (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
17.233 * [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
17.233 * [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
17.233 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
17.233 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.233 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.233 * [taylor]: Taking taylor expansion of 1.0 in k
17.233 * [backup-simplify]: Simplify 1.0 into 1.0
17.233 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.241 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.241 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
17.241 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
17.241 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
17.241 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
17.241 * [taylor]: Taking taylor expansion of 0.5 in k
17.242 * [backup-simplify]: Simplify 0.5 into 0.5
17.242 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
17.242 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.242 * [taylor]: Taking taylor expansion of k in k
17.242 * [backup-simplify]: Simplify 0 into 0
17.242 * [backup-simplify]: Simplify 1 into 1
17.243 * [backup-simplify]: Simplify (/ 1 1) into 1
17.243 * [taylor]: Taking taylor expansion of 1.0 in k
17.243 * [backup-simplify]: Simplify 1.0 into 1.0
17.243 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
17.243 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
17.243 * [taylor]: Taking taylor expansion of -2.0 in k
17.243 * [backup-simplify]: Simplify -2.0 into -2.0
17.243 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.243 * [taylor]: Taking taylor expansion of PI in k
17.243 * [backup-simplify]: Simplify PI into PI
17.243 * [taylor]: Taking taylor expansion of n in k
17.243 * [backup-simplify]: Simplify n into n
17.243 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.243 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
17.243 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
17.244 * [backup-simplify]: Simplify (+ 1 0) into 1
17.245 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
17.245 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
17.245 * [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))))
17.245 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.245 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.245 * [taylor]: Taking taylor expansion of -1 in k
17.245 * [backup-simplify]: Simplify -1 into -1
17.245 * [taylor]: Taking taylor expansion of k in k
17.245 * [backup-simplify]: Simplify 0 into 0
17.245 * [backup-simplify]: Simplify 1 into 1
17.246 * [backup-simplify]: Simplify (/ -1 1) into -1
17.246 * [backup-simplify]: Simplify (sqrt 0) into 0
17.248 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.249 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.251 * [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)))))
17.252 * [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))))))
17.253 * [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
17.253 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
17.253 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
17.253 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
17.253 * [taylor]: Taking taylor expansion of 1.0 in n
17.253 * [backup-simplify]: Simplify 1.0 into 1.0
17.253 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.254 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.254 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
17.254 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
17.254 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
17.254 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
17.254 * [taylor]: Taking taylor expansion of 0.5 in n
17.254 * [backup-simplify]: Simplify 0.5 into 0.5
17.254 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
17.254 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.254 * [taylor]: Taking taylor expansion of k in n
17.254 * [backup-simplify]: Simplify k into k
17.254 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.254 * [taylor]: Taking taylor expansion of 1.0 in n
17.255 * [backup-simplify]: Simplify 1.0 into 1.0
17.255 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
17.255 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
17.255 * [taylor]: Taking taylor expansion of -2.0 in n
17.255 * [backup-simplify]: Simplify -2.0 into -2.0
17.255 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.255 * [taylor]: Taking taylor expansion of PI in n
17.255 * [backup-simplify]: Simplify PI into PI
17.255 * [taylor]: Taking taylor expansion of n in n
17.255 * [backup-simplify]: Simplify 0 into 0
17.255 * [backup-simplify]: Simplify 1 into 1
17.255 * [backup-simplify]: Simplify (/ PI 1) into PI
17.256 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
17.257 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
17.257 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
17.257 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
17.259 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
17.260 * [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)))
17.262 * [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))))
17.262 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
17.262 * [taylor]: Taking taylor expansion of (/ -1 k) in n
17.262 * [taylor]: Taking taylor expansion of -1 in n
17.262 * [backup-simplify]: Simplify -1 into -1
17.262 * [taylor]: Taking taylor expansion of k in n
17.262 * [backup-simplify]: Simplify k into k
17.262 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
17.262 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
17.262 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
17.262 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
17.264 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.265 * [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)))))
17.267 * [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)))
17.267 * [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
17.267 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
17.267 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
17.267 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
17.267 * [taylor]: Taking taylor expansion of 1.0 in n
17.267 * [backup-simplify]: Simplify 1.0 into 1.0
17.267 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.268 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.268 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
17.268 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
17.268 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
17.268 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
17.268 * [taylor]: Taking taylor expansion of 0.5 in n
17.268 * [backup-simplify]: Simplify 0.5 into 0.5
17.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
17.268 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.268 * [taylor]: Taking taylor expansion of k in n
17.268 * [backup-simplify]: Simplify k into k
17.268 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.268 * [taylor]: Taking taylor expansion of 1.0 in n
17.268 * [backup-simplify]: Simplify 1.0 into 1.0
17.268 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
17.268 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
17.268 * [taylor]: Taking taylor expansion of -2.0 in n
17.268 * [backup-simplify]: Simplify -2.0 into -2.0
17.268 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.268 * [taylor]: Taking taylor expansion of PI in n
17.268 * [backup-simplify]: Simplify PI into PI
17.268 * [taylor]: Taking taylor expansion of n in n
17.268 * [backup-simplify]: Simplify 0 into 0
17.268 * [backup-simplify]: Simplify 1 into 1
17.269 * [backup-simplify]: Simplify (/ PI 1) into PI
17.269 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
17.270 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
17.270 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
17.270 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
17.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
17.271 * [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)))
17.272 * [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))))
17.272 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
17.272 * [taylor]: Taking taylor expansion of (/ -1 k) in n
17.272 * [taylor]: Taking taylor expansion of -1 in n
17.272 * [backup-simplify]: Simplify -1 into -1
17.272 * [taylor]: Taking taylor expansion of k in n
17.272 * [backup-simplify]: Simplify k into k
17.272 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
17.273 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
17.273 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
17.273 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
