53.465 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.209 * * * [progress]: [2/2] Setting up program. 0.212 * [progress]: [Phase 2 of 3] Improving. 0.212 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.212 * * [simplify]: Extracting # 0 : cost 0 0.212 * * [simplify]: Extracting # 1 : cost 0 0.212 * * [simplify]: Extracting # 2 : cost 0 0.212 * * [simplify]: Extracting # 3 : cost 0 0.212 * * [simplify]: Extracting # 4 : cost 0 0.213 * * [simplify]: Extracting # 5 : cost 0 0.213 * * [simplify]: Extracting # 6 : cost 0 0.213 * * [simplify]: Extracting # 7 : cost 0 0.213 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.216 * * [simplify]: Extracting # 0 : cost 0 0.216 * * [simplify]: Extracting # 1 : cost 0 0.216 * * [simplify]: Extracting # 2 : cost 0 0.216 * * [simplify]: Extracting # 3 : cost 0 0.216 * * [simplify]: Extracting # 4 : cost 0 0.216 * * [simplify]: Extracting # 5 : cost 0 0.216 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.225 * * [simplify]: Extracting # 0 : cost 0 0.225 * * [simplify]: Extracting # 1 : cost 0 0.225 * * [simplify]: Extracting # 2 : cost 0 0.225 * * [simplify]: Extracting # 3 : cost 0 0.226 * * [simplify]: Extracting # 4 : cost 0 0.226 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.253 * * [simplify]: Extracting # 0 : cost 0 0.253 * * [simplify]: Extracting # 1 : cost 0 0.253 * * [simplify]: Extracting # 2 : cost 0 0.254 * * [simplify]: Extracting # 3 : cost 0 0.254 * * [simplify]: Extracting # 4 : cost 0 0.254 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.319 * * [simplify]: Extracting # 0 : cost 0 0.319 * * [simplify]: Extracting # 1 : cost 0 0.320 * * [simplify]: Extracting # 2 : cost 0 0.320 * * [simplify]: Extracting # 3 : cost 0 0.337 * * [simplify]: Extracting # 4 : cost 0 0.337 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.573 * * [simplify]: Extracting # 0 : cost 0 0.574 * * [simplify]: Extracting # 1 : cost 0 0.575 * * [simplify]: Extracting # 2 : cost 0 0.575 * * [simplify]: Extracting # 3 : cost 0 0.576 * * [simplify]: Extracting # 4 : cost 0 0.577 * * [simplify]: iteration 5 : 843 enodes (cost 16 ) 2.097 * * [simplify]: Extracting # 0 : cost 0 2.100 * * [simplify]: Extracting # 1 : cost 0 2.103 * * [simplify]: Extracting # 2 : cost 0 2.106 * * [simplify]: Extracting # 3 : cost 0 2.111 * * [simplify]: Extracting # 4 : cost 0 2.114 * * [simplify]: iteration 6 : 3221 enodes (cost 16 ) 3.943 * * [simplify]: Extracting # 0 : cost 0 3.951 * * [simplify]: Extracting # 1 : cost 0 3.957 * * [simplify]: Extracting # 2 : cost 0 3.961 * * [simplify]: Extracting # 3 : cost 0 3.966 * * [simplify]: Extracting # 4 : cost 0 3.970 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 3.971 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3.971 * * [progress]: iteration 1 / 4 3.971 * * * [progress]: picking best candidate 3.974 * * * * [pick]: Picked # 3.974 * * * [progress]: localizing error 4.004 * * * [progress]: generating rewritten candidates 4.004 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.051 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 4.059 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 4.078 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.154 * * * [progress]: generating series expansions 4.154 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.156 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.156 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.156 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.156 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.156 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.156 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.156 * [taylor]: Taking taylor expansion of 0.5 in k 4.156 * [backup-simplify]: Simplify 0.5 into 0.5 4.156 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.156 * [taylor]: Taking taylor expansion of 1.0 in k 4.156 * [backup-simplify]: Simplify 1.0 into 1.0 4.156 * [taylor]: Taking taylor expansion of k in k 4.156 * [backup-simplify]: Simplify 0 into 0 4.156 * [backup-simplify]: Simplify 1 into 1 4.156 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.156 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.156 * [taylor]: Taking taylor expansion of 2.0 in k 4.156 * [backup-simplify]: Simplify 2.0 into 2.0 4.156 * [taylor]: Taking taylor expansion of (* n PI) in k 4.156 * [taylor]: Taking taylor expansion of n in k 4.156 * [backup-simplify]: Simplify n into n 4.156 * [taylor]: Taking taylor expansion of PI in k 4.156 * [backup-simplify]: Simplify PI into PI 4.156 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.157 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.157 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.157 * [backup-simplify]: Simplify (- 0) into 0 4.158 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.158 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.158 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.159 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.159 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.159 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.159 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.159 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.159 * [taylor]: Taking taylor expansion of 0.5 in n 4.159 * [backup-simplify]: Simplify 0.5 into 0.5 4.159 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.159 * [taylor]: Taking taylor expansion of 1.0 in n 4.159 * [backup-simplify]: Simplify 1.0 into 1.0 4.159 * [taylor]: Taking taylor expansion of k in n 4.159 * [backup-simplify]: Simplify k into k 4.159 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.159 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.159 * [taylor]: Taking taylor expansion of 2.0 in n 4.159 * [backup-simplify]: Simplify 2.0 into 2.0 4.159 * [taylor]: Taking taylor expansion of (* n PI) in n 4.159 * [taylor]: Taking taylor expansion of n in n 4.159 * [backup-simplify]: Simplify 0 into 0 4.159 * [backup-simplify]: Simplify 1 into 1 4.159 * [taylor]: Taking taylor expansion of PI in n 4.159 * [backup-simplify]: Simplify PI into PI 4.160 * [backup-simplify]: Simplify (* 0 PI) into 0 4.160 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.162 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.164 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.165 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.165 * [backup-simplify]: Simplify (- k) into (- k) 4.165 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.165 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.167 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.168 * [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)))) 4.169 * [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))))) 4.169 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.169 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.169 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.169 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.169 * [taylor]: Taking taylor expansion of 0.5 in n 4.170 * [backup-simplify]: Simplify 0.5 into 0.5 4.170 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.170 * [taylor]: Taking taylor expansion of 1.0 in n 4.170 * [backup-simplify]: Simplify 1.0 into 1.0 4.170 * [taylor]: Taking taylor expansion of k in n 4.170 * [backup-simplify]: Simplify k into k 4.170 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.170 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.170 * [taylor]: Taking taylor expansion of 2.0 in n 4.170 * [backup-simplify]: Simplify 2.0 into 2.0 4.170 * [taylor]: Taking taylor expansion of (* n PI) in n 4.170 * [taylor]: Taking taylor expansion of n in n 4.170 * [backup-simplify]: Simplify 0 into 0 4.170 * [backup-simplify]: Simplify 1 into 1 4.170 * [taylor]: Taking taylor expansion of PI in n 4.170 * [backup-simplify]: Simplify PI into PI 4.171 * [backup-simplify]: Simplify (* 0 PI) into 0 4.171 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.173 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.175 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.176 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.176 * [backup-simplify]: Simplify (- k) into (- k) 4.176 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.176 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.178 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.179 * [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)))) 4.180 * [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))))) 4.180 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.180 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.180 * [taylor]: Taking taylor expansion of 0.5 in k 4.180 * [backup-simplify]: Simplify 0.5 into 0.5 4.180 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.180 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.181 * [taylor]: Taking taylor expansion of 1.0 in k 4.181 * [backup-simplify]: Simplify 1.0 into 1.0 4.181 * [taylor]: Taking taylor expansion of k in k 4.181 * [backup-simplify]: Simplify 0 into 0 4.181 * [backup-simplify]: Simplify 1 into 1 4.181 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.181 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.181 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.181 * [taylor]: Taking taylor expansion of 2.0 in k 4.181 * [backup-simplify]: Simplify 2.0 into 2.0 4.181 * [taylor]: Taking taylor expansion of PI in k 4.181 * [backup-simplify]: Simplify PI into PI 4.181 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.182 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.183 * [taylor]: Taking taylor expansion of (log n) in k 4.183 * [taylor]: Taking taylor expansion of n in k 4.183 * [backup-simplify]: Simplify n into n 4.183 * [backup-simplify]: Simplify (log n) into (log n) 4.183 * [backup-simplify]: Simplify (- 0) into 0 4.184 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.185 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.186 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.187 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.188 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.190 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.191 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.192 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.194 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.194 * [backup-simplify]: Simplify (- 0) into 0 4.195 * [backup-simplify]: Simplify (+ 0 0) into 0 4.195 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.197 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.198 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.200 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.200 * [taylor]: Taking taylor expansion of 0 in k 4.200 * [backup-simplify]: Simplify 0 into 0 4.200 * [backup-simplify]: Simplify 0 into 0 4.201 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.203 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.204 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.205 * [backup-simplify]: Simplify (+ 0 0) into 0 4.205 * [backup-simplify]: Simplify (- 1) into -1 4.205 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.207 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.209 * [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)))) 4.213 * [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)))))) 4.216 * [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)))))) 4.217 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.219 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.230 * [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 4.231 * [backup-simplify]: Simplify (- 0) into 0 4.231 * [backup-simplify]: Simplify (+ 0 0) into 0 4.232 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.234 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.235 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.238 * [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 4.238 * [taylor]: Taking taylor expansion of 0 in k 4.238 * [backup-simplify]: Simplify 0 into 0 4.238 * [backup-simplify]: Simplify 0 into 0 4.238 * [backup-simplify]: Simplify 0 into 0 4.239 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.243 * [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 4.245 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.246 * [backup-simplify]: Simplify (+ 0 0) into 0 4.246 * [backup-simplify]: Simplify (- 0) into 0 4.246 * [backup-simplify]: Simplify (+ 0 0) into 0 4.248 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.251 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.256 * [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 (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.262 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.273 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 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 (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.274 * [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)))) 4.275 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.275 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.275 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.275 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.275 * [taylor]: Taking taylor expansion of 0.5 in k 4.275 * [backup-simplify]: Simplify 0.5 into 0.5 4.275 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.275 * [taylor]: Taking taylor expansion of 1.0 in k 4.275 * [backup-simplify]: Simplify 1.0 into 1.0 4.275 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.275 * [taylor]: Taking taylor expansion of k in k 4.275 * [backup-simplify]: Simplify 0 into 0 4.275 * [backup-simplify]: Simplify 1 into 1 4.275 * [backup-simplify]: Simplify (/ 1 1) into 1 4.275 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.276 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.276 * [taylor]: Taking taylor expansion of 2.0 in k 4.276 * [backup-simplify]: Simplify 2.0 into 2.0 4.276 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.276 * [taylor]: Taking taylor expansion of PI in k 4.276 * [backup-simplify]: Simplify PI into PI 4.276 * [taylor]: Taking taylor expansion of n in k 4.276 * [backup-simplify]: Simplify n into n 4.276 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.276 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.276 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.276 * [backup-simplify]: Simplify (- 1) into -1 4.277 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.277 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.278 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.278 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.278 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.278 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.278 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.278 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.278 * [taylor]: Taking taylor expansion of 0.5 in n 4.278 * [backup-simplify]: Simplify 0.5 into 0.5 4.278 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.278 * [taylor]: Taking taylor expansion of 1.0 in n 4.278 * [backup-simplify]: Simplify 1.0 into 1.0 4.278 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.278 * [taylor]: Taking taylor expansion of k in n 4.278 * [backup-simplify]: Simplify k into k 4.278 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.278 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.278 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.278 * [taylor]: Taking taylor expansion of 2.0 in n 4.279 * [backup-simplify]: Simplify 2.0 into 2.0 4.279 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.279 * [taylor]: Taking taylor expansion of PI in n 4.279 * [backup-simplify]: Simplify PI into PI 4.279 * [taylor]: Taking taylor expansion of n in n 4.279 * [backup-simplify]: Simplify 0 into 0 4.279 * [backup-simplify]: Simplify 1 into 1 4.279 * [backup-simplify]: Simplify (/ PI 1) into PI 4.280 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.281 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.281 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.281 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.281 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.283 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.284 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.285 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.285 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.285 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.285 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.285 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.286 * [taylor]: Taking taylor expansion of 0.5 in n 4.286 * [backup-simplify]: Simplify 0.5 into 0.5 4.286 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.286 * [taylor]: Taking taylor expansion of 1.0 in n 4.286 * [backup-simplify]: Simplify 1.0 into 1.0 4.286 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.286 * [taylor]: Taking taylor expansion of k in n 4.286 * [backup-simplify]: Simplify k into k 4.286 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.286 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.286 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.286 * [taylor]: Taking taylor expansion of 2.0 in n 4.286 * [backup-simplify]: Simplify 2.0 into 2.0 4.286 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.286 * [taylor]: Taking taylor expansion of PI in n 4.286 * [backup-simplify]: Simplify PI into PI 4.286 * [taylor]: Taking taylor expansion of n in n 4.286 * [backup-simplify]: Simplify 0 into 0 4.286 * [backup-simplify]: Simplify 1 into 1 4.287 * [backup-simplify]: Simplify (/ PI 1) into PI 4.287 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.288 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.288 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.289 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.289 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.292 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.293 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.294 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.294 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.294 * [taylor]: Taking taylor expansion of 0.5 in k 4.294 * [backup-simplify]: Simplify 0.5 into 0.5 4.294 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.294 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.294 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.294 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.294 * [taylor]: Taking taylor expansion of 2.0 in k 4.294 * [backup-simplify]: Simplify 2.0 into 2.0 4.294 * [taylor]: Taking taylor expansion of PI in k 4.294 * [backup-simplify]: Simplify PI into PI 4.294 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.296 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.296 * [taylor]: Taking taylor expansion of (log n) in k 4.296 * [taylor]: Taking taylor expansion of n in k 4.296 * [backup-simplify]: Simplify n into n 4.296 * [backup-simplify]: Simplify (log n) into (log n) 4.296 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.296 * [taylor]: Taking taylor expansion of 1.0 in k 4.296 * [backup-simplify]: Simplify 1.0 into 1.0 4.296 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.296 * [taylor]: Taking taylor expansion of k in k 4.296 * [backup-simplify]: Simplify 0 into 0 4.296 * [backup-simplify]: Simplify 1 into 1 4.296 * [backup-simplify]: Simplify (/ 1 1) into 1 4.297 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.298 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.298 * [backup-simplify]: Simplify (- 1) into -1 4.299 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.300 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.301 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.302 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.304 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.306 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.308 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.309 * [backup-simplify]: Simplify (- 0) into 0 4.309 * [backup-simplify]: Simplify (+ 0 0) into 0 4.310 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.313 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.315 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.315 * [taylor]: Taking taylor expansion of 0 in k 4.315 * [backup-simplify]: Simplify 0 into 0 4.315 * [backup-simplify]: Simplify 0 into 0 4.315 * [backup-simplify]: Simplify 0 into 0 4.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.317 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.319 * [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 4.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.319 * [backup-simplify]: Simplify (- 0) into 0 4.320 * [backup-simplify]: Simplify (+ 0 0) into 0 4.320 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.321 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.322 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.324 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.324 * [taylor]: Taking taylor expansion of 0 in k 4.324 * [backup-simplify]: Simplify 0 into 0 4.324 * [backup-simplify]: Simplify 0 into 0 4.324 * [backup-simplify]: Simplify 0 into 0 4.324 * [backup-simplify]: Simplify 0 into 0 4.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.326 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.329 * [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 4.329 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.329 * [backup-simplify]: Simplify (- 0) into 0 4.330 * [backup-simplify]: Simplify (+ 0 0) into 0 4.331 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.333 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.335 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.335 * [taylor]: Taking taylor expansion of 0 in k 4.335 * [backup-simplify]: Simplify 0 into 0 4.335 * [backup-simplify]: Simplify 0 into 0 4.335 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.336 * [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))) 4.336 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.336 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.336 * [taylor]: Taking taylor expansion of 0.5 in k 4.336 * [backup-simplify]: Simplify 0.5 into 0.5 4.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.336 * [taylor]: Taking taylor expansion of k in k 4.336 * [backup-simplify]: Simplify 0 into 0 4.336 * [backup-simplify]: Simplify 1 into 1 4.337 * [backup-simplify]: Simplify (/ 1 1) into 1 4.337 * [taylor]: Taking taylor expansion of 1.0 in k 4.337 * [backup-simplify]: Simplify 1.0 into 1.0 4.337 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.337 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.337 * [taylor]: Taking taylor expansion of -2.0 in k 4.337 * [backup-simplify]: Simplify -2.0 into -2.0 4.337 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.337 * [taylor]: Taking taylor expansion of PI in k 4.337 * [backup-simplify]: Simplify PI into PI 4.337 * [taylor]: Taking taylor expansion of n in k 4.337 * [backup-simplify]: Simplify n into n 4.337 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.337 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.337 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.337 * [backup-simplify]: Simplify (+ 1 0) into 1 4.338 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.338 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.338 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.338 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.338 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.338 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.338 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.338 * [taylor]: Taking taylor expansion of 0.5 in n 4.338 * [backup-simplify]: Simplify 0.5 into 0.5 4.338 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.338 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.338 * [taylor]: Taking taylor expansion of k in n 4.338 * [backup-simplify]: Simplify k into k 4.338 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.338 * [taylor]: Taking taylor expansion of 1.0 in n 4.338 * [backup-simplify]: Simplify 1.0 into 1.0 4.338 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.338 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.338 * [taylor]: Taking taylor expansion of -2.0 in n 4.338 * [backup-simplify]: Simplify -2.0 into -2.0 4.338 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.338 * [taylor]: Taking taylor expansion of PI in n 4.338 * [backup-simplify]: Simplify PI into PI 4.338 * [taylor]: Taking taylor expansion of n in n 4.338 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify 1 into 1 4.339 * [backup-simplify]: Simplify (/ PI 1) into PI 4.339 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.340 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.340 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.340 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.341 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.342 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.342 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.342 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.343 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.343 * [taylor]: Taking taylor expansion of 0.5 in n 4.343 * [backup-simplify]: Simplify 0.5 into 0.5 4.343 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.343 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.343 * [taylor]: Taking taylor expansion of k in n 4.343 * [backup-simplify]: Simplify k into k 4.343 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.343 * [taylor]: Taking taylor expansion of 1.0 in n 4.343 * [backup-simplify]: Simplify 1.0 into 1.0 4.343 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.343 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.343 * [taylor]: Taking taylor expansion of -2.0 in n 4.343 * [backup-simplify]: Simplify -2.0 into -2.0 4.343 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.343 * [taylor]: Taking taylor expansion of PI in n 4.343 * [backup-simplify]: Simplify PI into PI 4.343 * [taylor]: Taking taylor expansion of n in n 4.343 * [backup-simplify]: Simplify 0 into 0 4.343 * [backup-simplify]: Simplify 1 into 1 4.343 * [backup-simplify]: Simplify (/ PI 1) into PI 4.344 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.344 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.344 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.344 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.346 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.347 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.347 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.347 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.347 * [taylor]: Taking taylor expansion of 0.5 in k 4.347 * [backup-simplify]: Simplify 0.5 into 0.5 4.347 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.347 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.347 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.347 * [taylor]: Taking taylor expansion of k in k 4.347 * [backup-simplify]: Simplify 0 into 0 4.347 * [backup-simplify]: Simplify 1 into 1 4.348 * [backup-simplify]: Simplify (/ 1 1) into 1 4.348 * [taylor]: Taking taylor expansion of 1.0 in k 4.348 * [backup-simplify]: Simplify 1.0 into 1.0 4.348 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.348 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.348 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.348 * [taylor]: Taking taylor expansion of -2.0 in k 4.348 * [backup-simplify]: Simplify -2.0 into -2.0 4.348 * [taylor]: Taking taylor expansion of PI in k 4.348 * [backup-simplify]: Simplify PI into PI 4.348 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.349 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.349 * [taylor]: Taking taylor expansion of (log n) in k 4.349 * [taylor]: Taking taylor expansion of n in k 4.349 * [backup-simplify]: Simplify n into n 4.349 * [backup-simplify]: Simplify (log n) into (log n) 4.349 * [backup-simplify]: Simplify (+ 1 0) into 1 4.349 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.350 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.351 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.351 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.352 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.353 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.354 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.355 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.355 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.356 * [backup-simplify]: Simplify (+ 0 0) into 0 4.356 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.358 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.359 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.359 * [taylor]: Taking taylor expansion of 0 in k 4.359 * [backup-simplify]: Simplify 0 into 0 4.360 * [backup-simplify]: Simplify 0 into 0 4.360 * [backup-simplify]: Simplify 0 into 0 4.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.361 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.369 * [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 4.369 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.370 * [backup-simplify]: Simplify (+ 0 0) into 0 4.370 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.373 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.374 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.374 * [taylor]: Taking taylor expansion of 0 in k 4.374 * [backup-simplify]: Simplify 0 into 0 4.374 * [backup-simplify]: Simplify 0 into 0 4.375 * [backup-simplify]: Simplify 0 into 0 4.375 * [backup-simplify]: Simplify 0 into 0 4.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.376 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.379 * [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 4.380 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.380 * [backup-simplify]: Simplify (+ 0 0) into 0 4.381 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.382 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.383 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.385 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.385 * [taylor]: Taking taylor expansion of 0 in k 4.385 * [backup-simplify]: Simplify 0 into 0 4.385 * [backup-simplify]: Simplify 0 into 0 4.386 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.386 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 4.386 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.386 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.386 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.386 * [taylor]: Taking taylor expansion of 1.0 in k 4.386 * [backup-simplify]: Simplify 1.0 into 1.0 4.386 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.386 * [taylor]: Taking taylor expansion of k in k 4.386 * [backup-simplify]: Simplify 0 into 0 4.386 * [backup-simplify]: Simplify 1 into 1 4.386 * [backup-simplify]: Simplify (/ 1 1) into 1 4.387 * [backup-simplify]: Simplify (sqrt 0) into 0 4.388 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.388 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.388 * [taylor]: Taking taylor expansion of 1.0 in k 4.388 * [backup-simplify]: Simplify 1.0 into 1.0 4.388 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.388 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.388 * [taylor]: Taking taylor expansion of k in k 4.388 * [backup-simplify]: Simplify 0 into 0 4.388 * [backup-simplify]: Simplify 1 into 1 4.388 * [backup-simplify]: Simplify (/ 1 1) into 1 4.388 * [backup-simplify]: Simplify (sqrt 0) into 0 4.389 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.389 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.389 * [backup-simplify]: Simplify 0 into 0 4.390 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.391 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.391 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.393 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.396 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.396 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.397 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.401 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.403 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.404 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.405 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.405 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.405 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.405 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.405 * [taylor]: Taking taylor expansion of 1.0 in k 4.406 * [backup-simplify]: Simplify 1.0 into 1.0 4.406 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.406 * [taylor]: Taking taylor expansion of k in k 4.406 * [backup-simplify]: Simplify 0 into 0 4.406 * [backup-simplify]: Simplify 1 into 1 4.406 * [backup-simplify]: Simplify (sqrt 0) into 0 4.407 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.407 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.407 * [taylor]: Taking taylor expansion of 1.0 in k 4.408 * [backup-simplify]: Simplify 1.0 into 1.0 4.408 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.408 * [taylor]: Taking taylor expansion of k in k 4.408 * [backup-simplify]: Simplify 0 into 0 4.408 * [backup-simplify]: Simplify 1 into 1 4.408 * [backup-simplify]: Simplify (sqrt 0) into 0 4.409 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.410 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.410 * [backup-simplify]: Simplify 0 into 0 4.412 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.412 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.415 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.418 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.418 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.423 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.425 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.426 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.427 * [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)))))))) 4.427 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.428 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.428 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.428 * [taylor]: Taking taylor expansion of 1.0 in k 4.428 * [backup-simplify]: Simplify 1.0 into 1.0 4.428 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.428 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.428 * [taylor]: Taking taylor expansion of -1 in k 4.428 * [backup-simplify]: Simplify -1 into -1 4.428 * [taylor]: Taking taylor expansion of k in k 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 1 into 1 4.428 * [backup-simplify]: Simplify (/ -1 1) into -1 4.429 * [backup-simplify]: Simplify (sqrt 0) into 0 4.430 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.430 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.431 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.431 * [taylor]: Taking taylor expansion of 1.0 in k 4.431 * [backup-simplify]: Simplify 1.0 into 1.0 4.431 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.431 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.431 * [taylor]: Taking taylor expansion of -1 in k 4.431 * [backup-simplify]: Simplify -1 into -1 4.431 * [taylor]: Taking taylor expansion of k in k 4.431 * [backup-simplify]: Simplify 0 into 0 4.431 * [backup-simplify]: Simplify 1 into 1 4.431 * [backup-simplify]: Simplify (/ -1 1) into -1 4.432 * [backup-simplify]: Simplify (sqrt 0) into 0 4.433 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.433 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.434 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.437 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.440 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.441 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.446 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.450 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.450 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.452 * [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))))) 4.452 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 4.452 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.452 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.452 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.453 * [taylor]: Taking taylor expansion of 2.0 in n 4.453 * [backup-simplify]: Simplify 2.0 into 2.0 4.453 * [taylor]: Taking taylor expansion of (* n PI) in n 4.453 * [taylor]: Taking taylor expansion of n in n 4.453 * [backup-simplify]: Simplify 0 into 0 4.453 * [backup-simplify]: Simplify 1 into 1 4.453 * [taylor]: Taking taylor expansion of PI in n 4.453 * [backup-simplify]: Simplify PI into PI 4.453 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.453 * [taylor]: Taking taylor expansion of 2.0 in n 4.453 * [backup-simplify]: Simplify 2.0 into 2.0 4.453 * [taylor]: Taking taylor expansion of (* n PI) in n 4.453 * [taylor]: Taking taylor expansion of n in n 4.453 * [backup-simplify]: Simplify 0 into 0 4.453 * [backup-simplify]: Simplify 1 into 1 4.453 * [taylor]: Taking taylor expansion of PI in n 4.453 * [backup-simplify]: Simplify PI into PI 4.454 * [backup-simplify]: Simplify (* 0 PI) into 0 4.454 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.454 * [backup-simplify]: Simplify 0 into 0 4.456 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.458 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.458 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.459 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.459 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.459 * [backup-simplify]: Simplify 0 into 0 4.460 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.461 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.461 * [backup-simplify]: Simplify 0 into 0 4.462 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.463 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.463 * [backup-simplify]: Simplify 0 into 0 4.463 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.464 * [backup-simplify]: Simplify 0 into 0 4.465 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.467 * [backup-simplify]: Simplify 0 into 0 4.468 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.469 * [backup-simplify]: Simplify 0 into 0 4.469 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.470 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.470 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.470 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.470 * [taylor]: Taking taylor expansion of 2.0 in n 4.470 * [backup-simplify]: Simplify 2.0 into 2.0 4.470 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.470 * [taylor]: Taking taylor expansion of PI in n 4.470 * [backup-simplify]: Simplify PI into PI 4.470 * [taylor]: Taking taylor expansion of n in n 4.470 * [backup-simplify]: Simplify 0 into 0 4.470 * [backup-simplify]: Simplify 1 into 1 4.470 * [backup-simplify]: Simplify (/ PI 1) into PI 4.470 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.470 * [taylor]: Taking taylor expansion of 2.0 in n 4.470 * [backup-simplify]: Simplify 2.0 into 2.0 4.470 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.470 * [taylor]: Taking taylor expansion of PI in n 4.470 * [backup-simplify]: Simplify PI into PI 4.470 * [taylor]: Taking taylor expansion of n in n 4.470 * [backup-simplify]: Simplify 0 into 0 4.470 * [backup-simplify]: Simplify 1 into 1 4.471 * [backup-simplify]: Simplify (/ PI 1) into PI 4.471 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.471 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.472 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.473 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.473 * [backup-simplify]: Simplify 0 into 0 4.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.474 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.474 * [backup-simplify]: Simplify 0 into 0 4.475 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.475 * [backup-simplify]: Simplify 0 into 0 4.476 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.477 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.477 * [backup-simplify]: Simplify 0 into 0 4.478 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.478 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.478 * [backup-simplify]: Simplify 0 into 0 4.479 * [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 4.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.480 * [backup-simplify]: Simplify 0 into 0 4.481 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.481 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.481 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.481 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.481 * [taylor]: Taking taylor expansion of -2.0 in n 4.481 * [backup-simplify]: Simplify -2.0 into -2.0 4.481 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.481 * [taylor]: Taking taylor expansion of PI in n 4.481 * [backup-simplify]: Simplify PI into PI 4.481 * [taylor]: Taking taylor expansion of n in n 4.481 * [backup-simplify]: Simplify 0 into 0 4.481 * [backup-simplify]: Simplify 1 into 1 4.482 * [backup-simplify]: Simplify (/ PI 1) into PI 4.482 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.482 * [taylor]: Taking taylor expansion of -2.0 in n 4.482 * [backup-simplify]: Simplify -2.0 into -2.0 4.482 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.482 * [taylor]: Taking taylor expansion of PI in n 4.482 * [backup-simplify]: Simplify PI into PI 4.482 * [taylor]: Taking taylor expansion of n in n 4.482 * [backup-simplify]: Simplify 0 into 0 4.482 * [backup-simplify]: Simplify 1 into 1 4.482 * [backup-simplify]: Simplify (/ PI 1) into PI 4.482 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.483 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.484 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.484 * [backup-simplify]: Simplify 0 into 0 4.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.485 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.485 * [backup-simplify]: Simplify 0 into 0 4.486 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.487 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.487 * [backup-simplify]: Simplify 0 into 0 4.495 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.496 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.497 * [backup-simplify]: Simplify 0 into 0 4.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.498 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.499 * [backup-simplify]: Simplify 0 into 0 4.499 * [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 4.500 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.500 * [backup-simplify]: Simplify 0 into 0 4.501 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.501 * * * * [progress]: [ 4 / 4 ] generating series at (2) 4.501 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 4.502 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 4.502 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 4.502 * [taylor]: Taking taylor expansion of 1.0 in n 4.502 * [backup-simplify]: Simplify 1.0 into 1.0 4.502 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 4.502 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.502 * [taylor]: Taking taylor expansion of k in n 4.502 * [backup-simplify]: Simplify k into k 4.