52.179 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.149 * * * [progress]: [2/2] Setting up program. 0.154 * [progress]: [Phase 2 of 3] Improving. 0.154 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.154 * * [simplify]: iteration 0: 13 enodes 0.158 * * [simplify]: iteration 1: 29 enodes 0.169 * * [simplify]: iteration 2: 58 enodes 0.189 * * [simplify]: iteration 3: 114 enodes 0.255 * * [simplify]: iteration 4: 285 enodes 0.376 * * [simplify]: iteration 5: 806 enodes 1.289 * * [simplify]: iteration 6: 2693 enodes 2.315 * * [simplify]: iteration complete: 5001 enodes 2.315 * * [simplify]: Extracting #0: cost 1 inf + 0 2.316 * * [simplify]: Extracting #1: cost 108 inf + 0 2.319 * * [simplify]: Extracting #2: cost 443 inf + 1 2.324 * * [simplify]: Extracting #3: cost 1003 inf + 8 2.336 * * [simplify]: Extracting #4: cost 1325 inf + 10758 2.361 * * [simplify]: Extracting #5: cost 713 inf + 95758 2.481 * * [simplify]: Extracting #6: cost 212 inf + 355864 2.659 * * [simplify]: Extracting #7: cost 1 inf + 567087 2.835 * * [simplify]: Extracting #8: cost 0 inf + 554854 3.010 * [simplify]: Simplified to: (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) 3.012 * * [progress]: iteration 1 / 4 3.012 * * * [progress]: picking best candidate 3.021 * * * * [pick]: Picked # 3.021 * * * [progress]: localizing error 3.064 * * * [progress]: generating rewritten candidates 3.064 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.085 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 3.093 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 3.115 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.169 * * * [progress]: generating series expansions 3.169 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.170 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.170 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.170 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.170 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.170 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.170 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.170 * [taylor]: Taking taylor expansion of 0.5 in k 3.170 * [backup-simplify]: Simplify 0.5 into 0.5 3.170 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.170 * [taylor]: Taking taylor expansion of 1.0 in k 3.170 * [backup-simplify]: Simplify 1.0 into 1.0 3.170 * [taylor]: Taking taylor expansion of k in k 3.170 * [backup-simplify]: Simplify 0 into 0 3.170 * [backup-simplify]: Simplify 1 into 1 3.170 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.170 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.170 * [taylor]: Taking taylor expansion of 2.0 in k 3.170 * [backup-simplify]: Simplify 2.0 into 2.0 3.170 * [taylor]: Taking taylor expansion of (* n PI) in k 3.170 * [taylor]: Taking taylor expansion of n in k 3.170 * [backup-simplify]: Simplify n into n 3.170 * [taylor]: Taking taylor expansion of PI in k 3.170 * [backup-simplify]: Simplify PI into PI 3.170 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.170 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.170 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.171 * [backup-simplify]: Simplify (- 0) into 0 3.171 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.171 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.172 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.172 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.172 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.172 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.172 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.172 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.172 * [taylor]: Taking taylor expansion of 0.5 in n 3.172 * [backup-simplify]: Simplify 0.5 into 0.5 3.172 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.172 * [taylor]: Taking taylor expansion of 1.0 in n 3.172 * [backup-simplify]: Simplify 1.0 into 1.0 3.172 * [taylor]: Taking taylor expansion of k in n 3.172 * [backup-simplify]: Simplify k into k 3.172 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.172 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.172 * [taylor]: Taking taylor expansion of 2.0 in n 3.172 * [backup-simplify]: Simplify 2.0 into 2.0 3.172 * [taylor]: Taking taylor expansion of (* n PI) in n 3.172 * [taylor]: Taking taylor expansion of n in n 3.172 * [backup-simplify]: Simplify 0 into 0 3.172 * [backup-simplify]: Simplify 1 into 1 3.172 * [taylor]: Taking taylor expansion of PI in n 3.172 * [backup-simplify]: Simplify PI into PI 3.172 * [backup-simplify]: Simplify (* 0 PI) into 0 3.173 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.173 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.174 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.175 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.175 * [backup-simplify]: Simplify (- k) into (- k) 3.175 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.175 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.176 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.177 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.178 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.178 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.178 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.178 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.178 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.178 * [taylor]: Taking taylor expansion of 0.5 in n 3.178 * [backup-simplify]: Simplify 0.5 into 0.5 3.178 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.178 * [taylor]: Taking taylor expansion of 1.0 in n 3.178 * [backup-simplify]: Simplify 1.0 into 1.0 3.178 * [taylor]: Taking taylor expansion of k in n 3.178 * [backup-simplify]: Simplify k into k 3.178 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.178 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.178 * [taylor]: Taking taylor expansion of 2.0 in n 3.178 * [backup-simplify]: Simplify 2.0 into 2.0 3.178 * [taylor]: Taking taylor expansion of (* n PI) in n 3.178 * [taylor]: Taking taylor expansion of n in n 3.178 * [backup-simplify]: Simplify 0 into 0 3.178 * [backup-simplify]: Simplify 1 into 1 3.178 * [taylor]: Taking taylor expansion of PI in n 3.178 * [backup-simplify]: Simplify PI into PI 3.178 * [backup-simplify]: Simplify (* 0 PI) into 0 3.178 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.179 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.181 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.182 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.182 * [backup-simplify]: Simplify (- k) into (- k) 3.182 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.182 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.183 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.185 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.186 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.186 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.186 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.186 * [taylor]: Taking taylor expansion of 0.5 in k 3.186 * [backup-simplify]: Simplify 0.5 into 0.5 3.186 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.186 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.186 * [taylor]: Taking taylor expansion of 1.0 in k 3.186 * [backup-simplify]: Simplify 1.0 into 1.0 3.186 * [taylor]: Taking taylor expansion of k in k 3.186 * [backup-simplify]: Simplify 0 into 0 3.186 * [backup-simplify]: Simplify 1 into 1 3.186 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.186 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.186 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.186 * [taylor]: Taking taylor expansion of 2.0 in k 3.186 * [backup-simplify]: Simplify 2.0 into 2.0 3.186 * [taylor]: Taking taylor expansion of PI in k 3.186 * [backup-simplify]: Simplify PI into PI 3.187 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.188 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.188 * [taylor]: Taking taylor expansion of (log n) in k 3.188 * [taylor]: Taking taylor expansion of n in k 3.188 * [backup-simplify]: Simplify n into n 3.188 * [backup-simplify]: Simplify (log n) into (log n) 3.188 * [backup-simplify]: Simplify (- 0) into 0 3.189 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.190 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.195 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.196 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.197 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.198 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.198 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.199 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.200 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.200 * [backup-simplify]: Simplify (- 0) into 0 3.200 * [backup-simplify]: Simplify (+ 0 0) into 0 3.201 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.201 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.202 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.203 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.203 * [taylor]: Taking taylor expansion of 0 in k 3.203 * [backup-simplify]: Simplify 0 into 0 3.203 * [backup-simplify]: Simplify 0 into 0 3.204 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.205 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.205 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.206 * [backup-simplify]: Simplify (+ 0 0) into 0 3.206 * [backup-simplify]: Simplify (- 1) into -1 3.206 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.207 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.208 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3.210 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.212 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 3.213 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.214 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.216 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.216 * [backup-simplify]: Simplify (- 0) into 0 3.217 * [backup-simplify]: Simplify (+ 0 0) into 0 3.217 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.219 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.220 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.223 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.223 * [taylor]: Taking taylor expansion of 0 in k 3.223 * [backup-simplify]: Simplify 0 into 0 3.223 * [backup-simplify]: Simplify 0 into 0 3.223 * [backup-simplify]: Simplify 0 into 0 3.224 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.228 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.230 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.230 * [backup-simplify]: Simplify (+ 0 0) into 0 3.231 * [backup-simplify]: Simplify (- 0) into 0 3.231 * [backup-simplify]: Simplify (+ 0 0) into 0 3.233 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.236 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.240 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 3.243 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 3.249 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 3.250 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 3.250 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.250 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.250 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.250 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.250 * [taylor]: Taking taylor expansion of 0.5 in k 3.250 * [backup-simplify]: Simplify 0.5 into 0.5 3.250 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.250 * [taylor]: Taking taylor expansion of 1.0 in k 3.250 * [backup-simplify]: Simplify 1.0 into 1.0 3.250 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.250 * [taylor]: Taking taylor expansion of k in k 3.250 * [backup-simplify]: Simplify 0 into 0 3.250 * [backup-simplify]: Simplify 1 into 1 3.251 * [backup-simplify]: Simplify (/ 1 1) into 1 3.251 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.251 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.251 * [taylor]: Taking taylor expansion of 2.0 in k 3.251 * [backup-simplify]: Simplify 2.0 into 2.0 3.251 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.251 * [taylor]: Taking taylor expansion of PI in k 3.251 * [backup-simplify]: Simplify PI into PI 3.251 * [taylor]: Taking taylor expansion of n in k 3.251 * [backup-simplify]: Simplify n into n 3.251 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.251 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.251 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.251 * [backup-simplify]: Simplify (- 1) into -1 3.251 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.252 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.252 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.252 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 3.252 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.252 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.252 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.252 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.252 * [taylor]: Taking taylor expansion of 0.5 in n 3.252 * [backup-simplify]: Simplify 0.5 into 0.5 3.252 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.252 * [taylor]: Taking taylor expansion of 1.0 in n 3.252 * [backup-simplify]: Simplify 1.0 into 1.0 3.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.252 * [taylor]: Taking taylor expansion of k in n 3.252 * [backup-simplify]: Simplify k into k 3.252 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.252 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.252 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.252 * [taylor]: Taking taylor expansion of 2.0 in n 3.252 * [backup-simplify]: Simplify 2.0 into 2.0 3.252 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.252 * [taylor]: Taking taylor expansion of PI in n 3.252 * [backup-simplify]: Simplify PI into PI 3.252 * [taylor]: Taking taylor expansion of n in n 3.252 * [backup-simplify]: Simplify 0 into 0 3.252 * [backup-simplify]: Simplify 1 into 1 3.253 * [backup-simplify]: Simplify (/ PI 1) into PI 3.253 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.254 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.254 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.254 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.254 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.255 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.255 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.256 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.256 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.256 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.256 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.256 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.256 * [taylor]: Taking taylor expansion of 0.5 in n 3.256 * [backup-simplify]: Simplify 0.5 into 0.5 3.256 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.256 * [taylor]: Taking taylor expansion of 1.0 in n 3.256 * [backup-simplify]: Simplify 1.0 into 1.0 3.256 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.256 * [taylor]: Taking taylor expansion of k in n 3.256 * [backup-simplify]: Simplify k into k 3.256 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.256 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.256 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.256 * [taylor]: Taking taylor expansion of 2.0 in n 3.256 * [backup-simplify]: Simplify 2.0 into 2.0 3.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.256 * [taylor]: Taking taylor expansion of PI in n 3.256 * [backup-simplify]: Simplify PI into PI 3.256 * [taylor]: Taking taylor expansion of n in n 3.256 * [backup-simplify]: Simplify 0 into 0 3.256 * [backup-simplify]: Simplify 1 into 1 3.257 * [backup-simplify]: Simplify (/ PI 1) into PI 3.257 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.258 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.258 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.258 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.258 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.259 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.260 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.260 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.260 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 3.260 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 3.260 * [taylor]: Taking taylor expansion of 0.5 in k 3.260 * [backup-simplify]: Simplify 0.5 into 0.5 3.260 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 3.260 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.261 * [taylor]: Taking taylor expansion of 1.0 in k 3.261 * [backup-simplify]: Simplify 1.0 into 1.0 3.261 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.261 * [taylor]: Taking taylor expansion of k in k 3.261 * [backup-simplify]: Simplify 0 into 0 3.261 * [backup-simplify]: Simplify 1 into 1 3.261 * [backup-simplify]: Simplify (/ 1 1) into 1 3.261 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.261 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.261 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.261 * [taylor]: Taking taylor expansion of 2.0 in k 3.261 * [backup-simplify]: Simplify 2.0 into 2.0 3.261 * [taylor]: Taking taylor expansion of PI in k 3.261 * [backup-simplify]: Simplify PI into PI 3.261 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.262 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.262 * [taylor]: Taking taylor expansion of (log n) in k 3.262 * [taylor]: Taking taylor expansion of n in k 3.262 * [backup-simplify]: Simplify n into n 3.262 * [backup-simplify]: Simplify (log n) into (log n) 3.262 * [backup-simplify]: Simplify (- 1) into -1 3.262 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.263 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.263 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.264 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.265 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.265 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.266 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.267 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.268 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.269 * [backup-simplify]: Simplify (- 0) into 0 3.269 * [backup-simplify]: Simplify (+ 0 0) into 0 3.270 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.273 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.275 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.275 * [taylor]: Taking taylor expansion of 0 in k 3.275 * [backup-simplify]: Simplify 0 into 0 3.275 * [backup-simplify]: Simplify 0 into 0 3.275 * [backup-simplify]: Simplify 0 into 0 3.276 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.281 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.281 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.281 * [backup-simplify]: Simplify (- 0) into 0 3.282 * [backup-simplify]: Simplify (+ 0 0) into 0 3.283 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.285 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.286 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.289 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.289 * [taylor]: Taking taylor expansion of 0 in k 3.289 * [backup-simplify]: Simplify 0 into 0 3.289 * [backup-simplify]: Simplify 0 into 0 3.289 * [backup-simplify]: Simplify 0 into 0 3.289 * [backup-simplify]: Simplify 0 into 0 3.