17.273 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.275 * [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)))))
17.276 * [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)))
17.276 * [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
17.277 * [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
17.277 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
17.277 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
17.277 * [taylor]: Taking taylor expansion of 1.0 in k
17.277 * [backup-simplify]: Simplify 1.0 into 1.0
17.277 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
17.277 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
17.277 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
17.277 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
17.277 * [taylor]: Taking taylor expansion of 0.5 in k
17.277 * [backup-simplify]: Simplify 0.5 into 0.5
17.277 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
17.277 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
17.277 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
17.278 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
17.278 * [taylor]: Taking taylor expansion of -2.0 in k
17.278 * [backup-simplify]: Simplify -2.0 into -2.0
17.278 * [taylor]: Taking taylor expansion of PI in k
17.278 * [backup-simplify]: Simplify PI into PI
17.278 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
17.279 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
17.279 * [taylor]: Taking taylor expansion of (log n) in k
17.279 * [taylor]: Taking taylor expansion of n in k
17.279 * [backup-simplify]: Simplify n into n
17.279 * [backup-simplify]: Simplify (log n) into (log n)
17.279 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
17.279 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.279 * [taylor]: Taking taylor expansion of k in k
17.279 * [backup-simplify]: Simplify 0 into 0
17.279 * [backup-simplify]: Simplify 1 into 1
17.279 * [backup-simplify]: Simplify (/ 1 1) into 1
17.279 * [taylor]: Taking taylor expansion of 1.0 in k
17.279 * [backup-simplify]: Simplify 1.0 into 1.0
17.279 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.280 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
17.280 * [backup-simplify]: Simplify (+ 1 0) into 1
17.281 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
17.282 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
17.283 * [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))))
17.283 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.283 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.283 * [taylor]: Taking taylor expansion of -1 in k
17.283 * [backup-simplify]: Simplify -1 into -1
17.283 * [taylor]: Taking taylor expansion of k in k
17.283 * [backup-simplify]: Simplify 0 into 0
17.283 * [backup-simplify]: Simplify 1 into 1
17.283 * [backup-simplify]: Simplify (/ -1 1) into -1
17.283 * [backup-simplify]: Simplify (sqrt 0) into 0
17.284 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.285 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
17.286 * [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)))))
17.288 * [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))))))
17.289 * [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))))))
17.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.291 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
17.292 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
17.292 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.292 * [backup-simplify]: Simplify (+ 0 0) into 0
17.292 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
17.293 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
17.294 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
17.295 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.296 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.299 * [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
17.301 * [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
17.302 * [taylor]: Taking taylor expansion of 0 in k
17.302 * [backup-simplify]: Simplify 0 into 0
17.302 * [backup-simplify]: Simplify 0 into 0
17.302 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
17.304 * [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
17.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.309 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.312 * [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)))))))
17.314 * [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)))))))
17.314 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.315 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
17.317 * [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
17.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.318 * [backup-simplify]: Simplify (+ 0 0) into 0
17.318 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
17.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
17.320 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
17.322 * [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
17.323 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.323 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.325 * [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
17.325 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.325 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
17.327 * [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
17.327 * [taylor]: Taking taylor expansion of 0 in k
17.327 * [backup-simplify]: Simplify 0 into 0
17.327 * [backup-simplify]: Simplify 0 into 0
17.327 * [backup-simplify]: Simplify 0 into 0
17.328 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
17.329 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
17.330 * [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
17.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.333 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.337 * [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)))))))
17.339 * [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)))))))
17.347 * [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))))))))
17.347 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
17.348 * [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))))
17.348 * [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
17.349 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
17.349 * [taylor]: Taking taylor expansion of 1.0 in k
17.349 * [backup-simplify]: Simplify 1.0 into 1.0
17.349 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
17.349 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
17.349 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
17.349 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
17.349 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
17.349 * [taylor]: Taking taylor expansion of 0.5 in k
17.349 * [backup-simplify]: Simplify 0.5 into 0.5
17.349 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
17.349 * [taylor]: Taking taylor expansion of 1.0 in k
17.349 * [backup-simplify]: Simplify 1.0 into 1.0
17.349 * [taylor]: Taking taylor expansion of k in k
17.349 * [backup-simplify]: Simplify 0 into 0
17.349 * [backup-simplify]: Simplify 1 into 1
17.349 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
17.349 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
17.349 * [taylor]: Taking taylor expansion of 2.0 in k
17.349 * [backup-simplify]: Simplify 2.0 into 2.0
17.349 * [taylor]: Taking taylor expansion of (* n PI) in k
17.349 * [taylor]: Taking taylor expansion of n in k
17.349 * [backup-simplify]: Simplify n into n
17.349 * [taylor]: Taking taylor expansion of PI in k
17.349 * [backup-simplify]: Simplify PI into PI
17.349 * [backup-simplify]: Simplify (* n PI) into (* n PI)
17.349 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
17.349 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
17.350 * [backup-simplify]: Simplify (- 0) into 0
17.350 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
17.351 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
17.351 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
17.351 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
17.351 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.351 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.351 * [taylor]: Taking taylor expansion of k in k
17.351 * [backup-simplify]: Simplify 0 into 0
17.351 * [backup-simplify]: Simplify 1 into 1
17.352 * [backup-simplify]: Simplify (/ 1 1) into 1
17.352 * [backup-simplify]: Simplify (sqrt 0) into 0
17.353 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.354 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
17.354 * [taylor]: Taking taylor expansion of 1.0 in n
17.354 * [backup-simplify]: Simplify 1.0 into 1.0
17.354 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