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.502 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.502 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.502 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.502 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.502 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.502 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.502 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.502 * [taylor]: Taking taylor expansion of 0.5 in n 4.502 * [backup-simplify]: Simplify 0.5 into 0.5 4.502 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.502 * [taylor]: Taking taylor expansion of 1.0 in n 4.502 * [backup-simplify]: Simplify 1.0 into 1.0 4.502 * [taylor]: Taking taylor expansion of k in n 4.502 * [backup-simplify]: Simplify k into k 4.502 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.502 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.502 * [taylor]: Taking taylor expansion of 2.0 in n 4.502 * [backup-simplify]: Simplify 2.0 into 2.0 4.502 * [taylor]: Taking taylor expansion of (* n PI) in n 4.502 * [taylor]: Taking taylor expansion of n in n 4.502 * [backup-simplify]: Simplify 0 into 0 4.502 * [backup-simplify]: Simplify 1 into 1 4.502 * [taylor]: Taking taylor expansion of PI in n 4.502 * [backup-simplify]: Simplify PI into PI 4.503 * [backup-simplify]: Simplify (* 0 PI) into 0 4.503 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.504 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.505 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.506 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.506 * [backup-simplify]: Simplify (- k) into (- k) 4.506 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.506 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.507 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.508 * [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)))) 4.508 * [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))))) 4.508 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.508 * [taylor]: Taking taylor expansion of 1.0 in k 4.508 * [backup-simplify]: Simplify 1.0 into 1.0 4.508 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.509 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.509 * [taylor]: Taking taylor expansion of k in k 4.509 * [backup-simplify]: Simplify 0 into 0 4.509 * [backup-simplify]: Simplify 1 into 1 4.509 * [backup-simplify]: Simplify (/ 1 1) into 1 4.509 * [backup-simplify]: Simplify (sqrt 0) into 0 4.510 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.510 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.510 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.510 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.510 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.510 * [taylor]: Taking taylor expansion of 0.5 in k 4.510 * [backup-simplify]: Simplify 0.5 into 0.5 4.510 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.510 * [taylor]: Taking taylor expansion of 1.0 in k 4.510 * [backup-simplify]: Simplify 1.0 into 1.0 4.510 * [taylor]: Taking taylor expansion of k in k 4.510 * [backup-simplify]: Simplify 0 into 0 4.510 * [backup-simplify]: Simplify 1 into 1 4.510 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.510 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.510 * [taylor]: Taking taylor expansion of 2.0 in k 4.510 * [backup-simplify]: Simplify 2.0 into 2.0 4.510 * [taylor]: Taking taylor expansion of (* n PI) in k 4.510 * [taylor]: Taking taylor expansion of n in k 4.510 * [backup-simplify]: Simplify n into n 4.510 * [taylor]: Taking taylor expansion of PI in k 4.510 * [backup-simplify]: Simplify PI into PI 4.510 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.511 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.511 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.511 * [backup-simplify]: Simplify (- 0) into 0 4.511 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.511 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.512 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.512 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.512 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.512 * [taylor]: Taking taylor expansion of 1.0 in k 4.512 * [backup-simplify]: Simplify 1.0 into 1.0 4.512 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.512 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.512 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.512 * [taylor]: Taking taylor expansion of k in k 4.512 * [backup-simplify]: Simplify 0 into 0 4.512 * [backup-simplify]: Simplify 1 into 1 4.512 * [backup-simplify]: Simplify (/ 1 1) into 1 4.512 * [backup-simplify]: Simplify (sqrt 0) into 0 4.513 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.513 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.513 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.513 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.513 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.513 * [taylor]: Taking taylor expansion of 0.5 in k 4.513 * [backup-simplify]: Simplify 0.5 into 0.5 4.513 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.513 * [taylor]: Taking taylor expansion of 1.0 in k 4.513 * [backup-simplify]: Simplify 1.0 into 1.0 4.513 * [taylor]: Taking taylor expansion of k in k 4.513 * [backup-simplify]: Simplify 0 into 0 4.513 * [backup-simplify]: Simplify 1 into 1 4.513 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.513 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.513 * [taylor]: Taking taylor expansion of 2.0 in k 4.513 * [backup-simplify]: Simplify 2.0 into 2.0 4.513 * [taylor]: Taking taylor expansion of (* n PI) in k 4.513 * [taylor]: Taking taylor expansion of n in k 4.514 * [backup-simplify]: Simplify n into n 4.514 * [taylor]: Taking taylor expansion of PI in k 4.514 * [backup-simplify]: Simplify PI into PI 4.514 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.514 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.514 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.514 * [backup-simplify]: Simplify (- 0) into 0 4.514 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.515 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.515 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.515 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.515 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.515 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.515 * [taylor]: Taking taylor expansion of 0 in n 4.515 * [backup-simplify]: Simplify 0 into 0 4.515 * [backup-simplify]: Simplify 0 into 0 4.516 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.516 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.517 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.517 * [backup-simplify]: Simplify (- 1) into -1 4.517 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.518 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.519 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.519 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.520 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.521 * [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))) 4.521 * [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 4.521 * [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 4.521 * [taylor]: Taking taylor expansion of +nan.0 in n 4.521 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.521 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.522 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.522 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.522 * [taylor]: Taking taylor expansion of 0.5 in n 4.522 * [backup-simplify]: Simplify 0.5 into 0.5 4.522 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.522 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.522 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.522 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.522 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.522 * [taylor]: Taking taylor expansion of 1.0 in n 4.522 * [backup-simplify]: Simplify 1.0 into 1.0 4.522 * [taylor]: Taking taylor expansion of (log PI) in n 4.522 * [taylor]: Taking taylor expansion of PI in n 4.522 * [backup-simplify]: Simplify PI into PI 4.522 * [backup-simplify]: Simplify (log PI) into (log PI) 4.523 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.524 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.524 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.524 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.524 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.524 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.524 * [taylor]: Taking taylor expansion of 1.0 in n 4.524 * [backup-simplify]: Simplify 1.0 into 1.0 4.524 * [taylor]: Taking taylor expansion of (log n) in n 4.524 * [taylor]: Taking taylor expansion of n in n 4.524 * [backup-simplify]: Simplify 0 into 0 4.524 * [backup-simplify]: Simplify 1 into 1 4.524 * [backup-simplify]: Simplify (log 1) into 0 4.525 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.525 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.525 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.525 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.525 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.525 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.525 * [taylor]: Taking taylor expansion of 1.0 in n 4.525 * [backup-simplify]: Simplify 1.0 into 1.0 4.525 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.525 * [taylor]: Taking taylor expansion of 2.0 in n 4.525 * [backup-simplify]: Simplify 2.0 into 2.0 4.525 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.526 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.527 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.527 * [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) 4.528 * [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) 4.529 * [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)) 4.530 * [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))) 4.531 * [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) 4.532 * [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)) 4.533 * [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))) 4.534 * [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))) 4.534 * [backup-simplify]: Simplify 0 into 0 4.534 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.535 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.536 * [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 4.536 * [backup-simplify]: Simplify (- 0) into 0 4.537 * [backup-simplify]: Simplify (+ 0 0) into 0 4.538 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.539 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.541 * [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 (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.541 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.545 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.549 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.554 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 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)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.554 * [taylor]: Taking taylor expansion of (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 4.554 * [taylor]: Taking taylor expansion of (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 4.554 * [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 4.554 * [taylor]: Taking taylor expansion of +nan.0 in n 4.554 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.554 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.554 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.555 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.555 * [taylor]: Taking taylor expansion of 0.5 in n 4.555 * [backup-simplify]: Simplify 0.5 into 0.5 4.555 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.555 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.555 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.555 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.555 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.555 * [taylor]: Taking taylor expansion of 1.0 in n 4.555 * [backup-simplify]: Simplify 1.0 into 1.0 4.555 * [taylor]: Taking taylor expansion of (log PI) in n 4.555 * [taylor]: Taking taylor expansion of PI in n 4.555 * [backup-simplify]: Simplify PI into PI 4.555 * [backup-simplify]: Simplify (log PI) into (log PI) 4.557 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.558 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.558 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.558 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.558 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.558 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.558 * [taylor]: Taking taylor expansion of 1.0 in n 4.559 * [backup-simplify]: Simplify 1.0 into 1.0 4.559 * [taylor]: Taking taylor expansion of (log n) in n 4.559 * [taylor]: Taking taylor expansion of n in n 4.559 * [backup-simplify]: Simplify 0 into 0 4.559 * [backup-simplify]: Simplify 1 into 1 4.559 * [backup-simplify]: Simplify (log 1) into 0 4.559 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.560 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.560 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.560 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.560 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.560 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.560 * [taylor]: Taking taylor expansion of 1.0 in n 4.560 * [backup-simplify]: Simplify 1.0 into 1.0 4.560 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.560 * [taylor]: Taking taylor expansion of 2.0 in n 4.560 * [backup-simplify]: Simplify 2.0 into 2.0 4.560 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.561 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.563 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.564 * [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) 4.565 * [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) 4.566 * [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)) 4.566 * [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))) 4.567 * [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) 4.567 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 4.567 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 4.567 * [taylor]: Taking taylor expansion of +nan.0 in n 4.568 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.568 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 4.568 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.568 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.568 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.568 * [taylor]: Taking taylor expansion of 0.5 in n 4.568 * [backup-simplify]: Simplify 0.5 into 0.5 4.568 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.568 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.568 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.568 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.568 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.568 * [taylor]: Taking taylor expansion of 1.0 in n 4.568 * [backup-simplify]: Simplify 1.0 into 1.0 4.568 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.568 * [taylor]: Taking taylor expansion of 2.0 in n 4.568 * [backup-simplify]: Simplify 2.0 into 2.0 4.568 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.569 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.570 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.570 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.570 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.570 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.570 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.570 * [taylor]: Taking taylor expansion of 1.0 in n 4.570 * [backup-simplify]: Simplify 1.0 into 1.0 4.570 * [taylor]: Taking taylor expansion of (log PI) in n 4.570 * [taylor]: Taking taylor expansion of PI in n 4.570 * [backup-simplify]: Simplify PI into PI 4.570 * [backup-simplify]: Simplify (log PI) into (log PI) 4.571 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.572 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.572 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.572 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.572 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.572 * [taylor]: Taking taylor expansion of 1.0 in n 4.572 * [backup-simplify]: Simplify 1.0 into 1.0 4.572 * [taylor]: Taking taylor expansion of (log n) in n 4.572 * [taylor]: Taking taylor expansion of n in n 4.572 * [backup-simplify]: Simplify 0 into 0 4.572 * [backup-simplify]: Simplify 1 into 1 4.572 * [backup-simplify]: Simplify (log 1) into 0 4.573 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.573 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.573 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.574 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.574 * [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) 4.575 * [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)) 4.576 * [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))) 4.577 * [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) 4.577 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.577 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.577 * [taylor]: Taking taylor expansion of 2.0 in n 4.577 * [backup-simplify]: Simplify 2.0 into 2.0 4.577 * [taylor]: Taking taylor expansion of (* n PI) in n 4.577 * [taylor]: Taking taylor expansion of n in n 4.577 * [backup-simplify]: Simplify 0 into 0 4.577 * [backup-simplify]: Simplify 1 into 1 4.577 * [taylor]: Taking taylor expansion of PI in n 4.577 * [backup-simplify]: Simplify PI into PI 4.578 * [backup-simplify]: Simplify (* 0 PI) into 0 4.578 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.579 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.580 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.581 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.582 * [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)) 4.583 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.584 * [backup-simplify]: Simplify (* (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) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.586 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.588 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 4.591 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (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)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.597 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (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)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.604 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (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)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.606 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 4.607 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 4.608 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 4.610 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.611 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.611 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 4.612 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 4.613 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 4.615 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 4.623 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 4.625 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 4.627 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 4.629 * [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 4.631 * [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 4.634 * [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 4.636 * [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 4.636 * [backup-simplify]: Simplify (- 0) into 0 4.636 * [backup-simplify]: Simplify 0 into 0 4.636 * [backup-simplify]: Simplify 0 into 0 4.637 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.639 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 4.642 * [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 4.642 * [backup-simplify]: Simplify (- 0) into 0 4.643 * [backup-simplify]: Simplify (+ 0 0) into 0 4.644 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.646 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 4.648 * [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 (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.649 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.653 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.659 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 4.671 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +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 PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 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)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 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 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 4.671 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 4.671 * [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 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 4.671 * [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 4.671 * [taylor]: Taking taylor expansion of +nan.0 in n 4.671 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.671 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 4.671 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 4.671 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 4.671 * [taylor]: Taking taylor expansion of 0.5 in n 4.671 * [backup-simplify]: Simplify 0.5 into 0.5 4.671 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 4.671 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 4.671 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.671 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.671 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.671 * [taylor]: Taking taylor expansion of 1.0 in n 4.672 * [backup-simplify]: Simplify 1.0 into 1.0 4.672 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.672 * [taylor]: Taking taylor expansion of 2.0 in n 4.672 * [backup-simplify]: Simplify 2.0 into 2.0 4.672 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.673 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.675 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.675 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 4.675 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.675 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.675 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.675 * [taylor]: Taking taylor expansion of 1.0 in n 4.675 * [backup-simplify]: Simplify 1.0 into 1.0 4.675 * [taylor]: Taking taylor expansion of (log n) in n 4.675 * [taylor]: Taking taylor expansion of n in n 4.675 * [backup-simplify]: Simplify 0 into 0 4.675 * [backup-simplify]: Simplify 1 into 1 4.676 * [backup-simplify]: Simplify (log 1) into 0 4.676 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.676 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.676 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.676 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.676 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.676 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.676 * [taylor]: Taking taylor expansion of 1.0 in n 4.676 * [backup-simplify]: Simplify 1.0 into 1.0 4.676 * [taylor]: Taking taylor expansion of (log PI) in n 4.676 * [taylor]: Taking taylor expansion of PI in n 4.676 * [backup-simplify]: Simplify PI into PI 4.677 * [backup-simplify]: Simplify (log PI) into (log PI) 4.678 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.680 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.680 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.682 * [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) 4.683 * [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)) 4.685 * [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))) 4.687 * [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) 4.687 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 4.687 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 4.687 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 4.687 * [taylor]: Taking taylor expansion of +nan.0 in n 4.687 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.687 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 4.687 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.687 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.687 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.687 * [taylor]: Taking taylor expansion of 0.5 in n 4.687 * [backup-simplify]: Simplify 0.5 into 0.5 4.687 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.687 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.687 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.687 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.687 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.687 * [taylor]: Taking taylor expansion of 1.0 in n 4.687 * [backup-simplify]: Simplify 1.0 into 1.0 4.688 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.688 * [taylor]: Taking taylor expansion of 2.0 in n 4.688 * [backup-simplify]: Simplify 2.0 into 2.0 4.688 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.689 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.690 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.690 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.690 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.690 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.691 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.691 * [taylor]: Taking taylor expansion of 1.0 in n 4.691 * [backup-simplify]: Simplify 1.0 into 1.0 4.691 * [taylor]: Taking taylor expansion of (log PI) in n 4.691 * [taylor]: Taking taylor expansion of PI in n 4.691 * [backup-simplify]: Simplify PI into PI 4.691 * [backup-simplify]: Simplify (log PI) into (log PI) 4.692 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.694 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.694 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.694 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.694 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.694 * [taylor]: Taking taylor expansion of 1.0 in n 4.694 * [backup-simplify]: Simplify 1.0 into 1.0 4.694 * [taylor]: Taking taylor expansion of (log n) in n 4.694 * [taylor]: Taking taylor expansion of n in n 4.694 * [backup-simplify]: Simplify 0 into 0 4.694 * [backup-simplify]: Simplify 1 into 1 4.695 * [backup-simplify]: Simplify (log 1) into 0 4.695 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.695 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.695 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.696 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.697 * [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) 4.699 * [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)) 4.700 * [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))) 4.702 * [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) 4.702 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.702 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.702 * [taylor]: Taking taylor expansion of 2.0 in n 4.702 * [backup-simplify]: Simplify 2.0 into 2.0 4.702 * [taylor]: Taking taylor expansion of (* n PI) in n 4.702 * [taylor]: Taking taylor expansion of n in n 4.702 * [backup-simplify]: Simplify 0 into 0 4.702 * [backup-simplify]: Simplify 1 into 1 4.702 * [taylor]: Taking taylor expansion of PI in n 4.702 * [backup-simplify]: Simplify PI into PI 4.702 * [backup-simplify]: Simplify (* 0 PI) into 0 4.703 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.704 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.706 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.707 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.707 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 4.707 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 4.707 * [taylor]: Taking taylor expansion of +nan.0 in n 4.707 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.707 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 4.708 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.708 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.708 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.708 * [taylor]: Taking taylor expansion of 0.5 in n 4.708 * [backup-simplify]: Simplify 0.5 into 0.5 4.708 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.708 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.708 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.708 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.708 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.708 * [taylor]: Taking taylor expansion of 1.0 in n 4.708 * [backup-simplify]: Simplify 1.0 into 1.0 4.708 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.708 * [taylor]: Taking taylor expansion of 2.0 in n 4.708 * [backup-simplify]: Simplify 2.0 into 2.0 4.708 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.709 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.710 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.710 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.710 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.710 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.710 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.710 * [taylor]: Taking taylor expansion of 1.0 in n 4.710 * [backup-simplify]: Simplify 1.0 into 1.0 4.710 * [taylor]: Taking taylor expansion of (log PI) in n 4.710 * [taylor]: Taking taylor expansion of PI in n 4.710 * [backup-simplify]: Simplify PI into PI 4.711 * [backup-simplify]: Simplify (log PI) into (log PI) 4.711 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.712 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.712 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.712 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.712 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.712 * [taylor]: Taking taylor expansion of 1.0 in n 4.712 * [backup-simplify]: Simplify 1.0 into 1.0 4.712 * [taylor]: Taking taylor expansion of (log n) in n 4.712 * [taylor]: Taking taylor expansion of n in n 4.712 * [backup-simplify]: Simplify 0 into 0 4.712 * [backup-simplify]: Simplify 1 into 1 4.713 * [backup-simplify]: Simplify (log 1) into 0 4.713 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.713 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.713 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.714 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.714 * [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) 4.715 * [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)) 4.716 * [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))) 4.717 * [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) 4.717 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 4.717 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.717 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.717 * [taylor]: Taking taylor expansion of 2.0 in n 4.717 * [backup-simplify]: Simplify 2.0 into 2.0 4.717 * [taylor]: Taking taylor expansion of (* n PI) in n 4.717 * [taylor]: Taking taylor expansion of n in n 4.717 * [backup-simplify]: Simplify 0 into 0 4.717 * [backup-simplify]: Simplify 1 into 1 4.717 * [taylor]: Taking taylor expansion of PI in n 4.717 * [backup-simplify]: Simplify PI into PI 4.718 * [backup-simplify]: Simplify (* 0 PI) into 0 4.718 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.719 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.720 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.721 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.722 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.723 * [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)) 4.724 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.725 * [backup-simplify]: Simplify (* (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) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.727 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.728 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.729 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.731 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 4.732 * [backup-simplify]: Simplify (* (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) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.734 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.736 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.748 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 4.762 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 4.777 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (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)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.788 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (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)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.804 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.831 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (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)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 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 k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 4.833 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 4.833 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 4.833 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 4.833 * [taylor]: Taking taylor expansion of 1.0 in n 4.833 * [backup-simplify]: Simplify 1.0 into 1.0 4.833 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 4.833 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.833 * [taylor]: Taking taylor expansion of k in n 4.833 * [backup-simplify]: Simplify k into k 4.833 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.833 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.833 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.833 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.833 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.833 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.834 * [taylor]: Taking taylor expansion of 0.5 in n 4.834 * [backup-simplify]: Simplify 0.5 into 0.5 4.834 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.834 * [taylor]: Taking taylor expansion of 1.0 in n 4.834 * [backup-simplify]: Simplify 1.0 into 1.0 4.834 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.834 * [taylor]: Taking taylor expansion of k in n 4.834 * [backup-simplify]: Simplify k into k 4.834 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.834 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.834 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.834 * [taylor]: Taking taylor expansion of 2.0 in n 4.834 * [backup-simplify]: Simplify 2.0 into 2.0 4.834 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.834 * [taylor]: Taking taylor expansion of PI in n 4.834 * [backup-simplify]: Simplify PI into PI 4.834 * [taylor]: Taking taylor expansion of n in n 4.834 * [backup-simplify]: Simplify 0 into 0 4.834 * [backup-simplify]: Simplify 1 into 1 4.835 * [backup-simplify]: Simplify (/ PI 1) into PI 4.835 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.837 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.837 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.837 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.837 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.840 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.841 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.841 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.841 * [taylor]: Taking taylor expansion of 1.0 in k 4.841 * [backup-simplify]: Simplify 1.0 into 1.0 4.841 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.841 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.841 * [taylor]: Taking taylor expansion of k in k 4.841 * [backup-simplify]: Simplify 0 into 0 4.841 * [backup-simplify]: Simplify 1 into 1 4.842 * [backup-simplify]: Simplify (sqrt 0) into 0 4.843 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.844 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.844 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.844 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.844 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.844 * [taylor]: Taking taylor expansion of 0.5 in k 4.844 * [backup-simplify]: Simplify 0.5 into 0.5 4.844 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.844 * [taylor]: Taking taylor expansion of 1.0 in k 4.844 * [backup-simplify]: Simplify 1.0 into 1.0 4.844 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.844 * [taylor]: Taking taylor expansion of k in k 4.844 * [backup-simplify]: Simplify 0 into 0 4.844 * [backup-simplify]: Simplify 1 into 1 4.845 * [backup-simplify]: Simplify (/ 1 1) into 1 4.845 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.845 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.845 * [taylor]: Taking taylor expansion of 2.0 in k 4.845 * [backup-simplify]: Simplify 2.0 into 2.0 4.845 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.845 * [taylor]: Taking taylor expansion of PI in k 4.845 * [backup-simplify]: Simplify PI into PI 4.845 * [taylor]: Taking taylor expansion of n in k 4.845 * [backup-simplify]: Simplify n into n 4.845 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.845 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.845 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.846 * [backup-simplify]: Simplify (- 1) into -1 4.846 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.847 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.847 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.847 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.847 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.847 * [taylor]: Taking taylor expansion of 1.0 in k 4.847 * [backup-simplify]: Simplify 1.0 into 1.0 4.847 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.847 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.847 * [taylor]: Taking taylor expansion of k in k 4.847 * [backup-simplify]: Simplify 0 into 0 4.847 * [backup-simplify]: Simplify 1 into 1 4.848 * [backup-simplify]: Simplify (sqrt 0) into 0 4.849 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.849 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.849 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.849 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.849 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.849 * [taylor]: Taking taylor expansion of 0.5 in k 4.849 * [backup-simplify]: Simplify 0.5 into 0.5 4.849 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.849 * [taylor]: Taking taylor expansion of 1.0 in k 4.849 * [backup-simplify]: Simplify 1.0 into 1.0 4.849 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.849 * [taylor]: Taking taylor expansion of k in k 4.849 * [backup-simplify]: Simplify 0 into 0 4.849 * [backup-simplify]: Simplify 1 into 1 4.850 * [backup-simplify]: Simplify (/ 1 1) into 1 4.850 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.850 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.850 * [taylor]: Taking taylor expansion of 2.0 in k 4.850 * [backup-simplify]: Simplify 2.0 into 2.0 4.850 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.850 * [taylor]: Taking taylor expansion of PI in k 4.850 * [backup-simplify]: Simplify PI into PI 4.850 * [taylor]: Taking taylor expansion of n in k 4.850 * [backup-simplify]: Simplify n into n 4.850 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.850 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.850 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.851 * [backup-simplify]: Simplify (- 1) into -1 4.851 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.852 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.852 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.852 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.853 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 4.853 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.853 * [taylor]: Taking taylor expansion of 0 in n 4.853 * [backup-simplify]: Simplify 0 into 0 4.853 * [backup-simplify]: Simplify 0 into 0 4.854 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.855 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.855 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.855 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.855 * [taylor]: Taking taylor expansion of +nan.0 in n 4.855 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.855 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.855 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.855 * [taylor]: Taking taylor expansion of 0.5 in n 4.855 * [backup-simplify]: Simplify 0.5 into 0.5 4.855 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.855 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.855 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.855 * [taylor]: Taking taylor expansion of 2.0 in n 4.855 * [backup-simplify]: Simplify 2.0 into 2.0 4.855 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.855 * [taylor]: Taking taylor expansion of PI in n 4.855 * [backup-simplify]: Simplify PI into PI 4.855 * [taylor]: Taking taylor expansion of n in n 4.855 * [backup-simplify]: Simplify 0 into 0 4.855 * [backup-simplify]: Simplify 1 into 1 4.856 * [backup-simplify]: Simplify (/ PI 1) into PI 4.856 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.857 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.857 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.857 * [taylor]: Taking taylor expansion of 1.0 in n 4.857 * [backup-simplify]: Simplify 1.0 into 1.0 4.857 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.857 * [taylor]: Taking taylor expansion of k in n 4.858 * [backup-simplify]: Simplify k into k 4.858 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.859 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.859 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.861 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.862 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.863 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.865 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 4.866 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.868 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.868 * [backup-simplify]: Simplify 0 into 0 4.871 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.872 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.873 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.873 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.873 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.874 * [taylor]: Taking taylor expansion of +nan.0 in n 4.874 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.874 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.874 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.874 * [taylor]: Taking taylor expansion of 0.5 in n 4.874 * [backup-simplify]: Simplify 0.5 into 0.5 4.874 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.874 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.874 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.874 * [taylor]: Taking taylor expansion of 2.0 in n 4.874 * [backup-simplify]: Simplify 2.0 into 2.0 4.874 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.874 * [taylor]: Taking taylor expansion of PI in n 4.874 * [backup-simplify]: Simplify PI into PI 4.874 * [taylor]: Taking taylor expansion of n in n 4.874 * [backup-simplify]: Simplify 0 into 0 4.874 * [backup-simplify]: Simplify 1 into 1 4.875 * [backup-simplify]: Simplify (/ PI 1) into PI 4.875 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.876 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.876 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.876 * [taylor]: Taking taylor expansion of 1.0 in n 4.876 * [backup-simplify]: Simplify 1.0 into 1.0 4.876 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.876 * [taylor]: Taking taylor expansion of k in n 4.876 * [backup-simplify]: Simplify k into k 4.876 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.878 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.878 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.879 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 4.881 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.882 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.883 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 4.885 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.886 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 4.