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.291 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.298 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 3.298 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.298 * [backup-simplify]: Simplify (- 0) into 0 3.299 * [backup-simplify]: Simplify (+ 0 0) into 0 3.300 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.304 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.313 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.313 * [taylor]: Taking taylor expansion of 0 in k 3.313 * [backup-simplify]: Simplify 0 into 0 3.313 * [backup-simplify]: Simplify 0 into 0 3.315 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 3.316 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 3.316 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.316 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.316 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.316 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.316 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.316 * [taylor]: Taking taylor expansion of 0.5 in k 3.316 * [backup-simplify]: Simplify 0.5 into 0.5 3.316 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.316 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.316 * [taylor]: Taking taylor expansion of k in k 3.316 * [backup-simplify]: Simplify 0 into 0 3.316 * [backup-simplify]: Simplify 1 into 1 3.317 * [backup-simplify]: Simplify (/ 1 1) into 1 3.317 * [taylor]: Taking taylor expansion of 1.0 in k 3.317 * [backup-simplify]: Simplify 1.0 into 1.0 3.317 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.317 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.317 * [taylor]: Taking taylor expansion of -2.0 in k 3.317 * [backup-simplify]: Simplify -2.0 into -2.0 3.317 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.317 * [taylor]: Taking taylor expansion of PI in k 3.317 * [backup-simplify]: Simplify PI into PI 3.317 * [taylor]: Taking taylor expansion of n in k 3.317 * [backup-simplify]: Simplify n into n 3.317 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.317 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.317 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.318 * [backup-simplify]: Simplify (+ 1 0) into 1 3.318 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.319 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.319 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 3.319 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.319 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.319 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.319 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.319 * [taylor]: Taking taylor expansion of 0.5 in n 3.319 * [backup-simplify]: Simplify 0.5 into 0.5 3.319 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.319 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.319 * [taylor]: Taking taylor expansion of k in n 3.319 * [backup-simplify]: Simplify k into k 3.319 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.319 * [taylor]: Taking taylor expansion of 1.0 in n 3.319 * [backup-simplify]: Simplify 1.0 into 1.0 3.319 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.319 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.319 * [taylor]: Taking taylor expansion of -2.0 in n 3.319 * [backup-simplify]: Simplify -2.0 into -2.0 3.319 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.319 * [taylor]: Taking taylor expansion of PI in n 3.320 * [backup-simplify]: Simplify PI into PI 3.320 * [taylor]: Taking taylor expansion of n in n 3.320 * [backup-simplify]: Simplify 0 into 0 3.320 * [backup-simplify]: Simplify 1 into 1 3.320 * [backup-simplify]: Simplify (/ PI 1) into PI 3.321 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.322 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.322 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.322 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.323 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.324 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.325 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.325 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.325 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.325 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.325 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.326 * [taylor]: Taking taylor expansion of 0.5 in n 3.326 * [backup-simplify]: Simplify 0.5 into 0.5 3.326 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.326 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.326 * [taylor]: Taking taylor expansion of k in n 3.326 * [backup-simplify]: Simplify k into k 3.326 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.326 * [taylor]: Taking taylor expansion of 1.0 in n 3.326 * [backup-simplify]: Simplify 1.0 into 1.0 3.326 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.326 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.326 * [taylor]: Taking taylor expansion of -2.0 in n 3.326 * [backup-simplify]: Simplify -2.0 into -2.0 3.326 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.326 * [taylor]: Taking taylor expansion of PI in n 3.326 * [backup-simplify]: Simplify PI into PI 3.326 * [taylor]: Taking taylor expansion of n in n 3.326 * [backup-simplify]: Simplify 0 into 0 3.326 * [backup-simplify]: Simplify 1 into 1 3.326 * [backup-simplify]: Simplify (/ PI 1) into PI 3.327 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.328 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.328 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.328 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.331 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.332 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.332 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 3.332 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 3.332 * [taylor]: Taking taylor expansion of 0.5 in k 3.332 * [backup-simplify]: Simplify 0.5 into 0.5 3.332 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 3.332 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.332 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.332 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.332 * [taylor]: Taking taylor expansion of -2.0 in k 3.332 * [backup-simplify]: Simplify -2.0 into -2.0 3.332 * [taylor]: Taking taylor expansion of PI in k 3.333 * [backup-simplify]: Simplify PI into PI 3.333 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.334 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.334 * [taylor]: Taking taylor expansion of (log n) in k 3.334 * [taylor]: Taking taylor expansion of n in k 3.334 * [backup-simplify]: Simplify n into n 3.334 * [backup-simplify]: Simplify (log n) into (log n) 3.334 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.334 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.334 * [taylor]: Taking taylor expansion of k in k 3.334 * [backup-simplify]: Simplify 0 into 0 3.334 * [backup-simplify]: Simplify 1 into 1 3.335 * [backup-simplify]: Simplify (/ 1 1) into 1 3.335 * [taylor]: Taking taylor expansion of 1.0 in k 3.335 * [backup-simplify]: Simplify 1.0 into 1.0 3.335 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.336 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.336 * [backup-simplify]: Simplify (+ 1 0) into 1 3.338 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 3.339 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.340 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.341 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.342 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.343 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.345 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.345 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.346 * [backup-simplify]: Simplify (+ 0 0) into 0 3.346 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.349 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.351 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.351 * [taylor]: Taking taylor expansion of 0 in k 3.351 * [backup-simplify]: Simplify 0 into 0 3.351 * [backup-simplify]: Simplify 0 into 0 3.351 * [backup-simplify]: Simplify 0 into 0 3.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.353 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.357 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 3.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.358 * [backup-simplify]: Simplify (+ 0 0) into 0 3.359 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.360 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.362 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.364 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.364 * [taylor]: Taking taylor expansion of 0 in k 3.364 * [backup-simplify]: Simplify 0 into 0 3.364 * [backup-simplify]: Simplify 0 into 0 3.364 * [backup-simplify]: Simplify 0 into 0 3.364 * [backup-simplify]: Simplify 0 into 0 3.366 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.367 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.373 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 3.373 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.373 * [backup-simplify]: Simplify (+ 0 0) into 0 3.375 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.376 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.378 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.381 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 3.381 * [taylor]: Taking taylor expansion of 0 in k 3.381 * [backup-simplify]: Simplify 0 into 0 3.381 * [backup-simplify]: Simplify 0 into 0 3.383 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 3.383 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 3.383 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.383 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.383 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.383 * [taylor]: Taking taylor expansion of 1.0 in k 3.383 * [backup-simplify]: Simplify 1.0 into 1.0 3.383 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.383 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.383 * [taylor]: Taking taylor expansion of k in k 3.383 * [backup-simplify]: Simplify 0 into 0 3.383 * [backup-simplify]: Simplify 1 into 1 3.383 * [backup-simplify]: Simplify (/ 1 1) into 1 3.384 * [backup-simplify]: Simplify (sqrt 0) into 0 3.386 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.386 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.386 * [taylor]: Taking taylor expansion of 1.0 in k 3.386 * [backup-simplify]: Simplify 1.0 into 1.0 3.386 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.386 * [taylor]: Taking taylor expansion of k in k 3.386 * [backup-simplify]: Simplify 0 into 0 3.386 * [backup-simplify]: Simplify 1 into 1 3.386 * [backup-simplify]: Simplify (/ 1 1) into 1 3.387 * [backup-simplify]: Simplify (sqrt 0) into 0 3.388 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.388 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.388 * [backup-simplify]: Simplify 0 into 0 3.390 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.390 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.392 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.395 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.397 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.397 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.398 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.402 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.405 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.405 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.407 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 3.407 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.407 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.407 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.407 * [taylor]: Taking taylor expansion of 1.0 in k 3.407 * [backup-simplify]: Simplify 1.0 into 1.0 3.407 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.407 * [taylor]: Taking taylor expansion of k in k 3.407 * [backup-simplify]: Simplify 0 into 0 3.407 * [backup-simplify]: Simplify 1 into 1 3.408 * [backup-simplify]: Simplify (sqrt 0) into 0 3.409 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.409 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.409 * [taylor]: Taking taylor expansion of 1.0 in k 3.409 * [backup-simplify]: Simplify 1.0 into 1.0 3.409 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.409 * [taylor]: Taking taylor expansion of k in k 3.409 * [backup-simplify]: Simplify 0 into 0 3.409 * [backup-simplify]: Simplify 1 into 1 3.410 * [backup-simplify]: Simplify (sqrt 0) into 0 3.411 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.411 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.411 * [backup-simplify]: Simplify 0 into 0 3.413 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.413 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.416 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.418 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.419 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.423 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.425 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.425 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.427 * [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)))))))) 3.427 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.427 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.427 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.427 * [taylor]: Taking taylor expansion of 1.0 in k 3.427 * [backup-simplify]: Simplify 1.0 into 1.0 3.427 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.427 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.427 * [taylor]: Taking taylor expansion of -1 in k 3.427 * [backup-simplify]: Simplify -1 into -1 3.427 * [taylor]: Taking taylor expansion of k in k 3.428 * [backup-simplify]: Simplify 0 into 0 3.428 * [backup-simplify]: Simplify 1 into 1 3.428 * [backup-simplify]: Simplify (/ -1 1) into -1 3.428 * [backup-simplify]: Simplify (sqrt 0) into 0 3.430 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.430 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.430 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.430 * [taylor]: Taking taylor expansion of 1.0 in k 3.430 * [backup-simplify]: Simplify 1.0 into 1.0 3.430 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.430 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.430 * [taylor]: Taking taylor expansion of -1 in k 3.430 * [backup-simplify]: Simplify -1 into -1 3.430 * [taylor]: Taking taylor expansion of k in k 3.430 * [backup-simplify]: Simplify 0 into 0 3.430 * [backup-simplify]: Simplify 1 into 1 3.431 * [backup-simplify]: Simplify (/ -1 1) into -1 3.431 * [backup-simplify]: Simplify (sqrt 0) into 0 3.433 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.433 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.433 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.437 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.440 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.440 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.441 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.445 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.450 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.450 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.451 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 3.451 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 3.452 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.452 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.452 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.452 * [taylor]: Taking taylor expansion of 2.0 in n 3.452 * [backup-simplify]: Simplify 2.0 into 2.0 3.452 * [taylor]: Taking taylor expansion of (* n PI) in n 3.452 * [taylor]: Taking taylor expansion of n in n 3.452 * [backup-simplify]: Simplify 0 into 0 3.452 * [backup-simplify]: Simplify 1 into 1 3.452 * [taylor]: Taking taylor expansion of PI in n 3.452 * [backup-simplify]: Simplify PI into PI 3.452 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.452 * [taylor]: Taking taylor expansion of 2.0 in n 3.452 * [backup-simplify]: Simplify 2.0 into 2.0 3.452 * [taylor]: Taking taylor expansion of (* n PI) in n 3.452 * [taylor]: Taking taylor expansion of n in n 3.452 * [backup-simplify]: Simplify 0 into 0 3.452 * [backup-simplify]: Simplify 1 into 1 3.452 * [taylor]: Taking taylor expansion of PI in n 3.452 * [backup-simplify]: Simplify PI into PI 3.453 * [backup-simplify]: Simplify (* 0 PI) into 0 3.454 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.454 * [backup-simplify]: Simplify 0 into 0 3.455 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.457 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.457 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.465 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.465 * [backup-simplify]: Simplify 0 into 0 3.467 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.468 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.468 * [backup-simplify]: Simplify 0 into 0 3.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.471 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.471 * [backup-simplify]: Simplify 0 into 0 3.473 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.474 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.474 * [backup-simplify]: Simplify 0 into 0 3.476 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.478 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.478 * [backup-simplify]: Simplify 0 into 0 3.480 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.482 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.482 * [backup-simplify]: Simplify 0 into 0 3.482 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.483 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.483 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.483 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.483 * [taylor]: Taking taylor expansion of 2.0 in n 3.483 * [backup-simplify]: Simplify 2.0 into 2.0 3.483 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.483 * [taylor]: Taking taylor expansion of PI in n 3.483 * [backup-simplify]: Simplify PI into PI 3.483 * [taylor]: Taking taylor expansion of n in n 3.483 * [backup-simplify]: Simplify 0 into 0 3.483 * [backup-simplify]: Simplify 1 into 1 3.484 * [backup-simplify]: Simplify (/ PI 1) into PI 3.484 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.484 * [taylor]: Taking taylor expansion of 2.0 in n 3.484 * [backup-simplify]: Simplify 2.0 into 2.0 3.484 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.484 * [taylor]: Taking taylor expansion of PI in n 3.484 * [backup-simplify]: Simplify PI into PI 3.484 * [taylor]: Taking taylor expansion of n in n 3.484 * [backup-simplify]: Simplify 0 into 0 3.484 * [backup-simplify]: Simplify 1 into 1 3.485 * [backup-simplify]: Simplify (/ PI 1) into PI 3.485 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.486 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.487 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.487 * [backup-simplify]: Simplify 0 into 0 3.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.489 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.490 * [backup-simplify]: Simplify 0 into 0 3.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.492 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.492 * [backup-simplify]: Simplify 0 into 0 3.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.494 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.494 * [backup-simplify]: Simplify 0 into 0 3.496 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.497 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.497 * [backup-simplify]: Simplify 0 into 0 3.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.500 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.500 * [backup-simplify]: Simplify 0 into 0 3.501 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.501 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.501 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.501 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.501 * [taylor]: Taking taylor expansion of -2.0 in n 3.501 * [backup-simplify]: Simplify -2.0 into -2.0 3.501 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.501 * [taylor]: Taking taylor expansion of PI in n 3.501 * [backup-simplify]: Simplify PI into PI 3.501 * [taylor]: Taking taylor expansion of n in n 3.501 * [backup-simplify]: Simplify 0 into 0 3.502 * [backup-simplify]: Simplify 1 into 1 3.502 * [backup-simplify]: Simplify (/ PI 1) into PI 3.502 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.502 * [taylor]: Taking taylor expansion of -2.0 in n 3.502 * [backup-simplify]: Simplify -2.0 into -2.0 3.502 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.502 * [taylor]: Taking taylor expansion of PI in n 3.502 * [backup-simplify]: Simplify PI into PI 3.502 * [taylor]: Taking taylor expansion of n in n 3.502 * [backup-simplify]: Simplify 0 into 0 3.502 * [backup-simplify]: Simplify 1 into 1 3.503 * [backup-simplify]: Simplify (/ PI 1) into PI 3.504 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.504 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.506 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.506 * [backup-simplify]: Simplify 0 into 0 3.507 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.508 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.508 * [backup-simplify]: Simplify 0 into 0 3.509 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.510 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.510 * [backup-simplify]: Simplify 0 into 0 3.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.513 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.513 * [backup-simplify]: Simplify 0 into 0 3.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.516 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.516 * [backup-simplify]: Simplify 0 into 0 3.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.519 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.519 * [backup-simplify]: Simplify 0 into 0 3.519 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.520 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.520 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 3.520 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0 3.520 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 3.520 * [taylor]: Taking taylor expansion of 1.0 in n 3.520 * [backup-simplify]: Simplify 1.0 into 1.0 3.520 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 3.520 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.520 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.520 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.520 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.520 * [taylor]: Taking taylor expansion of 0.5 in n 3.520 * [backup-simplify]: Simplify 0.5 into 0.5 3.520 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.520 * [taylor]: Taking taylor expansion of 1.0 in n 3.521 * [backup-simplify]: Simplify 1.0 into 1.0 3.521 * [taylor]: Taking taylor expansion of k in n 3.521 * [backup-simplify]: Simplify k into k 3.521 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.521 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.521 * [taylor]: Taking taylor expansion of 2.0 in n 3.521 * [backup-simplify]: Simplify 2.0 into 2.0 3.521 * [taylor]: Taking taylor expansion of (* n PI) in n 3.521 * [taylor]: Taking taylor expansion of n in n 3.521 * [backup-simplify]: Simplify 0 into 0 3.521 * [backup-simplify]: Simplify 1 into 1 3.521 * [taylor]: Taking taylor expansion of PI in n 3.521 * [backup-simplify]: Simplify PI into PI 3.521 * [backup-simplify]: Simplify (* 0 PI) into 0 3.521 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.522 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.523 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.524 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.524 * [backup-simplify]: Simplify (- k) into (- k) 3.524 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.524 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.525 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.525 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.526 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.526 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.526 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.526 * [taylor]: Taking taylor expansion of k in n 3.526 * [backup-simplify]: Simplify k into k 3.526 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.526 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.526 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.526 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.526 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.526 * [taylor]: Taking taylor expansion of 1.0 in k 3.526 * [backup-simplify]: Simplify 1.0 into 1.0 3.527 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.527 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.527 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.527 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.527 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.527 * [taylor]: Taking taylor expansion of 0.5 in k 3.527 * [backup-simplify]: Simplify 0.5 into 0.5 3.527 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.527 * [taylor]: Taking taylor expansion of 1.0 in k 3.527 * [backup-simplify]: Simplify 1.0 into 1.0 3.527 * [taylor]: Taking taylor expansion of k in k 3.527 * [backup-simplify]: Simplify 0 into 0 3.527 * [backup-simplify]: Simplify 1 into 1 3.527 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.527 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.527 * [taylor]: Taking taylor expansion of 2.0 in k 3.527 * [backup-simplify]: Simplify 2.0 into 2.0 3.527 * [taylor]: Taking taylor expansion of (* n PI) in k 3.527 * [taylor]: Taking taylor expansion of n in k 3.527 * [backup-simplify]: Simplify n into n 3.527 * [taylor]: Taking taylor expansion of PI in k 3.527 * [backup-simplify]: Simplify PI into PI 3.527 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.527 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.527 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.527 * [backup-simplify]: Simplify (- 0) into 0 3.527 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.528 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.528 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.528 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.528 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.528 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.528 * [taylor]: Taking taylor expansion of k in k 3.528 * [backup-simplify]: Simplify 0 into 0 3.528 * [backup-simplify]: Simplify 1 into 1 3.528 * [backup-simplify]: Simplify (/ 1 1) into 1 3.528 * [backup-simplify]: Simplify (sqrt 0) into 0 3.529 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.529 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.529 * [taylor]: Taking taylor expansion of 1.0 in k 3.529 * [backup-simplify]: Simplify 1.0 into 1.0 3.529 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.529 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.529 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.529 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.529 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.529 * [taylor]: Taking taylor expansion of 0.5 in k 3.530 * [backup-simplify]: Simplify 0.5 into 0.5 3.530 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.530 * [taylor]: Taking taylor expansion of 1.0 in k 3.530 * [backup-simplify]: Simplify 1.0 into 1.0 3.530 * [taylor]: Taking taylor expansion of k in k 3.530 * [backup-simplify]: Simplify 0 into 0 3.530 * [backup-simplify]: Simplify 1 into 1 3.530 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.530 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.530 * [taylor]: Taking taylor expansion of 2.0 in k 3.530 * [backup-simplify]: Simplify 2.0 into 2.0 3.530 * [taylor]: Taking taylor expansion of (* n PI) in k 3.530 * [taylor]: Taking taylor expansion of n in k 3.530 * [backup-simplify]: Simplify n into n 3.530 * [taylor]: Taking taylor expansion of PI in k 3.530 * [backup-simplify]: Simplify PI into PI 3.530 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.530 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.530 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.530 * [backup-simplify]: Simplify (- 0) into 0 3.530 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.531 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.531 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.531 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.531 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.531 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.531 * [taylor]: Taking taylor expansion of k in k 3.531 * [backup-simplify]: Simplify 0 into 0 3.531 * [backup-simplify]: Simplify 1 into 1 3.531 * [backup-simplify]: Simplify (/ 1 1) into 1 3.531 * [backup-simplify]: Simplify (sqrt 0) into 0 3.532 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.532 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 3.533 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.533 * [taylor]: Taking taylor expansion of 0 in n 3.533 * [backup-simplify]: Simplify 0 into 0 3.533 * [backup-simplify]: Simplify 0 into 0 3.533 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 3.