17.354 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
17.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
17.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
17.354 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
17.354 * [taylor]: Taking taylor expansion of 0.5 in n
17.354 * [backup-simplify]: Simplify 0.5 into 0.5
17.354 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
17.354 * [taylor]: Taking taylor expansion of 1.0 in n
17.354 * [backup-simplify]: Simplify 1.0 into 1.0
17.354 * [taylor]: Taking taylor expansion of k in n
17.354 * [backup-simplify]: Simplify k into k
17.354 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
17.354 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
17.354 * [taylor]: Taking taylor expansion of 2.0 in n
17.354 * [backup-simplify]: Simplify 2.0 into 2.0
17.354 * [taylor]: Taking taylor expansion of (* n PI) in n
17.354 * [taylor]: Taking taylor expansion of n in n
17.354 * [backup-simplify]: Simplify 0 into 0
17.354 * [backup-simplify]: Simplify 1 into 1
17.354 * [taylor]: Taking taylor expansion of PI in n
17.354 * [backup-simplify]: Simplify PI into PI
17.355 * [backup-simplify]: Simplify (* 0 PI) into 0
17.355 * [backup-simplify]: Simplify (* 2.0 0) into 0
17.357 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.359 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
17.360 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.360 * [backup-simplify]: Simplify (- k) into (- k)
17.360 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
17.360 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
17.722 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
17.723 * [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))))
17.724 * [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)))))
17.724 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
17.724 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.724 * [taylor]: Taking taylor expansion of k in n
17.724 * [backup-simplify]: Simplify k into k
17.724 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.724 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
17.724 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.724 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
17.724 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
17.724 * [taylor]: Taking taylor expansion of 1.0 in n
17.724 * [backup-simplify]: Simplify 1.0 into 1.0
17.724 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
17.724 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
17.724 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
17.724 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
17.724 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
17.725 * [taylor]: Taking taylor expansion of 0.5 in n
17.725 * [backup-simplify]: Simplify 0.5 into 0.5
17.725 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
17.725 * [taylor]: Taking taylor expansion of 1.0 in n
17.725 * [backup-simplify]: Simplify 1.0 into 1.0
17.725 * [taylor]: Taking taylor expansion of k in n
17.725 * [backup-simplify]: Simplify k into k
17.725 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
17.725 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
17.725 * [taylor]: Taking taylor expansion of 2.0 in n
17.725 * [backup-simplify]: Simplify 2.0 into 2.0
17.725 * [taylor]: Taking taylor expansion of (* n PI) in n
17.725 * [taylor]: Taking taylor expansion of n in n
17.725 * [backup-simplify]: Simplify 0 into 0
17.725 * [backup-simplify]: Simplify 1 into 1
17.725 * [taylor]: Taking taylor expansion of PI in n
17.725 * [backup-simplify]: Simplify PI into PI
17.725 * [backup-simplify]: Simplify (* 0 PI) into 0
17.725 * [backup-simplify]: Simplify (* 2.0 0) into 0
17.726 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.727 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
17.728 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.728 * [backup-simplify]: Simplify (- k) into (- k)
17.728 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
17.728 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
17.730 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
17.731 * [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))))
17.736 * [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)))))
17.736 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
17.736 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.736 * [taylor]: Taking taylor expansion of k in n
17.736 * [backup-simplify]: Simplify k into k
17.736 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.736 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
17.736 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.736 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
17.738 * [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)))
17.739 * [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))))
17.739 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
17.739 * [taylor]: Taking taylor expansion of 1.0 in k
17.739 * [backup-simplify]: Simplify 1.0 into 1.0
17.739 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
17.739 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
17.740 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
17.740 * [taylor]: Taking taylor expansion of 0.5 in k
17.740 * [backup-simplify]: Simplify 0.5 into 0.5
17.740 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
17.740 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
17.740 * [taylor]: Taking taylor expansion of 1.0 in k
17.740 * [backup-simplify]: Simplify 1.0 into 1.0
17.740 * [taylor]: Taking taylor expansion of k in k
17.740 * [backup-simplify]: Simplify 0 into 0
17.740 * [backup-simplify]: Simplify 1 into 1
17.740 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
17.740 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
17.740 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
17.740 * [taylor]: Taking taylor expansion of 2.0 in k
17.740 * [backup-simplify]: Simplify 2.0 into 2.0
17.740 * [taylor]: Taking taylor expansion of PI in k
17.740 * [backup-simplify]: Simplify PI into PI
17.740 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.742 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.742 * [taylor]: Taking taylor expansion of (log n) in k
17.742 * [taylor]: Taking taylor expansion of n in k
17.742 * [backup-simplify]: Simplify n into n
17.742 * [backup-simplify]: Simplify (log n) into (log n)
17.742 * [backup-simplify]: Simplify (- 0) into 0
17.743 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
17.744 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
17.745 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
17.746 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
17.747 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
17.747 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
17.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.747 * [taylor]: Taking taylor expansion of k in k
17.747 * [backup-simplify]: Simplify 0 into 0
17.748 * [backup-simplify]: Simplify 1 into 1
17.748 * [backup-simplify]: Simplify (/ 1 1) into 1
17.748 * [backup-simplify]: Simplify (sqrt 0) into 0
17.749 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.750 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
17.750 * [backup-simplify]: Simplify (* 1.0 0) into 0
17.750 * [backup-simplify]: Simplify 0 into 0
17.751 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.751 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
17.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
17.753 * [backup-simplify]: Simplify (- 0) into 0
17.753 * [backup-simplify]: Simplify (+ 0 0) into 0
17.753 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
17.754 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
17.755 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
17.756 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.757 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
17.758 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
17.758 * [taylor]: Taking taylor expansion of 0 in k
17.758 * [backup-simplify]: Simplify 0 into 0
17.758 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
17.760 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
17.760 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
17.760 * [backup-simplify]: Simplify (+ 0 0) into 0
17.761 * [backup-simplify]: Simplify (- 1) into -1
17.761 * [backup-simplify]: Simplify (+ 0 -1) into -1
17.762 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
17.763 * [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))))
17.766 * [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))))))
17.768 * [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))))))
17.769 * [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))))))
17.770 * [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))))))