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.888 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.889 * [backup-simplify]: Simplify (- 0) into 0 4.889 * [backup-simplify]: Simplify (+ 0 0) into 0 4.889 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.890 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.891 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.892 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.893 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 4.894 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.895 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 4.895 * [backup-simplify]: Simplify (- 0) into 0 4.895 * [backup-simplify]: Simplify 0 into 0 4.895 * [backup-simplify]: Simplify 0 into 0 4.898 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.899 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.900 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.900 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.900 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.900 * [taylor]: Taking taylor expansion of +nan.0 in n 4.900 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.900 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.900 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.900 * [taylor]: Taking taylor expansion of 0.5 in n 4.900 * [backup-simplify]: Simplify 0.5 into 0.5 4.900 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.900 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.900 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.900 * [taylor]: Taking taylor expansion of 2.0 in n 4.900 * [backup-simplify]: Simplify 2.0 into 2.0 4.900 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.900 * [taylor]: Taking taylor expansion of PI in n 4.900 * [backup-simplify]: Simplify PI into PI 4.900 * [taylor]: Taking taylor expansion of n in n 4.900 * [backup-simplify]: Simplify 0 into 0 4.900 * [backup-simplify]: Simplify 1 into 1 5.325 * [backup-simplify]: Simplify (/ PI 1) into PI 5.326 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.327 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.327 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.327 * [taylor]: Taking taylor expansion of 1.0 in n 5.328 * [backup-simplify]: Simplify 1.0 into 1.0 5.328 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.328 * [taylor]: Taking taylor expansion of k in n 5.328 * [backup-simplify]: Simplify k into k 5.328 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.329 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.329 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.331 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.332 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.333 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.335 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.339 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.340 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.346 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 5.347 * [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)))) 5.347 * [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 5.347 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 5.347 * [taylor]: Taking taylor expansion of 1.0 in n 5.347 * [backup-simplify]: Simplify 1.0 into 1.0 5.347 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 5.347 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.347 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.347 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.347 * [taylor]: Taking taylor expansion of 0.5 in n 5.347 * [backup-simplify]: Simplify 0.5 into 0.5 5.347 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.347 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.347 * [taylor]: Taking taylor expansion of k in n 5.348 * [backup-simplify]: Simplify k into k 5.348 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.348 * [taylor]: Taking taylor expansion of 1.0 in n 5.348 * [backup-simplify]: Simplify 1.0 into 1.0 5.348 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.348 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.348 * [taylor]: Taking taylor expansion of -2.0 in n 5.348 * [backup-simplify]: Simplify -2.0 into -2.0 5.348 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.348 * [taylor]: Taking taylor expansion of PI in n 5.348 * [backup-simplify]: Simplify PI into PI 5.348 * [taylor]: Taking taylor expansion of n in n 5.348 * [backup-simplify]: Simplify 0 into 0 5.348 * [backup-simplify]: Simplify 1 into 1 5.349 * [backup-simplify]: Simplify (/ PI 1) into PI 5.349 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.350 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.350 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.350 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.353 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.355 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.355 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 5.355 * [taylor]: Taking taylor expansion of (/ -1 k) in n 5.355 * [taylor]: Taking taylor expansion of -1 in n 5.355 * [backup-simplify]: Simplify -1 into -1 5.355 * [taylor]: Taking taylor expansion of k in n 5.355 * [backup-simplify]: Simplify k into k 5.355 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 5.355 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 5.355 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 5.355 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 5.357 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 5.357 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 5.357 * [taylor]: Taking taylor expansion of 1.0 in k 5.357 * [backup-simplify]: Simplify 1.0 into 1.0 5.357 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 5.357 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.357 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.357 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.357 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.357 * [taylor]: Taking taylor expansion of 0.5 in k 5.357 * [backup-simplify]: Simplify 0.5 into 0.5 5.357 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.357 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.357 * [taylor]: Taking taylor expansion of k in k 5.357 * [backup-simplify]: Simplify 0 into 0 5.357 * [backup-simplify]: Simplify 1 into 1 5.358 * [backup-simplify]: Simplify (/ 1 1) into 1 5.358 * [taylor]: Taking taylor expansion of 1.0 in k 5.358 * [backup-simplify]: Simplify 1.0 into 1.0 5.358 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.358 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.358 * [taylor]: Taking taylor expansion of -2.0 in k 5.358 * [backup-simplify]: Simplify -2.0 into -2.0 5.358 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.358 * [taylor]: Taking taylor expansion of PI in k 5.358 * [backup-simplify]: Simplify PI into PI 5.358 * [taylor]: Taking taylor expansion of n in k 5.358 * [backup-simplify]: Simplify n into n 5.358 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.358 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.358 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.359 * [backup-simplify]: Simplify (+ 1 0) into 1 5.359 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.359 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.360 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.360 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.360 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.360 * [taylor]: Taking taylor expansion of -1 in k 5.360 * [backup-simplify]: Simplify -1 into -1 5.360 * [taylor]: Taking taylor expansion of k in k 5.360 * [backup-simplify]: Simplify 0 into 0 5.360 * [backup-simplify]: Simplify 1 into 1 5.360 * [backup-simplify]: Simplify (/ -1 1) into -1 5.361 * [backup-simplify]: Simplify (sqrt 0) into 0 5.362 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.363 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.363 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 5.363 * [taylor]: Taking taylor expansion of 1.0 in k 5.363 * [backup-simplify]: Simplify 1.0 into 1.0 5.363 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 5.363 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.363 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.363 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.363 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.363 * [taylor]: Taking taylor expansion of 0.5 in k 5.363 * [backup-simplify]: Simplify 0.5 into 0.5 5.363 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.363 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.363 * [taylor]: Taking taylor expansion of k in k 5.363 * [backup-simplify]: Simplify 0 into 0 5.363 * [backup-simplify]: Simplify 1 into 1 5.364 * [backup-simplify]: Simplify (/ 1 1) into 1 5.364 * [taylor]: Taking taylor expansion of 1.0 in k 5.364 * [backup-simplify]: Simplify 1.0 into 1.0 5.364 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.364 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.364 * [taylor]: Taking taylor expansion of -2.0 in k 5.364 * [backup-simplify]: Simplify -2.0 into -2.0 5.364 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.364 * [taylor]: Taking taylor expansion of PI in k 5.364 * [backup-simplify]: Simplify PI into PI 5.364 * [taylor]: Taking taylor expansion of n in k 5.364 * [backup-simplify]: Simplify n into n 5.364 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.364 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.364 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.365 * [backup-simplify]: Simplify (+ 1 0) into 1 5.365 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.366 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.366 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.366 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.366 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.366 * [taylor]: Taking taylor expansion of -1 in k 5.366 * [backup-simplify]: Simplify -1 into -1 5.366 * [taylor]: Taking taylor expansion of k in k 5.366 * [backup-simplify]: Simplify 0 into 0 5.366 * [backup-simplify]: Simplify 1 into 1 5.367 * [backup-simplify]: Simplify (/ -1 1) into -1 5.367 * [backup-simplify]: Simplify (sqrt 0) into 0 5.368 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.369 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.369 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.369 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.369 * [taylor]: Taking taylor expansion of +nan.0 in n 5.369 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.369 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.369 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.369 * [taylor]: Taking taylor expansion of 0.5 in n 5.369 * [backup-simplify]: Simplify 0.5 into 0.5 5.369 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.369 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.369 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.369 * [taylor]: Taking taylor expansion of k in n 5.370 * [backup-simplify]: Simplify k into k 5.370 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.370 * [taylor]: Taking taylor expansion of 1.0 in n 5.370 * [backup-simplify]: Simplify 1.0 into 1.0 5.370 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.370 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.370 * [taylor]: Taking taylor expansion of -2.0 in n 5.370 * [backup-simplify]: Simplify -2.0 into -2.0 5.370 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.370 * [taylor]: Taking taylor expansion of PI in n 5.370 * [backup-simplify]: Simplify PI into PI 5.370 * [taylor]: Taking taylor expansion of n in n 5.370 * [backup-simplify]: Simplify 0 into 0 5.370 * [backup-simplify]: Simplify 1 into 1 5.371 * [backup-simplify]: Simplify (/ PI 1) into PI 5.371 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.372 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.372 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.375 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.377 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.378 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.379 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.381 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 5.385 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.385 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.386 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.386 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 5.386 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.386 * [taylor]: Taking taylor expansion of +nan.0 in n 5.386 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.386 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.386 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.386 * [taylor]: Taking taylor expansion of 0.5 in n 5.386 * [backup-simplify]: Simplify 0.5 into 0.5 5.386 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.386 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.386 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.386 * [taylor]: Taking taylor expansion of k in n 5.386 * [backup-simplify]: Simplify k into k 5.386 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.386 * [taylor]: Taking taylor expansion of 1.0 in n 5.386 * [backup-simplify]: Simplify 1.0 into 1.0 5.386 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.386 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.386 * [taylor]: Taking taylor expansion of -2.0 in n 5.386 * [backup-simplify]: Simplify -2.0 into -2.0 5.386 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.386 * [taylor]: Taking taylor expansion of PI in n 5.386 * [backup-simplify]: Simplify PI into PI 5.386 * [taylor]: Taking taylor expansion of n in n 5.386 * [backup-simplify]: Simplify 0 into 0 5.386 * [backup-simplify]: Simplify 1 into 1 5.387 * [backup-simplify]: Simplify (/ PI 1) into PI 5.387 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.388 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.388 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.389 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.390 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.390 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.391 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.392 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.393 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.394 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.394 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.395 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.396 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 5.396 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.396 * [backup-simplify]: Simplify (+ 0 0) into 0 5.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.398 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 5.399 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 5.400 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.401 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 5.401 * [backup-simplify]: Simplify 0 into 0 5.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.404 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.405 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.406 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.406 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 5.406 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.406 * [taylor]: Taking taylor expansion of +nan.0 in n 5.406 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.406 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.406 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.406 * [taylor]: Taking taylor expansion of 0.5 in n 5.406 * [backup-simplify]: Simplify 0.5 into 0.5 5.406 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.406 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.406 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.406 * [taylor]: Taking taylor expansion of k in n 5.406 * [backup-simplify]: Simplify k into k 5.406 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.406 * [taylor]: Taking taylor expansion of 1.0 in n 5.406 * [backup-simplify]: Simplify 1.0 into 1.0 5.406 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.406 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.406 * [taylor]: Taking taylor expansion of -2.0 in n 5.407 * [backup-simplify]: Simplify -2.0 into -2.0 5.407 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.407 * [taylor]: Taking taylor expansion of PI in n 5.407 * [backup-simplify]: Simplify PI into PI 5.407 * [taylor]: Taking taylor expansion of n in n 5.407 * [backup-simplify]: Simplify 0 into 0 5.407 * [backup-simplify]: Simplify 1 into 1 5.407 * [backup-simplify]: Simplify (/ PI 1) into PI 5.407 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.408 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.408 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.410 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.411 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.411 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.412 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.413 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.414 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.417 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +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))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.473 * * * [progress]: simplifying candidates 5.476 * [simplify]: Simplifying: (* (+ (+ (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)) (- (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))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +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 k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (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 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.480 * * [simplify]: Extracting # 0 : cost 0 5.481 * * [simplify]: Extracting # 1 : cost 0 5.481 * * [simplify]: Extracting # 2 : cost 0 5.481 * * [simplify]: Extracting # 3 : cost 0 5.482 * * [simplify]: Extracting # 4 : cost 0 5.482 * * [simplify]: Extracting # 5 : cost 0 5.482 * * [simplify]: Extracting # 6 : cost 0 5.483 * * [simplify]: Extracting # 7 : cost 0 5.483 * * [simplify]: Extracting # 8 : cost 0 5.484 * * [simplify]: Extracting # 9 : cost 0 5.484 * * [simplify]: Extracting # 10 : cost 0 5.485 * * [simplify]: Extracting # 11 : cost 0 5.485 * * [simplify]: Extracting # 12 : cost 0 5.486 * * [simplify]: Extracting # 13 : cost 0 5.486 * * [simplify]: Extracting # 14 : cost 0 5.487 * * [simplify]: Extracting # 15 : cost 0 5.488 * * [simplify]: Extracting # 16 : cost 0 5.488 * * [simplify]: Extracting # 17 : cost 0 5.489 * * [simplify]: Extracting # 18 : cost 0 5.489 * * [simplify]: Extracting # 19 : cost 0 5.490 * * [simplify]: Extracting # 20 : cost 0 5.490 * * [simplify]: Extracting # 21 : cost 0 5.491 * * [simplify]: Extracting # 22 : cost 0 5.497 * * [simplify]: Extracting # 23 : cost 0 5.498 * * [simplify]: Extracting # 24 : cost 0 5.498 * * [simplify]: Extracting # 25 : cost 0 5.499 * * [simplify]: Extracting # 26 : cost 0 5.500 * * [simplify]: Extracting # 27 : cost 0 5.500 * * [simplify]: Extracting # 28 : cost 0 5.501 * * [simplify]: Extracting # 29 : cost 0 5.501 * * [simplify]: Extracting # 30 : cost 0 5.502 * * [simplify]: Extracting # 31 : cost 0 5.502 * * [simplify]: Extracting # 32 : cost 0 5.503 * * [simplify]: Extracting # 33 : cost 0 5.504 * * [simplify]: iteration 0 : 361 enodes (cost 2800 ) 5.674 * * [simplify]: Extracting # 0 : cost 0 5.677 * * [simplify]: Extracting # 1 : cost 0 5.680 * * [simplify]: Extracting # 2 : cost 0 5.682 * * [simplify]: Extracting # 3 : cost 0 5.683 * * [simplify]: Extracting # 4 : cost 0 5.685 * * [simplify]: Extracting # 5 : cost 0 5.686 * * [simplify]: Extracting # 6 : cost 0 5.687 * * [simplify]: iteration 1 : 931 enodes (cost 2635 ) 6.246 * * [simplify]: Extracting # 0 : cost 0 6.254 * * [simplify]: Extracting # 1 : cost 0 6.262 * * [simplify]: Extracting # 2 : cost 0 6.267 * * [simplify]: Extracting # 3 : cost 0 6.274 * * [simplify]: Extracting # 4 : cost 0 6.282 * * [simplify]: Extracting # 5 : cost 0 6.290 * * [simplify]: iteration 2 : 3051 enodes (cost 2471 ) 7.589 * * [simplify]: Extracting # 0 : cost 0 7.601 * * [simplify]: Extracting # 1 : cost 0 7.613 * * [simplify]: Extracting # 2 : cost 0 7.621 * * [simplify]: Extracting # 3 : cost 0 7.632 * * [simplify]: Extracting # 4 : cost 0 7.638 * * [simplify]: iteration done: 5001 enodes (cost 2471 ) 7.640 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* PI (* 2.0 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 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (pow (* PI (* 2.0 n)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (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)) (fabs (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)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (log (* PI (* 2.0 n))) (log (* PI (* 2.0 n))) (log (* PI (* 2.0 n))) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (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) (log (* (/ 1.0 (sqrt k)) (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)))) (log (* (/ 1.0 (sqrt k)) (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)))) (log (* (/ 1.0 (sqrt k)) (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)))) (log (* (/ 1.0 (sqrt k)) (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)))) (log (* (/ 1.0 (sqrt k)) (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)))) (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)))) (* (/ (/ (pow 1.0 3) k) (sqrt k)) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (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)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (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)) (* (/ 1.0 (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))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 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))) (- (+ (+ (pow (* (* 2.0 PI) n) 0.5) (* (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (* 2.0 PI) n) 0.5)) 0.25)) (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2))))) (* (* 0.5 k) (+ (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow (exp (* 0.5 (- 1.0 k))) (- (log (* -2.0 PI)) (log (/ -1 n)))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) +nan.0)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (+ (+ (- (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) (- (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) (+ (* (- +nan.0) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3))) (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) k)))) (+ (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (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)))) 7.641 * * * [progress]: adding candidates to table 8.357 * * [progress]: iteration 2 / 4 8.358 * * * [progress]: picking best candidate 8.388 * * * * [pick]: Picked # 8.388 * * * [progress]: localizing error 8.415 * * * [progress]: generating rewritten candidates 8.415 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.450 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.491 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 8.504 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 8.544 * * * [progress]: generating series expansions 8.544 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.545 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.545 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.545 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.545 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.545 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.545 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.545 * [taylor]: Taking taylor expansion of 0.25 in k 8.545 * [backup-simplify]: Simplify 0.25 into 0.25 8.545 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.545 * [taylor]: Taking taylor expansion of 1.0 in k 8.545 * [backup-simplify]: Simplify 1.0 into 1.0 8.545 * [taylor]: Taking taylor expansion of k in k 8.546 * [backup-simplify]: Simplify 0 into 0 8.546 * [backup-simplify]: Simplify 1 into 1 8.546 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.546 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.546 * [taylor]: Taking taylor expansion of 2.0 in k 8.546 * [backup-simplify]: Simplify 2.0 into 2.0 8.546 * [taylor]: Taking taylor expansion of (* n PI) in k 8.546 * [taylor]: Taking taylor expansion of n in k 8.546 * [backup-simplify]: Simplify n into n 8.546 * [taylor]: Taking taylor expansion of PI in k 8.546 * [backup-simplify]: Simplify PI into PI 8.546 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.546 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.546 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.546 * [backup-simplify]: Simplify (- 0) into 0 8.546 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.547 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.547 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.547 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.547 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.547 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.547 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.547 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.547 * [taylor]: Taking taylor expansion of 0.25 in n 8.547 * [backup-simplify]: Simplify 0.25 into 0.25 8.547 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.547 * [taylor]: Taking taylor expansion of 1.0 in n 8.547 * [backup-simplify]: Simplify 1.0 into 1.0 8.547 * [taylor]: Taking taylor expansion of k in n 8.547 * [backup-simplify]: Simplify k into k 8.547 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.547 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.547 * [taylor]: Taking taylor expansion of 2.0 in n 8.547 * [backup-simplify]: Simplify 2.0 into 2.0 8.547 * [taylor]: Taking taylor expansion of (* n PI) in n 8.547 * [taylor]: Taking taylor expansion of n in n 8.547 * [backup-simplify]: Simplify 0 into 0 8.547 * [backup-simplify]: Simplify 1 into 1 8.547 * [taylor]: Taking taylor expansion of PI in n 8.547 * [backup-simplify]: Simplify PI into PI 8.548 * [backup-simplify]: Simplify (* 0 PI) into 0 8.548 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.549 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.550 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.551 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.551 * [backup-simplify]: Simplify (- k) into (- k) 8.551 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.551 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.552 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.553 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.554 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.554 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.554 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.554 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.554 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.554 * [taylor]: Taking taylor expansion of 0.25 in n 8.554 * [backup-simplify]: Simplify 0.25 into 0.25 8.554 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.554 * [taylor]: Taking taylor expansion of 1.0 in n 8.554 * [backup-simplify]: Simplify 1.0 into 1.0 8.554 * [taylor]: Taking taylor expansion of k in n 8.554 * [backup-simplify]: Simplify k into k 8.554 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.554 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.554 * [taylor]: Taking taylor expansion of 2.0 in n 8.554 * [backup-simplify]: Simplify 2.0 into 2.0 8.554 * [taylor]: Taking taylor expansion of (* n PI) in n 8.554 * [taylor]: Taking taylor expansion of n in n 8.554 * [backup-simplify]: Simplify 0 into 0 8.554 * [backup-simplify]: Simplify 1 into 1 8.554 * [taylor]: Taking taylor expansion of PI in n 8.554 * [backup-simplify]: Simplify PI into PI 8.554 * [backup-simplify]: Simplify (* 0 PI) into 0 8.555 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.556 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.557 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.557 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.557 * [backup-simplify]: Simplify (- k) into (- k) 8.558 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.558 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.558 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.559 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.560 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.560 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.560 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.560 * [taylor]: Taking taylor expansion of 0.25 in k 8.560 * [backup-simplify]: Simplify 0.25 into 0.25 8.560 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.560 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.560 * [taylor]: Taking taylor expansion of 1.0 in k 8.560 * [backup-simplify]: Simplify 1.0 into 1.0 8.560 * [taylor]: Taking taylor expansion of k in k 8.560 * [backup-simplify]: Simplify 0 into 0 8.560 * [backup-simplify]: Simplify 1 into 1 8.560 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.560 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.560 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.560 * [taylor]: Taking taylor expansion of 2.0 in k 8.560 * [backup-simplify]: Simplify 2.0 into 2.0 8.560 * [taylor]: Taking taylor expansion of PI in k 8.560 * [backup-simplify]: Simplify PI into PI 8.561 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.561 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.562 * [taylor]: Taking taylor expansion of (log n) in k 8.562 * [taylor]: Taking taylor expansion of n in k 8.562 * [backup-simplify]: Simplify n into n 8.562 * [backup-simplify]: Simplify (log n) into (log n) 8.562 * [backup-simplify]: Simplify (- 0) into 0 8.562 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.563 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.564 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.565 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.566 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.567 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.569 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.570 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.572 * [backup-simplify]: Simplify (- 0) into 0 8.573 * [backup-simplify]: Simplify (+ 0 0) into 0 8.573 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.575 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.576 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.578 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.578 * [taylor]: Taking taylor expansion of 0 in k 8.578 * [backup-simplify]: Simplify 0 into 0 8.578 * [backup-simplify]: Simplify 0 into 0 8.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.582 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.583 * [backup-simplify]: Simplify (+ 0 0) into 0 8.583 * [backup-simplify]: Simplify (- 1) into -1 8.583 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.585 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.588 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.597 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.599 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.600 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.601 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.603 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.603 * [backup-simplify]: Simplify (- 0) into 0 8.604 * [backup-simplify]: Simplify (+ 0 0) into 0 8.604 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.606 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.608 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.608 * [taylor]: Taking taylor expansion of 0 in k 8.608 * [backup-simplify]: Simplify 0 into 0 8.608 * [backup-simplify]: Simplify 0 into 0 8.608 * [backup-simplify]: Simplify 0 into 0 8.609 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.611 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.612 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.612 * [backup-simplify]: Simplify (+ 0 0) into 0 8.613 * [backup-simplify]: Simplify (- 0) into 0 8.613 * [backup-simplify]: Simplify (+ 0 0) into 0 8.614 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.616 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.618 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.622 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.631 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.632 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.632 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.632 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.632 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.632 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.632 * [taylor]: Taking taylor expansion of 0.25 in k 8.632 * [backup-simplify]: Simplify 0.25 into 0.25 8.632 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.632 * [taylor]: Taking taylor expansion of 1.0 in k 8.632 * [backup-simplify]: Simplify 1.0 into 1.0 8.632 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.632 * [taylor]: Taking taylor expansion of k in k 8.632 * [backup-simplify]: Simplify 0 into 0 8.632 * [backup-simplify]: Simplify 1 into 1 8.633 * [backup-simplify]: Simplify (/ 1 1) into 1 8.633 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.633 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.633 * [taylor]: Taking taylor expansion of 2.0 in k 8.633 * [backup-simplify]: Simplify 2.0 into 2.0 8.633 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.633 * [taylor]: Taking taylor expansion of PI in k 8.633 * [backup-simplify]: Simplify PI into PI 8.633 * [taylor]: Taking taylor expansion of n in k 8.633 * [backup-simplify]: Simplify n into n 8.633 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.633 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.633 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.634 * [backup-simplify]: Simplify (- 1) into -1 8.634 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.634 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.635 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.635 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.635 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.635 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.635 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.635 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.635 * [taylor]: Taking taylor expansion of 0.25 in n 8.635 * [backup-simplify]: Simplify 0.25 into 0.25 8.635 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.635 * [taylor]: Taking taylor expansion of 1.0 in n 8.635 * [backup-simplify]: Simplify 1.0 into 1.0 8.635 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.635 * [taylor]: Taking taylor expansion of k in n 8.635 * [backup-simplify]: Simplify k into k 8.635 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.635 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.635 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.635 * [taylor]: Taking taylor expansion of 2.0 in n 8.635 * [backup-simplify]: Simplify 2.0 into 2.0 8.635 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.636 * [taylor]: Taking taylor expansion of PI in n 8.636 * [backup-simplify]: Simplify PI into PI 8.636 * [taylor]: Taking taylor expansion of n in n 8.636 * [backup-simplify]: Simplify 0 into 0 8.636 * [backup-simplify]: Simplify 1 into 1 8.636 * [backup-simplify]: Simplify (/ PI 1) into PI 8.637 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.638 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.638 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.638 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.638 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.641 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.642 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.642 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.642 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.642 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.642 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.642 * [taylor]: Taking taylor expansion of 0.25 in n 8.643 * [backup-simplify]: Simplify 0.25 into 0.25 8.643 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.643 * [taylor]: Taking taylor expansion of 1.0 in n 8.643 * [backup-simplify]: Simplify 1.0 into 1.0 8.643 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.643 * [taylor]: Taking taylor expansion of k in n 8.643 * [backup-simplify]: Simplify k into k 8.643 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.643 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.643 * [taylor]: Taking taylor expansion of 2.0 in n 8.643 * [backup-simplify]: Simplify 2.0 into 2.0 8.643 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.643 * [taylor]: Taking taylor expansion of PI in n 8.643 * [backup-simplify]: Simplify PI into PI 8.643 * [taylor]: Taking taylor expansion of n in n 8.643 * [backup-simplify]: Simplify 0 into 0 8.643 * [backup-simplify]: Simplify 1 into 1 8.644 * [backup-simplify]: Simplify (/ PI 1) into PI 8.644 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.646 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.646 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.646 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.646 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.649 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.650 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.650 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.650 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.650 * [taylor]: Taking taylor expansion of 0.25 in k 8.650 * [backup-simplify]: Simplify 0.25 into 0.25 8.650 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.650 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.650 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.650 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.650 * [taylor]: Taking taylor expansion of 2.0 in k 8.651 * [backup-simplify]: Simplify 2.0 into 2.0 8.651 * [taylor]: Taking taylor expansion of PI in k 8.651 * [backup-simplify]: Simplify PI into PI 8.651 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.652 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.652 * [taylor]: Taking taylor expansion of (log n) in k 8.652 * [taylor]: Taking taylor expansion of n in k 8.652 * [backup-simplify]: Simplify n into n 8.652 * [backup-simplify]: Simplify (log n) into (log n) 8.652 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.652 * [taylor]: Taking taylor expansion of 1.0 in k 8.652 * [backup-simplify]: Simplify 1.0 into 1.0 8.652 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.653 * [taylor]: Taking taylor expansion of k in k 8.653 * [backup-simplify]: Simplify 0 into 0 8.653 * [backup-simplify]: Simplify 1 into 1 8.653 * [backup-simplify]: Simplify (/ 1 1) into 1 8.653 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.654 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.655 * [backup-simplify]: Simplify (- 1) into -1 8.655 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.656 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.657 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.659 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.660 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.664 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.664 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.664 * [backup-simplify]: Simplify (- 0) into 0 8.665 * [backup-simplify]: Simplify (+ 0 0) into 0 8.665 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.667 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.668 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.670 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.670 * [taylor]: Taking taylor expansion of 0 in k 8.670 * [backup-simplify]: Simplify 0 into 0 8.670 * [backup-simplify]: Simplify 0 into 0 8.671 * [backup-simplify]: Simplify 0 into 0 8.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.676 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.677 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.677 * [backup-simplify]: Simplify (- 0) into 0 8.678 * [backup-simplify]: Simplify (+ 0 0) into 0 8.678 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.682 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.684 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.684 * [taylor]: Taking taylor expansion of 0 in k 8.684 * [backup-simplify]: Simplify 0 into 0 8.684 * [backup-simplify]: Simplify 0 into 0 8.684 * [backup-simplify]: Simplify 0 into 0 8.684 * [backup-simplify]: Simplify 0 into 0 8.