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 3.534 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 3.534 * [backup-simplify]: Simplify (- 1) into -1 3.534 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.535 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.536 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 3.536 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 3.537 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 3.538 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 3.538 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 3.538 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 3.538 * [taylor]: Taking taylor expansion of +nan.0 in n 3.538 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.538 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.538 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.538 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.538 * [taylor]: Taking taylor expansion of 0.5 in n 3.538 * [backup-simplify]: Simplify 0.5 into 0.5 3.538 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.539 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.539 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.539 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.539 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.539 * [taylor]: Taking taylor expansion of 1.0 in n 3.539 * [backup-simplify]: Simplify 1.0 into 1.0 3.539 * [taylor]: Taking taylor expansion of (log PI) in n 3.539 * [taylor]: Taking taylor expansion of PI in n 3.539 * [backup-simplify]: Simplify PI into PI 3.539 * [backup-simplify]: Simplify (log PI) into (log PI) 3.540 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.541 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.541 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.541 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.541 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.541 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.541 * [taylor]: Taking taylor expansion of 1.0 in n 3.541 * [backup-simplify]: Simplify 1.0 into 1.0 3.541 * [taylor]: Taking taylor expansion of (log n) in n 3.541 * [taylor]: Taking taylor expansion of n in n 3.541 * [backup-simplify]: Simplify 0 into 0 3.541 * [backup-simplify]: Simplify 1 into 1 3.541 * [backup-simplify]: Simplify (log 1) into 0 3.541 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.541 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.541 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.541 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.541 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.541 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.541 * [taylor]: Taking taylor expansion of 1.0 in n 3.541 * [backup-simplify]: Simplify 1.0 into 1.0 3.541 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.541 * [taylor]: Taking taylor expansion of 2.0 in n 3.541 * [backup-simplify]: Simplify 2.0 into 2.0 3.542 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.542 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.543 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.544 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.544 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.545 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.546 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.547 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.548 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 3.549 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 3.549 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 3.549 * [backup-simplify]: Simplify 0 into 0 3.550 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.552 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.552 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 3.553 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 3.554 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 3.554 * [backup-simplify]: Simplify (- 0) into 0 3.554 * [backup-simplify]: Simplify (+ 0 0) into 0 3.555 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.556 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 3.556 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 3.558 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))) 3.562 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) 3.562 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n 3.562 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n 3.562 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 3.562 * [taylor]: Taking taylor expansion of +nan.0 in n 3.562 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.562 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 3.562 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.562 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.562 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.562 * [taylor]: Taking taylor expansion of 0.5 in n 3.562 * [backup-simplify]: Simplify 0.5 into 0.5 3.562 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.562 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.562 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.562 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.562 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.562 * [taylor]: Taking taylor expansion of 1.0 in n 3.562 * [backup-simplify]: Simplify 1.0 into 1.0 3.562 * [taylor]: Taking taylor expansion of (log PI) in n 3.562 * [taylor]: Taking taylor expansion of PI in n 3.562 * [backup-simplify]: Simplify PI into PI 3.562 * [backup-simplify]: Simplify (log PI) into (log PI) 3.563 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.564 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.564 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.564 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.564 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.564 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.564 * [taylor]: Taking taylor expansion of 1.0 in n 3.564 * [backup-simplify]: Simplify 1.0 into 1.0 3.564 * [taylor]: Taking taylor expansion of (log n) in n 3.564 * [taylor]: Taking taylor expansion of n in n 3.564 * [backup-simplify]: Simplify 0 into 0 3.564 * [backup-simplify]: Simplify 1 into 1 3.564 * [backup-simplify]: Simplify (log 1) into 0 3.565 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.565 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.565 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.565 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.565 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.565 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.565 * [taylor]: Taking taylor expansion of 1.0 in n 3.565 * [backup-simplify]: Simplify 1.0 into 1.0 3.565 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.565 * [taylor]: Taking taylor expansion of 2.0 in n 3.565 * [backup-simplify]: Simplify 2.0 into 2.0 3.565 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.566 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.567 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.567 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.568 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.569 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.569 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.570 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.570 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.570 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.570 * [taylor]: Taking taylor expansion of 2.0 in n 3.570 * [backup-simplify]: Simplify 2.0 into 2.0 3.570 * [taylor]: Taking taylor expansion of (* n PI) in n 3.570 * [taylor]: Taking taylor expansion of n in n 3.570 * [backup-simplify]: Simplify 0 into 0 3.570 * [backup-simplify]: Simplify 1 into 1 3.570 * [taylor]: Taking taylor expansion of PI in n 3.570 * [backup-simplify]: Simplify PI into PI 3.571 * [backup-simplify]: Simplify (* 0 PI) into 0 3.571 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.572 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.573 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.573 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.573 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 3.574 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 3.574 * [taylor]: Taking taylor expansion of +nan.0 in n 3.574 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.574 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.574 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.574 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.574 * [taylor]: Taking taylor expansion of 0.5 in n 3.574 * [backup-simplify]: Simplify 0.5 into 0.5 3.574 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.574 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.574 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.574 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.574 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.574 * [taylor]: Taking taylor expansion of 1.0 in n 3.574 * [backup-simplify]: Simplify 1.0 into 1.0 3.574 * [taylor]: Taking taylor expansion of (log PI) in n 3.574 * [taylor]: Taking taylor expansion of PI in n 3.574 * [backup-simplify]: Simplify PI into PI 3.574 * [backup-simplify]: Simplify (log PI) into (log PI) 3.575 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.576 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.576 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.576 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.576 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.576 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.576 * [taylor]: Taking taylor expansion of 1.0 in n 3.576 * [backup-simplify]: Simplify 1.0 into 1.0 3.576 * [taylor]: Taking taylor expansion of (log n) in n 3.576 * [taylor]: Taking taylor expansion of n in n 3.576 * [backup-simplify]: Simplify 0 into 0 3.576 * [backup-simplify]: Simplify 1 into 1 3.576 * [backup-simplify]: Simplify (log 1) into 0 3.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.576 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.576 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.576 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.576 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.577 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.577 * [taylor]: Taking taylor expansion of 1.0 in n 3.577 * [backup-simplify]: Simplify 1.0 into 1.0 3.577 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.577 * [taylor]: Taking taylor expansion of 2.0 in n 3.577 * [backup-simplify]: Simplify 2.0 into 2.0 3.581 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.582 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.584 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.584 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.585 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.587 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.588 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.589 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.591 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.593 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 3.595 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 3.597 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 3.598 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 3.602 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 3.608 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) 3.614 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) 3.616 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 3.617 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 3.619 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 3.620 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.621 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.621 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 3.622 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.623 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 3.625 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 3.625 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 3.627 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 3.629 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 3.631 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 3.633 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 3.635 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.637 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 3.637 * [backup-simplify]: Simplify (- 0) into 0 3.637 * [backup-simplify]: Simplify 0 into 0 3.637 * [backup-simplify]: Simplify 0 into 0 3.638 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.642 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.643 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 3.647 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 3.648 * [backup-simplify]: Simplify (- 0) into 0 3.648 * [backup-simplify]: Simplify (+ 0 0) into 0 3.650 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 3.651 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 3.653 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 3.659 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 3.670 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 3.670 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 3.670 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 3.670 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 3.670 * [taylor]: Taking taylor expansion of +nan.0 in n 3.670 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.670 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 3.670 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.670 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.670 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.670 * [taylor]: Taking taylor expansion of 0.5 in n 3.670 * [backup-simplify]: Simplify 0.5 into 0.5 3.670 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.670 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.671 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.671 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.671 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.671 * [taylor]: Taking taylor expansion of 1.0 in n 3.671 * [backup-simplify]: Simplify 1.0 into 1.0 3.671 * [taylor]: Taking taylor expansion of (log PI) in n 3.671 * [taylor]: Taking taylor expansion of PI in n 3.671 * [backup-simplify]: Simplify PI into PI 3.671 * [backup-simplify]: Simplify (log PI) into (log PI) 3.672 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.674 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.674 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.674 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.674 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.674 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.674 * [taylor]: Taking taylor expansion of 1.0 in n 3.674 * [backup-simplify]: Simplify 1.0 into 1.0 3.674 * [taylor]: Taking taylor expansion of (log n) in n 3.674 * [taylor]: Taking taylor expansion of n in n 3.674 * [backup-simplify]: Simplify 0 into 0 3.674 * [backup-simplify]: Simplify 1 into 1 3.675 * [backup-simplify]: Simplify (log 1) into 0 3.675 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.675 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.675 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.675 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.675 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.675 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.675 * [taylor]: Taking taylor expansion of 1.0 in n 3.675 * [backup-simplify]: Simplify 1.0 into 1.0 3.675 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.675 * [taylor]: Taking taylor expansion of 2.0 in n 3.675 * [backup-simplify]: Simplify 2.0 into 2.0 3.676 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.677 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.678 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.679 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.680 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.681 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.683 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.684 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.684 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.684 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.684 * [taylor]: Taking taylor expansion of 2.0 in n 3.684 * [backup-simplify]: Simplify 2.0 into 2.0 3.684 * [taylor]: Taking taylor expansion of (* n PI) in n 3.684 * [taylor]: Taking taylor expansion of n in n 3.685 * [backup-simplify]: Simplify 0 into 0 3.685 * [backup-simplify]: Simplify 1 into 1 3.685 * [taylor]: Taking taylor expansion of PI in n 3.685 * [backup-simplify]: Simplify PI into PI 3.685 * [backup-simplify]: Simplify (* 0 PI) into 0 3.685 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.687 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.689 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.690 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.690 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 3.690 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 3.690 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 3.690 * [taylor]: Taking taylor expansion of +nan.0 in n 3.690 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.690 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.690 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.690 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.690 * [taylor]: Taking taylor expansion of 0.5 in n 3.690 * [backup-simplify]: Simplify 0.5 into 0.5 3.690 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.690 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.690 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.690 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.691 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.691 * [taylor]: Taking taylor expansion of 1.0 in n 3.691 * [backup-simplify]: Simplify 1.0 into 1.0 3.691 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.691 * [taylor]: Taking taylor expansion of 2.0 in n 3.691 * [backup-simplify]: Simplify 2.0 into 2.0 3.691 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.692 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.693 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.694 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.694 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.694 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.694 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.694 * [taylor]: Taking taylor expansion of 1.0 in n 3.694 * [backup-simplify]: Simplify 1.0 into 1.0 3.694 * [taylor]: Taking taylor expansion of (log n) in n 3.694 * [taylor]: Taking taylor expansion of n in n 3.694 * [backup-simplify]: Simplify 0 into 0 3.694 * [backup-simplify]: Simplify 1 into 1 3.694 * [backup-simplify]: Simplify (log 1) into 0 3.695 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.695 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.695 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.695 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.695 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.695 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.695 * [taylor]: Taking taylor expansion of 1.0 in n 3.695 * [backup-simplify]: Simplify 1.0 into 1.0 3.695 * [taylor]: Taking taylor expansion of (log PI) in n 3.695 * [taylor]: Taking taylor expansion of PI in n 3.695 * [backup-simplify]: Simplify PI into PI 3.696 * [backup-simplify]: Simplify (log PI) into (log PI) 3.696 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.698 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.699 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.700 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 3.701 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 3.703 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 3.704 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.704 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 3.704 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 3.704 * [taylor]: Taking taylor expansion of +nan.0 in n 3.704 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.704 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 3.704 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.704 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.705 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.705 * [taylor]: Taking taylor expansion of 0.5 in n 3.705 * [backup-simplify]: Simplify 0.5 into 0.5 3.705 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.705 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.705 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.705 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.705 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.705 * [taylor]: Taking taylor expansion of 1.0 in n 3.705 * [backup-simplify]: Simplify 1.0 into 1.0 3.705 * [taylor]: Taking taylor expansion of (log PI) in n 3.705 * [taylor]: Taking taylor expansion of PI in n 3.705 * [backup-simplify]: Simplify PI into PI 3.705 * [backup-simplify]: Simplify (log PI) into (log PI) 3.706 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.708 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.708 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.708 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.708 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.708 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.708 * [taylor]: Taking taylor expansion of 1.0 in n 3.708 * [backup-simplify]: Simplify 1.0 into 1.0 3.708 * [taylor]: Taking taylor expansion of (log n) in n 3.708 * [taylor]: Taking taylor expansion of n in n 3.708 * [backup-simplify]: Simplify 0 into 0 3.708 * [backup-simplify]: Simplify 1 into 1 3.709 * [backup-simplify]: Simplify (log 1) into 0 3.709 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.709 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.709 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.709 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.709 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.709 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.709 * [taylor]: Taking taylor expansion of 1.0 in n 3.709 * [backup-simplify]: Simplify 1.0 into 1.0 3.710 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.710 * [taylor]: Taking taylor expansion of 2.0 in n 3.710 * [backup-simplify]: Simplify 2.0 into 2.0 3.710 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.711 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.712 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.713 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 3.714 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 3.716 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 3.717 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 3.719 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.719 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.719 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.719 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.719 * [taylor]: Taking taylor expansion of 2.0 in n 3.719 * [backup-simplify]: Simplify 2.0 into 2.0 3.719 * [taylor]: Taking taylor expansion of (* n PI) in n 3.719 * [taylor]: Taking taylor expansion of n in n 3.719 * [backup-simplify]: Simplify 0 into 0 3.719 * [backup-simplify]: Simplify 1 into 1 3.719 * [taylor]: Taking taylor expansion of PI in n 3.719 * [backup-simplify]: Simplify PI into PI 3.720 * [backup-simplify]: Simplify (* 0 PI) into 0 3.720 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.721 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.722 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.723 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.723 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.724 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.726 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))) 3.732 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) 3.733 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 3.733 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.734 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.736 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.737 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) 3.739 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) 3.741 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))) 3.747 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) 3.753 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2)))))))))) 3.761 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 3.771 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) 3.781 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) 3.796 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) 3.797 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 3.797 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0 3.797 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 3.797 * [taylor]: Taking taylor expansion of 1.0 in n 3.797 * [backup-simplify]: Simplify 1.0 into 1.0 3.797 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 3.797 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.797 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.797 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.797 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.797 * [taylor]: Taking taylor expansion of 0.5 in n 3.797 * [backup-simplify]: Simplify 0.5 into 0.5 3.798 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.798 * [taylor]: Taking taylor expansion of 1.0 in n 3.798 * [backup-simplify]: Simplify 1.0 into 1.0 3.798 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.798 * [taylor]: Taking taylor expansion of k in n 3.798 * [backup-simplify]: Simplify k into k 3.798 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.798 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.798 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.798 * [taylor]: Taking taylor expansion of 2.0 in n 3.798 * [backup-simplify]: Simplify 2.0 into 2.0 3.798 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.798 * [taylor]: Taking taylor expansion of PI in n 3.798 * [backup-simplify]: Simplify PI into PI 3.798 * [taylor]: Taking taylor expansion of n in n 3.798 * [backup-simplify]: Simplify 0 into 0 3.798 * [backup-simplify]: Simplify 1 into 1 3.798 * [backup-simplify]: Simplify (/ PI 1) into PI 3.799 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.800 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.800 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.800 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.800 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.802 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.803 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.803 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.803 * [taylor]: Taking taylor expansion of k in n 3.803 * [backup-simplify]: Simplify k into k 3.803 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.803 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.803 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.803 * [taylor]: Taking taylor expansion of 1.0 in k 3.803 * [backup-simplify]: Simplify 1.0 into 1.0 3.803 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.803 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.803 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.803 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.803 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.803 * [taylor]: Taking taylor expansion of 0.5 in k 3.803 * [backup-simplify]: Simplify 0.5 into 0.5 3.803 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.803 * [taylor]: Taking taylor expansion of 1.0 in k 3.803 * [backup-simplify]: Simplify 1.0 into 1.0 3.803 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.803 * [taylor]: Taking taylor expansion of k in k 3.803 * [backup-simplify]: Simplify 0 into 0 3.803 * [backup-simplify]: Simplify 1 into 1 3.803 * [backup-simplify]: Simplify (/ 1 1) into 1 3.803 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.803 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.803 * [taylor]: Taking taylor expansion of 2.0 in k 3.803 * [backup-simplify]: Simplify 2.0 into 2.0 3.803 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.803 * [taylor]: Taking taylor expansion of PI in k 3.803 * [backup-simplify]: Simplify PI into PI 3.803 * [taylor]: Taking taylor expansion of n in k 3.803 * [backup-simplify]: Simplify n into n 3.803 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.803 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.804 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.804 * [backup-simplify]: Simplify (- 1) into -1 3.804 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.804 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.804 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.805 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 3.805 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.805 * [taylor]: Taking taylor expansion of k in k 3.805 * [backup-simplify]: Simplify 0 into 0 3.805 * [backup-simplify]: Simplify 1 into 1 3.805 * [backup-simplify]: Simplify (sqrt 0) into 0 3.806 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.806 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.806 * [taylor]: Taking taylor expansion of 1.0 in k 3.806 * [backup-simplify]: Simplify 1.0 into 1.0 3.806 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.806 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.806 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.806 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.806 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.806 * [taylor]: Taking taylor expansion of 0.5 in k 3.806 * [backup-simplify]: Simplify 0.5 into 0.5 3.806 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.806 * [taylor]: Taking taylor expansion of 1.0 in k 3.806 * [backup-simplify]: Simplify 1.0 into 1.0 3.806 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.806 * [taylor]: Taking taylor expansion of k in k 3.806 * [backup-simplify]: Simplify 0 into 0 3.806 * [backup-simplify]: Simplify 1 into 1 3.806 * [backup-simplify]: Simplify (/ 1 1) into 1 3.807 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.807 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.807 * [taylor]: Taking taylor expansion of 2.0 in k 3.807 * [backup-simplify]: Simplify 2.0 into 2.0 3.807 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.807 * [taylor]: Taking taylor expansion of PI in k 3.807 * [backup-simplify]: Simplify PI into PI 3.807 * [taylor]: Taking taylor expansion of n in k 3.807 * [backup-simplify]: Simplify n into n 3.807 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.807 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.807 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.807 * [backup-simplify]: Simplify (- 1) into -1 3.807 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.808 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.808 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.808 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 3.808 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.808 * [taylor]: Taking taylor expansion of k in k 3.808 * [backup-simplify]: Simplify 0 into 0 3.808 * [backup-simplify]: Simplify 1 into 1 3.808 * [backup-simplify]: Simplify (sqrt 0) into 0 3.809 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.809 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 3.810 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.810 * [taylor]: Taking taylor expansion of 0 in n 3.810 * [backup-simplify]: Simplify 0 into 0 3.810 * [backup-simplify]: Simplify 0 into 0 3.810 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.810 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.810 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.810 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.811 * [taylor]: Taking taylor expansion of +nan.0 in n 3.811 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.811 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.811 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.811 * [taylor]: Taking taylor expansion of 0.5 in n 3.811 * [backup-simplify]: Simplify 0.5 into 0.5 3.811 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.811 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.811 * [taylor]: Taking taylor expansion of 1.0 in n 3.811 * [backup-simplify]: Simplify 1.0 into 1.0 3.811 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.811 * [taylor]: Taking taylor expansion of k in n 3.811 * [backup-simplify]: Simplify k into k 3.811 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.811 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.811 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.811 * [taylor]: Taking taylor expansion of 2.0 in n 3.811 * [backup-simplify]: Simplify 2.0 into 2.0 3.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.811 * [taylor]: Taking taylor expansion of PI in n 3.811 * [backup-simplify]: Simplify PI into PI 3.811 * [taylor]: Taking taylor expansion of n in n 3.811 * [backup-simplify]: Simplify 0 into 0 3.811 * [backup-simplify]: Simplify 1 into 1 3.811 * [backup-simplify]: Simplify (/ PI 1) into PI 3.812 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.812 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.812 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.812 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.815 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.816 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.817 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.817 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.818 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.819 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.819 * [backup-simplify]: Simplify 0 into 0 3.825 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.825 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.826 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.826 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.826 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.826 * [taylor]: Taking taylor expansion of +nan.0 in n 3.826 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.826 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.826 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.826 * [taylor]: Taking taylor expansion of 0.5 in n 3.826 * [backup-simplify]: Simplify 0.5 into 0.5 3.826 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.826 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.826 * [taylor]: Taking taylor expansion of 1.0 in n 3.826 * [backup-simplify]: Simplify 1.0 into 1.0 3.826 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.826 * [taylor]: Taking taylor expansion of k in n 3.826 * [backup-simplify]: Simplify k into k 3.826 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.826 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.826 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.826 * [taylor]: Taking taylor expansion of 2.0 in n 3.826 * [backup-simplify]: Simplify 2.0 into 2.0 3.826 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.827 * [taylor]: Taking taylor expansion of PI in n 3.827 * [backup-simplify]: Simplify PI into PI 3.827 * [taylor]: Taking taylor expansion of n in n 3.827 * [backup-simplify]: Simplify 0 into 0 3.827 * [backup-simplify]: Simplify 1 into 1 3.827 * [backup-simplify]: Simplify (/ PI 1) into PI 3.827 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.828 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.828 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.828 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.829 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.830 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.830 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.831 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.832 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.833 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.833 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.834 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.834 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.835 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.836 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.836 * [backup-simplify]: Simplify (- 0) into 0 3.836 * [backup-simplify]: Simplify (+ 0 0) into 0 3.837 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.838 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.839 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 3.840 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.841 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 3.841 * [backup-simplify]: Simplify (- 0) into 0 3.841 * [backup-simplify]: Simplify 0 into 0 3.841 * [backup-simplify]: Simplify 0 into 0 3.844 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.844 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.845 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.845 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.845 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.845 * [taylor]: Taking taylor expansion of +nan.0 in n 3.845 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.845 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.845 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.845 * [taylor]: Taking taylor expansion of 0.5 in n 3.845 * [backup-simplify]: Simplify 0.5 into 0.5 3.845 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.845 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.845 * [taylor]: Taking taylor expansion of 1.0 in n 3.845 * [backup-simplify]: Simplify 1.0 into 1.0 3.845 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.845 * [taylor]: Taking taylor expansion of k in n 3.845 * [backup-simplify]: Simplify k into k 3.845 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.845 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.845 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.845 * [taylor]: Taking taylor expansion of 2.0 in n 3.845 * [backup-simplify]: Simplify 2.0 into 2.0 3.845 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.845 * [taylor]: Taking taylor expansion of PI in n 3.845 * [backup-simplify]: Simplify PI into PI 3.845 * [taylor]: Taking taylor expansion of n in n 3.845 * [backup-simplify]: Simplify 0 into 0 3.845 * [backup-simplify]: Simplify 1 into 1 3.846 * [backup-simplify]: Simplify (/ PI 1) into PI 3.846 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.847 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.847 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.847 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.848 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.848 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.849 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 3.850 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.851 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.851 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.852 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.855 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 3.856 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 3.856 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 3.856 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 3.856 * [taylor]: Taking taylor expansion of 1.0 in n 3.856 * [backup-simplify]: Simplify 1.0 into 1.0 3.856 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 3.856 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.856 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.856 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.856 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.856 * [taylor]: Taking taylor expansion of 0.5 in n 3.856 * [backup-simplify]: Simplify 0.5 into 0.5 3.856 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.856 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.856 * [taylor]: Taking taylor expansion of k in n 3.856 * [backup-simplify]: Simplify k into k 3.856 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.856 * [taylor]: Taking taylor expansion of 1.0 in n 3.856 * [backup-simplify]: Simplify 1.0 into 1.0 3.856 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.856 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.856 * [taylor]: Taking taylor expansion of -2.0 in n 3.856 * [backup-simplify]: Simplify -2.0 into -2.0 3.856 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.856 * [taylor]: Taking taylor expansion of PI in n 3.856 * [backup-simplify]: Simplify PI into PI 3.856 * [taylor]: Taking taylor expansion of n in n 3.856 * [backup-simplify]: Simplify 0 into 0 3.856 * [backup-simplify]: Simplify 1 into 1 3.856 * [backup-simplify]: Simplify (/ PI 1) into PI 3.857 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.857 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.857 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.858 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.858 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.859 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.860 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.860 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.860 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.860 * [taylor]: Taking taylor expansion of -1 in n 3.860 * [backup-simplify]: Simplify -1 into -1 3.860 * [taylor]: Taking taylor expansion of k in n 3.860 * [backup-simplify]: Simplify k into k 3.860 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.860 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.860 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.860 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.861 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 3.861 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.861 * [taylor]: Taking taylor expansion of 1.0 in k 3.861 * [backup-simplify]: Simplify 1.0 into 1.0 3.861 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.861 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.861 