17.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.771 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
17.772 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.772 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.774 * [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
17.775 * [backup-simplify]: Simplify (- 0) into 0
17.775 * [backup-simplify]: Simplify (+ 0 0) into 0
17.776 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
17.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
17.779 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
17.781 * [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
17.783 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
17.785 * [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
17.785 * [taylor]: Taking taylor expansion of 0 in k
17.785 * [backup-simplify]: Simplify 0 into 0
17.785 * [backup-simplify]: Simplify 0 into 0
17.786 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
17.789 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
17.793 * [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
17.795 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
17.796 * [backup-simplify]: Simplify (+ 0 0) into 0
17.796 * [backup-simplify]: Simplify (- 0) into 0
17.796 * [backup-simplify]: Simplify (+ 0 0) into 0
17.798 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
17.801 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
17.805 * [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))))))
17.815 * [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)))))))))))
17.822 * [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)))))))))))
17.827 * [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)))))))))))
17.827 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.828 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
17.830 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.831 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
17.837 * [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
17.838 * [backup-simplify]: Simplify (- 0) into 0
17.838 * [backup-simplify]: Simplify (+ 0 0) into 0
17.839 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
17.841 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
17.843 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
17.845 * [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
17.853 * [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
17.855 * [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
17.855 * [taylor]: Taking taylor expansion of 0 in k
17.855 * [backup-simplify]: Simplify 0 into 0
17.856 * [backup-simplify]: Simplify 0 into 0
17.856 * [backup-simplify]: Simplify 0 into 0
17.857 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.860 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.868 * [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
17.871 * [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
17.872 * [backup-simplify]: Simplify (+ 0 0) into 0
17.872 * [backup-simplify]: Simplify (- 0) into 0
17.872 * [backup-simplify]: Simplify (+ 0 0) into 0
17.875 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
17.878 * [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
17.884 * [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))))))
17.904 * [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)))))))))))))))))
17.926 * [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)))))))))))))))))
17.939 * [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)))))))))))))))))
17.960 * [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)))))))))))))))))))))
17.961 * [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)))
17.962 * [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
17.962 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
17.962 * [taylor]: Taking taylor expansion of 1.0 in k
17.962 * [backup-simplify]: Simplify 1.0 into 1.0
17.962 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
17.962 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
17.962 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
17.962 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
17.962 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
17.962 * [taylor]: Taking taylor expansion of 0.5 in k
17.962 * [backup-simplify]: Simplify 0.5 into 0.5
17.962 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
17.962 * [taylor]: Taking taylor expansion of 1.0 in k
17.962 * [backup-simplify]: Simplify 1.0 into 1.0
17.962 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.962 * [taylor]: Taking taylor expansion of k in k
17.962 * [backup-simplify]: Simplify 0 into 0
17.962 * [backup-simplify]: Simplify 1 into 1
17.962 * [backup-simplify]: Simplify (/ 1 1) into 1
17.962 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
17.962 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
17.962 * [taylor]: Taking taylor expansion of 2.0 in k
17.963 * [backup-simplify]: Simplify 2.0 into 2.0
17.963 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.963 * [taylor]: Taking taylor expansion of PI in k
17.963 * [backup-simplify]: Simplify PI into PI
17.963 * [taylor]: Taking taylor expansion of n in k
17.963 * [backup-simplify]: Simplify n into n
17.963 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.963 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
17.963 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
17.963 * [backup-simplify]: Simplify (- 1) into -1
17.964 * [backup-simplify]: Simplify (+ 0 -1) into -1
17.964 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
17.964 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
17.964 * [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))))))
17.965 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.965 * [taylor]: Taking taylor expansion of k in k
17.965 * [backup-simplify]: Simplify 0 into 0
17.965 * [backup-simplify]: Simplify 1 into 1
17.965 * [backup-simplify]: Simplify (sqrt 0) into 0
17.966 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
17.966 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
17.966 * [taylor]: Taking taylor expansion of 1.0 in n
17.966 * [backup-simplify]: Simplify 1.0 into 1.0
17.967 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
17.967 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
17.967 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
17.967 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
17.967 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
17.967 * [taylor]: Taking taylor expansion of 0.5 in n
17.967 * [backup-simplify]: Simplify 0.5 into 0.5
17.967 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
17.967 * [taylor]: Taking taylor expansion of 1.0 in n
17.967 * [backup-simplify]: Simplify 1.0 into 1.0
17.967 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.967 * [taylor]: Taking taylor expansion of k in n
17.967 * [backup-simplify]: Simplify k into k
17.967 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.967 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
17.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
17.967 * [taylor]: Taking taylor expansion of 2.0 in n
17.967 * [backup-simplify]: Simplify 2.0 into 2.0
17.967 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.967 * [taylor]: Taking taylor expansion of PI in n
17.967 * [backup-simplify]: Simplify PI into PI
17.967 * [taylor]: Taking taylor expansion of n in n
17.967 * [backup-simplify]: Simplify 0 into 0
17.967 * [backup-simplify]: Simplify 1 into 1
17.968 * [backup-simplify]: Simplify (/ PI 1) into PI
17.968 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.969 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.970 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
17.970 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
17.970 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
17.971 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.972 * [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))))
17.974 * [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)))))
17.974 * [taylor]: Taking taylor expansion of (sqrt k) in n
17.974 * [taylor]: Taking taylor expansion of k in n
17.974 * [backup-simplify]: Simplify k into k
17.974 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
17.974 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
17.974 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
17.974 * [taylor]: Taking taylor expansion of 1.0 in n
17.974 * [backup-simplify]: Simplify 1.0 into 1.0
17.974 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
17.974 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
17.974 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
17.974 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