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.694 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.694 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.694 * [backup-simplify]: Simplify (- 0) into 0 8.695 * [backup-simplify]: Simplify (+ 0 0) into 0 8.696 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.700 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.703 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.703 * [taylor]: Taking taylor expansion of 0 in k 8.703 * [backup-simplify]: Simplify 0 into 0 8.703 * [backup-simplify]: Simplify 0 into 0 8.704 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 8.705 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 8.705 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.705 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.705 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.705 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.705 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.705 * [taylor]: Taking taylor expansion of 0.25 in k 8.705 * [backup-simplify]: Simplify 0.25 into 0.25 8.705 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.705 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.705 * [taylor]: Taking taylor expansion of k in k 8.706 * [backup-simplify]: Simplify 0 into 0 8.706 * [backup-simplify]: Simplify 1 into 1 8.706 * [backup-simplify]: Simplify (/ 1 1) into 1 8.706 * [taylor]: Taking taylor expansion of 1.0 in k 8.706 * [backup-simplify]: Simplify 1.0 into 1.0 8.706 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.706 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.706 * [taylor]: Taking taylor expansion of -2.0 in k 8.706 * [backup-simplify]: Simplify -2.0 into -2.0 8.706 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.706 * [taylor]: Taking taylor expansion of PI in k 8.706 * [backup-simplify]: Simplify PI into PI 8.706 * [taylor]: Taking taylor expansion of n in k 8.706 * [backup-simplify]: Simplify n into n 8.706 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.706 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.707 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.707 * [backup-simplify]: Simplify (+ 1 0) into 1 8.708 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.708 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.708 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 8.708 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.708 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.708 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.708 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.708 * [taylor]: Taking taylor expansion of 0.25 in n 8.708 * [backup-simplify]: Simplify 0.25 into 0.25 8.708 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.708 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.708 * [taylor]: Taking taylor expansion of k in n 8.708 * [backup-simplify]: Simplify k into k 8.708 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.708 * [taylor]: Taking taylor expansion of 1.0 in n 8.708 * [backup-simplify]: Simplify 1.0 into 1.0 8.708 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.709 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.709 * [taylor]: Taking taylor expansion of -2.0 in n 8.709 * [backup-simplify]: Simplify -2.0 into -2.0 8.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.709 * [taylor]: Taking taylor expansion of PI in n 8.709 * [backup-simplify]: Simplify PI into PI 8.709 * [taylor]: Taking taylor expansion of n in n 8.709 * [backup-simplify]: Simplify 0 into 0 8.709 * [backup-simplify]: Simplify 1 into 1 8.709 * [backup-simplify]: Simplify (/ PI 1) into PI 8.710 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.711 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.711 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.711 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.713 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.714 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.715 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.715 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.715 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.715 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.715 * [taylor]: Taking taylor expansion of 0.25 in n 8.716 * [backup-simplify]: Simplify 0.25 into 0.25 8.716 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.716 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.716 * [taylor]: Taking taylor expansion of k in n 8.716 * [backup-simplify]: Simplify k into k 8.716 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.716 * [taylor]: Taking taylor expansion of 1.0 in n 8.716 * [backup-simplify]: Simplify 1.0 into 1.0 8.716 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.716 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.716 * [taylor]: Taking taylor expansion of -2.0 in n 8.716 * [backup-simplify]: Simplify -2.0 into -2.0 8.716 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.716 * [taylor]: Taking taylor expansion of PI in n 8.716 * [backup-simplify]: Simplify PI into PI 8.716 * [taylor]: Taking taylor expansion of n in n 8.716 * [backup-simplify]: Simplify 0 into 0 8.716 * [backup-simplify]: Simplify 1 into 1 8.717 * [backup-simplify]: Simplify (/ PI 1) into PI 8.717 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.718 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.718 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.718 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.721 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.722 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.722 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.723 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.723 * [taylor]: Taking taylor expansion of 0.25 in k 8.723 * [backup-simplify]: Simplify 0.25 into 0.25 8.723 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.723 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.723 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.723 * [taylor]: Taking taylor expansion of k in k 8.723 * [backup-simplify]: Simplify 0 into 0 8.723 * [backup-simplify]: Simplify 1 into 1 8.723 * [backup-simplify]: Simplify (/ 1 1) into 1 8.723 * [taylor]: Taking taylor expansion of 1.0 in k 8.723 * [backup-simplify]: Simplify 1.0 into 1.0 8.723 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.723 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.723 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.723 * [taylor]: Taking taylor expansion of -2.0 in k 8.723 * [backup-simplify]: Simplify -2.0 into -2.0 8.723 * [taylor]: Taking taylor expansion of PI in k 8.723 * [backup-simplify]: Simplify PI into PI 8.724 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.725 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.725 * [taylor]: Taking taylor expansion of (log n) in k 8.725 * [taylor]: Taking taylor expansion of n in k 8.725 * [backup-simplify]: Simplify n into n 8.725 * [backup-simplify]: Simplify (log n) into (log n) 8.726 * [backup-simplify]: Simplify (+ 1 0) into 1 8.726 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.727 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.728 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.729 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.731 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.732 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.738 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.740 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.741 * [backup-simplify]: Simplify (+ 0 0) into 0 8.741 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.744 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.746 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.746 * [taylor]: Taking taylor expansion of 0 in k 8.746 * [backup-simplify]: Simplify 0 into 0 8.747 * [backup-simplify]: Simplify 0 into 0 8.747 * [backup-simplify]: Simplify 0 into 0 8.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.752 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.753 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.753 * [backup-simplify]: Simplify (+ 0 0) into 0 8.754 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.757 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.760 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.760 * [taylor]: Taking taylor expansion of 0 in k 8.760 * [backup-simplify]: Simplify 0 into 0 8.760 * [backup-simplify]: Simplify 0 into 0 8.760 * [backup-simplify]: Simplify 0 into 0 8.760 * [backup-simplify]: Simplify 0 into 0 8.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.762 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.768 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.769 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.769 * [backup-simplify]: Simplify (+ 0 0) into 0 8.770 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.774 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.777 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.777 * [taylor]: Taking taylor expansion of 0 in k 8.777 * [backup-simplify]: Simplify 0 into 0 8.778 * [backup-simplify]: Simplify 0 into 0 8.779 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.779 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.780 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.780 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.780 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.780 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.780 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.780 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.780 * [taylor]: Taking taylor expansion of 0.25 in k 8.780 * [backup-simplify]: Simplify 0.25 into 0.25 8.780 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.780 * [taylor]: Taking taylor expansion of 1.0 in k 8.780 * [backup-simplify]: Simplify 1.0 into 1.0 8.780 * [taylor]: Taking taylor expansion of k in k 8.780 * [backup-simplify]: Simplify 0 into 0 8.780 * [backup-simplify]: Simplify 1 into 1 8.780 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.780 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.780 * [taylor]: Taking taylor expansion of 2.0 in k 8.781 * [backup-simplify]: Simplify 2.0 into 2.0 8.781 * [taylor]: Taking taylor expansion of (* n PI) in k 8.781 * [taylor]: Taking taylor expansion of n in k 8.781 * [backup-simplify]: Simplify n into n 8.781 * [taylor]: Taking taylor expansion of PI in k 8.781 * [backup-simplify]: Simplify PI into PI 8.781 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.781 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.781 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.781 * [backup-simplify]: Simplify (- 0) into 0 8.782 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.782 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.782 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.783 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.783 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.783 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.783 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.783 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.783 * [taylor]: Taking taylor expansion of 0.25 in n 8.783 * [backup-simplify]: Simplify 0.25 into 0.25 8.783 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.783 * [taylor]: Taking taylor expansion of 1.0 in n 8.783 * [backup-simplify]: Simplify 1.0 into 1.0 8.783 * [taylor]: Taking taylor expansion of k in n 8.783 * [backup-simplify]: Simplify k into k 8.783 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.783 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.783 * [taylor]: Taking taylor expansion of 2.0 in n 8.783 * [backup-simplify]: Simplify 2.0 into 2.0 8.783 * [taylor]: Taking taylor expansion of (* n PI) in n 8.783 * [taylor]: Taking taylor expansion of n in n 8.783 * [backup-simplify]: Simplify 0 into 0 8.783 * [backup-simplify]: Simplify 1 into 1 8.783 * [taylor]: Taking taylor expansion of PI in n 8.783 * [backup-simplify]: Simplify PI into PI 8.784 * [backup-simplify]: Simplify (* 0 PI) into 0 8.784 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.786 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.787 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.788 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.789 * [backup-simplify]: Simplify (- k) into (- k) 8.789 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.789 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.790 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.790 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.791 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.791 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.791 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.791 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.791 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.791 * [taylor]: Taking taylor expansion of 0.25 in n 8.791 * [backup-simplify]: Simplify 0.25 into 0.25 8.791 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.791 * [taylor]: Taking taylor expansion of 1.0 in n 8.791 * [backup-simplify]: Simplify 1.0 into 1.0 8.791 * [taylor]: Taking taylor expansion of k in n 8.791 * [backup-simplify]: Simplify k into k 8.791 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.791 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.791 * [taylor]: Taking taylor expansion of 2.0 in n 8.791 * [backup-simplify]: Simplify 2.0 into 2.0 8.791 * [taylor]: Taking taylor expansion of (* n PI) in n 8.791 * [taylor]: Taking taylor expansion of n in n 8.791 * [backup-simplify]: Simplify 0 into 0 8.791 * [backup-simplify]: Simplify 1 into 1 8.791 * [taylor]: Taking taylor expansion of PI in n 8.792 * [backup-simplify]: Simplify PI into PI 8.792 * [backup-simplify]: Simplify (* 0 PI) into 0 8.792 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.793 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.794 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.795 * [backup-simplify]: Simplify (- k) into (- k) 8.795 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.795 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.796 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.797 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.797 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.797 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.798 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.798 * [taylor]: Taking taylor expansion of 0.25 in k 8.798 * [backup-simplify]: Simplify 0.25 into 0.25 8.798 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.798 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.798 * [taylor]: Taking taylor expansion of 1.0 in k 8.798 * [backup-simplify]: Simplify 1.0 into 1.0 8.798 * [taylor]: Taking taylor expansion of k in k 8.798 * [backup-simplify]: Simplify 0 into 0 8.798 * [backup-simplify]: Simplify 1 into 1 8.798 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.798 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.798 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.798 * [taylor]: Taking taylor expansion of 2.0 in k 8.798 * [backup-simplify]: Simplify 2.0 into 2.0 8.798 * [taylor]: Taking taylor expansion of PI in k 8.798 * [backup-simplify]: Simplify PI into PI 8.798 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.799 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.799 * [taylor]: Taking taylor expansion of (log n) in k 8.799 * [taylor]: Taking taylor expansion of n in k 8.799 * [backup-simplify]: Simplify n into n 8.799 * [backup-simplify]: Simplify (log n) into (log n) 8.799 * [backup-simplify]: Simplify (- 0) into 0 8.799 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.800 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.801 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.802 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.802 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.803 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.804 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.804 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.806 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.806 * [backup-simplify]: Simplify (- 0) into 0 8.806 * [backup-simplify]: Simplify (+ 0 0) into 0 8.807 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.808 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.808 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.810 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.810 * [taylor]: Taking taylor expansion of 0 in k 8.810 * [backup-simplify]: Simplify 0 into 0 8.810 * [backup-simplify]: Simplify 0 into 0 8.810 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.811 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.812 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.812 * [backup-simplify]: Simplify (+ 0 0) into 0 8.813 * [backup-simplify]: Simplify (- 1) into -1 8.813 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.815 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.817 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.821 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.824 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.825 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.827 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.831 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.831 * [backup-simplify]: Simplify (- 0) into 0 8.832 * [backup-simplify]: Simplify (+ 0 0) into 0 8.833 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.834 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.836 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.838 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.838 * [taylor]: Taking taylor expansion of 0 in k 8.838 * [backup-simplify]: Simplify 0 into 0 8.838 * [backup-simplify]: Simplify 0 into 0 8.839 * [backup-simplify]: Simplify 0 into 0 8.840 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.844 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.846 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.847 * [backup-simplify]: Simplify (+ 0 0) into 0 8.847 * [backup-simplify]: Simplify (- 0) into 0 8.847 * [backup-simplify]: Simplify (+ 0 0) into 0 8.849 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.853 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.857 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.863 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.875 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.876 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.876 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.876 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.876 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.876 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.876 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.876 * [taylor]: Taking taylor expansion of 0.25 in k 8.876 * [backup-simplify]: Simplify 0.25 into 0.25 8.876 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.876 * [taylor]: Taking taylor expansion of 1.0 in k 8.876 * [backup-simplify]: Simplify 1.0 into 1.0 8.876 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.877 * [taylor]: Taking taylor expansion of k in k 8.877 * [backup-simplify]: Simplify 0 into 0 8.877 * [backup-simplify]: Simplify 1 into 1 8.877 * [backup-simplify]: Simplify (/ 1 1) into 1 8.877 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.877 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.877 * [taylor]: Taking taylor expansion of 2.0 in k 8.877 * [backup-simplify]: Simplify 2.0 into 2.0 8.877 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.877 * [taylor]: Taking taylor expansion of PI in k 8.877 * [backup-simplify]: Simplify PI into PI 8.877 * [taylor]: Taking taylor expansion of n in k 8.877 * [backup-simplify]: Simplify n into n 8.878 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.878 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.878 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.878 * [backup-simplify]: Simplify (- 1) into -1 8.884 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.884 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.885 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.885 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.885 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.885 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.885 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.885 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.885 * [taylor]: Taking taylor expansion of 0.25 in n 8.885 * [backup-simplify]: Simplify 0.25 into 0.25 8.885 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.885 * [taylor]: Taking taylor expansion of 1.0 in n 8.885 * [backup-simplify]: Simplify 1.0 into 1.0 8.885 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.885 * [taylor]: Taking taylor expansion of k in n 8.885 * [backup-simplify]: Simplify k into k 8.885 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.886 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.886 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.886 * [taylor]: Taking taylor expansion of 2.0 in n 8.886 * [backup-simplify]: Simplify 2.0 into 2.0 8.886 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.886 * [taylor]: Taking taylor expansion of PI in n 8.886 * [backup-simplify]: Simplify PI into PI 8.886 * [taylor]: Taking taylor expansion of n in n 8.886 * [backup-simplify]: Simplify 0 into 0 8.886 * [backup-simplify]: Simplify 1 into 1 8.886 * [backup-simplify]: Simplify (/ PI 1) into PI 8.887 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.888 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.888 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.888 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.888 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.890 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.891 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.891 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.891 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.891 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.891 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.891 * [taylor]: Taking taylor expansion of 0.25 in n 8.891 * [backup-simplify]: Simplify 0.25 into 0.25 8.891 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.891 * [taylor]: Taking taylor expansion of 1.0 in n 8.891 * [backup-simplify]: Simplify 1.0 into 1.0 8.891 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.891 * [taylor]: Taking taylor expansion of k in n 8.891 * [backup-simplify]: Simplify k into k 8.891 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.891 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.891 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.892 * [taylor]: Taking taylor expansion of 2.0 in n 8.892 * [backup-simplify]: Simplify 2.0 into 2.0 8.892 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.892 * [taylor]: Taking taylor expansion of PI in n 8.892 * [backup-simplify]: Simplify PI into PI 8.892 * [taylor]: Taking taylor expansion of n in n 8.892 * [backup-simplify]: Simplify 0 into 0 8.892 * [backup-simplify]: Simplify 1 into 1 8.892 * [backup-simplify]: Simplify (/ PI 1) into PI 8.892 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.893 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.893 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.893 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.893 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.895 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.896 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.896 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.896 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.896 * [taylor]: Taking taylor expansion of 0.25 in k 8.896 * [backup-simplify]: Simplify 0.25 into 0.25 8.896 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.896 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.896 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.896 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.896 * [taylor]: Taking taylor expansion of 2.0 in k 8.896 * [backup-simplify]: Simplify 2.0 into 2.0 8.896 * [taylor]: Taking taylor expansion of PI in k 8.896 * [backup-simplify]: Simplify PI into PI 8.896 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.897 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.897 * [taylor]: Taking taylor expansion of (log n) in k 8.897 * [taylor]: Taking taylor expansion of n in k 8.897 * [backup-simplify]: Simplify n into n 8.897 * [backup-simplify]: Simplify (log n) into (log n) 8.897 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.897 * [taylor]: Taking taylor expansion of 1.0 in k 8.897 * [backup-simplify]: Simplify 1.0 into 1.0 8.897 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.897 * [taylor]: Taking taylor expansion of k in k 8.897 * [backup-simplify]: Simplify 0 into 0 8.897 * [backup-simplify]: Simplify 1 into 1 8.898 * [backup-simplify]: Simplify (/ 1 1) into 1 8.898 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.898 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.899 * [backup-simplify]: Simplify (- 1) into -1 8.899 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.900 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.900 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.901 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.902 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.903 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.903 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.904 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.904 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.905 * [backup-simplify]: Simplify (- 0) into 0 8.905 * [backup-simplify]: Simplify (+ 0 0) into 0 8.905 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.907 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.909 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.909 * [taylor]: Taking taylor expansion of 0 in k 8.909 * [backup-simplify]: Simplify 0 into 0 8.909 * [backup-simplify]: Simplify 0 into 0 8.909 * [backup-simplify]: Simplify 0 into 0 8.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.910 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.912 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.912 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.913 * [backup-simplify]: Simplify (- 0) into 0 8.913 * [backup-simplify]: Simplify (+ 0 0) into 0 8.913 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.915 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.917 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.917 * [taylor]: Taking taylor expansion of 0 in k 8.917 * [backup-simplify]: Simplify 0 into 0 8.917 * [backup-simplify]: Simplify 0 into 0 8.917 * [backup-simplify]: Simplify 0 into 0 8.917 * [backup-simplify]: Simplify 0 into 0 8.918 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.919 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.924 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.924 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.924 * [backup-simplify]: Simplify (- 0) into 0 8.925 * [backup-simplify]: Simplify (+ 0 0) into 0 8.926 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.928 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.930 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.933 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.933 * [taylor]: Taking taylor expansion of 0 in k 8.933 * [backup-simplify]: Simplify 0 into 0 8.933 * [backup-simplify]: Simplify 0 into 0 8.935 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 8.936 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 8.936 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.936 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.936 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.936 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.936 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.936 * [taylor]: Taking taylor expansion of 0.25 in k 8.936 * [backup-simplify]: Simplify 0.25 into 0.25 8.936 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.936 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.936 * [taylor]: Taking taylor expansion of k in k 8.936 * [backup-simplify]: Simplify 0 into 0 8.936 * [backup-simplify]: Simplify 1 into 1 8.936 * [backup-simplify]: Simplify (/ 1 1) into 1 8.937 * [taylor]: Taking taylor expansion of 1.0 in k 8.937 * [backup-simplify]: Simplify 1.0 into 1.0 8.937 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.937 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.937 * [taylor]: Taking taylor expansion of -2.0 in k 8.937 * [backup-simplify]: Simplify -2.0 into -2.0 8.937 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.937 * [taylor]: Taking taylor expansion of PI in k 8.937 * [backup-simplify]: Simplify PI into PI 8.937 * [taylor]: Taking taylor expansion of n in k 8.937 * [backup-simplify]: Simplify n into n 8.937 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.937 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.937 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.938 * [backup-simplify]: Simplify (+ 1 0) into 1 8.938 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.938 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.938 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 8.939 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.939 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.939 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.939 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.939 * [taylor]: Taking taylor expansion of 0.25 in n 8.939 * [backup-simplify]: Simplify 0.25 into 0.25 8.939 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.939 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.939 * [taylor]: Taking taylor expansion of k in n 8.939 * [backup-simplify]: Simplify k into k 8.939 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.939 * [taylor]: Taking taylor expansion of 1.0 in n 8.939 * [backup-simplify]: Simplify 1.0 into 1.0 8.939 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.939 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.939 * [taylor]: Taking taylor expansion of -2.0 in n 8.939 * [backup-simplify]: Simplify -2.0 into -2.0 8.939 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.939 * [taylor]: Taking taylor expansion of PI in n 8.939 * [backup-simplify]: Simplify PI into PI 8.939 * [taylor]: Taking taylor expansion of n in n 8.939 * [backup-simplify]: Simplify 0 into 0 8.939 * [backup-simplify]: Simplify 1 into 1 8.940 * [backup-simplify]: Simplify (/ PI 1) into PI 8.940 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.941 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.941 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.941 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.942 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.943 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.944 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.944 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.944 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.944 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.944 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.944 * [taylor]: Taking taylor expansion of 0.25 in n 8.944 * [backup-simplify]: Simplify 0.25 into 0.25 8.944 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.944 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.944 * [taylor]: Taking taylor expansion of k in n 8.944 * [backup-simplify]: Simplify k into k 8.944 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.944 * [taylor]: Taking taylor expansion of 1.0 in n 8.944 * [backup-simplify]: Simplify 1.0 into 1.0 8.944 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.944 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.944 * [taylor]: Taking taylor expansion of -2.0 in n 8.944 * [backup-simplify]: Simplify -2.0 into -2.0 8.944 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.944 * [taylor]: Taking taylor expansion of PI in n 8.944 * [backup-simplify]: Simplify PI into PI 8.944 * [taylor]: Taking taylor expansion of n in n 8.944 * [backup-simplify]: Simplify 0 into 0 8.944 * [backup-simplify]: Simplify 1 into 1 8.945 * [backup-simplify]: Simplify (/ PI 1) into PI 8.945 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.946 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.946 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.946 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.947 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.948 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.949 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.949 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.949 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.949 * [taylor]: Taking taylor expansion of 0.25 in k 8.949 * [backup-simplify]: Simplify 0.25 into 0.25 8.949 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.949 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.949 * [taylor]: Taking taylor expansion of k in k 8.949 * [backup-simplify]: Simplify 0 into 0 8.949 * [backup-simplify]: Simplify 1 into 1 8.949 * [backup-simplify]: Simplify (/ 1 1) into 1 8.949 * [taylor]: Taking taylor expansion of 1.0 in k 8.949 * [backup-simplify]: Simplify 1.0 into 1.0 8.949 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.949 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.949 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.949 * [taylor]: Taking taylor expansion of -2.0 in k 8.949 * [backup-simplify]: Simplify -2.0 into -2.0 8.949 * [taylor]: Taking taylor expansion of PI in k 8.949 * [backup-simplify]: Simplify PI into PI 8.950 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.950 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.950 * [taylor]: Taking taylor expansion of (log n) in k 8.950 * [taylor]: Taking taylor expansion of n in k 8.950 * [backup-simplify]: Simplify n into n 8.951 * [backup-simplify]: Simplify (log n) into (log n) 8.951 * [backup-simplify]: Simplify (+ 1 0) into 1 8.951 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.952 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.952 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.953 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.954 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.955 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.956 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.957 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.957 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.958 * [backup-simplify]: Simplify (+ 0 0) into 0 8.958 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.960 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.961 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.961 * [taylor]: Taking taylor expansion of 0 in k 8.961 * [backup-simplify]: Simplify 0 into 0 8.961 * [backup-simplify]: Simplify 0 into 0 8.961 * [backup-simplify]: Simplify 0 into 0 8.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.963 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.965 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.965 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.965 * [backup-simplify]: Simplify (+ 0 0) into 0 8.966 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.968 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.970 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.970 * [taylor]: Taking taylor expansion of 0 in k 8.970 * [backup-simplify]: Simplify 0 into 0 8.970 * [backup-simplify]: Simplify 0 into 0 8.970 * [backup-simplify]: Simplify 0 into 0 8.970 * [backup-simplify]: Simplify 0 into 0 8.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.971 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.975 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.975 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.975 * [backup-simplify]: Simplify (+ 0 0) into 0 8.976 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.980 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.983 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.984 * [taylor]: Taking taylor expansion of 0 in k 8.984 * [backup-simplify]: Simplify 0 into 0 8.984 * [backup-simplify]: Simplify 0 into 0 8.985 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.985 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 8.986 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.986 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.986 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.986 * [taylor]: Taking taylor expansion of 1.0 in k 8.986 * [backup-simplify]: Simplify 1.0 into 1.0 8.986 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.986 * [taylor]: Taking taylor expansion of k in k 8.986 * [backup-simplify]: Simplify 0 into 0 8.986 * [backup-simplify]: Simplify 1 into 1 8.986 * [backup-simplify]: Simplify (/ 1 1) into 1 8.987 * [backup-simplify]: Simplify (sqrt 0) into 0 8.988 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.988 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.988 * [taylor]: Taking taylor expansion of 1.0 in k 8.988 * [backup-simplify]: Simplify 1.0 into 1.0 8.988 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.989 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.989 * [taylor]: Taking taylor expansion of k in k 8.989 * [backup-simplify]: Simplify 0 into 0 8.989 * [backup-simplify]: Simplify 1 into 1 8.989 * [backup-simplify]: Simplify (/ 1 1) into 1 8.989 * [backup-simplify]: Simplify (sqrt 0) into 0 8.991 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.991 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.991 * [backup-simplify]: Simplify 0 into 0 8.993 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.994 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.994 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.998 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.000 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.000 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.006 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.011 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.014 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.014 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.016 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 9.016 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.016 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.016 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.016 * [taylor]: Taking taylor expansion of 1.0 in k 9.016 * [backup-simplify]: Simplify 1.0 into 1.0 9.016 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.016 * [taylor]: Taking taylor expansion of k in k 9.016 * [backup-simplify]: Simplify 0 into 0 9.016 * [backup-simplify]: Simplify 1 into 1 9.017 * [backup-simplify]: Simplify (sqrt 0) into 0 9.018 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.018 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.018 * [taylor]: Taking taylor expansion of 1.0 in k 9.018 * [backup-simplify]: Simplify 1.0 into 1.0 9.018 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.018 * [taylor]: Taking taylor expansion of k in k 9.018 * [backup-simplify]: Simplify 0 into 0 9.018 * [backup-simplify]: Simplify 1 into 1 9.019 * [backup-simplify]: Simplify (sqrt 0) into 0 9.020 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.020 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.021 * [backup-simplify]: Simplify 0 into 0 9.022 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.023 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.026 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.028 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.028 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.033 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.035 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.036 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.038 * [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)))))))) 9.038 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.038 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.038 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.038 * [taylor]: Taking taylor expansion of 1.0 in k 9.038 * [backup-simplify]: Simplify 1.0 into 1.0 9.038 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.038 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.038 * [taylor]: Taking taylor expansion of -1 in k 9.038 * [backup-simplify]: Simplify -1 into -1 9.038 * [taylor]: Taking taylor expansion of k in k 9.038 * [backup-simplify]: Simplify 0 into 0 9.038 * [backup-simplify]: Simplify 1 into 1 9.039 * [backup-simplify]: Simplify (/ -1 1) into -1 9.039 * [backup-simplify]: Simplify (sqrt 0) into 0 9.040 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.041 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.041 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.041 * [taylor]: Taking taylor expansion of 1.0 in k 9.041 * [backup-simplify]: Simplify 1.0 into 1.0 9.041 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.041 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.041 * [taylor]: Taking taylor expansion of -1 in k 9.041 * [backup-simplify]: Simplify -1 into -1 9.041 * [taylor]: Taking taylor expansion of k in k 9.041 * [backup-simplify]: Simplify 0 into 0 9.041 * [backup-simplify]: Simplify 1 into 1 9.042 * [backup-simplify]: Simplify (/ -1 1) into -1 9.042 * [backup-simplify]: Simplify (sqrt 0) into 0 9.043 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.044 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.044 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.045 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.048 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.051 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.051 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.056 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.061 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.061 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.062 * [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))))) 9.062 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 9.063 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.063 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.063 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.063 * [taylor]: Taking taylor expansion of 2.0 in n 9.063 * [backup-simplify]: Simplify 2.0 into 2.0 9.063 * [taylor]: Taking taylor expansion of (* n PI) in n 9.063 * [taylor]: Taking taylor expansion of n in n 9.063 * [backup-simplify]: Simplify 0 into 0 9.063 * [backup-simplify]: Simplify 1 into 1 9.063 * [taylor]: Taking taylor expansion of PI in n 9.063 * [backup-simplify]: Simplify PI into PI 9.063 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.063 * [taylor]: Taking taylor expansion of 2.0 in n 9.063 * [backup-simplify]: Simplify 2.0 into 2.0 9.063 * [taylor]: Taking taylor expansion of (* n PI) in n 9.063 * [taylor]: Taking taylor expansion of n in n 9.063 * [backup-simplify]: Simplify 0 into 0 9.063 * [backup-simplify]: Simplify 1 into 1 9.063 * [taylor]: Taking taylor expansion of PI in n 9.063 * [backup-simplify]: Simplify PI into PI 9.064 * [backup-simplify]: Simplify (* 0 PI) into 0 9.064 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.065 * [backup-simplify]: Simplify 0 into 0 9.066 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.068 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.068 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.069 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.070 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.070 * [backup-simplify]: Simplify 0 into 0 9.070 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.071 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.071 * [backup-simplify]: Simplify 0 into 0 9.072 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.073 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.073 * [backup-simplify]: Simplify 0 into 0 9.074 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.075 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.075 * [backup-simplify]: Simplify 0 into 0 9.076 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.077 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.077 * [backup-simplify]: Simplify 0 into 0 9.078 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.079 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.079 * [backup-simplify]: Simplify 0 into 0 9.079 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.080 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.080 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.080 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.080 * [taylor]: Taking taylor expansion of 2.0 in n 9.080 * [backup-simplify]: Simplify 2.0 into 2.0 9.080 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.080 * [taylor]: Taking taylor expansion of PI in n 9.080 * [backup-simplify]: Simplify PI into PI 9.080 * [taylor]: Taking taylor expansion of n in n 9.080 * [backup-simplify]: Simplify 0 into 0 9.080 * [backup-simplify]: Simplify 1 into 1 9.080 * [backup-simplify]: Simplify (/ PI 1) into PI 9.080 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.080 * [taylor]: Taking taylor expansion of 2.0 in n 9.080 * [backup-simplify]: Simplify 2.0 into 2.0 9.080 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.080 * [taylor]: Taking taylor expansion of PI in n 9.080 * [backup-simplify]: Simplify PI into PI 9.080 * [taylor]: Taking taylor expansion of n in n 9.080 * [backup-simplify]: Simplify 0 into 0 9.080 * [backup-simplify]: Simplify 1 into 1 9.081 * [backup-simplify]: Simplify (/ PI 1) into PI 9.081 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.081 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.082 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.083 * [backup-simplify]: Simplify 0 into 0 9.083 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.084 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.084 * [backup-simplify]: Simplify 0 into 0 9.