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.861 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.861 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.861 * [taylor]: Taking taylor expansion of 0.5 in k 3.861 * [backup-simplify]: Simplify 0.5 into 0.5 3.861 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.861 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.861 * [taylor]: Taking taylor expansion of k in k 3.861 * [backup-simplify]: Simplify 0 into 0 3.861 * [backup-simplify]: Simplify 1 into 1 3.862 * [backup-simplify]: Simplify (/ 1 1) into 1 3.862 * [taylor]: Taking taylor expansion of 1.0 in k 3.862 * [backup-simplify]: Simplify 1.0 into 1.0 3.862 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.862 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.862 * [taylor]: Taking taylor expansion of -2.0 in k 3.862 * [backup-simplify]: Simplify -2.0 into -2.0 3.862 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.862 * [taylor]: Taking taylor expansion of PI in k 3.862 * [backup-simplify]: Simplify PI into PI 3.862 * [taylor]: Taking taylor expansion of n in k 3.862 * [backup-simplify]: Simplify n into n 3.862 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.862 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.862 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.862 * [backup-simplify]: Simplify (+ 1 0) into 1 3.862 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.862 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.863 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 3.863 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.863 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.863 * [taylor]: Taking taylor expansion of -1 in k 3.863 * [backup-simplify]: Simplify -1 into -1 3.863 * [taylor]: Taking taylor expansion of k in k 3.863 * [backup-simplify]: Simplify 0 into 0 3.863 * [backup-simplify]: Simplify 1 into 1 3.863 * [backup-simplify]: Simplify (/ -1 1) into -1 3.863 * [backup-simplify]: Simplify (sqrt 0) into 0 3.864 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.864 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.864 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.864 * [taylor]: Taking taylor expansion of 1.0 in k 3.864 * [backup-simplify]: Simplify 1.0 into 1.0 3.864 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.864 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.864 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.864 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.864 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.864 * [taylor]: Taking taylor expansion of 0.5 in k 3.864 * [backup-simplify]: Simplify 0.5 into 0.5 3.864 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.864 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.864 * [taylor]: Taking taylor expansion of k in k 3.864 * [backup-simplify]: Simplify 0 into 0 3.864 * [backup-simplify]: Simplify 1 into 1 3.865 * [backup-simplify]: Simplify (/ 1 1) into 1 3.865 * [taylor]: Taking taylor expansion of 1.0 in k 3.865 * [backup-simplify]: Simplify 1.0 into 1.0 3.865 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.865 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.865 * [taylor]: Taking taylor expansion of -2.0 in k 3.865 * [backup-simplify]: Simplify -2.0 into -2.0 3.865 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.865 * [taylor]: Taking taylor expansion of PI in k 3.865 * [backup-simplify]: Simplify PI into PI 3.865 * [taylor]: Taking taylor expansion of n in k 3.865 * [backup-simplify]: Simplify n into n 3.865 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.865 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.865 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.865 * [backup-simplify]: Simplify (+ 1 0) into 1 3.866 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.866 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.866 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 3.866 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.866 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.866 * [taylor]: Taking taylor expansion of -1 in k 3.866 * [backup-simplify]: Simplify -1 into -1 3.866 * [taylor]: Taking taylor expansion of k in k 3.866 * [backup-simplify]: Simplify 0 into 0 3.866 * [backup-simplify]: Simplify 1 into 1 3.866 * [backup-simplify]: Simplify (/ -1 1) into -1 3.867 * [backup-simplify]: Simplify (sqrt 0) into 0 3.867 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.868 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.868 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.868 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.868 * [taylor]: Taking taylor expansion of +nan.0 in n 3.868 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.868 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.868 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.868 * [taylor]: Taking taylor expansion of 0.5 in n 3.868 * [backup-simplify]: Simplify 0.5 into 0.5 3.868 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.868 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.868 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.868 * [taylor]: Taking taylor expansion of -2.0 in n 3.868 * [backup-simplify]: Simplify -2.0 into -2.0 3.868 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.868 * [taylor]: Taking taylor expansion of PI in n 3.868 * [backup-simplify]: Simplify PI into PI 3.868 * [taylor]: Taking taylor expansion of n in n 3.868 * [backup-simplify]: Simplify 0 into 0 3.868 * [backup-simplify]: Simplify 1 into 1 3.868 * [backup-simplify]: Simplify (/ PI 1) into PI 3.869 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.869 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.869 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.869 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.869 * [taylor]: Taking taylor expansion of k in n 3.869 * [backup-simplify]: Simplify k into k 3.870 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.870 * [taylor]: Taking taylor expansion of 1.0 in n 3.870 * [backup-simplify]: Simplify 1.0 into 1.0 3.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.870 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.871 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.872 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.873 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.873 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.874 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.876 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.877 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.877 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.878 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.878 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.878 * [taylor]: Taking taylor expansion of +nan.0 in n 3.878 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.878 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.878 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.878 * [taylor]: Taking taylor expansion of 0.5 in n 3.878 * [backup-simplify]: Simplify 0.5 into 0.5 3.878 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.878 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.878 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.878 * [taylor]: Taking taylor expansion of -2.0 in n 3.878 * [backup-simplify]: Simplify -2.0 into -2.0 3.878 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.878 * [taylor]: Taking taylor expansion of PI in n 3.878 * [backup-simplify]: Simplify PI into PI 3.878 * [taylor]: Taking taylor expansion of n in n 3.878 * [backup-simplify]: Simplify 0 into 0 3.878 * [backup-simplify]: Simplify 1 into 1 3.878 * [backup-simplify]: Simplify (/ PI 1) into PI 3.878 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.879 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.879 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.879 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.879 * [taylor]: Taking taylor expansion of k in n 3.879 * [backup-simplify]: Simplify k into k 3.879 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.879 * [taylor]: Taking taylor expansion of 1.0 in n 3.879 * [backup-simplify]: Simplify 1.0 into 1.0 3.880 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.880 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.882 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.883 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.884 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.885 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.887 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.888 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.890 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.890 * [backup-simplify]: Simplify (+ 0 0) into 0 3.891 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.892 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.894 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.895 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.897 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 3.899 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.900 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 3.900 * [backup-simplify]: Simplify 0 into 0 3.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.906 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.908 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.909 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.909 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.909 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.909 * [taylor]: Taking taylor expansion of +nan.0 in n 3.909 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.909 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.909 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.909 * [taylor]: Taking taylor expansion of 0.5 in n 3.909 * [backup-simplify]: Simplify 0.5 into 0.5 3.909 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.909 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.909 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.910 * [taylor]: Taking taylor expansion of -2.0 in n 3.910 * [backup-simplify]: Simplify -2.0 into -2.0 3.910 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.910 * [taylor]: Taking taylor expansion of PI in n 3.910 * [backup-simplify]: Simplify PI into PI 3.910 * [taylor]: Taking taylor expansion of n in n 3.910 * [backup-simplify]: Simplify 0 into 0 3.910 * [backup-simplify]: Simplify 1 into 1 3.910 * [backup-simplify]: Simplify (/ PI 1) into PI 3.911 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.912 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.912 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.912 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.912 * [taylor]: Taking taylor expansion of k in n 3.912 * [backup-simplify]: Simplify k into k 3.912 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.912 * [taylor]: Taking taylor expansion of 1.0 in n 3.912 * [backup-simplify]: Simplify 1.0 into 1.0 3.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.914 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.915 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.916 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.917 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 3.918 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.919 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.919 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.922 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 3.922 * * * [progress]: simplifying candidates 3.924 * [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 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(- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 3.928 * * [simplify]: iteration 0: 353 enodes 4.046 * * [simplify]: iteration 1: 975 enodes 4.487 * * [simplify]: iteration 2: 3265 enodes 5.579 * * [simplify]: iteration complete: 5003 enodes 5.579 * * [simplify]: Extracting #0: cost 117 inf + 0 5.582 * * [simplify]: Extracting #1: cost 596 inf + 2 5.588 * * [simplify]: Extracting #2: cost 1008 inf + 4271 5.603 * * [simplify]: Extracting #3: cost 1200 inf + 33936 5.655 * * [simplify]: Extracting #4: cost 816 inf + 166432 5.725 * * [simplify]: Extracting #5: cost 465 inf + 368931 5.827 * * [simplify]: Extracting #6: cost 443 inf + 462195 5.946 * * [simplify]: Extracting #7: cost 181 inf + 659600 6.102 * * [simplify]: Extracting #8: cost 55 inf + 774574 6.301 * * [simplify]: Extracting #9: cost 8 inf + 830419 6.498 * * [simplify]: Extracting #10: cost 0 inf + 837854 6.664 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0)) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* PI n)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* 2.0 (* PI n)) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) 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(* (* (* 2.0 (* PI n)) (* 2.0 (* PI n))) (* 2.0 (* PI n))) (* (* (* 2.0 (* PI n)) (* 2.0 (* PI n))) (* 2.0 (* PI n))) (* (cbrt (* 2.0 (* PI n))) (cbrt (* 2.0 (* PI n)))) (cbrt (* 2.0 (* PI n))) (* (* (* 2.0 (* PI n)) (* 2.0 (* PI n))) (* 2.0 (* PI n))) (sqrt (* 2.0 (* PI n))) (sqrt (* 2.0 (* PI n))) (* (* (* (cbrt n) (cbrt n)) 2.0) PI) (* (* 2.0 PI) (sqrt n)) (* PI 2.0) (* PI n) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (+ (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (log (/ 1.0 (sqrt k)))) (exp (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (* (cbrt (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (sqrt (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* 1.0 (pow (* 2.0 (* PI n)) (/ 1.0 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 (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))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (cbrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))) (/ (* (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))) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (/ (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (cbrt 1.0) (/ (sqrt k) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (cbrt 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 1.0) (cbrt (sqrt k)))) (/ (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (cbrt k))) (* (/ (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))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k)))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (/ (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (* (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)) (sqrt k)) (/ (* 1.0 (pow (* 2.0 (* PI n)) (/ 1.0 2.0))) (sqrt k)) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) 1.0) (- (+ (+ (+ (* (* (log (* PI 2.0)) (exp (* (log (* 2.0 (* PI n))) 0.5))) (* (* (log n) (* k k)) 0.25)) (* (* 0.125 (* (log n) (* (log n) (* k k)))) (exp (* (log (* 2.0 (* PI n))) 0.5)))) (* (* (* (* (log (* PI 2.0)) (log (* PI 2.0))) 0.125) (* k k)) (exp (* (log (* 2.0 (* PI n))) 0.5)))) (exp (* (log (* 2.0 (* PI n))) 0.5))) (* (* k (+ (* (exp (* (log (* 2.0 (* PI n))) 0.5)) (log n)) (* (log (* PI 2.0)) (exp (* (log (* 2.0 (* PI n))) 0.5))))) 0.5)) (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 (* PI n)))))) (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) (+ (* (- +nan.0) (* k k)) (- +nan.0 (* +nan.0 k))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k)))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) +nan.0)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (+ (* (- (* +nan.0 k)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (+ (- (* (* +nan.0 (* k k)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (log n) (* k k))) +nan.0)) (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* +nan.0 (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (* (log (* PI 2.0)) k) (* (log (* PI 2.0)) k)))) (+ (- (* +nan.0 (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* (* k k) (* (log n) (log (* PI 2.0)))))) (* +nan.0 (* (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (log (* PI 2.0))) k))) (- (* (* +nan.0 (* k (log n))) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (* (* +nan.0 (* k k)) (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (log (* PI 2.0))) (* (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5) (* +nan.0 (* (* k (log n)) (* k (log n)))))))))))) (+ (- (/ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 (* PI n))))))) (* k k))) (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 (* PI n)))))) k)) (* (/ (- +nan.0) (* k k)) (/ (exp (* 0.5 (* (- 1.0 k) (log (* 2.0 (* PI n)))))) k)))) (+ (* +nan.0 (- (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))))) (* +nan.0 (+ (- (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) (* k k))) (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k)))) 6.686 * * * [progress]: adding candidates to table 7.605 * * [progress]: iteration 2 / 4 7.606 * * * [progress]: picking best candidate 7.713 * * * * [pick]: Picked # 7.713 * * * [progress]: localizing error 7.750 * * * [progress]: generating rewritten candidates 7.750 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 7.783 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 1) 7.788 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 7.793 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1) 7.814 * * * [progress]: generating series expansions 7.814 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 7.815 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 7.815 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 7.815 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 7.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 7.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 7.816 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 7.816 * [taylor]: Taking taylor expansion of 0.5 in k 7.816 * [backup-simplify]: Simplify 0.5 into 0.5 7.816 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 7.816 * [taylor]: Taking taylor expansion of 1.0 in k 7.816 * [backup-simplify]: Simplify 1.0 into 1.0 7.816 * [taylor]: Taking taylor expansion of k in k 7.816 * [backup-simplify]: Simplify 0 into 0 7.816 * [backup-simplify]: Simplify 1 into 1 7.816 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 7.816 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 7.816 * [taylor]: Taking taylor expansion of 2.0 in k 7.816 * [backup-simplify]: Simplify 2.0 into 2.0 7.816 * [taylor]: Taking taylor expansion of (* n PI) in k 7.816 * [taylor]: Taking taylor expansion of n in k 7.816 * [backup-simplify]: Simplify n into n 7.816 * [taylor]: Taking taylor expansion of PI in k 7.816 * [backup-simplify]: Simplify PI into PI 7.816 * [backup-simplify]: Simplify (* n PI) into (* n PI) 7.816 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 7.816 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 7.817 * [backup-simplify]: Simplify (- 0) into 0 7.817 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 7.818 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 7.818 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 7.818 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 7.818 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 7.818 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 7.818 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 7.818 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 7.818 * [taylor]: Taking taylor expansion of 0.5 in n 7.818 * [backup-simplify]: Simplify 0.5 into 0.5 7.818 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 7.818 * [taylor]: Taking taylor expansion of 1.0 in n 7.818 * [backup-simplify]: Simplify 1.0 into 1.0 7.818 * [taylor]: Taking taylor expansion of k in n 7.818 * [backup-simplify]: Simplify k into k 7.818 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 7.818 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.818 * [taylor]: Taking taylor expansion of 2.0 in n 7.818 * [backup-simplify]: Simplify 2.0 into 2.0 7.818 * [taylor]: Taking taylor expansion of (* n PI) in n 7.818 * [taylor]: Taking taylor expansion of n in n 7.818 * [backup-simplify]: Simplify 0 into 0 7.818 * [backup-simplify]: Simplify 1 into 1 7.818 * [taylor]: Taking taylor expansion of PI in n 7.818 * [backup-simplify]: Simplify PI into PI 7.819 * [backup-simplify]: Simplify (* 0 PI) into 0 7.819 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.821 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.822 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.824 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.824 * [backup-simplify]: Simplify (- k) into (- k) 7.824 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 7.824 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 7.826 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.828 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 7.829 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 7.829 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 7.829 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 7.829 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 7.829 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 7.829 * [taylor]: Taking taylor expansion of 0.5 in n 7.829 * [backup-simplify]: Simplify 0.5 into 0.5 7.829 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 7.829 * [taylor]: Taking taylor expansion of 1.0 in n 7.829 * [backup-simplify]: Simplify 1.0 into 1.0 7.829 * [taylor]: Taking taylor expansion of k in n 7.829 * [backup-simplify]: Simplify k into k 7.829 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 7.829 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 7.829 * [taylor]: Taking taylor expansion of 2.0 in n 7.829 * [backup-simplify]: Simplify 2.0 into 2.0 7.829 * [taylor]: Taking taylor expansion of (* n PI) in n 7.829 * [taylor]: Taking taylor expansion of n in n 7.829 * [backup-simplify]: Simplify 0 into 0 7.829 * [backup-simplify]: Simplify 1 into 1 7.829 * [taylor]: Taking taylor expansion of PI in n 7.829 * [backup-simplify]: Simplify PI into PI 7.830 * [backup-simplify]: Simplify (* 0 PI) into 0 7.830 * [backup-simplify]: Simplify (* 2.0 0) into 0 7.832 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 7.834 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 7.835 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.835 * [backup-simplify]: Simplify (- k) into (- k) 7.835 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 7.835 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 7.836 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.838 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 7.839 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 7.839 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 7.839 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 7.839 * [taylor]: Taking taylor expansion of 0.5 in k 7.839 * [backup-simplify]: Simplify 