17.975 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
17.975 * [taylor]: Taking taylor expansion of 0.5 in n
17.975 * [backup-simplify]: Simplify 0.5 into 0.5
17.975 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
17.975 * [taylor]: Taking taylor expansion of 1.0 in n
17.975 * [backup-simplify]: Simplify 1.0 into 1.0
17.975 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.975 * [taylor]: Taking taylor expansion of k in n
17.975 * [backup-simplify]: Simplify k into k
17.975 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.975 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
17.975 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
17.975 * [taylor]: Taking taylor expansion of 2.0 in n
17.975 * [backup-simplify]: Simplify 2.0 into 2.0
17.975 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.975 * [taylor]: Taking taylor expansion of PI in n
17.975 * [backup-simplify]: Simplify PI into PI
17.975 * [taylor]: Taking taylor expansion of n in n
17.975 * [backup-simplify]: Simplify 0 into 0
17.975 * [backup-simplify]: Simplify 1 into 1
17.976 * [backup-simplify]: Simplify (/ PI 1) into PI
17.976 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.977 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.977 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
17.977 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
17.977 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
17.979 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
17.980 * [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))))
17.981 * [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)))))
17.981 * [taylor]: Taking taylor expansion of (sqrt k) in n
17.981 * [taylor]: Taking taylor expansion of k in n
17.981 * [backup-simplify]: Simplify k into k
17.981 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
17.981 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
17.983 * [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))
17.984 * [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)))
17.984 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
17.984 * [taylor]: Taking taylor expansion of 1.0 in k
17.984 * [backup-simplify]: Simplify 1.0 into 1.0
17.985 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
17.985 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
17.985 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
17.985 * [taylor]: Taking taylor expansion of 0.5 in k
17.985 * [backup-simplify]: Simplify 0.5 into 0.5
17.985 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
17.985 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
17.985 * [taylor]: Taking taylor expansion of 1.0 in k
17.985 * [backup-simplify]: Simplify 1.0 into 1.0
17.985 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.985 * [taylor]: Taking taylor expansion of k in k
17.985 * [backup-simplify]: Simplify 0 into 0
17.985 * [backup-simplify]: Simplify 1 into 1
17.985 * [backup-simplify]: Simplify (/ 1 1) into 1
17.985 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
17.985 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
17.985 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
17.985 * [taylor]: Taking taylor expansion of 2.0 in k
17.985 * [backup-simplify]: Simplify 2.0 into 2.0
17.985 * [taylor]: Taking taylor expansion of PI in k
17.985 * [backup-simplify]: Simplify PI into PI
17.986 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
17.987 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
17.987 * [taylor]: Taking taylor expansion of (log n) in k
17.987 * [taylor]: Taking taylor expansion of n in k
17.987 * [backup-simplify]: Simplify n into n
17.987 * [backup-simplify]: Simplify (log n) into (log n)
17.987 * [backup-simplify]: Simplify (- 1) into -1
17.988 * [backup-simplify]: Simplify (+ 0 -1) into -1
17.988 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.989 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
17.990 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
17.991 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
17.992 * [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)))))
17.993 * [taylor]: Taking taylor expansion of (sqrt k) in k
17.993 * [taylor]: Taking taylor expansion of k in k
17.993 * [backup-simplify]: Simplify 0 into 0
17.993 * [backup-simplify]: Simplify 1 into 1
17.993 * [backup-simplify]: Simplify (sqrt 0) into 0
17.994 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.000 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
18.001 * [backup-simplify]: Simplify (* 1.0 0) into 0
18.001 * [backup-simplify]: Simplify 0 into 0
18.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.003 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
18.004 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
18.005 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.005 * [backup-simplify]: Simplify (- 0) into 0
18.005 * [backup-simplify]: Simplify (+ 0 0) into 0
18.006 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
18.007 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.008 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
18.009 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.010 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
18.011 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
18.011 * [taylor]: Taking taylor expansion of 0 in k
18.011 * [backup-simplify]: Simplify 0 into 0
18.011 * [backup-simplify]: Simplify 0 into 0
18.012 * [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)))))))
18.013 * [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)))))))
18.014 * [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)))))))
18.015 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
18.015 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.016 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.018 * [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
18.018 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.018 * [backup-simplify]: Simplify (- 0) into 0
18.019 * [backup-simplify]: Simplify (+ 0 0) into 0
18.019 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
18.020 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.021 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
18.023 * [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
18.024 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
18.025 * [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
18.026 * [taylor]: Taking taylor expansion of 0 in k
18.026 * [backup-simplify]: Simplify 0 into 0
18.026 * [backup-simplify]: Simplify 0 into 0
18.026 * [backup-simplify]: Simplify 0 into 0
18.028 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.029 * [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)))))))
18.031 * [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)))))))
18.032 * [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)))))))
18.033 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
18.034 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.035 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.042 * [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
18.042 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.043 * [backup-simplify]: Simplify (- 0) into 0
18.043 * [backup-simplify]: Simplify (+ 0 0) into 0
18.045 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
18.046 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.048 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
18.050 * [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
18.051 * [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
18.052 * [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
18.053 * [taylor]: Taking taylor expansion of 0 in k
18.053 * [backup-simplify]: Simplify 0 into 0
18.053 * [backup-simplify]: Simplify 0 into 0
18.053 * [backup-simplify]: Simplify 0 into 0
18.053 * [backup-simplify]: Simplify 0 into 0
18.055 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.056 * [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)))))))
18.059 * [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)))))))
18.060 * [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)))))))
18.063 * [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))))))))
18.063 * [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))))
18.063 * [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
18.063 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
18.063 * [taylor]: Taking taylor expansion of 1.0 in k
18.063 * [backup-simplify]: Simplify 1.0 into 1.0
18.063 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
18.063 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
18.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
18.064 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