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.085 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.085 * [backup-simplify]: Simplify 0 into 0 9.086 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.087 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.087 * [backup-simplify]: Simplify 0 into 0 9.087 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.088 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.088 * [backup-simplify]: Simplify 0 into 0 9.089 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.090 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.090 * [backup-simplify]: Simplify 0 into 0 9.090 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.091 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.091 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.091 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.091 * [taylor]: Taking taylor expansion of -2.0 in n 9.091 * [backup-simplify]: Simplify -2.0 into -2.0 9.091 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.091 * [taylor]: Taking taylor expansion of PI in n 9.091 * [backup-simplify]: Simplify PI into PI 9.091 * [taylor]: Taking taylor expansion of n in n 9.091 * [backup-simplify]: Simplify 0 into 0 9.091 * [backup-simplify]: Simplify 1 into 1 9.091 * [backup-simplify]: Simplify (/ PI 1) into PI 9.091 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.091 * [taylor]: Taking taylor expansion of -2.0 in n 9.091 * [backup-simplify]: Simplify -2.0 into -2.0 9.091 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.091 * [taylor]: Taking taylor expansion of PI in n 9.091 * [backup-simplify]: Simplify PI into PI 9.091 * [taylor]: Taking taylor expansion of n in n 9.091 * [backup-simplify]: Simplify 0 into 0 9.091 * [backup-simplify]: Simplify 1 into 1 9.092 * [backup-simplify]: Simplify (/ PI 1) into PI 9.092 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.092 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.094 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.094 * [backup-simplify]: Simplify 0 into 0 9.094 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.095 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.095 * [backup-simplify]: Simplify 0 into 0 9.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.096 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.096 * [backup-simplify]: Simplify 0 into 0 9.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.098 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.098 * [backup-simplify]: Simplify 0 into 0 9.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.099 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.099 * [backup-simplify]: Simplify 0 into 0 9.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.101 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.101 * [backup-simplify]: Simplify 0 into 0 9.102 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.102 * * * [progress]: simplifying candidates 9.106 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ 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(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) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +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)) 9.113 * * [simplify]: Extracting # 0 : cost 0 9.114 * * [simplify]: Extracting # 1 : cost 0 9.114 * * [simplify]: Extracting # 2 : cost 0 9.115 * * [simplify]: Extracting # 3 : cost 0 9.116 * * [simplify]: Extracting # 4 : cost 0 9.117 * * [simplify]: Extracting # 5 : cost 0 9.117 * * [simplify]: Extracting # 6 : cost 0 9.118 * * [simplify]: Extracting # 7 : cost 0 9.118 * * [simplify]: Extracting # 8 : cost 0 9.119 * * [simplify]: Extracting # 9 : cost 0 9.119 * * [simplify]: Extracting # 10 : cost 0 9.120 * * [simplify]: Extracting # 11 : cost 0 9.120 * * [simplify]: Extracting # 12 : cost 0 9.121 * * [simplify]: Extracting # 13 : cost 0 9.125 * * [simplify]: Extracting # 14 : cost 0 9.126 * * [simplify]: iteration 0 : 326 enodes (cost 3510 ) 9.275 * * [simplify]: Extracting # 0 : cost 0 9.277 * * [simplify]: Extracting # 1 : cost 0 9.278 * * [simplify]: Extracting # 2 : cost 0 9.279 * * [simplify]: Extracting # 3 : cost 0 9.280 * * [simplify]: Extracting # 4 : cost 0 9.281 * * [simplify]: Extracting # 5 : cost 0 9.283 * * [simplify]: iteration 1 : 839 enodes (cost 3234 ) 9.869 * * [simplify]: Extracting # 0 : cost 0 9.873 * * [simplify]: Extracting # 1 : cost 0 9.876 * * [simplify]: Extracting # 2 : cost 0 9.880 * * [simplify]: Extracting # 3 : cost 0 9.883 * * [simplify]: Extracting # 4 : cost 0 9.887 * * [simplify]: Extracting # 5 : cost 0 9.890 * * [simplify]: iteration 2 : 2444 enodes (cost 3128 ) 10.917 * * [simplify]: Extracting # 0 : cost 0 10.925 * * [simplify]: Extracting # 1 : cost 0 10.933 * * [simplify]: Extracting # 2 : cost 0 10.940 * * [simplify]: Extracting # 3 : cost 0 10.947 * * [simplify]: Extracting # 4 : cost 0 10.965 * * [simplify]: iteration done: 5000 enodes (cost 3080 ) 10.968 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (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))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* PI n)) (- 1.0 k)) (* 2.0 (* PI n)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (/ (/ (- 1.0 k) 2) 2.0) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (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))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* PI n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* PI n)) (- 1.0 k)) (* 2.0 (* PI n)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (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)) (fabs (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)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (log (* 2.0 (* PI n))) (log (* 2.0 (* PI n))) (log (* 2.0 (* PI n))) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (pow (* 2.0 (* PI n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (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) (* PI n) (- (+ (+ (pow (* 2.0 (* PI n)) 0.25) (* (* 0.0625 (pow k 2)) (* (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n))))) (* (* (* 0.03125 (pow k 2)) (pow (* 2.0 (* PI n)) 0.25)) (+ (pow (log n) 2) (pow (log (* 2.0 PI)) 2)))) (* (* 0.25 k) (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 (* PI n)))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (+ (pow (* 2.0 (* PI n)) 0.25) (* (* 0.0625 (pow k 2)) (* (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n))))) (* (* (* 0.03125 (pow k 2)) (pow (* 2.0 (* PI n)) 0.25)) (+ (pow (log n) 2) (pow (log (* 2.0 PI)) 2)))) (* (* 0.25 k) (* (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 (* PI n)))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (- k (* k k))) +nan.0)) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) 10.971 * * * [progress]: adding candidates to table 12.127 * * [progress]: iteration 3 / 4 12.127 * * * [progress]: picking best candidate 12.158 * * * * [pick]: Picked # 12.158 * * * [progress]: localizing error 12.213 * * * [progress]: generating rewritten candidates 12.213 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 12.234 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 12.281 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 12.291 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 12.311 * * * [progress]: generating series expansions 12.311 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 12.311 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.311 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.311 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.311 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.311 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.311 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.311 * [taylor]: Taking taylor expansion of 0.5 in k 12.311 * [backup-simplify]: Simplify 0.5 into 0.5 12.311 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.311 * [taylor]: Taking taylor expansion of 1.0 in k 12.311 * [backup-simplify]: Simplify 1.0 into 1.0 12.311 * [taylor]: Taking taylor expansion of k in k 12.311 * [backup-simplify]: Simplify 0 into 0 12.311 * [backup-simplify]: Simplify 1 into 1 12.311 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.311 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.311 * [taylor]: Taking taylor expansion of 2.0 in k 12.311 * [backup-simplify]: Simplify 2.0 into 2.0 12.311 * [taylor]: Taking taylor expansion of (* n PI) in k 12.311 * [taylor]: Taking taylor expansion of n in k 12.311 * [backup-simplify]: Simplify n into n 12.311 * [taylor]: Taking taylor expansion of PI in k 12.311 * [backup-simplify]: Simplify PI into PI 12.311 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.312 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.312 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.312 * [backup-simplify]: Simplify (- 0) into 0 12.312 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.313 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.313 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.313 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.313 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.313 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.313 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.313 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.313 * [taylor]: Taking taylor expansion of 0.5 in n 12.313 * [backup-simplify]: Simplify 0.5 into 0.5 12.313 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.313 * [taylor]: Taking taylor expansion of 1.0 in n 12.313 * [backup-simplify]: Simplify 1.0 into 1.0 12.313 * [taylor]: Taking taylor expansion of k in n 12.313 * [backup-simplify]: Simplify k into k 12.313 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.313 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.313 * [taylor]: Taking taylor expansion of 2.0 in n 12.313 * [backup-simplify]: Simplify 2.0 into 2.0 12.313 * [taylor]: Taking taylor expansion of (* n PI) in n 12.313 * [taylor]: Taking taylor expansion of n in n 12.313 * [backup-simplify]: Simplify 0 into 0 12.313 * [backup-simplify]: Simplify 1 into 1 12.313 * [taylor]: Taking taylor expansion of PI in n 12.313 * [backup-simplify]: Simplify PI into PI 12.314 * [backup-simplify]: Simplify (* 0 PI) into 0 12.314 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.315 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.316 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.317 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.317 * [backup-simplify]: Simplify (- k) into (- k) 12.317 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.317 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.318 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.319 * [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)))) 12.320 * [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))))) 12.320 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.320 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.320 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.320 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.320 * [taylor]: Taking taylor expansion of 0.5 in n 12.320 * [backup-simplify]: Simplify 0.5 into 0.5 12.320 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.320 * [taylor]: Taking taylor expansion of 1.0 in n 12.320 * [backup-simplify]: Simplify 1.0 into 1.0 12.320 * [taylor]: Taking taylor expansion of k in n 12.320 * [backup-simplify]: Simplify k into k 12.320 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.320 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.320 * [taylor]: Taking taylor expansion of 2.0 in n 12.320 * [backup-simplify]: Simplify 2.0 into 2.0 12.320 * [taylor]: Taking taylor expansion of (* n PI) in n 12.320 * [taylor]: Taking taylor expansion of n in n 12.320 * [backup-simplify]: Simplify 0 into 0 12.320 * [backup-simplify]: Simplify 1 into 1 12.320 * [taylor]: Taking taylor expansion of PI in n 12.320 * [backup-simplify]: Simplify PI into PI 12.320 * [backup-simplify]: Simplify (* 0 PI) into 0 12.321 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.322 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.324 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.325 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.325 * [backup-simplify]: Simplify (- k) into (- k) 12.325 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.325 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.326 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.328 * [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)))) 12.329 * [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))))) 12.329 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.329 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.329 * [taylor]: Taking taylor expansion of 0.5 in k 12.329 * [backup-simplify]: Simplify 0.5 into 0.5 12.329 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.329 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.329 * [taylor]: Taking taylor expansion of 1.0 in k 12.329 * [backup-simplify]: Simplify 1.0 into 1.0 12.329 * [taylor]: Taking taylor expansion of k in k 12.329 * [backup-simplify]: Simplify 0 into 0 12.329 * [backup-simplify]: Simplify 1 into 1 12.329 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.329 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.329 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.329 * [taylor]: Taking taylor expansion of 2.0 in k 12.329 * [backup-simplify]: Simplify 2.0 into 2.0 12.329 * [taylor]: Taking taylor expansion of PI in k 12.329 * [backup-simplify]: Simplify PI into PI 12.330 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.331 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.331 * [taylor]: Taking taylor expansion of (log n) in k 12.331 * [taylor]: Taking taylor expansion of n in k 12.331 * [backup-simplify]: Simplify n into n 12.331 * [backup-simplify]: Simplify (log n) into (log n) 12.331 * [backup-simplify]: Simplify (- 0) into 0 12.332 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.333 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.334 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.334 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.335 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.336 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.337 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.337 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.338 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.339 * [backup-simplify]: Simplify (- 0) into 0 12.339 * [backup-simplify]: Simplify (+ 0 0) into 0 12.339 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.340 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.341 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.342 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.342 * [taylor]: Taking taylor expansion of 0 in k 12.342 * [backup-simplify]: Simplify 0 into 0 12.342 * [backup-simplify]: Simplify 0 into 0 12.343 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.344 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.344 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.345 * [backup-simplify]: Simplify (+ 0 0) into 0 12.345 * [backup-simplify]: Simplify (- 1) into -1 12.345 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.346 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.348 * [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)))) 12.350 * [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)))))) 12.351 * [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)))))) 12.352 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.353 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.355 * [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 12.355 * [backup-simplify]: Simplify (- 0) into 0 12.356 * [backup-simplify]: Simplify (+ 0 0) into 0 12.356 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.358 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.359 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.362 * [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 12.362 * [taylor]: Taking taylor expansion of 0 in k 12.362 * [backup-simplify]: Simplify 0 into 0 12.362 * [backup-simplify]: Simplify 0 into 0 12.362 * [backup-simplify]: Simplify 0 into 0 12.363 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.366 * [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 12.368 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.369 * [backup-simplify]: Simplify (+ 0 0) into 0 12.369 * [backup-simplify]: Simplify (- 0) into 0 12.369 * [backup-simplify]: Simplify (+ 0 0) into 0 12.371 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.374 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.378 * [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 (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.382 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.389 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 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 (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.389 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.389 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.389 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.389 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.389 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.389 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.389 * [taylor]: Taking taylor expansion of 0.5 in k 12.389 * [backup-simplify]: Simplify 0.5 into 0.5 12.389 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.389 * [taylor]: Taking taylor expansion of 1.0 in k 12.389 * [backup-simplify]: Simplify 1.0 into 1.0 12.389 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.389 * [taylor]: Taking taylor expansion of k in k 12.389 * [backup-simplify]: Simplify 0 into 0 12.389 * [backup-simplify]: Simplify 1 into 1 12.390 * [backup-simplify]: Simplify (/ 1 1) into 1 12.390 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.390 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.390 * [taylor]: Taking taylor expansion of 2.0 in k 12.390 * [backup-simplify]: Simplify 2.0 into 2.0 12.390 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.390 * [taylor]: Taking taylor expansion of PI in k 12.390 * [backup-simplify]: Simplify PI into PI 12.390 * [taylor]: Taking taylor expansion of n in k 12.390 * [backup-simplify]: Simplify n into n 12.390 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.390 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.390 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.390 * [backup-simplify]: Simplify (- 1) into -1 12.391 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.391 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.391 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.391 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.391 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.391 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.391 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.391 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.391 * [taylor]: Taking taylor expansion of 0.5 in n 12.391 * [backup-simplify]: Simplify 0.5 into 0.5 12.391 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.391 * [taylor]: Taking taylor expansion of 1.0 in n 12.391 * [backup-simplify]: Simplify 1.0 into 1.0 12.391 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.391 * [taylor]: Taking taylor expansion of k in n 12.391 * [backup-simplify]: Simplify k into k 12.391 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.391 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.391 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.391 * [taylor]: Taking taylor expansion of 2.0 in n 12.391 * [backup-simplify]: Simplify 2.0 into 2.0 12.391 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.391 * [taylor]: Taking taylor expansion of PI in n 12.391 * [backup-simplify]: Simplify PI into PI 12.391 * [taylor]: Taking taylor expansion of n in n 12.392 * [backup-simplify]: Simplify 0 into 0 12.392 * [backup-simplify]: Simplify 1 into 1 12.392 * [backup-simplify]: Simplify (/ PI 1) into PI 12.392 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.393 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.393 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.393 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.393 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.394 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.395 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.395 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.396 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.396 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.396 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.396 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.396 * [taylor]: Taking taylor expansion of 0.5 in n 12.396 * [backup-simplify]: Simplify 0.5 into 0.5 12.396 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.396 * [taylor]: Taking taylor expansion of 1.0 in n 12.396 * [backup-simplify]: Simplify 1.0 into 1.0 12.396 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.396 * [taylor]: Taking taylor expansion of k in n 12.396 * [backup-simplify]: Simplify k into k 12.396 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.396 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.396 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.396 * [taylor]: Taking taylor expansion of 2.0 in n 12.396 * [backup-simplify]: Simplify 2.0 into 2.0 12.396 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.396 * [taylor]: Taking taylor expansion of PI in n 12.396 * [backup-simplify]: Simplify PI into PI 12.396 * [taylor]: Taking taylor expansion of n in n 12.396 * [backup-simplify]: Simplify 0 into 0 12.396 * [backup-simplify]: Simplify 1 into 1 12.396 * [backup-simplify]: Simplify (/ PI 1) into PI 12.397 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.397 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.397 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.397 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.398 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.398 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.399 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.400 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.400 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.400 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.400 * [taylor]: Taking taylor expansion of 0.5 in k 12.400 * [backup-simplify]: Simplify 0.5 into 0.5 12.400 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.400 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.400 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.400 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.400 * [taylor]: Taking taylor expansion of 2.0 in k 12.400 * [backup-simplify]: Simplify 2.0 into 2.0 12.400 * [taylor]: Taking taylor expansion of PI in k 12.400 * [backup-simplify]: Simplify PI into PI 12.401 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.402 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.402 * [taylor]: Taking taylor expansion of (log n) in k 12.402 * [taylor]: Taking taylor expansion of n in k 12.402 * [backup-simplify]: Simplify n into n 12.402 * [backup-simplify]: Simplify (log n) into (log n) 12.402 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.402 * [taylor]: Taking taylor expansion of 1.0 in k 12.402 * [backup-simplify]: Simplify 1.0 into 1.0 12.402 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.402 * [taylor]: Taking taylor expansion of k in k 12.402 * [backup-simplify]: Simplify 0 into 0 12.402 * [backup-simplify]: Simplify 1 into 1 12.402 * [backup-simplify]: Simplify (/ 1 1) into 1 12.402 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.403 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.403 * [backup-simplify]: Simplify (- 1) into -1 12.403 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.404 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.413 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.414 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.416 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.418 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.419 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.420 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.420 * [backup-simplify]: Simplify (- 0) into 0 12.420 * [backup-simplify]: Simplify (+ 0 0) into 0 12.421 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.422 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.424 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.426 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.426 * [taylor]: Taking taylor expansion of 0 in k 12.426 * [backup-simplify]: Simplify 0 into 0 12.426 * [backup-simplify]: Simplify 0 into 0 12.426 * [backup-simplify]: Simplify 0 into 0 12.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.428 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.432 * [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 12.432 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.433 * [backup-simplify]: Simplify (- 0) into 0 12.433 * [backup-simplify]: Simplify (+ 0 0) into 0 12.434 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.435 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.437 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.440 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.440 * [taylor]: Taking taylor expansion of 0 in k 12.440 * [backup-simplify]: Simplify 0 into 0 12.440 * [backup-simplify]: Simplify 0 into 0 12.440 * [backup-simplify]: Simplify 0 into 0 12.440 * [backup-simplify]: Simplify 0 into 0 12.442 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.443 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.449 * [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 12.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.450 * [backup-simplify]: Simplify (- 0) into 0 12.451 * [backup-simplify]: Simplify (+ 0 0) into 0 12.452 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.455 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.458 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.458 * [taylor]: Taking taylor expansion of 0 in k 12.459 * [backup-simplify]: Simplify 0 into 0 12.459 * [backup-simplify]: Simplify 0 into 0 12.460 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.460 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.460 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.460 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.460 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.461 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.461 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.461 * [taylor]: Taking taylor expansion of 0.5 in k 12.461 * [backup-simplify]: Simplify 0.5 into 0.5 12.461 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.461 * [taylor]: Taking taylor expansion of k in k 12.461 * [backup-simplify]: Simplify 0 into 0 12.461 * [backup-simplify]: Simplify 1 into 1 12.461 * [backup-simplify]: Simplify (/ 1 1) into 1 12.461 * [taylor]: Taking taylor expansion of 1.0 in k 12.461 * [backup-simplify]: Simplify 1.0 into 1.0 12.461 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.461 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.461 * [taylor]: Taking taylor expansion of -2.0 in k 12.461 * [backup-simplify]: Simplify -2.0 into -2.0 12.461 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.461 * [taylor]: Taking taylor expansion of PI in k 12.462 * [backup-simplify]: Simplify PI into PI 12.462 * [taylor]: Taking taylor expansion of n in k 12.462 * [backup-simplify]: Simplify n into n 12.462 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.462 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.462 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.462 * [backup-simplify]: Simplify (+ 1 0) into 1 12.463 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.463 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.463 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.463 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.463 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.463 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.463 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.463 * [taylor]: Taking taylor expansion of 0.5 in n 12.463 * [backup-simplify]: Simplify 0.5 into 0.5 12.463 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.463 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.464 * [taylor]: Taking taylor expansion of k in n 12.464 * [backup-simplify]: Simplify k into k 12.464 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.464 * [taylor]: Taking taylor expansion of 1.0 in n 12.464 * [backup-simplify]: Simplify 1.0 into 1.0 12.464 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.464 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.464 * [taylor]: Taking taylor expansion of -2.0 in n 12.464 * [backup-simplify]: Simplify -2.0 into -2.0 12.464 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.464 * [taylor]: Taking taylor expansion of PI in n 12.464 * [backup-simplify]: Simplify PI into PI 12.464 * [taylor]: Taking taylor expansion of n in n 12.464 * [backup-simplify]: Simplify 0 into 0 12.464 * [backup-simplify]: Simplify 1 into 1 12.465 * [backup-simplify]: Simplify (/ PI 1) into PI 12.465 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.466 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.466 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.466 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.469 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.471 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.471 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.471 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.471 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.471 * [taylor]: Taking taylor expansion of 0.5 in n 12.471 * [backup-simplify]: Simplify 0.5 into 0.5 12.471 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.471 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.471 * [taylor]: Taking taylor expansion of k in n 12.471 * [backup-simplify]: Simplify k into k 12.471 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.471 * [taylor]: Taking taylor expansion of 1.0 in n 12.471 * [backup-simplify]: Simplify 1.0 into 1.0 12.471 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.471 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.471 * [taylor]: Taking taylor expansion of -2.0 in n 12.471 * [backup-simplify]: Simplify -2.0 into -2.0 12.471 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.471 * [taylor]: Taking taylor expansion of PI in n 12.471 * [backup-simplify]: Simplify PI into PI 12.471 * [taylor]: Taking taylor expansion of n in n 12.471 * [backup-simplify]: Simplify 0 into 0 12.471 * [backup-simplify]: Simplify 1 into 1 12.472 * [backup-simplify]: Simplify (/ PI 1) into PI 12.472 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.473 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.473 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.474 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.475 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.476 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.478 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.478 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.478 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.478 * [taylor]: Taking taylor expansion of 0.5 in k 12.478 * [backup-simplify]: Simplify 0.5 into 0.5 12.478 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.478 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.478 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.478 * [taylor]: Taking taylor expansion of k in k 12.478 * [backup-simplify]: Simplify 0 into 0 12.478 * [backup-simplify]: Simplify 1 into 1 12.479 * [backup-simplify]: Simplify (/ 1 1) into 1 12.479 * [taylor]: Taking taylor expansion of 1.0 in k 12.479 * [backup-simplify]: Simplify 1.0 into 1.0 12.479 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.479 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.479 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.479 * [taylor]: Taking taylor expansion of -2.0 in k 12.479 * [backup-simplify]: Simplify -2.0 into -2.0 12.479 * [taylor]: Taking taylor expansion of PI in k 12.479 * [backup-simplify]: Simplify PI into PI 12.479 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.480 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.480 * [taylor]: Taking taylor expansion of (log n) in k 12.481 * [taylor]: Taking taylor expansion of n in k 12.481 * [backup-simplify]: Simplify n into n 12.481 * [backup-simplify]: Simplify (log n) into (log n) 12.481 * [backup-simplify]: Simplify (+ 1 0) into 1 12.481 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.482 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.483 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.485 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.486 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.487 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.489 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.491 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.491 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.492 * [backup-simplify]: Simplify (+ 0 0) into 0 12.492 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.494 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.495 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.498 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.498 * [taylor]: Taking taylor expansion of 0 in k 12.498 * [backup-simplify]: Simplify 0 into 0 12.498 * [backup-simplify]: Simplify 0 into 0 12.498 * [backup-simplify]: Simplify 0 into 0 12.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.500 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.504 * [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 12.504 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.505 * [backup-simplify]: Simplify (+ 0 0) into 0 12.505 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.509 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.512 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.512 * [taylor]: Taking taylor expansion of 0 in k 12.512 * [backup-simplify]: Simplify 0 into 0 12.512 * [backup-simplify]: Simplify 0 into 0 12.512 * [backup-simplify]: Simplify 0 into 0 12.512 * [backup-simplify]: Simplify 0 into 0 12.513 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.515 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.521 * [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 12.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.522 * [backup-simplify]: Simplify (+ 0 0) into 0 12.523 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.527 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.530 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.530 * [taylor]: Taking taylor expansion of 0 in k 12.530 * [backup-simplify]: Simplify 0 into 0 12.530 * [backup-simplify]: Simplify 0 into 0 12.532 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.532 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 12.532 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 12.533 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.533 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.533 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.533 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.533 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.533 * [taylor]: Taking taylor expansion of 0.25 in k 12.533 * [backup-simplify]: Simplify 0.25 into 0.25 12.533 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.533 * [taylor]: Taking taylor expansion of 1.0 in k 12.533 * [backup-simplify]: Simplify 1.0 into 1.0 12.533 * [taylor]: Taking taylor expansion of k in k 12.533 * [backup-simplify]: Simplify 0 into 0 12.533 * [backup-simplify]: Simplify 1 into 1 12.533 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.533 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.533 * [taylor]: Taking taylor expansion of 2.0 in k 12.533 * [backup-simplify]: Simplify 2.0 into 2.0 12.533 * [taylor]: Taking taylor expansion of (* n PI) in k 12.533 * [taylor]: Taking taylor expansion of n in k 12.533 * [backup-simplify]: Simplify n into n 12.533 * [taylor]: Taking taylor expansion of PI in k 12.533 * [backup-simplify]: Simplify PI into PI 12.533 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.533 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.534 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.534 * [backup-simplify]: Simplify (- 0) into 0 12.534 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.535 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.535 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.535 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.535 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.535 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.535 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.535 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.535 * [taylor]: Taking taylor expansion of 0.25 in n 12.535 * [backup-simplify]: Simplify 0.25 into 0.25 12.535 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.535 * [taylor]: Taking taylor expansion of 1.0 in n 12.535 * [backup-simplify]: Simplify 1.0 into 1.0 12.535 * [taylor]: Taking taylor expansion of k in n 12.536 * [backup-simplify]: Simplify k into k 12.536 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.536 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.536 * [taylor]: Taking taylor expansion of 2.0 in n 12.536 * [backup-simplify]: Simplify 2.0 into 2.0 12.536 * [taylor]: Taking taylor expansion of (* n PI) in n 12.536 * [taylor]: Taking taylor expansion of n in n 12.536 * [backup-simplify]: Simplify 0 into 0 12.536 * [backup-simplify]: Simplify 1 into 1 12.536 * [taylor]: Taking taylor expansion of PI in n 12.536 * [backup-simplify]: Simplify PI into PI 12.536 * [backup-simplify]: Simplify (* 0 PI) into 0 12.537 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.538 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.540 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.541 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.541 * [backup-simplify]: Simplify (- k) into (- k) 12.541 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.541 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.543 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.544 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.545 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.545 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.546 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.546 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.546 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.546 * [taylor]: Taking taylor expansion of 0.25 in n 12.546 * [backup-simplify]: Simplify 0.25 into 0.25 12.546 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.546 * [taylor]: Taking taylor expansion of 1.0 in n 12.546 * [backup-simplify]: Simplify 1.0 into 1.0 12.546 * [taylor]: Taking taylor expansion of k in n 12.546 * [backup-simplify]: Simplify k into k 12.546 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.546 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.546 * [taylor]: Taking taylor expansion of 2.0 in n 12.546 * [backup-simplify]: Simplify 2.0 into 2.0 12.546 * [taylor]: Taking taylor expansion of (* n PI) in n 12.546 * [taylor]: Taking taylor expansion of n in n 12.546 * [backup-simplify]: Simplify 0 into 0 12.546 * [backup-simplify]: Simplify 1 into 1 12.546 * [taylor]: Taking taylor expansion of PI in n 12.546 * [backup-simplify]: Simplify PI into PI 12.547 * [backup-simplify]: Simplify (* 0 PI) into 0 12.547 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.549 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.550 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.552 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.552 * [backup-simplify]: Simplify (- k) into (- k) 12.552 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.552 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.553 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.555 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.556 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.556 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.556 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.556 * [taylor]: Taking taylor expansion of 0.25 in k 12.556 * [backup-simplify]: Simplify 0.25 into 0.25 12.556 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.556 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.556 * [taylor]: Taking taylor expansion of 1.0 in k 12.556 * [backup-simplify]: Simplify 1.0 into 1.0 12.556 * [taylor]: Taking taylor expansion of k in k 12.556 * [backup-simplify]: Simplify 0 into 0 12.556 * [backup-simplify]: Simplify 1 into 1 12.556 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.556 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.557 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.557 * [taylor]: Taking taylor expansion of 2.0 in k 12.557 * [backup-simplify]: Simplify 2.0 into 2.0 12.557 * [taylor]: Taking taylor expansion of PI in k 12.557 * [backup-simplify]: Simplify PI into PI 12.557 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.559 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.559 * [taylor]: Taking taylor expansion of (log n) in k 12.559 * [taylor]: Taking taylor expansion of n in k 12.559 * [backup-simplify]: Simplify n into n 12.559 * [backup-simplify]: Simplify (log n) into (log n) 12.559 * [backup-simplify]: Simplify (- 0) into 0 12.560 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.561 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.561 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.562 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.563 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.563 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.564 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.565 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.571 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.572 * [backup-simplify]: Simplify (- 0) into 0 12.572 * [backup-simplify]: Simplify (+ 0 0) into 0 12.572 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.573 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.574 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.575 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.576 * [taylor]: Taking taylor expansion of 0 in k 12.576 * [backup-simplify]: Simplify 0 into 0 12.576 * [backup-simplify]: Simplify 0 into 0 12.