0.5 into 0.5 7.839 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 7.839 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 7.839 * [taylor]: Taking taylor expansion of 1.0 in k 7.839 * [backup-simplify]: Simplify 1.0 into 1.0 7.839 * [taylor]: Taking taylor expansion of k in k 7.839 * [backup-simplify]: Simplify 0 into 0 7.839 * [backup-simplify]: Simplify 1 into 1 7.839 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 7.839 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 7.839 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 7.839 * [taylor]: Taking taylor expansion of 2.0 in k 7.840 * [backup-simplify]: Simplify 2.0 into 2.0 7.840 * [taylor]: Taking taylor expansion of PI in k 7.840 * [backup-simplify]: Simplify PI into PI 7.840 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.841 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.841 * [taylor]: Taking taylor expansion of (log n) in k 7.841 * [taylor]: Taking taylor expansion of n in k 7.841 * [backup-simplify]: Simplify n into n 7.841 * [backup-simplify]: Simplify (log n) into (log n) 7.842 * [backup-simplify]: Simplify (- 0) into 0 7.842 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 7.844 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 7.845 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 7.846 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 7.847 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 7.849 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 7.850 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 7.851 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 7.853 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.853 * [backup-simplify]: Simplify (- 0) into 0 7.853 * [backup-simplify]: Simplify (+ 0 0) into 0 7.854 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 7.855 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.857 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 7.859 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.859 * [taylor]: Taking taylor expansion of 0 in k 7.859 * [backup-simplify]: Simplify 0 into 0 7.859 * [backup-simplify]: Simplify 0 into 0 7.859 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.861 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.862 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 7.863 * [backup-simplify]: Simplify (+ 0 0) into 0 7.863 * [backup-simplify]: Simplify (- 1) into -1 7.863 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.865 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 7.867 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 7.870 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 7.879 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 7.880 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 7.882 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 7.886 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 7.886 * [backup-simplify]: Simplify (- 0) into 0 7.886 * [backup-simplify]: Simplify (+ 0 0) into 0 7.887 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 7.889 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 7.890 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 7.893 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.893 * [taylor]: Taking taylor expansion of 0 in k 7.893 * [backup-simplify]: Simplify 0 into 0 7.893 * [backup-simplify]: Simplify 0 into 0 7.893 * [backup-simplify]: Simplify 0 into 0 7.894 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.897 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 7.899 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 7.900 * [backup-simplify]: Simplify (+ 0 0) into 0 7.900 * [backup-simplify]: Simplify (- 0) into 0 7.900 * [backup-simplify]: Simplify (+ 0 0) into 0 7.902 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 7.905 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 7.909 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 7.914 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 7.924 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 7.925 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 7.925 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 7.925 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 7.925 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 7.925 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 7.925 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 7.925 * [taylor]: Taking taylor expansion of 0.5 in k 7.925 * [backup-simplify]: Simplify 0.5 into 0.5 7.925 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 7.925 * [taylor]: Taking taylor expansion of 1.0 in k 7.925 * [backup-simplify]: Simplify 1.0 into 1.0 7.925 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.925 * [taylor]: Taking taylor expansion of k in k 7.925 * [backup-simplify]: Simplify 0 into 0 7.925 * [backup-simplify]: Simplify 1 into 1 7.926 * [backup-simplify]: Simplify (/ 1 1) into 1 7.926 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 7.926 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 7.926 * [taylor]: Taking taylor expansion of 2.0 in k 7.926 * [backup-simplify]: Simplify 2.0 into 2.0 7.926 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.926 * [taylor]: Taking taylor expansion of PI in k 7.926 * [backup-simplify]: Simplify PI into PI 7.926 * [taylor]: Taking taylor expansion of n in k 7.926 * [backup-simplify]: Simplify n into n 7.926 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.926 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 7.926 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 7.927 * [backup-simplify]: Simplify (- 1) into -1 7.927 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.927 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 7.928 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 7.928 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 7.928 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 7.928 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 7.928 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 7.928 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 7.928 * [taylor]: Taking taylor expansion of 0.5 in n 7.928 * [backup-simplify]: Simplify 0.5 into 0.5 7.928 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 7.928 * [taylor]: Taking taylor expansion of 1.0 in n 7.928 * [backup-simplify]: Simplify 1.0 into 1.0 7.928 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.928 * [taylor]: Taking taylor expansion of k in n 7.928 * [backup-simplify]: Simplify k into k 7.928 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.928 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 7.928 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.928 * [taylor]: Taking taylor expansion of 2.0 in n 7.928 * [backup-simplify]: Simplify 2.0 into 2.0 7.928 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.928 * [taylor]: Taking taylor expansion of PI in n 7.928 * [backup-simplify]: Simplify PI into PI 7.929 * [taylor]: Taking taylor expansion of n in n 7.929 * [backup-simplify]: Simplify 0 into 0 7.929 * [backup-simplify]: Simplify 1 into 1 7.929 * [backup-simplify]: Simplify (/ PI 1) into PI 7.930 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.931 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.931 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.931 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 7.931 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 7.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.934 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 7.935 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.935 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 7.935 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 7.936 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 7.936 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 7.936 * [taylor]: Taking taylor expansion of 0.5 in n 7.936 * [backup-simplify]: Simplify 0.5 into 0.5 7.936 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 7.936 * [taylor]: Taking taylor expansion of 1.0 in n 7.936 * [backup-simplify]: Simplify 1.0 into 1.0 7.936 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.936 * [taylor]: Taking taylor expansion of k in n 7.936 * [backup-simplify]: Simplify k into k 7.936 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.936 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 7.936 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 7.936 * [taylor]: Taking taylor expansion of 2.0 in n 7.936 * [backup-simplify]: Simplify 2.0 into 2.0 7.936 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.936 * [taylor]: Taking taylor expansion of PI in n 7.936 * [backup-simplify]: Simplify PI into PI 7.936 * [taylor]: Taking taylor expansion of n in n 7.936 * [backup-simplify]: Simplify 0 into 0 7.936 * [backup-simplify]: Simplify 1 into 1 7.937 * [backup-simplify]: Simplify (/ PI 1) into PI 7.937 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.938 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.938 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 7.938 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 7.938 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 7.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.941 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 7.942 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.942 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 7.942 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 7.942 * [taylor]: Taking taylor expansion of 0.5 in k 7.943 * [backup-simplify]: Simplify 0.5 into 0.5 7.943 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 7.943 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 7.943 * [taylor]: Taking taylor expansion of 1.0 in k 7.943 * [backup-simplify]: Simplify 1.0 into 1.0 7.943 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.943 * [taylor]: Taking taylor expansion of k in k 7.943 * [backup-simplify]: Simplify 0 into 0 7.943 * [backup-simplify]: Simplify 1 into 1 7.943 * [backup-simplify]: Simplify (/ 1 1) into 1 7.943 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 7.944 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 7.944 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 7.944 * [taylor]: Taking taylor expansion of 2.0 in k 7.944 * [backup-simplify]: Simplify 2.0 into 2.0 7.944 * [taylor]: Taking taylor expansion of PI in k 7.944 * [backup-simplify]: Simplify PI into PI 7.944 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 7.945 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 7.945 * [taylor]: Taking taylor expansion of (log n) in k 7.945 * [taylor]: Taking taylor expansion of n in k 7.945 * [backup-simplify]: Simplify n into n 7.946 * [backup-simplify]: Simplify (log n) into (log n) 7.946 * [backup-simplify]: Simplify (- 1) into -1 7.946 * [backup-simplify]: Simplify (+ 0 -1) into -1 7.946 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.948 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 7.949 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 7.950 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 7.951 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.952 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 7.953 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 7.956 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 7.956 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.956 * [backup-simplify]: Simplify (- 0) into 0 7.957 * [backup-simplify]: Simplify (+ 0 0) into 0 7.957 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 7.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.960 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 7.962 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.962 * [taylor]: Taking taylor expansion of 0 in k 7.962 * [backup-simplify]: Simplify 0 into 0 7.962 * [backup-simplify]: Simplify 0 into 0 7.962 * [backup-simplify]: Simplify 0 into 0 7.963 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.963 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.965 * [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 7.965 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.966 * [backup-simplify]: Simplify (- 0) into 0 7.966 * [backup-simplify]: Simplify (+ 0 0) into 0 7.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 7.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.968 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 7.970 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 7.970 * [taylor]: Taking taylor expansion of 0 in k 7.970 * [backup-simplify]: Simplify 0 into 0 7.970 * [backup-simplify]: Simplify 0 into 0 7.970 * [backup-simplify]: Simplify 0 into 0 7.970 * [backup-simplify]: Simplify 0 into 0 7.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.975 * [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 7.975 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.975 * [backup-simplify]: Simplify (- 0) into 0 7.975 * [backup-simplify]: Simplify (+ 0 0) into 0 7.976 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 7.977 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.978 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 7.980 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 7.980 * [taylor]: Taking taylor expansion of 0 in k 7.980 * [backup-simplify]: Simplify 0 into 0 7.980 * [backup-simplify]: Simplify 0 into 0 7.981 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 7.981 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 7.981 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 7.981 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 7.981 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 7.981 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 7.981 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 7.981 * [taylor]: Taking taylor expansion of 0.5 in k 7.981 * [backup-simplify]: Simplify 0.5 into 0.5 7.981 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.981 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.981 * [taylor]: Taking taylor expansion of k in k 7.981 * [backup-simplify]: Simplify 0 into 0 7.981 * [backup-simplify]: Simplify 1 into 1 7.981 * [backup-simplify]: Simplify (/ 1 1) into 1 7.981 * [taylor]: Taking taylor expansion of 1.0 in k 7.982 * [backup-simplify]: Simplify 1.0 into 1.0 7.982 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 7.982 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 7.982 * [taylor]: Taking taylor expansion of -2.0 in k 7.982 * [backup-simplify]: Simplify -2.0 into -2.0 7.982 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.982 * [taylor]: Taking taylor expansion of PI in k 7.982 * [backup-simplify]: Simplify PI into PI 7.982 * [taylor]: Taking taylor expansion of n in k 7.982 * [backup-simplify]: Simplify n into n 7.982 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.982 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 7.982 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 7.982 * [backup-simplify]: Simplify (+ 1 0) into 1 7.982 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 7.982 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 7.983 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 7.983 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.983 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.983 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.983 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.983 * [taylor]: Taking taylor expansion of 0.5 in n 7.983 * [backup-simplify]: Simplify 0.5 into 0.5 7.983 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.983 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.983 * [taylor]: Taking taylor expansion of k in n 7.983 * [backup-simplify]: Simplify k into k 7.983 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.983 * [taylor]: Taking taylor expansion of 1.0 in n 7.983 * [backup-simplify]: Simplify 1.0 into 1.0 7.983 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.983 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.983 * [taylor]: Taking taylor expansion of -2.0 in n 7.983 * [backup-simplify]: Simplify -2.0 into -2.0 7.983 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.983 * [taylor]: Taking taylor expansion of PI in n 7.983 * [backup-simplify]: Simplify PI into PI 7.983 * [taylor]: Taking taylor expansion of n in n 7.983 * [backup-simplify]: Simplify 0 into 0 7.983 * [backup-simplify]: Simplify 1 into 1 7.983 * [backup-simplify]: Simplify (/ PI 1) into PI 7.984 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.984 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.984 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.984 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.985 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.986 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 7.987 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.987 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.987 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.987 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.987 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.987 * [taylor]: Taking taylor expansion of 0.5 in n 7.987 * [backup-simplify]: Simplify 0.5 into 0.5 7.987 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.987 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.987 * [taylor]: Taking taylor expansion of k in n 7.987 * [backup-simplify]: Simplify k into k 7.987 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.987 * [taylor]: Taking taylor expansion of 1.0 in n 7.987 * [backup-simplify]: Simplify 1.0 into 1.0 7.987 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.987 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.987 * [taylor]: Taking taylor expansion of -2.0 in n 7.987 * [backup-simplify]: Simplify -2.0 into -2.0 7.987 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.987 * [taylor]: Taking taylor expansion of PI in n 7.987 * [backup-simplify]: Simplify PI into PI 7.987 * [taylor]: Taking taylor expansion of n in n 7.987 * [backup-simplify]: Simplify 0 into 0 7.987 * [backup-simplify]: Simplify 1 into 1 7.987 * [backup-simplify]: Simplify (/ PI 1) into PI 7.988 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.988 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.988 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.988 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.989 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.990 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 7.991 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.991 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 7.991 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 7.991 * [taylor]: Taking taylor expansion of 0.5 in k 7.991 * [backup-simplify]: Simplify 0.5 into 0.5 7.991 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 7.991 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 7.991 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 7.991 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 7.991 * [taylor]: Taking taylor expansion of -2.0 in k 7.991 * [backup-simplify]: Simplify -2.0 into -2.0 7.991 * [taylor]: Taking taylor expansion of PI in k 7.991 * [backup-simplify]: Simplify PI into PI 7.991 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.992 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.992 * [taylor]: Taking taylor expansion of (log n) in k 7.992 * [taylor]: Taking taylor expansion of n in k 7.992 * [backup-simplify]: Simplify n into n 7.992 * [backup-simplify]: Simplify (log n) into (log n) 7.992 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.992 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.992 * [taylor]: Taking taylor expansion of k in k 7.992 * [backup-simplify]: Simplify 0 into 0 7.992 * [backup-simplify]: Simplify 1 into 1 7.992 * [backup-simplify]: Simplify (/ 1 1) into 1 7.992 * [taylor]: Taking taylor expansion of 1.0 in k 7.992 * [backup-simplify]: Simplify 1.0 into 1.0 7.992 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.993 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 7.994 * [backup-simplify]: Simplify (+ 1 0) into 1 7.994 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 7.995 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 7.996 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.997 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 7.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.999 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.000 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.001 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.007 * [backup-simplify]: Simplify (+ 0 0) into 0 8.008 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.009 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.011 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.013 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 8.013 * [taylor]: Taking taylor expansion of 0 in k 8.013 * [backup-simplify]: Simplify 0 into 0 8.013 * [backup-simplify]: Simplify 0 into 0 8.013 * [backup-simplify]: Simplify 0 into 0 8.014 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.015 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.018 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.019 * [backup-simplify]: Simplify (+ 0 0) into 0 8.020 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.021 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.023 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.025 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.026 * [taylor]: Taking taylor expansion of 0 in k 8.026 * [backup-simplify]: Simplify 0 into 0 8.026 * [backup-simplify]: Simplify 0 into 0 8.026 * [backup-simplify]: Simplify 0 into 0 8.026 * [backup-simplify]: Simplify 0 into 0 8.