18.064 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
18.064 * [taylor]: Taking taylor expansion of 0.5 in k
18.064 * [backup-simplify]: Simplify 0.5 into 0.5
18.064 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
18.064 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.064 * [taylor]: Taking taylor expansion of k in k
18.064 * [backup-simplify]: Simplify 0 into 0
18.064 * [backup-simplify]: Simplify 1 into 1
18.064 * [backup-simplify]: Simplify (/ 1 1) into 1
18.064 * [taylor]: Taking taylor expansion of 1.0 in k
18.064 * [backup-simplify]: Simplify 1.0 into 1.0
18.064 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
18.064 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
18.064 * [taylor]: Taking taylor expansion of -2.0 in k
18.064 * [backup-simplify]: Simplify -2.0 into -2.0
18.064 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.064 * [taylor]: Taking taylor expansion of PI in k
18.064 * [backup-simplify]: Simplify PI into PI
18.064 * [taylor]: Taking taylor expansion of n in k
18.064 * [backup-simplify]: Simplify n into n
18.064 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.064 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
18.064 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
18.065 * [backup-simplify]: Simplify (+ 1 0) into 1
18.065 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
18.065 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
18.065 * [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))))
18.065 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.065 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.065 * [taylor]: Taking taylor expansion of -1 in k
18.065 * [backup-simplify]: Simplify -1 into -1
18.065 * [taylor]: Taking taylor expansion of k in k
18.065 * [backup-simplify]: Simplify 0 into 0
18.065 * [backup-simplify]: Simplify 1 into 1
18.065 * [backup-simplify]: Simplify (/ -1 1) into -1
18.066 * [backup-simplify]: Simplify (sqrt 0) into 0
18.067 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.067 * [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)))))
18.067 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
18.067 * [taylor]: Taking taylor expansion of 1.0 in n
18.067 * [backup-simplify]: Simplify 1.0 into 1.0
18.067 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
18.067 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
18.067 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
18.067 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
18.067 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
18.067 * [taylor]: Taking taylor expansion of 0.5 in n
18.067 * [backup-simplify]: Simplify 0.5 into 0.5
18.067 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
18.067 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.067 * [taylor]: Taking taylor expansion of k in n
18.067 * [backup-simplify]: Simplify k into k
18.067 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.067 * [taylor]: Taking taylor expansion of 1.0 in n
18.067 * [backup-simplify]: Simplify 1.0 into 1.0
18.067 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
18.067 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.067 * [taylor]: Taking taylor expansion of -2.0 in n
18.067 * [backup-simplify]: Simplify -2.0 into -2.0
18.067 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.067 * [taylor]: Taking taylor expansion of PI in n
18.067 * [backup-simplify]: Simplify PI into PI
18.067 * [taylor]: Taking taylor expansion of n in n
18.067 * [backup-simplify]: Simplify 0 into 0
18.067 * [backup-simplify]: Simplify 1 into 1
18.068 * [backup-simplify]: Simplify (/ PI 1) into PI
18.068 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.069 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
18.069 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
18.069 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
18.070 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.071 * [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)))
18.071 * [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))))
18.071 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
18.071 * [taylor]: Taking taylor expansion of (/ -1 k) in n
18.071 * [taylor]: Taking taylor expansion of -1 in n
18.071 * [backup-simplify]: Simplify -1 into -1
18.071 * [taylor]: Taking taylor expansion of k in n
18.071 * [backup-simplify]: Simplify k into k
18.071 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
18.072 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
18.072 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
18.072 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
18.072 * [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)))
18.073 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
18.073 * [taylor]: Taking taylor expansion of 1.0 in n
18.073 * [backup-simplify]: Simplify 1.0 into 1.0
18.073 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
18.073 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
18.073 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
18.073 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
18.073 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
18.073 * [taylor]: Taking taylor expansion of 0.5 in n
18.073 * [backup-simplify]: Simplify 0.5 into 0.5
18.073 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
18.073 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.073 * [taylor]: Taking taylor expansion of k in n
18.073 * [backup-simplify]: Simplify k into k
18.073 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.073 * [taylor]: Taking taylor expansion of 1.0 in n
18.073 * [backup-simplify]: Simplify 1.0 into 1.0
18.073 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
18.073 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.073 * [taylor]: Taking taylor expansion of -2.0 in n
18.073 * [backup-simplify]: Simplify -2.0 into -2.0
18.073 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.073 * [taylor]: Taking taylor expansion of PI in n
18.073 * [backup-simplify]: Simplify PI into PI
18.073 * [taylor]: Taking taylor expansion of n in n
18.073 * [backup-simplify]: Simplify 0 into 0
18.073 * [backup-simplify]: Simplify 1 into 1
18.073 * [backup-simplify]: Simplify (/ PI 1) into PI
18.074 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.075 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
18.075 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
18.075 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
18.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.077 * [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)))
18.078 * [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))))
18.078 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
18.078 * [taylor]: Taking taylor expansion of (/ -1 k) in n
18.078 * [taylor]: Taking taylor expansion of -1 in n
18.078 * [backup-simplify]: Simplify -1 into -1
18.078 * [taylor]: Taking taylor expansion of k in n
18.078 * [backup-simplify]: Simplify k into k
18.078 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
18.079 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
18.079 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
18.079 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
18.080 * [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)))
18.081 * [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))))
18.082 * [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
18.082 * [taylor]: Taking taylor expansion of 1.0 in k
18.082 * [backup-simplify]: Simplify 1.0 into 1.0
18.082 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
18.082 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
18.082 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
18.082 * [taylor]: Taking taylor expansion of 0.5 in k
18.082 * [backup-simplify]: Simplify 0.5 into 0.5
18.082 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
18.082 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
18.082 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
18.082 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
18.082 * [taylor]: Taking taylor expansion of -2.0 in k
18.082 * [backup-simplify]: Simplify -2.0 into -2.0
18.082 * [taylor]: Taking taylor expansion of PI in k
18.082 * [backup-simplify]: Simplify PI into PI
18.082 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.084 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
18.084 * [taylor]: Taking taylor expansion of (log n) in k
18.084 * [taylor]: Taking taylor expansion of n in k
18.084 * [backup-simplify]: Simplify n into n
18.084 * [backup-simplify]: Simplify (log n) into (log n)
18.084 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
18.084 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.084 * [taylor]: Taking taylor expansion of k in k