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.577 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.578 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.578 * [backup-simplify]: Simplify (+ 0 0) into 0 12.578 * [backup-simplify]: Simplify (- 1) into -1 12.579 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.580 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.581 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 12.583 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.585 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.586 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.587 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.589 * [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 12.589 * [backup-simplify]: Simplify (- 0) into 0 12.589 * [backup-simplify]: Simplify (+ 0 0) into 0 12.590 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.591 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.592 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.594 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.594 * [taylor]: Taking taylor expansion of 0 in k 12.594 * [backup-simplify]: Simplify 0 into 0 12.594 * [backup-simplify]: Simplify 0 into 0 12.595 * [backup-simplify]: Simplify 0 into 0 12.596 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.599 * [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 12.602 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.602 * [backup-simplify]: Simplify (+ 0 0) into 0 12.602 * [backup-simplify]: Simplify (- 0) into 0 12.603 * [backup-simplify]: Simplify (+ 0 0) into 0 12.605 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.608 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.613 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 12.618 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 12.630 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.631 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 12.631 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.631 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.631 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.631 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.631 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.631 * [taylor]: Taking taylor expansion of 0.25 in k 12.631 * [backup-simplify]: Simplify 0.25 into 0.25 12.631 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.631 * [taylor]: Taking taylor expansion of 1.0 in k 12.631 * [backup-simplify]: Simplify 1.0 into 1.0 12.631 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.631 * [taylor]: Taking taylor expansion of k in k 12.631 * [backup-simplify]: Simplify 0 into 0 12.631 * [backup-simplify]: Simplify 1 into 1 12.631 * [backup-simplify]: Simplify (/ 1 1) into 1 12.631 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.632 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.632 * [taylor]: Taking taylor expansion of 2.0 in k 12.632 * [backup-simplify]: Simplify 2.0 into 2.0 12.632 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.632 * [taylor]: Taking taylor expansion of PI in k 12.632 * [backup-simplify]: Simplify PI into PI 12.632 * [taylor]: Taking taylor expansion of n in k 12.632 * [backup-simplify]: Simplify n into n 12.632 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.632 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.632 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.632 * [backup-simplify]: Simplify (- 1) into -1 12.633 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.633 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.633 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.634 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.634 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.634 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.634 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.634 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.634 * [taylor]: Taking taylor expansion of 0.25 in n 12.634 * [backup-simplify]: Simplify 0.25 into 0.25 12.634 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.634 * [taylor]: Taking taylor expansion of 1.0 in n 12.634 * [backup-simplify]: Simplify 1.0 into 1.0 12.634 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.634 * [taylor]: Taking taylor expansion of k in n 12.634 * [backup-simplify]: Simplify k into k 12.634 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.634 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.634 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.634 * [taylor]: Taking taylor expansion of 2.0 in n 12.634 * [backup-simplify]: Simplify 2.0 into 2.0 12.634 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.634 * [taylor]: Taking taylor expansion of PI in n 12.634 * [backup-simplify]: Simplify PI into PI 12.634 * [taylor]: Taking taylor expansion of n in n 12.635 * [backup-simplify]: Simplify 0 into 0 12.635 * [backup-simplify]: Simplify 1 into 1 12.635 * [backup-simplify]: Simplify (/ PI 1) into PI 12.636 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.637 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.637 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.637 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.637 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.640 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.641 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.641 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.641 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.641 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.641 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.641 * [taylor]: Taking taylor expansion of 0.25 in n 12.641 * [backup-simplify]: Simplify 0.25 into 0.25 12.641 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.642 * [taylor]: Taking taylor expansion of 1.0 in n 12.642 * [backup-simplify]: Simplify 1.0 into 1.0 12.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.642 * [taylor]: Taking taylor expansion of k in n 12.642 * [backup-simplify]: Simplify k into k 12.642 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.642 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.642 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.642 * [taylor]: Taking taylor expansion of 2.0 in n 12.642 * [backup-simplify]: Simplify 2.0 into 2.0 12.642 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.642 * [taylor]: Taking taylor expansion of PI in n 12.642 * [backup-simplify]: Simplify PI into PI 12.642 * [taylor]: Taking taylor expansion of n in n 12.642 * [backup-simplify]: Simplify 0 into 0 12.642 * [backup-simplify]: Simplify 1 into 1 12.642 * [backup-simplify]: Simplify (/ PI 1) into PI 12.643 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.644 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.644 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.644 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.644 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.647 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.648 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.648 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.648 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.648 * [taylor]: Taking taylor expansion of 0.25 in k 12.648 * [backup-simplify]: Simplify 0.25 into 0.25 12.649 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.649 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.649 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.649 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.649 * [taylor]: Taking taylor expansion of 2.0 in k 12.649 * [backup-simplify]: Simplify 2.0 into 2.0 12.649 * [taylor]: Taking taylor expansion of PI in k 12.649 * [backup-simplify]: Simplify PI into PI 12.649 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.650 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.650 * [taylor]: Taking taylor expansion of (log n) in k 12.650 * [taylor]: Taking taylor expansion of n in k 12.650 * [backup-simplify]: Simplify n into n 12.651 * [backup-simplify]: Simplify (log n) into (log n) 12.651 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.651 * [taylor]: Taking taylor expansion of 1.0 in k 12.651 * [backup-simplify]: Simplify 1.0 into 1.0 12.651 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.651 * [taylor]: Taking taylor expansion of k in k 12.651 * [backup-simplify]: Simplify 0 into 0 12.651 * [backup-simplify]: Simplify 1 into 1 12.651 * [backup-simplify]: Simplify (/ 1 1) into 1 12.651 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.652 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.653 * [backup-simplify]: Simplify (- 1) into -1 12.653 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.654 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.654 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.655 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.656 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.656 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.657 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.658 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.658 * [backup-simplify]: Simplify (- 0) into 0 12.659 * [backup-simplify]: Simplify (+ 0 0) into 0 12.659 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.661 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.662 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.662 * [taylor]: Taking taylor expansion of 0 in k 12.662 * [backup-simplify]: Simplify 0 into 0 12.662 * [backup-simplify]: Simplify 0 into 0 12.662 * [backup-simplify]: Simplify 0 into 0 12.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.665 * [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 12.666 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.666 * [backup-simplify]: Simplify (- 0) into 0 12.666 * [backup-simplify]: Simplify (+ 0 0) into 0 12.667 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.668 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.669 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.670 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.670 * [taylor]: Taking taylor expansion of 0 in k 12.670 * [backup-simplify]: Simplify 0 into 0 12.670 * [backup-simplify]: Simplify 0 into 0 12.670 * [backup-simplify]: Simplify 0 into 0 12.670 * [backup-simplify]: Simplify 0 into 0 12.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.675 * [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 12.675 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.675 * [backup-simplify]: Simplify (- 0) into 0 12.676 * [backup-simplify]: Simplify (+ 0 0) into 0 12.676 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.677 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.679 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.680 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.680 * [taylor]: Taking taylor expansion of 0 in k 12.681 * [backup-simplify]: Simplify 0 into 0 12.681 * [backup-simplify]: Simplify 0 into 0 12.682 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.683 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 12.683 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.683 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.683 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.683 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.683 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.683 * [taylor]: Taking taylor expansion of 0.25 in k 12.683 * [backup-simplify]: Simplify 0.25 into 0.25 12.683 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.683 * [taylor]: Taking taylor expansion of k in k 12.683 * [backup-simplify]: Simplify 0 into 0 12.683 * [backup-simplify]: Simplify 1 into 1 12.684 * [backup-simplify]: Simplify (/ 1 1) into 1 12.684 * [taylor]: Taking taylor expansion of 1.0 in k 12.684 * [backup-simplify]: Simplify 1.0 into 1.0 12.684 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.684 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.684 * [taylor]: Taking taylor expansion of -2.0 in k 12.684 * [backup-simplify]: Simplify -2.0 into -2.0 12.684 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.684 * [taylor]: Taking taylor expansion of PI in k 12.684 * [backup-simplify]: Simplify PI into PI 12.684 * [taylor]: Taking taylor expansion of n in k 12.684 * [backup-simplify]: Simplify n into n 12.684 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.684 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.684 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.685 * [backup-simplify]: Simplify (+ 1 0) into 1 12.685 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.685 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.686 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.686 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.686 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.686 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.686 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.686 * [taylor]: Taking taylor expansion of 0.25 in n 12.686 * [backup-simplify]: Simplify 0.25 into 0.25 12.686 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.686 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.686 * [taylor]: Taking taylor expansion of k in n 12.686 * [backup-simplify]: Simplify k into k 12.686 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.686 * [taylor]: Taking taylor expansion of 1.0 in n 12.686 * [backup-simplify]: Simplify 1.0 into 1.0 12.686 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.686 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.686 * [taylor]: Taking taylor expansion of -2.0 in n 12.686 * [backup-simplify]: Simplify -2.0 into -2.0 12.686 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.686 * [taylor]: Taking taylor expansion of PI in n 12.686 * [backup-simplify]: Simplify PI into PI 12.686 * [taylor]: Taking taylor expansion of n in n 12.686 * [backup-simplify]: Simplify 0 into 0 12.686 * [backup-simplify]: Simplify 1 into 1 12.687 * [backup-simplify]: Simplify (/ PI 1) into PI 12.687 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.688 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.689 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.689 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.690 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.691 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.701 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.701 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.701 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.701 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.701 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.701 * [taylor]: Taking taylor expansion of 0.25 in n 12.701 * [backup-simplify]: Simplify 0.25 into 0.25 12.701 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.701 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.701 * [taylor]: Taking taylor expansion of k in n 12.701 * [backup-simplify]: Simplify k into k 12.701 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.701 * [taylor]: Taking taylor expansion of 1.0 in n 12.701 * [backup-simplify]: Simplify 1.0 into 1.0 12.701 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.702 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.702 * [taylor]: Taking taylor expansion of -2.0 in n 12.702 * [backup-simplify]: Simplify -2.0 into -2.0 12.702 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.702 * [taylor]: Taking taylor expansion of PI in n 12.702 * [backup-simplify]: Simplify PI into PI 12.702 * [taylor]: Taking taylor expansion of n in n 12.702 * [backup-simplify]: Simplify 0 into 0 12.702 * [backup-simplify]: Simplify 1 into 1 12.703 * [backup-simplify]: Simplify (/ PI 1) into PI 12.703 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.704 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.705 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.705 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.708 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.709 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.710 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.710 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.710 * [taylor]: Taking taylor expansion of 0.25 in k 12.710 * [backup-simplify]: Simplify 0.25 into 0.25 12.710 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.710 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.710 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.710 * [taylor]: Taking taylor expansion of k in k 12.710 * [backup-simplify]: Simplify 0 into 0 12.710 * [backup-simplify]: Simplify 1 into 1 12.710 * [backup-simplify]: Simplify (/ 1 1) into 1 12.710 * [taylor]: Taking taylor expansion of 1.0 in k 12.710 * [backup-simplify]: Simplify 1.0 into 1.0 12.710 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.710 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.710 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.710 * [taylor]: Taking taylor expansion of -2.0 in k 12.711 * [backup-simplify]: Simplify -2.0 into -2.0 12.711 * [taylor]: Taking taylor expansion of PI in k 12.711 * [backup-simplify]: Simplify PI into PI 12.711 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.712 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.712 * [taylor]: Taking taylor expansion of (log n) in k 12.712 * [taylor]: Taking taylor expansion of n in k 12.712 * [backup-simplify]: Simplify n into n 12.712 * [backup-simplify]: Simplify (log n) into (log n) 12.713 * [backup-simplify]: Simplify (+ 1 0) into 1 12.713 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.714 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.716 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.717 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.718 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.719 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.721 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.721 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.723 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.723 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.724 * [backup-simplify]: Simplify (+ 0 0) into 0 12.724 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.726 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.727 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.729 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.729 * [taylor]: Taking taylor expansion of 0 in k 12.729 * [backup-simplify]: Simplify 0 into 0 12.729 * [backup-simplify]: Simplify 0 into 0 12.729 * [backup-simplify]: Simplify 0 into 0 12.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.730 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.732 * [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 12.733 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.733 * [backup-simplify]: Simplify (+ 0 0) into 0 12.733 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.734 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.735 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.737 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.737 * [taylor]: Taking taylor expansion of 0 in k 12.737 * [backup-simplify]: Simplify 0 into 0 12.737 * [backup-simplify]: Simplify 0 into 0 12.737 * [backup-simplify]: Simplify 0 into 0 12.737 * [backup-simplify]: Simplify 0 into 0 12.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.742 * [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 12.742 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.743 * [backup-simplify]: Simplify (+ 0 0) into 0 12.743 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.746 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.747 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.747 * [taylor]: Taking taylor expansion of 0 in k 12.747 * [backup-simplify]: Simplify 0 into 0 12.747 * [backup-simplify]: Simplify 0 into 0 12.748 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.748 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 12.749 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.749 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.749 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.749 * [taylor]: Taking taylor expansion of 1.0 in k 12.749 * [backup-simplify]: Simplify 1.0 into 1.0 12.749 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.749 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.749 * [taylor]: Taking taylor expansion of k in k 12.749 * [backup-simplify]: Simplify 0 into 0 12.749 * [backup-simplify]: Simplify 1 into 1 12.749 * [backup-simplify]: Simplify (/ 1 1) into 1 12.749 * [backup-simplify]: Simplify (sqrt 0) into 0 12.750 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.750 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.750 * [taylor]: Taking taylor expansion of 1.0 in k 12.750 * [backup-simplify]: Simplify 1.0 into 1.0 12.750 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.750 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.750 * [taylor]: Taking taylor expansion of k in k 12.750 * [backup-simplify]: Simplify 0 into 0 12.750 * [backup-simplify]: Simplify 1 into 1 12.751 * [backup-simplify]: Simplify (/ 1 1) into 1 12.751 * [backup-simplify]: Simplify (sqrt 0) into 0 12.752 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.752 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.752 * [backup-simplify]: Simplify 0 into 0 12.753 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.753 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.754 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.756 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.757 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.758 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.758 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.762 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.765 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.765 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.767 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 12.767 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.767 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.767 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.767 * [taylor]: Taking taylor expansion of 1.0 in k 12.767 * [backup-simplify]: Simplify 1.0 into 1.0 12.767 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.767 * [taylor]: Taking taylor expansion of k in k 12.767 * [backup-simplify]: Simplify 0 into 0 12.767 * [backup-simplify]: Simplify 1 into 1 12.768 * [backup-simplify]: Simplify (sqrt 0) into 0 12.769 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.769 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.769 * [taylor]: Taking taylor expansion of 1.0 in k 12.769 * [backup-simplify]: Simplify 1.0 into 1.0 12.769 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.769 * [taylor]: Taking taylor expansion of k in k 12.769 * [backup-simplify]: Simplify 0 into 0 12.769 * [backup-simplify]: Simplify 1 into 1 12.770 * [backup-simplify]: Simplify (sqrt 0) into 0 12.771 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.772 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.772 * [backup-simplify]: Simplify 0 into 0 12.773 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.773 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.775 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.776 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.777 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.779 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.780 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.781 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.782 * [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)))))))) 12.782 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 12.782 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 12.782 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.782 * [taylor]: Taking taylor expansion of 1.0 in k 12.782 * [backup-simplify]: Simplify 1.0 into 1.0 12.782 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.782 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.782 * [taylor]: Taking taylor expansion of -1 in k 12.782 * [backup-simplify]: Simplify -1 into -1 12.782 * [taylor]: Taking taylor expansion of k in k 12.782 * [backup-simplify]: Simplify 0 into 0 12.782 * [backup-simplify]: Simplify 1 into 1 12.782 * [backup-simplify]: Simplify (/ -1 1) into -1 12.783 * [backup-simplify]: Simplify (sqrt 0) into 0 12.783 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.784 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.784 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 12.784 * [taylor]: Taking taylor expansion of 1.0 in k 12.784 * [backup-simplify]: Simplify 1.0 into 1.0 12.784 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.784 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.784 * [taylor]: Taking taylor expansion of -1 in k 12.784 * [backup-simplify]: Simplify -1 into -1 12.784 * [taylor]: Taking taylor expansion of k in k 12.784 * [backup-simplify]: Simplify 0 into 0 12.784 * [backup-simplify]: Simplify 1 into 1 12.784 * [backup-simplify]: Simplify (/ -1 1) into -1 12.784 * [backup-simplify]: Simplify (sqrt 0) into 0 12.785 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.786 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 12.786 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.788 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.790 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 12.790 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.791 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.793 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.796 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 12.796 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.797 * [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))))) 12.797 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 12.797 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.797 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 12.797 * [taylor]: Taking taylor expansion of (* n PI) in n 12.797 * [taylor]: Taking taylor expansion of n in n 12.797 * [backup-simplify]: Simplify 0 into 0 12.797 * [backup-simplify]: Simplify 1 into 1 12.797 * [taylor]: Taking taylor expansion of PI in n 12.797 * [backup-simplify]: Simplify PI into PI 12.797 * [taylor]: Taking taylor expansion of (* n PI) in n 12.797 * [taylor]: Taking taylor expansion of n in n 12.797 * [backup-simplify]: Simplify 0 into 0 12.797 * [backup-simplify]: Simplify 1 into 1 12.797 * [taylor]: Taking taylor expansion of PI in n 12.797 * [backup-simplify]: Simplify PI into PI 12.797 * [backup-simplify]: Simplify (* 0 PI) into 0 12.797 * [backup-simplify]: Simplify 0 into 0 12.798 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.799 * [backup-simplify]: Simplify PI into PI 12.799 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.799 * [backup-simplify]: Simplify 0 into 0 12.800 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.800 * [backup-simplify]: Simplify 0 into 0 12.801 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.801 * [backup-simplify]: Simplify 0 into 0 12.802 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.802 * [backup-simplify]: Simplify 0 into 0 12.803 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.803 * [backup-simplify]: Simplify 0 into 0 12.804 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.804 * [backup-simplify]: Simplify 0 into 0 12.804 * [backup-simplify]: Simplify (* PI n) into (* n PI) 12.804 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 12.804 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 12.804 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.804 * [taylor]: Taking taylor expansion of PI in n 12.804 * [backup-simplify]: Simplify PI into PI 12.804 * [taylor]: Taking taylor expansion of n in n 12.804 * [backup-simplify]: Simplify 0 into 0 12.804 * [backup-simplify]: Simplify 1 into 1 12.805 * [backup-simplify]: Simplify (/ PI 1) into PI 12.805 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.805 * [taylor]: Taking taylor expansion of PI in n 12.805 * [backup-simplify]: Simplify PI into PI 12.805 * [taylor]: Taking taylor expansion of n in n 12.805 * [backup-simplify]: Simplify 0 into 0 12.805 * [backup-simplify]: Simplify 1 into 1 12.805 * [backup-simplify]: Simplify (/ PI 1) into PI 12.805 * [backup-simplify]: Simplify PI into PI 12.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.806 * [backup-simplify]: Simplify 0 into 0 12.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.806 * [backup-simplify]: Simplify 0 into 0 12.807 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.807 * [backup-simplify]: Simplify 0 into 0 12.808 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.808 * [backup-simplify]: Simplify 0 into 0 12.808 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.809 * [backup-simplify]: Simplify 0 into 0 12.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.809 * [backup-simplify]: Simplify 0 into 0 12.809 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 12.810 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 12.810 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 12.810 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.810 * [taylor]: Taking taylor expansion of -1 in n 12.810 * [backup-simplify]: Simplify -1 into -1 12.810 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.810 * [taylor]: Taking taylor expansion of PI in n 12.810 * [backup-simplify]: Simplify PI into PI 12.810 * [taylor]: Taking taylor expansion of n in n 12.810 * [backup-simplify]: Simplify 0 into 0 12.810 * [backup-simplify]: Simplify 1 into 1 12.810 * [backup-simplify]: Simplify (/ PI 1) into PI 12.810 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 12.810 * [taylor]: Taking taylor expansion of -1 in n 12.810 * [backup-simplify]: Simplify -1 into -1 12.810 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.810 * [taylor]: Taking taylor expansion of PI in n 12.810 * [backup-simplify]: Simplify PI into PI 12.810 * [taylor]: Taking taylor expansion of n in n 12.810 * [backup-simplify]: Simplify 0 into 0 12.810 * [backup-simplify]: Simplify 1 into 1 12.817 * [backup-simplify]: Simplify (/ PI 1) into PI 12.818 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.818 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 12.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.820 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 12.820 * [backup-simplify]: Simplify 0 into 0 12.820 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.821 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 12.821 * [backup-simplify]: Simplify 0 into 0 12.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.822 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.823 * [backup-simplify]: Simplify 0 into 0 12.823 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.824 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.824 * [backup-simplify]: Simplify 0 into 0 12.825 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.826 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.826 * [backup-simplify]: Simplify 0 into 0 12.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.827 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.827 * [backup-simplify]: Simplify 0 into 0 12.828 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 12.828 * * * [progress]: simplifying candidates 12.831 * [simplify]: Simplifying: (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 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 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) 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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) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +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))))) (* n PI) (* n PI) (* n PI) 12.835 * * [simplify]: Extracting # 0 : cost 0 12.836 * * [simplify]: Extracting # 1 : cost 0 12.836 * * [simplify]: Extracting # 2 : cost 0 12.837 * * [simplify]: Extracting # 3 : cost 0 12.838 * * [simplify]: Extracting # 4 : cost 0 12.838 * * [simplify]: Extracting # 5 : cost 0 12.839 * * [simplify]: Extracting # 6 : cost 0 12.839 * * [simplify]: Extracting # 7 : cost 0 12.840 * * [simplify]: Extracting # 8 : cost 0 12.841 * * [simplify]: Extracting # 9 : cost 0 12.841 * * [simplify]: Extracting # 10 : cost 0 12.842 * * [simplify]: Extracting # 11 : cost 0 12.843 * * [simplify]: Extracting # 12 : cost 0 12.843 * * [simplify]: Extracting # 13 : cost 0 12.844 * * [simplify]: iteration 0 : 390 enodes (cost 2642 ) 13.034 * * [simplify]: Extracting # 0 : cost 0 13.037 * * [simplify]: Extracting # 1 : cost 0 13.040 * * [simplify]: Extracting # 2 : cost 0 13.043 * * [simplify]: Extracting # 3 : cost 0 13.046 * * [simplify]: Extracting # 4 : cost 0 13.049 * * [simplify]: Extracting # 5 : cost 0 13.052 * * [simplify]: Extracting # 6 : cost 0 13.055 * * [simplify]: iteration 1 : 997 enodes (cost 2438 ) 13.675 * * [simplify]: Extracting # 0 : cost 0 13.681 * * [simplify]: Extracting # 1 : cost 0 13.689 * * [simplify]: Extracting # 2 : cost 0 13.696 * * [simplify]: Extracting # 3 : cost 0 13.704 * * [simplify]: Extracting # 4 : cost 0 13.711 * * [simplify]: Extracting # 5 : cost 0 13.718 * * [simplify]: iteration 2 : 2716 enodes (cost 2342 ) 14.688 * * [simplify]: Extracting # 0 : cost 0 14.695 * * [simplify]: Extracting # 1 : cost 0 14.702 * * [simplify]: Extracting # 2 : cost 0 14.709 * * [simplify]: Extracting # 3 : cost 0 14.729 * * [simplify]: Extracting # 4 : cost 0 14.742 * * [simplify]: iteration done: 5002 enodes (cost 2342 ) 14.745 * [simplify]: Simplified to: (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (* 2.0 (* n PI)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* 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(sqrt 2))) (pow (* 2.0 (* n PI)) (/ (* (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* n PI)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* n PI)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* 2.0 (* n PI)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* 2.0 (* n PI)) (- 1.0 k)) (* 2.0 (* n PI)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 4)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (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)) (fabs (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)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (pow (* n PI) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* n PI) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* 2.0 (* n PI)) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (log n) 2) (pow (* 2.0 (* n PI)) 0.5)))) (- (+ (pow (* 2.0 (* n PI)) 0.5) (* (* (* 0.25 (pow k 2)) (* (pow (* 2.0 (* n PI)) 0.5) (log n))) (log (* 2.0 PI)))) (* (* 0.5 k) (+ (* (pow (* 2.0 (* n PI)) 0.5) (log (* 2.0 PI))) (* (pow (* 2.0 (* n PI)) 0.5) (log n)))))) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* (* (pow (* 2.0 (* n PI)) 0.25) (pow (log (* 2.0 PI)) 2)) (* 0.03125 (pow k 2))) (+ (+ (pow (* 2.0 (* n PI)) 0.25) (* (* (pow (* 2.0 (* n PI)) 0.25) (pow (log n) 2)) (* 0.03125 (pow k 2)))) (* (* (* (pow k 2) (log (* 2.0 PI))) (* (pow (* 2.0 (* n PI)) 0.25) (log n))) 0.0625))) (* (* 0.25 k) (+ (* (pow (* 2.0 (* n PI)) 0.25) (log n)) (* (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.25))))) (pow (pow (* 2.0 (* n PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (pow k 2))) (* n PI) (* n PI) (* n PI) 14.748 * * * [progress]: adding candidates to table 15.930 * * [progress]: iteration 4 / 4 15.930 * * * [progress]: picking best candidate 15.961 * * * * [pick]: Picked # 15.961 * * * [progress]: localizing error 16.020 * * * [progress]: generating rewritten candidates 16.020 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 16.214 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 16.270 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 2 2 1) 16.271 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2 1 2) 16.282 * * * [progress]: generating series expansions 16.283 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 16.283 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 16.283 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 16.283 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 16.283 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 16.283 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 16.283 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 16.283 * [taylor]: Taking taylor expansion of 0.5 in k 16.283 * [backup-simplify]: Simplify 0.5 into 0.5 16.283 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.283 * [taylor]: Taking taylor expansion of 1.0 in k 16.283 * [backup-simplify]: Simplify 1.0 into 1.0 16.283 * [taylor]: Taking taylor expansion of k in k 16.283 * [backup-simplify]: Simplify 0 into 0 16.283 * [backup-simplify]: Simplify 1 into 1 16.283 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 16.283 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 16.283 * [taylor]: Taking taylor expansion of 2.0 in k 16.283 * [backup-simplify]: Simplify 2.0 into 2.0 16.283 * [taylor]: Taking taylor expansion of (* n PI) in k 16.283 * [taylor]: Taking taylor expansion of n in k 16.283 * [backup-simplify]: Simplify n into n 16.283 * [taylor]: Taking taylor expansion of PI in k 16.283 * [backup-simplify]: Simplify PI into PI 16.283 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.283 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 16.284 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 16.284 * [backup-simplify]: Simplify (- 0) into 0 16.284 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.285 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 16.285 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 16.285 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 16.285 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 16.285 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.285 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.285 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.285 * [taylor]: Taking taylor expansion of 0.5 in n 16.285 * [backup-simplify]: Simplify 0.5 into 0.5 16.285 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.285 * [taylor]: Taking taylor expansion of 1.0 in n 16.285 * [backup-simplify]: Simplify 1.0 into 1.0 16.285 * [taylor]: Taking taylor expansion of k in n 16.285 * [backup-simplify]: Simplify k into k 16.285 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.285 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.285 * [taylor]: Taking taylor expansion of 2.0 in n 16.285 * [backup-simplify]: Simplify 2.0 into 2.0 16.285 * [taylor]: Taking taylor expansion of (* n PI) in n 16.285 * [taylor]: Taking taylor expansion of n in n 16.285 * [backup-simplify]: Simplify 0 into 0 16.285 * [backup-simplify]: Simplify 1 into 1 16.285 * [taylor]: Taking taylor expansion of PI in n 16.285 * [backup-simplify]: Simplify PI into PI 16.286 * [backup-simplify]: Simplify (* 0 PI) into 0 16.286 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.287 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.288 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.289 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.289 * [backup-simplify]: Simplify (- k) into (- k) 16.289 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.289 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.290 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.291 * [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)))) 16.292 * [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))))) 16.292 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 16.