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.028 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.034 * [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 8.035 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.035 * [backup-simplify]: Simplify (+ 0 0) into 0 8.036 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.038 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.040 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.043 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.043 * [taylor]: Taking taylor expansion of 0 in k 8.043 * [backup-simplify]: Simplify 0 into 0 8.043 * [backup-simplify]: Simplify 0 into 0 8.044 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.045 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 1) 8.045 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.045 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.045 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.045 * [taylor]: Taking taylor expansion of 1.0 in k 8.045 * [backup-simplify]: Simplify 1.0 into 1.0 8.045 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.045 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.045 * [taylor]: Taking taylor expansion of k in k 8.045 * [backup-simplify]: Simplify 0 into 0 8.045 * [backup-simplify]: Simplify 1 into 1 8.045 * [backup-simplify]: Simplify (/ 1 1) into 1 8.046 * [backup-simplify]: Simplify (sqrt 0) into 0 8.047 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.047 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.047 * [taylor]: Taking taylor expansion of 1.0 in k 8.047 * [backup-simplify]: Simplify 1.0 into 1.0 8.047 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.047 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.047 * [taylor]: Taking taylor expansion of k in k 8.047 * [backup-simplify]: Simplify 0 into 0 8.047 * [backup-simplify]: Simplify 1 into 1 8.048 * [backup-simplify]: Simplify (/ 1 1) into 1 8.048 * [backup-simplify]: Simplify (sqrt 0) into 0 8.049 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.049 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.049 * [backup-simplify]: Simplify 0 into 0 8.050 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.050 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.051 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.052 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.054 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.054 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.054 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.056 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.058 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.058 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.059 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 8.059 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.059 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.059 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.059 * [taylor]: Taking taylor expansion of 1.0 in k 8.059 * [backup-simplify]: Simplify 1.0 into 1.0 8.059 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.059 * [taylor]: Taking taylor expansion of k in k 8.059 * [backup-simplify]: Simplify 0 into 0 8.059 * [backup-simplify]: Simplify 1 into 1 8.059 * [backup-simplify]: Simplify (sqrt 0) into 0 8.060 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.060 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.060 * [taylor]: Taking taylor expansion of 1.0 in k 8.060 * [backup-simplify]: Simplify 1.0 into 1.0 8.060 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.060 * [taylor]: Taking taylor expansion of k in k 8.060 * [backup-simplify]: Simplify 0 into 0 8.060 * [backup-simplify]: Simplify 1 into 1 8.060 * [backup-simplify]: Simplify (sqrt 0) into 0 8.061 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.061 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.061 * [backup-simplify]: Simplify 0 into 0 8.062 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.063 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.064 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.065 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.066 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.068 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.069 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.069 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.070 * [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)))))))) 8.070 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.070 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.070 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.070 * [taylor]: Taking taylor expansion of 1.0 in k 8.070 * [backup-simplify]: Simplify 1.0 into 1.0 8.071 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.071 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.071 * [taylor]: Taking taylor expansion of -1 in k 8.071 * [backup-simplify]: Simplify -1 into -1 8.071 * [taylor]: Taking taylor expansion of k in k 8.071 * [backup-simplify]: Simplify 0 into 0 8.071 * [backup-simplify]: Simplify 1 into 1 8.071 * [backup-simplify]: Simplify (/ -1 1) into -1 8.071 * [backup-simplify]: Simplify (sqrt 0) into 0 8.072 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.072 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.072 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.072 * [taylor]: Taking taylor expansion of 1.0 in k 8.072 * [backup-simplify]: Simplify 1.0 into 1.0 8.072 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.072 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.072 * [taylor]: Taking taylor expansion of -1 in k 8.072 * [backup-simplify]: Simplify -1 into -1 8.072 * [taylor]: Taking taylor expansion of k in k 8.072 * [backup-simplify]: Simplify 0 into 0 8.072 * [backup-simplify]: Simplify 1 into 1 8.073 * [backup-simplify]: Simplify (/ -1 1) into -1 8.073 * [backup-simplify]: Simplify (sqrt 0) into 0 8.074 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.074 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.074 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.074 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.076 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.078 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.078 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.081 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.085 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.086 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.087 * [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))))) 8.087 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 8.087 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 8.087 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 8.087 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.087 * [taylor]: Taking taylor expansion of 1.0 in k 8.087 * [backup-simplify]: Simplify 1.0 into 1.0 8.087 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.087 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.087 * [taylor]: Taking taylor expansion of k in k 8.087 * [backup-simplify]: Simplify 0 into 0 8.087 * [backup-simplify]: Simplify 1 into 1 8.088 * [backup-simplify]: Simplify (/ 1 1) into 1 8.088 * [backup-simplify]: Simplify (sqrt 0) into 0 8.089 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.089 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 8.089 * [taylor]: Taking taylor expansion of 1.0 in k 8.090 * [backup-simplify]: Simplify 1.0 into 1.0 8.090 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 8.090 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.090 * [taylor]: Taking taylor expansion of k in k 8.090 * [backup-simplify]: Simplify 0 into 0 8.090 * [backup-simplify]: Simplify 1 into 1 8.090 * [backup-simplify]: Simplify (/ 1 1) into 1 8.090 * [backup-simplify]: Simplify (sqrt 0) into 0 8.092 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.092 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.092 * [backup-simplify]: Simplify 0 into 0 8.094 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.094 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.095 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 8.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.101 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.101 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.102 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.105 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.106 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.106 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.107 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 8.107 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 8.107 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 8.107 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.107 * [taylor]: Taking taylor expansion of 1.0 in k 8.107 * [backup-simplify]: Simplify 1.0 into 1.0 8.108 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.108 * [taylor]: Taking taylor expansion of k in k 8.108 * [backup-simplify]: Simplify 0 into 0 8.108 * [backup-simplify]: Simplify 1 into 1 8.108 * [backup-simplify]: Simplify (sqrt 0) into 0 8.109 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.109 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 8.109 * [taylor]: Taking taylor expansion of 1.0 in k 8.109 * [backup-simplify]: Simplify 1.0 into 1.0 8.109 * [taylor]: Taking taylor expansion of (sqrt k) in k 8.109 * [taylor]: Taking taylor expansion of k in k 8.109 * [backup-simplify]: Simplify 0 into 0 8.109 * [backup-simplify]: Simplify 1 into 1 8.109 * [backup-simplify]: Simplify (sqrt 0) into 0 8.110 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 8.110 * [backup-simplify]: Simplify (* 1.0 0) into 0 8.110 * [backup-simplify]: Simplify 0 into 0 8.111 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 8.111 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.113 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.114 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 8.114 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.121 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.122 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 8.122 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.123 * [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)))))))) 8.124 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 8.124 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 8.124 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.124 * [taylor]: Taking taylor expansion of 1.0 in k 8.124 * [backup-simplify]: Simplify 1.0 into 1.0 8.124 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.124 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.124 * [taylor]: Taking taylor expansion of -1 in k 8.124 * [backup-simplify]: Simplify -1 into -1 8.124 * [taylor]: Taking taylor expansion of k in k 8.124 * [backup-simplify]: Simplify 0 into 0 8.124 * [backup-simplify]: Simplify 1 into 1 8.124 * [backup-simplify]: Simplify (/ -1 1) into -1 8.124 * [backup-simplify]: Simplify (sqrt 0) into 0 8.125 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.125 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.125 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 8.125 * [taylor]: Taking taylor expansion of 1.0 in k 8.125 * [backup-simplify]: Simplify 1.0 into 1.0 8.125 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 8.125 * [taylor]: Taking taylor expansion of (/ -1 k) in k 8.125 * [taylor]: Taking taylor expansion of -1 in k 8.125 * [backup-simplify]: Simplify -1 into -1 8.125 * [taylor]: Taking taylor expansion of k in k 8.125 * [backup-simplify]: Simplify 0 into 0 8.125 * [backup-simplify]: Simplify 1 into 1 8.126 * [backup-simplify]: Simplify (/ -1 1) into -1 8.126 * [backup-simplify]: Simplify (sqrt 0) into 0 8.127 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 8.127 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 8.127 * [backup-simplify]: Simplify +nan.0 into +nan.0 8.128 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 8.129 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 8.131 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 8.131 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.132 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.134 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 8.137 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 8.137 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 8.138 * [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))))) 8.138 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1) 8.139 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.139 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 8.139 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.139 * [taylor]: Taking taylor expansion of 2.0 in n 8.139 * [backup-simplify]: Simplify 2.0 into 2.0 8.139 * [taylor]: Taking taylor expansion of (* n PI) in n 8.139 * [taylor]: Taking taylor expansion of n in n 8.139 * [backup-simplify]: Simplify 0 into 0 8.139 * [backup-simplify]: Simplify 1 into 1 8.139 * [taylor]: Taking taylor expansion of PI in n 8.139 * [backup-simplify]: Simplify PI into PI 8.139 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.139 * [taylor]: Taking taylor expansion of 2.0 in n 8.139 * [backup-simplify]: Simplify 2.0 into 2.0 8.139 * [taylor]: Taking taylor expansion of (* n PI) in n 8.139 * [taylor]: Taking taylor expansion of n in n 8.139 * [backup-simplify]: Simplify 0 into 0 8.139 * [backup-simplify]: Simplify 1 into 1 8.139 * [taylor]: Taking taylor expansion of PI in n 8.139 * [backup-simplify]: Simplify PI into PI 8.140 * [backup-simplify]: Simplify (* 0 PI) into 0 8.140 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.140 * [backup-simplify]: Simplify 0 into 0 8.141 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.142 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.142 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.143 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.143 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.143 * [backup-simplify]: Simplify 0 into 0 8.144 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.145 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.145 * [backup-simplify]: Simplify 0 into 0 8.146 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.147 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 8.147 * [backup-simplify]: Simplify 0 into 0 8.148 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.148 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 8.148 * [backup-simplify]: Simplify 0 into 0 8.149 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.150 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 8.150 * [backup-simplify]: Simplify 0 into 0 8.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 8.153 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 8.153 * [backup-simplify]: Simplify 0 into 0 8.153 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 8.154 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 8.154 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 8.154 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.154 * [taylor]: Taking taylor expansion of 2.0 in n 8.154 * [backup-simplify]: Simplify 2.0 into 2.0 8.154 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.154 * [taylor]: Taking taylor expansion of PI in n 8.154 * [backup-simplify]: Simplify PI into PI 8.154 * [taylor]: Taking taylor expansion of n in n 8.154 * [backup-simplify]: Simplify 0 into 0 8.154 * [backup-simplify]: Simplify 1 into 1 8.154 * [backup-simplify]: Simplify (/ PI 1) into PI 8.154 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.154 * [taylor]: Taking taylor expansion of 2.0 in n 8.154 * [backup-simplify]: Simplify 2.0 into 2.0 8.154 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.154 * [taylor]: Taking taylor expansion of PI in n 8.154 * [backup-simplify]: Simplify PI into PI 8.154 * [taylor]: Taking taylor expansion of n in n 8.154 * [backup-simplify]: Simplify 0 into 0 8.154 * [backup-simplify]: Simplify 1 into 1 8.154 * [backup-simplify]: Simplify (/ PI 1) into PI 8.155 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.155 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.156 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.156 * [backup-simplify]: Simplify 0 into 0 8.157 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.157 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.157 * [backup-simplify]: Simplify 0 into 0 8.158 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.159 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.159 * [backup-simplify]: Simplify 0 into 0 8.159 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.160 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.160 * [backup-simplify]: Simplify 0 into 0 8.161 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.162 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.162 * [backup-simplify]: Simplify 0 into 0 8.162 * [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 8.163 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.163 * [backup-simplify]: Simplify 0 into 0 8.164 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 8.164 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 8.164 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 8.164 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.164 * [taylor]: Taking taylor expansion of -2.0 in n 8.164 * [backup-simplify]: Simplify -2.0 into -2.0 8.164 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.164 * [taylor]: Taking taylor expansion of PI in n 8.164 * [backup-simplify]: Simplify PI into PI 8.164 * [taylor]: Taking taylor expansion of n in n 8.164 * [backup-simplify]: Simplify 0 into 0 8.164 * [backup-simplify]: Simplify 1 into 1 8.164 * [backup-simplify]: Simplify (/ PI 1) into PI 8.164 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.164 * [taylor]: Taking taylor expansion of -2.0 in n 8.164 * [backup-simplify]: Simplify -2.0 into -2.0 8.165 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.165 * [taylor]: Taking taylor expansion of PI in n 8.165 * [backup-simplify]: Simplify PI into PI 8.165 * [taylor]: Taking taylor expansion of n in n 8.165 * [backup-simplify]: Simplify 0 into 0 8.165 * [backup-simplify]: Simplify 1 into 1 8.165 * [backup-simplify]: Simplify (/ PI 1) into PI 8.165 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.166 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.166 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.167 * [backup-simplify]: Simplify 0 into 0 8.167 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.168 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.168 * [backup-simplify]: Simplify 0 into 0 8.168 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.169 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.169 * [backup-simplify]: Simplify 0 into 0 8.170 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.170 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 8.170 * [backup-simplify]: Simplify 0 into 0 8.171 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.172 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 8.172 * [backup-simplify]: Simplify 0 into 0 8.173 * [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 8.175 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 8.175 * [backup-simplify]: Simplify 0 into 0 8.175 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 8.175 * * * [progress]: simplifying candidates 8.179 * [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) (- (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) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 8.184 * * [simplify]: iteration 0: 236 enodes 8.269 * * [simplify]: iteration 1: 601 enodes 8.546 * * [simplify]: iteration 2: 1810 enodes 9.234 * * [simplify]: iteration complete: 5000 enodes 9.234 * * [simplify]: Extracting #0: cost 81 inf + 0 9.235 * * [simplify]: Extracting #1: cost 678 inf + 2 9.240 * * [simplify]: Extracting #2: cost 1517 inf + 5547 9.262 * * [simplify]: Extracting #3: cost 1378 inf + 83918 9.346 * * [simplify]: Extracting #4: cost 604 inf + 291031 9.466 * * [simplify]: Extracting #5: cost 190 inf + 474955 9.607 * * [simplify]: Extracting #6: cost 19 inf + 536567 9.754 * * [simplify]: Extracting #7: cost 0 inf + 536604 9.858 * * [simplify]: Extracting #8: cost 0 inf + 535924 9.981 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI n) 2.0) (/ 1.0 2.0)) (pow (* (* PI n) 2.0) (/ k 2.0)) (pow (* (* PI n) 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* PI n) 2.0) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* PI n) 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow (* (* PI n) 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* PI n) 2.0) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI n) 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* PI n) 2.0) (sqrt (- 1.0 k))) (pow (* (* PI n) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ 1 (sqrt 2.0))) (* (* PI n) 2.0) (pow (* (* PI n) 2.0) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* PI n) 2.0) (+ (sqrt 1.0) (sqrt k))) (pow (* (* PI n) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ 1 (sqrt 2.0))) (* (* PI n) 2.0) (* (* PI n) 2.0) (pow (* (* PI n) 2.0) (- 1.0 k)) (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0))) (exp (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (pow (* (* PI n) 2.0) (* (/ (- 1.0 k) 2.0) 1/2)) (pow (* (* PI n) 2.0) (* (/ (- 1.0 k) 2.0) 1/2)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* PI n) 2.0) (* (* PI n) 2.0) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (exp (* (* PI n) 2.0)) (* (* (* n 2.0) PI) (* (* (* n 2.0) PI) (* (* n 2.0) PI))) (* (* (* n 2.0) PI) (* (* (* n 2.0) PI) (* (* n 2.0) PI))) (* (cbrt (* (* PI n) 2.0)) (cbrt (* (* PI n) 2.0))) (cbrt (* (* PI n) 2.0)) (* (* (* n 2.0) PI) (* (* (* n 2.0) PI) (* (* n 2.0) PI))) (sqrt (* (* PI n) 2.0)) (sqrt (* (* PI n) 2.0)) (* 2.0 (* (* PI (cbrt n)) (cbrt n))) (* (* (sqrt n) 2.0) PI) (* PI 2.0) (* PI n) (+ (* (* (* k k) 0.125) (+ (* (* (log n) (log n)) (exp (* (log (* (* PI n) 2.0)) 0.5))) (* (* (exp (* (log (* (* PI n) 2.0)) 0.5)) (log (* PI 2.0))) (log (* PI 2.0))))) (+ (exp (* (log (* (* PI n) 2.0)) 0.5)) (- (* (* (* 0.25 (log (* PI 2.0))) (* (log n) (* k k))) (exp (* (log (* (* PI n) 2.0)) 0.5))) (* 0.5 (* (* (exp (* (log (* (* PI n) 2.0)) 0.5)) k) (log (* (* PI n) 2.0))))))) (exp (* (* (log (* (* PI n) 2.0)) 0.5) (- 1.0 k))) (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n))))) (+ (* (* k k) (- +nan.0)) (- +nan.0 (* +nan.0 k))) (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) (/ +nan.0 (* k (* k k))))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (* k k)))) (+ (* (* k k) (- +nan.0)) (- +nan.0 (* +nan.0 k))) (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) (/ +nan.0 (* k (* k k))))) (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (* k k)))) (* (* PI n) 2.0) (* (* PI n) 2.0) (* (* PI n) 2.0) 9.995 * * * [progress]: adding candidates to table 10.986 * * [progress]: iteration 3 / 4 10.986 * * * [progress]: picking best candidate 11.052 * * * * [pick]: Picked # 11.053 * * * [progress]: localizing error 11.117 * * * [progress]: generating rewritten candidates 11.117 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 11.134 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1) 11.145 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 11.170 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 11.205 * * * [progress]: generating series expansions 11.205 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 11.206 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 11.206 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 11.206 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 11.206 