18.084 * [backup-simplify]: Simplify 0 into 0
18.084 * [backup-simplify]: Simplify 1 into 1
18.084 * [backup-simplify]: Simplify (/ 1 1) into 1
18.084 * [taylor]: Taking taylor expansion of 1.0 in k
18.084 * [backup-simplify]: Simplify 1.0 into 1.0
18.084 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.085 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
18.086 * [backup-simplify]: Simplify (+ 1 0) into 1
18.087 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
18.088 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
18.089 * [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))))
18.089 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.089 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.089 * [taylor]: Taking taylor expansion of -1 in k
18.089 * [backup-simplify]: Simplify -1 into -1
18.089 * [taylor]: Taking taylor expansion of k in k
18.090 * [backup-simplify]: Simplify 0 into 0
18.090 * [backup-simplify]: Simplify 1 into 1
18.090 * [backup-simplify]: Simplify (/ -1 1) into -1
18.090 * [backup-simplify]: Simplify (sqrt 0) into 0
18.092 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.093 * [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)))))
18.094 * [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)))))
18.096 * [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)))))
18.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.098 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
18.100 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
18.100 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.100 * [backup-simplify]: Simplify (+ 0 0) into 0
18.101 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
18.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.104 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
18.105 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
18.106 * [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
18.107 * [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
18.107 * [taylor]: Taking taylor expansion of 0 in k
18.107 * [backup-simplify]: Simplify 0 into 0
18.107 * [backup-simplify]: Simplify 0 into 0
18.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
18.110 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.114 * [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))))))
18.116 * [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))))))
18.117 * [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))))))
18.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.118 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.120 * [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
18.121 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.121 * [backup-simplify]: Simplify (+ 0 0) into 0
18.121 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
18.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.123 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
18.125 * [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
18.125 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.126 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
18.127 * [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
18.128 * [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
18.128 * [taylor]: Taking taylor expansion of 0 in k
18.128 * [backup-simplify]: Simplify 0 into 0
18.128 * [backup-simplify]: Simplify 0 into 0
18.128 * [backup-simplify]: Simplify 0 into 0
18.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.131 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.134 * [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))))))
18.136 * [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))))))
18.137 * [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))))))
18.140 * [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))))))))
18.140 * * * [progress]: simplifying candidates
18.148 * [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)
  (* (/ (* 1.0 (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))) (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))) (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))) (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))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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)) (sqrt (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (sqrt k))))) (cbrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt 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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt 1)))))
  (* (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt 1))))
  (* (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (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 (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) 1)))
  (* (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 (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (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 (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (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 (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt 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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt (sqrt 1)))))
  (* (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) (sqrt 1))))
  (* (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 (sqrt k)))) (sqrt (sqrt (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 (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (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 (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (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 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (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 (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (* (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 (sqrt (sqrt k)))) (sqrt (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 (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (* (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 (sqrt 1))) (sqrt (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 1))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (* (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 (sqrt (sqrt k)))) (sqrt (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 (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (* (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 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (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))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (* (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 (sqrt (sqrt k)))) (sqrt (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 (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (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 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 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))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (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 (* (cbrt (sqrt k)) (cbrt (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 (sqrt (* (cbrt k) (cbrt 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 (sqrt (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 (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 (sqrt (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))))
  (* (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 (sqrt (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))) 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 (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (sqrt k))) (sqrt (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 (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)))))
  (- (+ (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))))))))
18.159 * * [simplify]: iteration 0: 560 enodes
18.382 * * [simplify]: iteration 1: 1335 enodes
18.706 * * [simplify]: iteration complete: 5001 enodes
18.707 * * [simplify]: Extracting #0: cost 102 inf + 0
18.709 * * [simplify]: Extracting #1: cost 773 inf + 1
18.714 * * [simplify]: Extracting #2: cost 1293 inf + 3487
18.724 * * [simplify]: Extracting #3: cost 1379 inf + 38882
18.762 * * [simplify]: Extracting #4: cost 1358 inf + 90579
18.843 * * [simplify]: Extracting #5: cost 818 inf + 394316
18.976 * * [simplify]: Extracting #6: cost 313 inf + 700455
19.158 * * [simplify]: Extracting #7: cost 152 inf + 795729
19.353 * * [simplify]: Extracting #8: cost 91 inf + 846815
19.539 * * [simplify]: Extracting #9: cost 57 inf + 864956
19.817 * * [simplify]: Extracting #10: cost 7 inf + 895472
20.070 * * [simplify]: Extracting #11: cost 0 inf + 899514
20.299 * * [simplify]: Extracting #12: cost 0 inf + 899474
20.524 * [simplify]: Simplified to:
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (exp (* (* n PI) 2.0))
  (* (* n (* n n)) (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) PI))
  (* (* (* (* 2.0 PI) (* (* 2.0 PI) (* 2.0 PI))) (* n n)) n)
  (* (cbrt (* (* n PI) 2.0)) (cbrt (* (* n PI) 2.0)))
  (cbrt (* (* n PI) 2.0))
  (* (* (* (* n PI) 2.0) (* (* n PI) 2.0)) (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (* (* (cbrt n) (cbrt n)) (* 2.0 PI))
  (* 2.0 (* PI (sqrt n)))
  (* 2.0 PI)
  (* n PI)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (log (* (* n PI) 2.0))
  (exp (* (* n PI) 2.0))
  (* (* n (* n n)) (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) PI))
  (* (* (* (* 2.0 PI) (* (* 2.0 PI) (* 2.0 PI))) (* n n)) n)
  (* (cbrt (* (* n PI) 2.0)) (cbrt (* (* n PI) 2.0)))
  (cbrt (* (* n PI) 2.0))
  (* (* (* (* n PI) 2.0) (* (* n PI) 2.0)) (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (sqrt (* (* n PI) 2.0))
  (* (* (cbrt n) (cbrt n)) (* 2.0 PI))
  (* 2.0 (* PI (sqrt n)))
  (* 2.0 PI)
  (* n PI)
  (* (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
  (* (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (- (log 1.0) (log (sqrt k))))
  (+ (/ (* (log (* (* n PI) 2.0)) (- 1.0 k)) 2.0) (- (log 1.0) (log (sqrt k))))
  (exp (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (* (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (* (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (cbrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (cbrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (fabs (cbrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (fabs (/ (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (fabs (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (/ (sqrt (fabs (cbrt k))) (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))))
  (* (sqrt (/ (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (fabs (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))
  (* (sqrt (/ (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (fabs (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))
  (* (sqrt (/ (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (/ (sqrt (sqrt (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (fabs (cbrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
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  (- (sqrt k))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (/ (sqrt k) 1.0) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (fabs (cbrt k)))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* 1.0 (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow (* (* n PI) 2.0) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* n PI) 2.0) (/ k 2.0)))
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (* (* n PI) 2.0)
  (+ (* (* 1.0 (* (log n) (* k (exp (* 0.5 (log (* (* n PI) 2.0))))))) (- +nan.0)) (- (* (* +nan.0 1.0) (* (exp (* 0.5 (log (* (* n PI) 2.0)))) k)) (- (- (* +nan.0 (* (* (* (log (* 2.0 PI)) 1.0) k) (exp (* 0.5 (log (* (* n PI) 2.0)))))) (* (* +nan.0 (log (* 2.0 PI))) (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* (* k k) 1.0)))) (+ (* (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* (* k k) 1.0)) (- +nan.0)) (+ (- (* (* (log (* 2.0 PI)) 1.0) (* (* +nan.0 (* (log n) (* k k))) (exp (* 0.5 (log (* (* n PI) 2.0)))))) (* (* (* (* k (log n)) (* k (log n))) (* +nan.0 (exp (* 0.5 (log (* (* n PI) 2.0)))))) 1.0)) (+ (- (* +nan.0 (* (exp (* 0.5 (log (* (* n PI) 2.0)))) 1.0)) (* (* (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* (* k k) +nan.0)) (* (log (* 2.0 PI)) (log (* 2.0 PI)))) 1.0)) (* (* (* +nan.0 (* (log n) (* k k))) (exp (* 0.5 (log (* (* n PI) 2.0))))) 1.0)))))))
  (+ (- (* +nan.0 (/ (exp (* (log (* (* n PI) 2.0)) (* (- 1.0 k) 0.5))) (/ k 1.0))) (* (/ +nan.0 k) (/ (exp (* (log (* (* n PI) 2.0)) (* (- 1.0 k) 0.5))) (/ k 1.0)))) (/ (- (* (* +nan.0 1.0) (exp (* (log (* (* n PI) 2.0)) (* (- 1.0 k) 0.5))))) (* (* k k) k)))
  (+ (* +nan.0 (- (* 1.0 (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (/ (* 1.0 (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (* k k)))) (/ (* (* (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) +nan.0) (- 1.0)) k))
  (- (+ (- (* (* (* +nan.0 (log (* 2.0 PI))) (* (log n) (* k k))) (exp (* 0.5 (log (* (* n PI) 2.0))))) (* +nan.0 (exp (* 0.5 (log (* (* n PI) 2.0)))))) (+ (- (* (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* (* k k) +nan.0)) (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* (* k k) +nan.0))) (+ (- (* (* (* k (log n)) (* k (log n))) (* +nan.0 (exp (* 0.5 (log (* (* n PI) 2.0)))))) (* (* +nan.0 (* (log n) (* k k))) (exp (* 0.5 (log (* (* n PI) 2.0)))))) (+ (- (* (log (* 2.0 PI)) (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* (* k k) +nan.0))) (* (exp (* 0.5 (log (* (* n PI) 2.0)))) (* +nan.0 (* (log n) k)))) (* (* (exp (* 0.5 (log (* (* n PI) 2.0)))) k) (- (* +nan.0 (log (* 2.0 PI))) +nan.0)))))))
  (+ (* +nan.0 (- (/ (exp (* (log (* (* n PI) 2.0)) (* (- 1.0 k) 0.5))) k) (/ (/ (/ (exp (* (log (* (* n PI) 2.0)) (* (- 1.0 k) 0.5))) k) k) k))) (* (/ (/ (exp (* (log (* (* n PI) 2.0)) (* (- 1.0 k) 0.5))) k) k) (- +nan.0)))
  (- (+ (- (* (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) +nan.0) (* +nan.0 (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k))) (/ (* (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) +nan.0) (* k k))))
20.569 * * * [progress]: adding candidates to table
22.598 * [progress]: [Phase 3 of 3] Extracting.
22.598 * * [regime]: Finding splitpoints for: (#<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) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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) (* (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 (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n PI) 2.0) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt 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 (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))>)
22.600 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
22.600 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<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) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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) (* (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 (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n PI) 2.0) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt 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 (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))>)
22.701 * * * * [regimes]: Trying to branch on n from (#<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) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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) (* (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 (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n PI) 2.0) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt 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 (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))>)
22.766 * * * * [regimes]: Trying to branch on k from (#<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) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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) (* (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 (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n PI) 2.0) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt 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 (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))>)
22.853 * * * [regime]: Found split indices: #<option (#s(si 4 255))>
22.854 * [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 (sqrt k))) (sqrt (sqrt k)))))
22.854 * * [simplify]: iteration 0: 19 enodes
22.856 * * [simplify]: iteration 1: 23 enodes
22.859 * * [simplify]: iteration complete: 23 enodes
22.859 * * [simplify]: Extracting #0: cost 1 inf + 0
22.859 * * [simplify]: Extracting #1: cost 3 inf + 0
22.859 * * [simplify]: Extracting #2: cost 5 inf + 0
22.859 * * [simplify]: Extracting #3: cost 9 inf + 0
22.859 * * [simplify]: Extracting #4: cost 12 inf + 0
22.860 * * [simplify]: Extracting #5: cost 10 inf + 124
22.860 * * [simplify]: Extracting #6: cost 14 inf + 124
22.860 * * [simplify]: Extracting #7: cost 12 inf + 168
22.860 * * [simplify]: Extracting #8: cost 7 inf + 752
22.861 * * [simplify]: Extracting #9: cost 3 inf + 2732
22.861 * * [simplify]: Extracting #10: cost 2 inf + 3307
22.862 * * [simplify]: Extracting #11: cost 0 inf + 4657
22.863 * [simplify]: Simplified to:
  (* (sqrt (/ (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
29.971 * [regime-testing]: Baseline error score: 0.42650952365267747
29.989 * [regime-testing]: Oracle error score: 0.06524875765765792
30.025 * [regime-testing]: End program error score: 0.42650952365267747