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.292 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.292 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.292 * [taylor]: Taking taylor expansion of 0.5 in n 16.292 * [backup-simplify]: Simplify 0.5 into 0.5 16.292 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.292 * [taylor]: Taking taylor expansion of 1.0 in n 16.292 * [backup-simplify]: Simplify 1.0 into 1.0 16.292 * [taylor]: Taking taylor expansion of k in n 16.292 * [backup-simplify]: Simplify k into k 16.292 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.292 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.292 * [taylor]: Taking taylor expansion of 2.0 in n 16.292 * [backup-simplify]: Simplify 2.0 into 2.0 16.292 * [taylor]: Taking taylor expansion of (* n PI) in n 16.292 * [taylor]: Taking taylor expansion of n in n 16.292 * [backup-simplify]: Simplify 0 into 0 16.292 * [backup-simplify]: Simplify 1 into 1 16.292 * [taylor]: Taking taylor expansion of PI in n 16.292 * [backup-simplify]: Simplify PI into PI 16.293 * [backup-simplify]: Simplify (* 0 PI) into 0 16.293 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.294 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.295 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.296 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.296 * [backup-simplify]: Simplify (- k) into (- k) 16.296 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.296 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.297 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.297 * [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)))) 16.298 * [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))))) 16.298 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 16.298 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 16.298 * [taylor]: Taking taylor expansion of 0.5 in k 16.298 * [backup-simplify]: Simplify 0.5 into 0.5 16.298 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 16.298 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.298 * [taylor]: Taking taylor expansion of 1.0 in k 16.298 * [backup-simplify]: Simplify 1.0 into 1.0 16.299 * [taylor]: Taking taylor expansion of k in k 16.299 * [backup-simplify]: Simplify 0 into 0 16.299 * [backup-simplify]: Simplify 1 into 1 16.299 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 16.299 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.299 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.299 * [taylor]: Taking taylor expansion of 2.0 in k 16.299 * [backup-simplify]: Simplify 2.0 into 2.0 16.299 * [taylor]: Taking taylor expansion of PI in k 16.299 * [backup-simplify]: Simplify PI into PI 16.299 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.300 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.300 * [taylor]: Taking taylor expansion of (log n) in k 16.300 * [taylor]: Taking taylor expansion of n in k 16.300 * [backup-simplify]: Simplify n into n 16.300 * [backup-simplify]: Simplify (log n) into (log n) 16.300 * [backup-simplify]: Simplify (- 0) into 0 16.300 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.301 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 16.302 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 16.303 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 16.304 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 16.304 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 16.305 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.306 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 16.307 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.307 * [backup-simplify]: Simplify (- 0) into 0 16.307 * [backup-simplify]: Simplify (+ 0 0) into 0 16.308 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 16.309 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.310 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 16.311 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.311 * [taylor]: Taking taylor expansion of 0 in k 16.311 * [backup-simplify]: Simplify 0 into 0 16.311 * [backup-simplify]: Simplify 0 into 0 16.311 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.313 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.313 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.313 * [backup-simplify]: Simplify (+ 0 0) into 0 16.314 * [backup-simplify]: Simplify (- 1) into -1 16.314 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.315 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 16.317 * [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)))) 16.319 * [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)))))) 16.321 * [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)))))) 16.322 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.323 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.325 * [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 16.325 * [backup-simplify]: Simplify (- 0) into 0 16.326 * [backup-simplify]: Simplify (+ 0 0) into 0 16.326 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.327 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.328 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.331 * [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 16.331 * [taylor]: Taking taylor expansion of 0 in k 16.331 * [backup-simplify]: Simplify 0 into 0 16.331 * [backup-simplify]: Simplify 0 into 0 16.331 * [backup-simplify]: Simplify 0 into 0 16.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.336 * [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 16.338 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.338 * [backup-simplify]: Simplify (+ 0 0) into 0 16.339 * [backup-simplify]: Simplify (- 0) into 0 16.339 * [backup-simplify]: Simplify (+ 0 0) into 0 16.341 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.344 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 16.349 * [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 (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 16.355 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 16.366 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 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 (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 16.367 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt (/ 1 n)) (cbrt (/ 1 n))) (* (cbrt (/ 1 n)) PI))) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 16.367 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 16.367 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 16.367 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 16.367 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 16.367 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 16.367 * [taylor]: Taking taylor expansion of 0.5 in k 16.367 * [backup-simplify]: Simplify 0.5 into 0.5 16.367 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.367 * [taylor]: Taking taylor expansion of 1.0 in k 16.367 * [backup-simplify]: Simplify 1.0 into 1.0 16.367 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.367 * [taylor]: Taking taylor expansion of k in k 16.367 * [backup-simplify]: Simplify 0 into 0 16.367 * [backup-simplify]: Simplify 1 into 1 16.368 * [backup-simplify]: Simplify (/ 1 1) into 1 16.368 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 16.368 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 16.368 * [taylor]: Taking taylor expansion of 2.0 in k 16.368 * [backup-simplify]: Simplify 2.0 into 2.0 16.368 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.368 * [taylor]: Taking taylor expansion of PI in k 16.368 * [backup-simplify]: Simplify PI into PI 16.368 * [taylor]: Taking taylor expansion of n in k 16.368 * [backup-simplify]: Simplify n into n 16.368 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.368 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 16.369 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 16.369 * [backup-simplify]: Simplify (- 1) into -1 16.369 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.370 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 16.370 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 16.370 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 16.370 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.370 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.371 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.371 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.371 * [taylor]: Taking taylor expansion of 0.5 in n 16.371 * [backup-simplify]: Simplify 0.5 into 0.5 16.371 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.371 * [taylor]: Taking taylor expansion of 1.0 in n 16.371 * [backup-simplify]: Simplify 1.0 into 1.0 16.371 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.371 * [taylor]: Taking taylor expansion of k in n 16.371 * [backup-simplify]: Simplify k into k 16.371 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.371 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.371 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.371 * [taylor]: Taking taylor expansion of 2.0 in n 16.371 * [backup-simplify]: Simplify 2.0 into 2.0 16.371 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.371 * [taylor]: Taking taylor expansion of PI in n 16.371 * [backup-simplify]: Simplify PI into PI 16.371 * [taylor]: Taking taylor expansion of n in n 16.371 * [backup-simplify]: Simplify 0 into 0 16.371 * [backup-simplify]: Simplify 1 into 1 16.372 * [backup-simplify]: Simplify (/ PI 1) into PI 16.372 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.374 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.374 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.374 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.374 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.376 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.377 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.378 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.378 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.378 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.378 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.378 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.378 * [taylor]: Taking taylor expansion of 0.5 in n 16.378 * [backup-simplify]: Simplify 0.5 into 0.5 16.378 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.379 * [taylor]: Taking taylor expansion of 1.0 in n 16.379 * [backup-simplify]: Simplify 1.0 into 1.0 16.379 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.379 * [taylor]: Taking taylor expansion of k in n 16.379 * [backup-simplify]: Simplify k into k 16.379 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.379 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.379 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.379 * [taylor]: Taking taylor expansion of 2.0 in n 16.379 * [backup-simplify]: Simplify 2.0 into 2.0 16.379 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.379 * [taylor]: Taking taylor expansion of PI in n 16.379 * [backup-simplify]: Simplify PI into PI 16.379 * [taylor]: Taking taylor expansion of n in n 16.379 * [backup-simplify]: Simplify 0 into 0 16.379 * [backup-simplify]: Simplify 1 into 1 16.380 * [backup-simplify]: Simplify (/ PI 1) into PI 16.380 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.381 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.381 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.381 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.381 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.384 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.385 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.385 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 16.385 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 16.385 * [taylor]: Taking taylor expansion of 0.5 in k 16.385 * [backup-simplify]: Simplify 0.5 into 0.5 16.385 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 16.385 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 16.386 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.386 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.386 * [taylor]: Taking taylor expansion of 2.0 in k 16.386 * [backup-simplify]: Simplify 2.0 into 2.0 16.386 * [taylor]: Taking taylor expansion of PI in k 16.386 * [backup-simplify]: Simplify PI into PI 16.386 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.387 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.387 * [taylor]: Taking taylor expansion of (log n) in k 16.387 * [taylor]: Taking taylor expansion of n in k 16.387 * [backup-simplify]: Simplify n into n 16.387 * [backup-simplify]: Simplify (log n) into (log n) 16.387 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.387 * [taylor]: Taking taylor expansion of 1.0 in k 16.387 * [backup-simplify]: Simplify 1.0 into 1.0 16.387 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.387 * [taylor]: Taking taylor expansion of k in k 16.387 * [backup-simplify]: Simplify 0 into 0 16.387 * [backup-simplify]: Simplify 1 into 1 16.387 * [backup-simplify]: Simplify (/ 1 1) into 1 16.387 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.388 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 16.388 * [backup-simplify]: Simplify (- 1) into -1 16.389 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.389 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 16.390 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 16.391 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.401 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.404 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.404 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.404 * [backup-simplify]: Simplify (- 0) into 0 16.404 * [backup-simplify]: Simplify (+ 0 0) into 0 16.405 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.406 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.406 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 16.408 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.408 * [taylor]: Taking taylor expansion of 0 in k 16.408 * [backup-simplify]: Simplify 0 into 0 16.408 * [backup-simplify]: Simplify 0 into 0 16.408 * [backup-simplify]: Simplify 0 into 0 16.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.409 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.411 * [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 16.411 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.412 * [backup-simplify]: Simplify (- 0) into 0 16.412 * [backup-simplify]: Simplify (+ 0 0) into 0 16.413 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.414 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.415 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 16.416 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.416 * [taylor]: Taking taylor expansion of 0 in k 16.416 * [backup-simplify]: Simplify 0 into 0 16.416 * [backup-simplify]: Simplify 0 into 0 16.416 * [backup-simplify]: Simplify 0 into 0 16.416 * [backup-simplify]: Simplify 0 into 0 16.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.419 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.427 * [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 16.427 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.428 * [backup-simplify]: Simplify (- 0) into 0 16.428 * [backup-simplify]: Simplify (+ 0 0) into 0 16.430 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.431 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.433 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 16.436 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.436 * [taylor]: Taking taylor expansion of 0 in k 16.437 * [backup-simplify]: Simplify 0 into 0 16.437 * [backup-simplify]: Simplify 0 into 0 16.438 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 16.439 * [backup-simplify]: Simplify (pow (* 2.0 (* (* (cbrt (/ 1 (- n))) (cbrt (/ 1 (- n)))) (* (cbrt (/ 1 (- n))) PI))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) 16.439 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 16.439 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 16.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 16.439 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 16.439 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 16.439 * [taylor]: Taking taylor expansion of 0.5 in k 16.439 * [backup-simplify]: Simplify 0.5 into 0.5 16.439 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.439 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.439 * [taylor]: Taking taylor expansion of k in k 16.439 * [backup-simplify]: Simplify 0 into 0 16.439 * [backup-simplify]: Simplify 1 into 1 16.440 * [backup-simplify]: Simplify (/ 1 1) into 1 16.440 * [taylor]: Taking taylor expansion of 1.0 in k 16.440 * [backup-simplify]: Simplify 1.0 into 1.0 16.440 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 16.440 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 16.440 * [taylor]: Taking taylor expansion of 2.0 in k 16.440 * [backup-simplify]: Simplify 2.0 into 2.0 16.440 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 16.440 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 16.440 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 16.440 * [taylor]: Taking taylor expansion of (cbrt -1) in k 16.440 * [taylor]: Taking taylor expansion of -1 in k 16.440 * [backup-simplify]: Simplify -1 into -1 16.441 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 16.442 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 16.442 * [taylor]: Taking taylor expansion of PI in k 16.442 * [backup-simplify]: Simplify PI into PI 16.442 * [taylor]: Taking taylor expansion of n in k 16.442 * [backup-simplify]: Simplify n into n 16.443 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 16.446 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 16.448 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 16.448 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 16.448 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 16.448 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 16.449 * [backup-simplify]: Simplify (+ 1 0) into 1 16.449 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 16.450 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 16.452 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 16.452 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 16.452 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 16.452 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 16.452 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 16.452 * [taylor]: Taking taylor expansion of 0.5 in n 16.452 * [backup-simplify]: Simplify 0.5 into 0.5 16.452 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.452 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.452 * [taylor]: Taking taylor expansion of k in n 16.452 * [backup-simplify]: Simplify k into k 16.452 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.452 * [taylor]: Taking taylor expansion of 1.0 in n 16.452 * [backup-simplify]: Simplify 1.0 into 1.0 16.452 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 16.452 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 16.452 * [taylor]: Taking taylor expansion of 2.0 in n 16.452 * [backup-simplify]: Simplify 2.0 into 2.0 16.452 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 16.452 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 16.453 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 16.453 * [taylor]: Taking taylor expansion of (cbrt -1) in n 16.453 * [taylor]: Taking taylor expansion of -1 in n 16.453 * [backup-simplify]: Simplify -1 into -1 16.453 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 16.453 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 16.453 * [taylor]: Taking taylor expansion of PI in n 16.453 * [backup-simplify]: Simplify PI into PI 16.454 * [taylor]: Taking taylor expansion of n in n 16.454 * [backup-simplify]: Simplify 0 into 0 16.454 * [backup-simplify]: Simplify 1 into 1 16.455 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 16.457 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 16.459 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 16.460 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 16.461 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 16.462 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.462 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.462 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 16.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.465 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 16.466 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.466 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 16.466 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 16.466 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 16.466 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 16.466 * [taylor]: Taking taylor expansion of 0.5 in n 16.466 * [backup-simplify]: Simplify 0.5 into 0.5 16.466 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.466 * [taylor]: Taking taylor expansion of k in n 16.467 * [backup-simplify]: Simplify k into k 16.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.467 * [taylor]: Taking taylor expansion of 1.0 in n 16.467 * [backup-simplify]: Simplify 1.0 into 1.0 16.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 16.467 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 16.467 * [taylor]: Taking taylor expansion of 2.0 in n 16.467 * [backup-simplify]: Simplify 2.0 into 2.0 16.467 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 16.467 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 16.467 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 16.467 * [taylor]: Taking taylor expansion of (cbrt -1) in n 16.467 * [taylor]: Taking taylor expansion of -1 in n 16.467 * [backup-simplify]: Simplify -1 into -1 16.467 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 16.468 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 16.468 * [taylor]: Taking taylor expansion of PI in n 16.468 * [backup-simplify]: Simplify PI into PI 16.468 * [taylor]: Taking taylor expansion of n in n 16.468 * [backup-simplify]: Simplify 0 into 0 16.468 * [backup-simplify]: Simplify 1 into 1 16.470 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 16.472 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 16.473 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 16.475 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 16.476 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 16.477 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.477 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.477 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 16.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.480 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 16.481 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.481 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 16.481 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 16.481 * [taylor]: Taking taylor expansion of 0.5 in k 16.481 * [backup-simplify]: Simplify 0.5 into 0.5 16.481 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 16.481 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.481 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.481 * [taylor]: Taking taylor expansion of k in k 16.481 * [backup-simplify]: Simplify 0 into 0 16.481 * [backup-simplify]: Simplify 1 into 1 16.482 * [backup-simplify]: Simplify (/ 1 1) into 1 16.482 * [taylor]: Taking taylor expansion of 1.0 in k 16.482 * [backup-simplify]: Simplify 1.0 into 1.0 16.482 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 16.482 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 16.482 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 16.482 * [taylor]: Taking taylor expansion of -2.0 in k 16.482 * [backup-simplify]: Simplify -2.0 into -2.0 16.482 * [taylor]: Taking taylor expansion of PI in k 16.482 * [backup-simplify]: Simplify PI into PI 16.483 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.484 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.484 * [taylor]: Taking taylor expansion of (log n) in k 16.484 * [taylor]: Taking taylor expansion of n in k 16.484 * [backup-simplify]: Simplify n into n 16.484 * [backup-simplify]: Simplify (log n) into (log n) 16.484 * [backup-simplify]: Simplify (+ 1 0) into 1 16.484 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.486 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 16.487 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 16.488 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 16.489 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.490 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.491 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 16.492 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 16.493 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 16.494 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 16.495 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 16.497 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 16.498 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.498 * [backup-simplify]: Simplify (+ 0 0) into 0 16.499 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 16.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.502 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 16.504 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.504 * [taylor]: Taking taylor expansion of 0 in k 16.504 * [backup-simplify]: Simplify 0 into 0 16.504 * [backup-simplify]: Simplify 0 into 0 16.504 * [backup-simplify]: Simplify 0 into 0 16.506 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 16.508 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 16.509 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 16.511 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 16.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.514 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 16.518 * [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 16.518 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.519 * [backup-simplify]: Simplify (+ 0 0) into 0 16.520 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 16.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.523 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 16.526 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.526 * [taylor]: Taking taylor expansion of 0 in k 16.526 * [backup-simplify]: Simplify 0 into 0 16.526 * [backup-simplify]: Simplify 0 into 0 16.526 * [backup-simplify]: Simplify 0 into 0 16.526 * [backup-simplify]: Simplify 0 into 0 16.528 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 16.529 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 16.530 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 16.531 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.532 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 16.536 * [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 16.536 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.536 * [backup-simplify]: Simplify (+ 0 0) into 0 16.537 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 16.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.546 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 16.548 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.548 * [taylor]: Taking taylor expansion of 0 in k 16.548 * [backup-simplify]: Simplify 0 into 0 16.548 * [backup-simplify]: Simplify 0 into 0 16.549 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 16.549 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 16.549 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 16.549 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 16.549 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 16.549 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 16.549 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 16.549 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 16.549 * [taylor]: Taking taylor expansion of 0.25 in k 16.549 * [backup-simplify]: Simplify 0.25 into 0.25 16.549 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.549 * [taylor]: Taking taylor expansion of 1.0 in k 16.549 * [backup-simplify]: Simplify 1.0 into 1.0 16.549 * [taylor]: Taking taylor expansion of k in k 16.549 * [backup-simplify]: Simplify 0 into 0 16.549 * [backup-simplify]: Simplify 1 into 1 16.549 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 16.549 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 16.549 * [taylor]: Taking taylor expansion of 2.0 in k 16.549 * [backup-simplify]: Simplify 2.0 into 2.0 16.549 * [taylor]: Taking taylor expansion of (* n PI) in k 16.550 * [taylor]: Taking taylor expansion of n in k 16.550 * [backup-simplify]: Simplify n into n 16.550 * [taylor]: Taking taylor expansion of PI in k 16.550 * [backup-simplify]: Simplify PI into PI 16.550 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.550 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 16.550 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 16.550 * [backup-simplify]: Simplify (- 0) into 0 16.550 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.551 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 16.551 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 16.551 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 16.551 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 16.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.551 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.551 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 16.551 * [taylor]: Taking taylor expansion of 0.25 in n 16.551 * [backup-simplify]: Simplify 0.25 into 0.25 16.551 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.551 * [taylor]: Taking taylor expansion of 1.0 in n 16.551 * [backup-simplify]: Simplify 1.0 into 1.0 16.551 * [taylor]: Taking taylor expansion of k in n 16.551 * [backup-simplify]: Simplify k into k 16.551 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.551 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.551 * [taylor]: Taking taylor expansion of 2.0 in n 16.551 * [backup-simplify]: Simplify 2.0 into 2.0 16.551 * [taylor]: Taking taylor expansion of (* n PI) in n 16.551 * [taylor]: Taking taylor expansion of n in n 16.551 * [backup-simplify]: Simplify 0 into 0 16.551 * [backup-simplify]: Simplify 1 into 1 16.551 * [taylor]: Taking taylor expansion of PI in n 16.551 * [backup-simplify]: Simplify PI into PI 16.551 * [backup-simplify]: Simplify (* 0 PI) into 0 16.552 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.553 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.554 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.555 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.555 * [backup-simplify]: Simplify (- k) into (- k) 16.555 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.555 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 16.556 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.556 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 16.557 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 16.557 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 16.557 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.557 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.557 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 16.557 * [taylor]: Taking taylor expansion of 0.25 in n 16.557 * [backup-simplify]: Simplify 0.25 into 0.25 16.557 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.557 * [taylor]: Taking taylor expansion of 1.0 in n 16.557 * [backup-simplify]: Simplify 1.0 into 1.0 16.557 * [taylor]: Taking taylor expansion of k in n 16.557 * [backup-simplify]: Simplify k into k 16.557 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.557 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.557 * [taylor]: Taking taylor expansion of 2.0 in n 16.557 * [backup-simplify]: Simplify 2.0 into 2.0 16.557 * [taylor]: Taking taylor expansion of (* n PI) in n 16.558 * [taylor]: Taking taylor expansion of n in n 16.558 * [backup-simplify]: Simplify 0 into 0 16.558 * [backup-simplify]: Simplify 1 into 1 16.558 * [taylor]: Taking taylor expansion of PI in n 16.558 * [backup-simplify]: Simplify PI into PI 16.558 * [backup-simplify]: Simplify (* 0 PI) into 0 16.558 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.559 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.560 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.561 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.561 * [backup-simplify]: Simplify (- k) into (- k) 16.561 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.561 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 16.562 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.563 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 16.564 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 16.564 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 16.564 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 16.564 * [taylor]: Taking taylor expansion of 0.25 in k 16.564 * [backup-simplify]: Simplify 0.25 into 0.25 16.564 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 16.564 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.564 * [taylor]: Taking taylor expansion of 1.0 in k 16.564 * [backup-simplify]: Simplify 1.0 into 1.0 16.564 * [taylor]: Taking taylor expansion of k in k 16.564 * [backup-simplify]: Simplify 0 into 0 16.564 * [backup-simplify]: Simplify 1 into 1 16.564 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 16.564 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.564 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.564 * [taylor]: Taking taylor expansion of 2.0 in k 16.564 * [backup-simplify]: Simplify 2.0 into 2.0 16.564 * [taylor]: Taking taylor expansion of PI in k 16.564 * [backup-simplify]: Simplify PI into PI 16.565 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.565 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.565 * [taylor]: Taking taylor expansion of (log n) in k 16.565 * [taylor]: Taking taylor expansion of n in k 16.565 * [backup-simplify]: Simplify n into n 16.565 * [backup-simplify]: Simplify (log n) into (log n) 16.566 * [backup-simplify]: Simplify (- 0) into 0 16.566 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.567 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 16.567 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 16.568 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 16.569 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 16.570 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 16.570 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.571 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 16.572 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.572 * [backup-simplify]: Simplify (- 0) into 0 16.573 * [backup-simplify]: Simplify (+ 0 0) into 0 16.573 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 16.574 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.575 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 16.576 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.576 * [taylor]: Taking taylor expansion of 0 in k 16.576 * [backup-simplify]: Simplify 0 into 0 16.576 * [backup-simplify]: Simplify 0 into 0 16.577 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.578 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.579 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.579 * [backup-simplify]: Simplify (+ 0 0) into 0 16.579 * [backup-simplify]: Simplify (- 1) into -1 16.579 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.581 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 16.582 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 16.584 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 16.586 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 16.587 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.588 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.590 * [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 16.591 * [backup-simplify]: Simplify (- 0) into 0 16.591 * [backup-simplify]: Simplify (+ 0 0) into 0 16.592 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.594 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.596 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.596 * [taylor]: Taking taylor expansion of 0 in k 16.596 * [backup-simplify]: Simplify 0 into 0 16.596 * [backup-simplify]: Simplify 0 into 0 16.596 * [backup-simplify]: Simplify 0 into 0 16.597 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.599 * [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 16.601 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.601 * [backup-simplify]: Simplify (+ 0 0) into 0 16.601 * [backup-simplify]: Simplify (- 0) into 0 16.601 * [backup-simplify]: Simplify (+ 0 0) into 0 16.603 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.604 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 16.607 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 16.610 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 16.617 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 16.618 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 16.618 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 16.618 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 16.618 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 16.618 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 16.618 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 16.618 * [taylor]: Taking taylor expansion of 0.25 in k 16.618 * [backup-simplify]: Simplify 0.25 into 0.25 16.618 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.618 * [taylor]: Taking taylor expansion of 1.0 in k 16.618 * [backup-simplify]: Simplify 1.0 into 1.0 16.618 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.618 * [taylor]: Taking taylor expansion of k in k 16.618 * [backup-simplify]: Simplify 0 into 0 16.618 * [backup-simplify]: Simplify 1 into 1 16.619 * [backup-simplify]: Simplify (/ 1 1) into 1 16.619 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 16.619 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 16.619 * [taylor]: Taking taylor expansion of 2.0 in k 16.619 * [backup-simplify]: Simplify 2.0 into 2.0 16.619 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.619 * [taylor]: Taking taylor expansion of PI in k 16.619 * [backup-simplify]: Simplify PI into PI 16.619 * [taylor]: Taking taylor expansion of n in k 16.619 * [backup-simplify]: Simplify n into n 16.619 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.619 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 16.619 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 16.619 * [backup-simplify]: Simplify (- 1) into -1 16.619 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.620 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 16.620 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 16.620 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 16.620 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 16.620 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.620 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.620 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 16.620 * [taylor]: Taking taylor expansion of 0.25 in n 16.620 * [backup-simplify]: Simplify 0.25 into 0.25 16.620 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.620 * [taylor]: Taking taylor expansion of 1.0 in n 16.620 * [backup-simplify]: Simplify 1.0 into 1.0 16.620 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.620 * [taylor]: Taking taylor expansion of k in n 16.620 * [backup-simplify]: Simplify k into k 16.620 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.620 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.620 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.620 * [taylor]: Taking taylor expansion of 2.0 in n 16.620 * [backup-simplify]: Simplify 2.0 into 2.0 16.620 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.620 * [taylor]: Taking taylor expansion of PI in n 16.620 * [backup-simplify]: Simplify PI into PI 16.620 * [taylor]: Taking taylor expansion of n in n 16.620 * [backup-simplify]: Simplify 0 into 0 16.620 * [backup-simplify]: Simplify 1 into 1 16.621 * [backup-simplify]: Simplify (/ PI 1) into PI 16.621 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.622 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.622 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.622 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.622 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 16.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.624 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.625 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.625 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 16.625 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.625 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.625 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 16.625 * [taylor]: Taking taylor expansion of 0.25 in n 16.625 * [backup-simplify]: Simplify 0.25 into 0.25 16.625 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.625 * [taylor]: Taking taylor expansion of 1.0 in n 16.625 * [backup-simplify]: Simplify 1.0 into 1.0 16.625 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.625 * [taylor]: Taking taylor expansion of k in n 16.625 * [backup-simplify]: Simplify k into k 16.625 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.625 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.625 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.625 * [taylor]: Taking taylor expansion of 2.0 in n 16.625 * [backup-simplify]: Simplify 2.0 into 2.0 16.625 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.625 * [taylor]: Taking taylor expansion of PI in n 16.625 * [backup-simplify]: Simplify PI into PI 16.625 * [taylor]: Taking taylor expansion of n in n 16.625 * [backup-simplify]: Simplify 0 into 0 16.625 * [backup-simplify]: Simplify 1 into 1 16.626 * [backup-simplify]: Simplify (/ PI 1) into PI 16.626 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.627 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.627 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.627 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.627 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 16.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.629 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.630 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.630 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 16.630 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 16.630 * [taylor]: Taking taylor expansion of 0.25 in k 16.630 * [backup-simplify]: Simplify 0.25 into 0.25 16.630 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 16.630 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 16.630 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.630 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.630 * [taylor]: Taking taylor expansion of 2.0 in k 16.630 * [backup-simplify]: Simplify 2.0 into 2.0 16.630 * [taylor]: Taking taylor expansion of PI in k 16.630 * [backup-simplify]: Simplify PI into PI 16.630 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.631 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.631 * [taylor]: Taking taylor expansion of (log n) in k 16.631 * [taylor]: Taking taylor expansion of n in k 16.631 * [backup-simplify]: Simplify n into n 16.631 * [backup-simplify]: Simplify (log n) into (log n) 16.631 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.631 * [taylor]: Taking taylor expansion of 1.0 in k 16.631 * [backup-simplify]: Simplify 1.0 into 1.0 16.631 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.631 * [taylor]: Taking taylor expansion of k in k 16.631 * [backup-simplify]: Simplify 0 into 0 16.631 * [backup-simplify]: Simplify 1 into 1 16.632 * [backup-simplify]: Simplify (/ 1 1) into 1 16.632 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.633 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 16.633 * [backup-simplify]: Simplify (- 1) into -1 16.633 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.635 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 16.636 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 16.637 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.639 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.641 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.643 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.643 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.643 * [backup-simplify]: Simplify (- 0) into 0 16.644 * [backup-simplify]: Simplify (+ 0 0) into 0 16.645 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.647 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 16.650 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.650 * [taylor]: Taking taylor expansion of 0 in k 16.650 * [backup-simplify]: Simplify 0 into 0 16.650 * [backup-simplify]: Simplify 0 into 0 16.650 * [backup-simplify]: Simplify 0 into 0 16.651 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.660 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.663 * [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 16.663 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.663 * [backup-simplify]: Simplify (- 0) into 0 16.663 * [backup-simplify]: Simplify (+ 0 0) into 0 16.664 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.665 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.666 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 16.668 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.668 * [taylor]: Taking taylor expansion of 0 in k 16.668 * [backup-simplify]: Simplify 0 into 0 16.668 * [backup-simplify]: Simplify 0 into 0 16.668 * [backup-simplify]: Simplify 0 into 0 16.668 * [backup-simplify]: Simplify 0 into 0 16.668 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.673 * [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 16.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.673 * [backup-simplify]: Simplify (- 0) into 0 16.673 * [backup-simplify]: Simplify (+ 0 0) into 0 16.674 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.676 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 16.678 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.678 * [taylor]: Taking taylor expansion of 0 in k 16.678 * [backup-simplify]: Simplify 0 into 0 16.678 * [backup-simplify]: Simplify 0 into 0 16.679 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 16.680 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 16.680 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 16.680 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 16.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 16.680 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 16.680 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 16.680 * [taylor]: Taking taylor expansion of 0.25 in k 16.680 * [backup-simplify]: Simplify 0.25 into 0.25 16.680 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.680 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.680 * [taylor]: Taking taylor expansion of k in k 16.680 * [backup-simplify]: Simplify 0 into 0 16.680 * [backup-simplify]: Simplify 1 into 1 16.680 * [backup-simplify]: Simplify (/ 1 1) into 1 16.680 * [taylor]: Taking taylor expansion of 1.0 in k 16.680 * [backup-simplify]: Simplify 1.0 into 1.0 16.680 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 16.680 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 16.680 * [taylor]: Taking taylor expansion of -2.0 in k 16.680 * [backup-simplify]: Simplify -2.0 into -2.0 16.680 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.680 * [taylor]: Taking taylor expansion of PI in k 16.680 * [backup-simplify]: Simplify PI into PI 16.680 * [taylor]: Taking taylor expansion of n in k 16.680 * [backup-simplify]: Simplify n into n 16.680 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.680 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 16.681 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 16.681 * [backup-simplify]: Simplify (+ 1 0) into 1 16.681 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 16.681 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 16.681 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 16.681 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 16.681 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 16.681 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 16.681 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 16.681 * [taylor]: Taking taylor expansion of 0.25 in n 16.681 * [backup-simplify]: Simplify 0.25 into 0.25 16.681 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.682 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.682 * [taylor]: Taking taylor expansion of k in n 16.682 * [backup-simplify]: Simplify k into k 16.682 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.682 * [taylor]: Taking taylor expansion of 1.0 in n 16.682 * [backup-simplify]: Simplify 1.0 into 1.0 16.682 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 16.682 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 16.682 * [taylor]: Taking taylor expansion of -2.0 in n 16.682 * [backup-simplify]: Simplify -2.0 into -2.0 16.682 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.682 * [taylor]: Taking taylor expansion of PI in n 16.682 * [backup-simplify]: Simplify PI into PI 16.682 * [taylor]: Taking taylor expansion of n in n 16.682 * [backup-simplify]: Simplify 0 into 0 16.682 * [backup-simplify]: Simplify 1 into 1 16.682 * [backup-simplify]: Simplify (/ PI 1) into PI 16.682 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.683 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.683 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.683 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 16.684 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.685 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 16.686 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.686 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 16.686 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 16.686 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 16.686 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 16.686 * [taylor]: Taking taylor expansion of 0.25 in n 16.686 * [backup-simplify]: Simplify 0.25 into 0.25 16.686 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.686 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.686 * [taylor]: Taking taylor expansion of k in n 16.686 * [backup-simplify]: Simplify k into k 16.686 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.686 * [taylor]: Taking taylor expansion of 1.0 in n 16.686 * [backup-simplify]: Simplify 1.0 into 1.0 16.686 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 16.686 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 16.686 * [taylor]: Taking taylor expansion of -2.0 in n 16.686 * [backup-simplify]: Simplify -2.0 into -2.0 16.686 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.686 * [taylor]: Taking taylor expansion of PI in n 16.686 * [backup-simplify]: Simplify PI into PI 16.686 * [taylor]: Taking taylor expansion of n in n 16.686 * [backup-simplify]: Simplify 0 into 0 16.686 * [backup-simplify]: Simplify 1 into 1 16.687 * [backup-simplify]: Simplify (/ PI 1) into PI 16.687 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.688 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.688 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.688 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 16.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.690 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 16.692 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.692 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 16.692 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 16.692 * [taylor]: Taking taylor expansion of 0.25 in k 16.692 * [backup-simplify]: Simplify 0.25 into 0.25 16.692 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 16.692 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.692 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.692 * [taylor]: Taking taylor expansion of k in k 16.692 * [backup-simplify]: Simplify 0 into 0 16.692 * [backup-simplify]: Simplify 1 into 1 16.693 * [backup-simplify]: Simplify (/ 1 1) into 1 16.693 * [taylor]: Taking taylor expansion of 1.0 in k 16.693 * [backup-simplify]: Simplify 1.0 into 1.0 16.693 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 16.693 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 16.693 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 16.693 * [taylor]: Taking taylor expansion of -2.0 in k 16.693 * [backup-simplify]: Simplify -2.0 into -2.0 16.693 * [taylor]: Taking taylor expansion of PI in k 16.693 * [backup-simplify]: Simplify PI into PI 16.693 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 16.695 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 16.695 * [taylor]: Taking taylor expansion of (log n) in k 16.695 * [taylor]: Taking taylor expansion of n in k 16.695 * [backup-simplify]: Simplify n into n 16.695 * [backup-simplify]: Simplify (log n) into (log n) 16.695 * [backup-simplify]: Simplify (+ 1 0) into 1 16.695 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.697 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 16.698 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 16.699 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 16.700 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.701 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 16.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.703 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 16.705 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 16.705 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.706 * [backup-simplify]: Simplify (+ 0 0) into 0 16.706 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 16.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.709 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 16.711 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.711 * [taylor]: Taking taylor expansion of 0 in k 16.711 * [backup-simplify]: Simplify 0 into 0 16.712 * [backup-simplify]: Simplify 0 into 0 16.712 * [backup-simplify]: Simplify 0 into 0 16.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.714 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.718 * [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 16.718 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.719 * [backup-simplify]: Simplify (+ 0 0) into 0 16.720 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 16.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.723 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 16.726 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.726 * [taylor]: Taking taylor expansion of 0 in k 16.726 * [backup-simplify]: Simplify 0 into 0 16.726 * [backup-simplify]: Simplify 0 into 0 16.726 * [backup-simplify]: Simplify 0 into 0 16.726 * [backup-simplify]: Simplify 0 into 0 16.727 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.729 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.735 * [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 16.735 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.736 * [backup-simplify]: Simplify (+ 0 0) into 0 16.737 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 16.739 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 16.741 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 16.744 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.744 * [taylor]: Taking taylor expansion of 0 in k 16.744 * [backup-simplify]: Simplify 0 into 0 16.745 * [backup-simplify]: Simplify 0 into 0 16.746 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 16.746 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 2 2 1) 16.746 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 16.746 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 16.746 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 16.746 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 16.746 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 16.746 * [taylor]: Taking taylor expansion of 1/3 in n 16.747 * [backup-simplify]: Simplify 1/3 into 1/3 16.747 * [taylor]: Taking taylor expansion of (log n) in n 16.747 * [taylor]: Taking taylor expansion of n in n 16.747 * [backup-simplify]: Simplify 0 into 0 16.747 * [backup-simplify]: Simplify 1 into 1 16.747 * [backup-simplify]: Simplify (log 1) into 0 16.748 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.748 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 16.748 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 16.748 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 16.748 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 16.748 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 16.748 * [taylor]: Taking taylor expansion of 1/3 in n 16.748 * [backup-simplify]: Simplify 1/3 into 1/3 16.748 * [taylor]: Taking taylor expansion of (log n) in n 16.748 * [taylor]: Taking taylor expansion of n in n 16.748 * [backup-simplify]: Simplify 0 into 0 16.748 * [backup-simplify]: Simplify 1 into 1 16.749 * [backup-simplify]: Simplify (log 1) into 0 16.749 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.749 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 16.749 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 16.750 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 16.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 16.751 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.752 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 16.753 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 16.753 * [backup-simplify]: Simplify 0 into 0 16.756 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 16.756 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.758 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 16.759 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.759 * [backup-simplify]: Simplify 0 into 0 16.764 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 16.765 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.766 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 16.768 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.768 * [backup-simplify]: Simplify 0 into 0 16.778 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 16.779 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.780 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 16.783 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.783 * [backup-simplify]: Simplify 0 into 0 16.808 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 16.809 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.812 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 16.816 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.816 * [backup-simplify]: Simplify 0 into 0 16.851 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 16.851 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 16.854 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 16.860 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.860 * [backup-simplify]: Simplify 0 into 0 16.860 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 16.861 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 16.861 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 16.861 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 16.861 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 16.861 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 16.861 * [taylor]: Taking taylor expansion of 1/3 in n 16.861 * [backup-simplify]: Simplify 1/3 into 1/3 16.861 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 16.861 * [taylor]: Taking taylor expansion of (/ 1 n) in n 16.861 * [taylor]: Taking taylor expansion of n in n 16.861 * [backup-simplify]: Simplify 0 into 0 16.861 * [backup-simplify]: Simplify 1 into 1 16.862 * [backup-simplify]: Simplify (/ 1 1) into 1 16.862 * [backup-simplify]: Simplify (log 1) into 0 16.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.863 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 16.863 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 16.863 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 16.863 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 16.863 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 16.863 * [taylor]: Taking taylor expansion of 1/3 in n 16.863 * [backup-simplify]: Simplify 1/3 into 1/3 16.863 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 16.863 * [taylor]: Taking taylor expansion of (/ 1 n) in n 16.863 * [taylor]: Taking taylor expansion of n in n 16.863 * [backup-simplify]: Simplify 0 into 0 16.863 * [backup-simplify]: Simplify 1 into 1 16.864 * [backup-simplify]: Simplify (/ 1 1) into 1 16.864 * [backup-simplify]: Simplify (log 1) into 0 16.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.865 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 16.865 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 16.865 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 16.866 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 16.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 16.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.868 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 16.869 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 16.870 * [backup-simplify]: Simplify 0 into 0 16.871 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.874 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 16.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.876 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 16.878 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.878 * [backup-simplify]: Simplify 0 into 0 16.879 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.885 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 16.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.887 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 16.889 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.890 * [backup-simplify]: Simplify 0 into 0 16.891 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.903 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 16.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.905 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 16.908 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.908 * [backup-simplify]: Simplify 0 into 0 16.909 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.927 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 16.928 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.930 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 16.934 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.934 * [backup-simplify]: Simplify 0 into 0 16.935 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.969 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 16.970 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.982 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 16.989 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.989 * [backup-simplify]: Simplify 0 into 0 16.989 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 16.989 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 16.990 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 16.990 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 16.990 * [taylor]: Taking taylor expansion of (cbrt -1) in n 16.990 * [taylor]: Taking taylor expansion of -1 in n 16.990 * [backup-simplify]: Simplify -1 into -1 16.990 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 16.991 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 16.991 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 16.991 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 16.991 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 16.991 * [taylor]: Taking taylor expansion of 1/3 in n 16.991 * [backup-simplify]: Simplify 1/3 into 1/3 16.991 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 16.991 * [taylor]: Taking taylor expansion of (/ 1 n) in n 16.991 * [taylor]: Taking taylor expansion of n in n 16.992 * [backup-simplify]: Simplify 0 into 0 16.992 * [backup-simplify]: Simplify 1 into 1 16.992 * [backup-simplify]: Simplify (/ 1 1) into 1 16.992 * [backup-simplify]: Simplify (log 1) into 0 16.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.993 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 16.993 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 16.993 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 16.993 * [taylor]: Taking taylor expansion of (cbrt -1) in n 16.993 * [taylor]: Taking taylor expansion of -1 in n 16.993 * [backup-simplify]: Simplify -1 into -1 16.993 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 16.994 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 16.994 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 16.994 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 16.994 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 16.994 * [taylor]: Taking taylor expansion of 1/3 in n 16.994 * [backup-simplify]: Simplify 1/3 into 1/3 16.994 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 16.994 * [taylor]: Taking taylor expansion of (/ 1 n) in n 16.994 * [taylor]: Taking taylor expansion of n in n 16.994 * [backup-simplify]: Simplify 0 into 0 16.994 * [backup-simplify]: Simplify 1 into 1 16.994 * [backup-simplify]: Simplify (/ 1 1) into 1 16.995 * [backup-simplify]: Simplify (log 1) into 0 16.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.995 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 16.995 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 16.996 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 16.996 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 16.997 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 16.997 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 16.998 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 16.998 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 16.999 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 16.999 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 16.999 * [backup-simplify]: Simplify 0 into 0 17.000 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.001 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.002 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.002 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.003 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.004 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.005 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 17.005 * [backup-simplify]: Simplify 0 into 0 17.006 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.010 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 17.010 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.011 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.012 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.013 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.014 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 17.014 * [backup-simplify]: Simplify 0 into 0 17.015 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.021 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.021 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.023 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.024 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.026 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.027 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 17.027 * [backup-simplify]: Simplify 0 into 0 17.028 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.039 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.040 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.042 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.046 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.048 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.050 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 17.050 * [backup-simplify]: Simplify 0 into 0 17.052 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.084 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.085 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.088 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 17.095 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.098 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.101 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 17.102 * [backup-simplify]: Simplify 0 into 0 17.102 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 17.102 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2 1 2) 17.102 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 17.103 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 17.103 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 17.103 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 17.103 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 17.103 * [taylor]: Taking taylor expansion of 1/3 in n 17.103 * [backup-simplify]: Simplify 1/3 into 1/3 17.103 * [taylor]: Taking taylor expansion of (log n) in n 17.103 * [taylor]: Taking taylor expansion of n in n 17.103 * [backup-simplify]: Simplify 0 into 0 17.103 * [backup-simplify]: Simplify 1 into 1 17.103 * [backup-simplify]: Simplify (log 1) into 0 17.104 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.104 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 17.104 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 17.104 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 17.104 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 17.104 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 17.104 * [taylor]: Taking taylor expansion of 1/3 in n 17.104 * [backup-simplify]: Simplify 1/3 into 1/3 17.104 * [taylor]: Taking taylor expansion of (log n) in n 17.104 * [taylor]: Taking taylor expansion of n in n 17.104 * [backup-simplify]: Simplify 0 into 0 17.104 * [backup-simplify]: Simplify 1 into 1 17.105 * [backup-simplify]: Simplify (log 1) into 0 17.105 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.105 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 17.105 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 17.106 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 17.107 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.108 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.108 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 17.109 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.109 * [backup-simplify]: Simplify 0 into 0 17.112 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.122 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.123 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 17.125 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.125 * [backup-simplify]: Simplify 0 into 0 17.131 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 17.131 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.133 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 17.135 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.135 * [backup-simplify]: Simplify 0 into 0 17.147 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.147 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.149 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 17.152 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.152 * [backup-simplify]: Simplify 0 into 0 17.171 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.172 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.174 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 17.178 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.178 * [backup-simplify]: Simplify 0 into 0 17.196 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.197 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 17.199 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 17.202 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.202 * [backup-simplify]: Simplify 0 into 0 17.202 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 17.202 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 17.202 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 17.202 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.202 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.202 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.202 * [taylor]: Taking taylor expansion of 1/3 in n 17.202 * [backup-simplify]: Simplify 1/3 into 1/3 17.203 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.203 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.203 * [taylor]: Taking taylor expansion of n in n 17.203 * [backup-simplify]: Simplify 0 into 0 17.203 * [backup-simplify]: Simplify 1 into 1 17.203 * [backup-simplify]: Simplify (/ 1 1) into 1 17.203 * [backup-simplify]: Simplify (log 1) into 0 17.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.204 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.204 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.204 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.204 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.204 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.204 * [taylor]: Taking taylor expansion of 1/3 in n 17.204 * [backup-simplify]: Simplify 1/3 into 1/3 17.204 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.204 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.204 * [taylor]: Taking taylor expansion of n in n 17.204 * [backup-simplify]: Simplify 0 into 0 17.204 * [backup-simplify]: Simplify 1 into 1 17.204 * [backup-simplify]: Simplify (/ 1 1) into 1 17.205 * [backup-simplify]: Simplify (log 1) into 0 17.205 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.205 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.205 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.205 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 17.206 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.207 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.207 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 17.208 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.208 * [backup-simplify]: Simplify 0 into 0 17.209 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.212 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.212 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.213 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.215 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.215 * [backup-simplify]: Simplify 0 into 0 17.216 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.222 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 17.223 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.224 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.227 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.227 * [backup-simplify]: Simplify 0 into 0 17.228 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.239 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.241 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.243 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.243 * [backup-simplify]: Simplify 0 into 0 17.244 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.260 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.261 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.262 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.264 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.264 * [backup-simplify]: Simplify 0 into 0 17.265 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.293 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.294 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.297 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 17.304 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.304 * [backup-simplify]: Simplify 0 into 0 17.304 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 17.305 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.305 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 17.305 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 17.305 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.305 * [taylor]: Taking taylor expansion of -1 in n 17.305 * [backup-simplify]: Simplify -1 into -1 17.306 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.307 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.307 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.307 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.307 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.307 * [taylor]: Taking taylor expansion of 1/3 in n 17.307 * [backup-simplify]: Simplify 1/3 into 1/3 17.307 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.307 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.307 * [taylor]: Taking taylor expansion of n in n 17.307 * [backup-simplify]: Simplify 0 into 0 17.307 * [backup-simplify]: Simplify 1 into 1 17.308 * [backup-simplify]: Simplify (/ 1 1) into 1 17.308 * [backup-simplify]: Simplify (log 1) into 0 17.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.309 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.309 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.309 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 17.309 * [taylor]: Taking taylor expansion of (cbrt -1) in n 17.309 * [taylor]: Taking taylor expansion of -1 in n 17.309 * [backup-simplify]: Simplify -1 into -1 17.309 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 17.310 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 17.310 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 17.310 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 17.310 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 17.310 * [taylor]: Taking taylor expansion of 1/3 in n 17.310 * [backup-simplify]: Simplify 1/3 into 1/3 17.310 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 17.310 * [taylor]: Taking taylor expansion of (/ 1 n) in n 17.310 * [taylor]: Taking taylor expansion of n in n 17.311 * [backup-simplify]: Simplify 0 into 0 17.311 * [backup-simplify]: Simplify 1 into 1 17.311 * [backup-simplify]: Simplify (/ 1 1) into 1 17.311 * [backup-simplify]: Simplify (log 1) into 0 17.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.312 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 17.312 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 17.313 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.314 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 17.315 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.316 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 17.317 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.317 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 17.318 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 17.319 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 17.319 * [backup-simplify]: Simplify 0 into 0 17.320 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.322 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 17.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.323 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 17.324 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.325 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.325 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 17.325 * [backup-simplify]: Simplify 0 into 0 17.326 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.329 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 17.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.330 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 17.331 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.332 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.333 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 17.333 * [backup-simplify]: Simplify 0 into 0 17.334 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.340 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 17.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.341 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 17.343 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.344 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.345 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 17.345 * [backup-simplify]: Simplify 0 into 0 17.346 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.363 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 17.363 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.365 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 17.370 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.371 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 17.374 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 17.374 * [backup-simplify]: Simplify 0 into 0 17.375 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.400 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 17.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 17.403 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 17.407 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.409 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 17.412 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 17.412 * [backup-simplify]: Simplify 0 into 0 17.413 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 17.413 * * * [progress]: simplifying candidates 17.418 * [simplify]: Simplifying: (* (+ (log 2.0) (+ (+ (log (cbrt n)) (log (cbrt n))) (+ (log (cbrt n)) (log PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (+ (log (cbrt n)) (log (cbrt n))) (log (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* (cbrt n) (cbrt n))) (+ (log (cbrt n)) (log PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (+ (log (* (cbrt n) (cbrt n))) (log (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 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 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1.0 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ k 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ 1 1)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) 1) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI)) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (* (cbrt n) (cbrt n))) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) (cbrt 1) (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) (* (* (cbrt n) (cbrt n)) (cbrt n)) (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 17.427 * * [simplify]: Extracting # 0 : cost 0 17.427 * * [simplify]: Extracting # 1 : cost 0 17.428 * * [simplify]: Extracting # 2 : cost 0 17.429 * * [simplify]: Extracting # 3 : cost 0 17.430 * * [simplify]: Extracting # 4 : cost 0 17.431 * * [simplify]: Extracting # 5 : cost 0 17.432 * * [simplify]: Extracting # 6 : cost 0 17.433 * * [simplify]: Extracting # 7 : cost 0 17.434 * * [simplify]: Extracting # 8 : cost 0 17.435 * * [simplify]: Extracting # 9 : cost 0 17.435 * * [simplify]: Extracting # 10 : cost 0 17.436 * * [simplify]: Extracting # 11 : cost 0 17.437 * * [simplify]: Extracting # 12 : cost 0 17.438 * * [simplify]: iteration 0 : 317 enodes (cost 2608 ) 17.584 * * [simplify]: Extracting # 0 : cost 0 17.587 * * [simplify]: Extracting # 1 : cost 0 17.589 * * [simplify]: Extracting # 2 : cost 0 17.592 * * [simplify]: Extracting # 3 : cost 0 17.595 * * [simplify]: Extracting # 4 : cost 0 17.597 * * [simplify]: Extracting # 5 : cost 0 17.599 * * [simplify]: iteration 1 : 847 enodes (cost 2419 ) 18.155 * * [simplify]: Extracting # 0 : cost 0 18.161 * * [simplify]: Extracting # 1 : cost 0 18.168 * * [simplify]: Extracting # 2 : cost 0 18.176 * * [simplify]: Extracting # 3 : cost 0 18.182 * * [simplify]: Extracting # 4 : cost 0 18.189 * * [simplify]: Extracting # 5 : cost 0 18.197 * * [simplify]: iteration 2 : 2475 enodes (cost 2180 ) 19.189 * * [simplify]: Extracting # 0 : cost 0 19.203 * * [simplify]: Extracting # 1 : cost 0 19.217 * * [simplify]: Extracting # 2 : cost 0 19.230 * * [simplify]: Extracting # 3 : cost 0 19.253 * * [simplify]: Extracting # 4 : cost 0 19.266 * * [simplify]: iteration done: 5000 enodes (cost 2057 ) 19.268 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n (* 2.0 PI)) (/ 1.0 2.0)) (pow (* n (* 2.0 PI)) (/ k 2.0)) (pow (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n (* 2.0 PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* PI n) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* n (* 2.0 PI)) (/ (- 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 (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* n (* 2.0 PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (pow (* n (* 2.0 PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* n (* 2.0 PI)) (/ (/ 1.0 2.0) 2)) (pow (* n (* 2.0 PI)) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (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))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (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)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* n (* 2.0 PI)) (- 1.0 k)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* n (* 2.0 PI)) (* (/ (- 1.0 k) 2.0) 1/2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) (log (cbrt n)) (exp (cbrt n)) (cbrt (pow n 2/3)) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (pow n 2/3)) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (- (+ (+ (pow (* (* 2.0 PI) n) 0.5) (* (* (log n) (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)))) (* 0.25 (pow k 2)))) (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5))))) (* (* 0.5 k) (+ (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (+ (+ (* (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.25)) (* 0.03125 (pow k 2))) (pow (* (* 2.0 PI) n) 0.25)) (* (* (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (* 2.0 PI) n) 0.25)) (log n)) 0.0625)) (* (* (pow (* (* 2.0 PI) n) 0.25) (pow (log n) 2)) (* 0.03125 (pow k 2)))) (* (* 0.25 k) (+ (* (log n) (pow (* (* 2.0 PI) n) 0.25)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25))))) (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) 19.270 * * * [progress]: adding candidates to table 20.317 * [progress]: [Phase 3 of 3] Extracting. 20.317 * * [regime]: Finding splitpoints for: (# # # # # # #) 20.322 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 20.322 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 20.369 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # #) 20.406 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 20.453 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 20.530 * * * [regime]: Found split indices: #