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 11.206 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 11.206 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 11.206 * [taylor]: Taking taylor expansion of 0.5 in k 11.206 * [backup-simplify]: Simplify 0.5 into 0.5 11.206 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.206 * [taylor]: Taking taylor expansion of 1.0 in k 11.206 * [backup-simplify]: Simplify 1.0 into 1.0 11.206 * [taylor]: Taking taylor expansion of k in k 11.206 * [backup-simplify]: Simplify 0 into 0 11.206 * [backup-simplify]: Simplify 1 into 1 11.206 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 11.206 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 11.206 * [taylor]: Taking taylor expansion of 2.0 in k 11.206 * [backup-simplify]: Simplify 2.0 into 2.0 11.206 * [taylor]: Taking taylor expansion of (* n PI) in k 11.206 * [taylor]: Taking taylor expansion of n in k 11.206 * [backup-simplify]: Simplify n into n 11.206 * [taylor]: Taking taylor expansion of PI in k 11.206 * [backup-simplify]: Simplify PI into PI 11.206 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.206 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 11.206 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 11.207 * [backup-simplify]: Simplify (- 0) into 0 11.207 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.207 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 11.207 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 11.207 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 11.208 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.208 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.208 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.208 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.208 * [taylor]: Taking taylor expansion of 0.5 in n 11.208 * [backup-simplify]: Simplify 0.5 into 0.5 11.208 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.208 * [taylor]: Taking taylor expansion of 1.0 in n 11.208 * [backup-simplify]: Simplify 1.0 into 1.0 11.208 * [taylor]: Taking taylor expansion of k in n 11.208 * [backup-simplify]: Simplify k into k 11.208 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.208 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.208 * [taylor]: Taking taylor expansion of 2.0 in n 11.208 * [backup-simplify]: Simplify 2.0 into 2.0 11.208 * [taylor]: Taking taylor expansion of (* n PI) in n 11.208 * [taylor]: Taking taylor expansion of n in n 11.208 * [backup-simplify]: Simplify 0 into 0 11.208 * [backup-simplify]: Simplify 1 into 1 11.208 * [taylor]: Taking taylor expansion of PI in n 11.208 * [backup-simplify]: Simplify PI into PI 11.208 * [backup-simplify]: Simplify (* 0 PI) into 0 11.208 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.209 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.210 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.211 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.211 * [backup-simplify]: Simplify (- k) into (- k) 11.211 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.211 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.212 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.213 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 11.214 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 11.214 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 11.214 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 11.214 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 11.214 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 11.214 * [taylor]: Taking taylor expansion of 0.5 in n 11.214 * [backup-simplify]: Simplify 0.5 into 0.5 11.214 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 11.214 * [taylor]: Taking taylor expansion of 1.0 in n 11.214 * [backup-simplify]: Simplify 1.0 into 1.0 11.214 * [taylor]: Taking taylor expansion of k in n 11.214 * [backup-simplify]: Simplify k into k 11.214 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 11.214 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 11.214 * [taylor]: Taking taylor expansion of 2.0 in n 11.214 * [backup-simplify]: Simplify 2.0 into 2.0 11.214 * [taylor]: Taking taylor expansion of (* n PI) in n 11.214 * [taylor]: Taking taylor expansion of n in n 11.214 * [backup-simplify]: Simplify 0 into 0 11.214 * [backup-simplify]: Simplify 1 into 1 11.214 * [taylor]: Taking taylor expansion of PI in n 11.214 * [backup-simplify]: Simplify PI into PI 11.214 * [backup-simplify]: Simplify (* 0 PI) into 0 11.215 * [backup-simplify]: Simplify (* 2.0 0) into 0 11.216 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.217 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 11.217 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.217 * [backup-simplify]: Simplify (- k) into (- k) 11.217 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 11.217 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 11.218 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.219 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 11.220 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 11.220 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 11.220 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 11.220 * [taylor]: Taking taylor expansion of 0.5 in k 11.220 * [backup-simplify]: Simplify 0.5 into 0.5 11.220 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 11.220 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 11.220 * [taylor]: Taking taylor expansion of 1.0 in k 11.220 * [backup-simplify]: Simplify 1.0 into 1.0 11.220 * [taylor]: Taking taylor expansion of k in k 11.220 * [backup-simplify]: Simplify 0 into 0 11.220 * [backup-simplify]: Simplify 1 into 1 11.220 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 11.220 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.220 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.220 * [taylor]: Taking taylor expansion of 2.0 in k 11.220 * [backup-simplify]: Simplify 2.0 into 2.0 11.220 * [taylor]: Taking taylor expansion of PI in k 11.220 * [backup-simplify]: Simplify PI into PI 11.221 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.221 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.221 * [taylor]: Taking taylor expansion of (log n) in k 11.221 * [taylor]: Taking taylor expansion of n in k 11.221 * [backup-simplify]: Simplify n into n 11.221 * [backup-simplify]: Simplify (log n) into (log n) 11.222 * [backup-simplify]: Simplify (- 0) into 0 11.222 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 11.223 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 11.223 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 11.224 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 11.225 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.226 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 11.226 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.227 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 11.228 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.228 * [backup-simplify]: Simplify (- 0) into 0 11.228 * [backup-simplify]: Simplify (+ 0 0) into 0 11.229 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 11.230 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.230 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 11.232 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.232 * [taylor]: Taking taylor expansion of 0 in k 11.232 * [backup-simplify]: Simplify 0 into 0 11.232 * [backup-simplify]: Simplify 0 into 0 11.232 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.233 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.234 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.234 * [backup-simplify]: Simplify (+ 0 0) into 0 11.234 * [backup-simplify]: Simplify (- 1) into -1 11.234 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.235 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 11.237 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 11.239 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 11.241 * [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)))))) 11.242 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.244 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 11.244 * [backup-simplify]: Simplify (- 0) into 0 11.245 * [backup-simplify]: Simplify (+ 0 0) into 0 11.245 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 11.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 11.247 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.249 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.249 * [taylor]: Taking taylor expansion of 0 in k 11.249 * [backup-simplify]: Simplify 0 into 0 11.249 * [backup-simplify]: Simplify 0 into 0 11.249 * [backup-simplify]: Simplify 0 into 0 11.249 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.251 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 11.252 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.253 * [backup-simplify]: Simplify (+ 0 0) into 0 11.253 * [backup-simplify]: Simplify (- 0) into 0 11.253 * [backup-simplify]: Simplify (+ 0 0) into 0 11.254 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 11.256 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 11.269 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 11.275 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 11.282 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 11.283 * [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)))) 11.283 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 11.283 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 11.283 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 11.283 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 11.283 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 11.283 * [taylor]: Taking taylor expansion of 0.5 in k 11.283 * [backup-simplify]: Simplify 0.5 into 0.5 11.283 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.283 * [taylor]: Taking taylor expansion of 1.0 in k 11.283 * [backup-simplify]: Simplify 1.0 into 1.0 11.283 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.283 * [taylor]: Taking taylor expansion of k in k 11.283 * [backup-simplify]: Simplify 0 into 0 11.283 * [backup-simplify]: Simplify 1 into 1 11.283 * [backup-simplify]: Simplify (/ 1 1) into 1 11.283 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 11.283 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 11.283 * [taylor]: Taking taylor expansion of 2.0 in k 11.283 * [backup-simplify]: Simplify 2.0 into 2.0 11.283 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.283 * [taylor]: Taking taylor expansion of PI in k 11.283 * [backup-simplify]: Simplify PI into PI 11.283 * [taylor]: Taking taylor expansion of n in k 11.283 * [backup-simplify]: Simplify n into n 11.283 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.283 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 11.283 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 11.284 * [backup-simplify]: Simplify (- 1) into -1 11.284 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.284 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 11.284 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 11.285 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 11.285 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.285 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.285 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.285 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.285 * [taylor]: Taking taylor expansion of 0.5 in n 11.285 * [backup-simplify]: Simplify 0.5 into 0.5 11.285 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.285 * [taylor]: Taking taylor expansion of 1.0 in n 11.285 * [backup-simplify]: Simplify 1.0 into 1.0 11.285 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.285 * [taylor]: Taking taylor expansion of k in n 11.285 * [backup-simplify]: Simplify k into k 11.285 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.285 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.285 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.285 * [taylor]: Taking taylor expansion of 2.0 in n 11.285 * [backup-simplify]: Simplify 2.0 into 2.0 11.285 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.285 * [taylor]: Taking taylor expansion of PI in n 11.285 * [backup-simplify]: Simplify PI into PI 11.285 * [taylor]: Taking taylor expansion of n in n 11.285 * [backup-simplify]: Simplify 0 into 0 11.285 * [backup-simplify]: Simplify 1 into 1 11.285 * [backup-simplify]: Simplify (/ PI 1) into PI 11.286 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.286 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.286 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.286 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.286 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.288 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 11.289 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 11.289 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 11.289 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 11.289 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 11.289 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 11.289 * [taylor]: Taking taylor expansion of 0.5 in n 11.289 * [backup-simplify]: Simplify 0.5 into 0.5 11.289 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 11.289 * [taylor]: Taking taylor expansion of 1.0 in n 11.289 * [backup-simplify]: Simplify 1.0 into 1.0 11.289 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.289 * [taylor]: Taking taylor expansion of k in n 11.289 * [backup-simplify]: Simplify k into k 11.289 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.289 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 11.289 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 11.289 * [taylor]: Taking taylor expansion of 2.0 in n 11.289 * [backup-simplify]: Simplify 2.0 into 2.0 11.289 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.289 * [taylor]: Taking taylor expansion of PI in n 11.289 * [backup-simplify]: Simplify PI into PI 11.289 * [taylor]: Taking taylor expansion of n in n 11.289 * [backup-simplify]: Simplify 0 into 0 11.289 * [backup-simplify]: Simplify 1 into 1 11.290 * [backup-simplify]: Simplify (/ PI 1) into PI 11.290 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.290 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.291 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 11.291 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 11.291 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 11.292 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.292 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 11.293 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 11.293 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 11.293 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 11.293 * [taylor]: Taking taylor expansion of 0.5 in k 11.293 * [backup-simplify]: Simplify 0.5 into 0.5 11.293 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 11.293 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 11.293 * [taylor]: Taking taylor expansion of 1.0 in k 11.293 * [backup-simplify]: Simplify 1.0 into 1.0 11.293 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.293 * [taylor]: Taking taylor expansion of k in k 11.293 * [backup-simplify]: Simplify 0 into 0 11.293 * [backup-simplify]: Simplify 1 into 1 11.294 * [backup-simplify]: Simplify (/ 1 1) into 1 11.294 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 11.294 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 11.294 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 11.294 * [taylor]: Taking taylor expansion of 2.0 in k 11.294 * [backup-simplify]: Simplify 2.0 into 2.0 11.294 * [taylor]: Taking taylor expansion of PI in k 11.294 * [backup-simplify]: Simplify PI into PI 11.294 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 11.295 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 11.295 * [taylor]: Taking taylor expansion of (log n) in k 11.295 * [taylor]: Taking taylor expansion of n in k 11.295 * [backup-simplify]: Simplify n into n 11.295 * [backup-simplify]: Simplify (log n) into (log n) 11.295 * [backup-simplify]: Simplify (- 1) into -1 11.295 * [backup-simplify]: Simplify (+ 0 -1) into -1 11.295 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.296 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 11.297 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 11.297 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 11.298 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 11.299 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 11.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.300 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 11.301 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 11.301 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.301 * [backup-simplify]: Simplify (- 0) into 0 11.302 * [backup-simplify]: Simplify (+ 0 0) into 0 11.302 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 11.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.304 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 11.305 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.305 * [taylor]: Taking taylor expansion of 0 in k 11.305 * [backup-simplify]: Simplify 0 into 0 11.305 * [backup-simplify]: Simplify 0 into 0 11.305 * [backup-simplify]: Simplify 0 into 0 11.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.309 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 11.309 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.310 * [backup-simplify]: Simplify (- 0) into 0 11.310 * [backup-simplify]: Simplify (+ 0 0) into 0 11.311 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 11.313 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.314 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 11.317 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.317 * [taylor]: Taking taylor expansion of 0 in k 11.317 * [backup-simplify]: Simplify 0 into 0 11.317 * [backup-simplify]: Simplify 0 into 0 11.317 * [backup-simplify]: Simplify 0 into 0 11.317 * [backup-simplify]: Simplify 0 into 0 11.319 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.327 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 11.328 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.328 * [backup-simplify]: Simplify (- 0) into 0 11.329 * [backup-simplify]: Simplify (+ 0 0) into 0 11.330 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 11.331 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 11.334 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 11.337 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.337 * [taylor]: Taking taylor expansion of 0 in k 11.337 * [backup-simplify]: Simplify 0 into 0 11.337 * [backup-simplify]: Simplify 0 into 0 11.338 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 11.339 * [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))) 11.339 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 11.339 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 11.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 11.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 11.339 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 11.339 * [taylor]: Taking taylor expansion of 0.5 in k 11.339 * [backup-simplify]: Simplify 0.5 into 0.5 11.339 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.339 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.339 * [taylor]: Taking taylor expansion of k in k 11.339 * [backup-simplify]: Simplify 0 into 0 11.339 * [backup-simplify]: Simplify 1 into 1 11.339 * [backup-simplify]: Simplify (/ 1 1) into 1 11.340 * [taylor]: Taking taylor expansion of 1.0 in k 11.340 * [backup-simplify]: Simplify 1.0 into 1.0 11.340 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 11.340 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 11.340 * [taylor]: Taking taylor expansion of -2.0 in k 11.340 * [backup-simplify]: Simplify -2.0 into -2.0 11.340 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.340 * [taylor]: Taking taylor expansion of PI in k 11.340 * [backup-simplify]: Simplify PI into PI 11.340 * [taylor]: Taking taylor expansion of n in k 11.340 * [backup-simplify]: Simplify n into n 11.340 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.340 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 11.340 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 11.340 * [backup-simplify]: Simplify (+ 1 0) into 1 11.341 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 11.341 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 11.341 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 11.341 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.341 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.341 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.341 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.341 * [taylor]: Taking taylor expansion of 0.5 in n 11.341 * [backup-simplify]: Simplify 0.5 into 0.5 11.341 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.341 * [taylor]: Taking taylor expansion of k in n 11.341 * [backup-simplify]: Simplify k into k 11.341 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.342 * [taylor]: Taking taylor expansion of 1.0 in n 11.342 * [backup-simplify]: Simplify 1.0 into 1.0 11.342 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.342 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.342 * [taylor]: Taking taylor expansion of -2.0 in n 11.342 * [backup-simplify]: Simplify -2.0 into -2.0 11.342 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.342 * [taylor]: Taking taylor expansion of PI in n 11.342 * [backup-simplify]: Simplify PI into PI 11.342 * [taylor]: Taking taylor expansion of n in n 11.342 * [backup-simplify]: Simplify 0 into 0 11.342 * [backup-simplify]: Simplify 1 into 1 11.342 * [backup-simplify]: Simplify (/ PI 1) into PI 11.343 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.344 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.344 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.344 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.346 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 11.348 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 11.348 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 11.348 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 11.348 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 11.348 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 11.348 * [taylor]: Taking taylor expansion of 0.5 in n 11.348 * [backup-simplify]: Simplify 0.5 into 0.5 11.348 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 11.348 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.348 * [taylor]: Taking taylor expansion of k in n 11.348 * [backup-simplify]: Simplify k into k 11.348 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.348 * [taylor]: Taking taylor expansion of 1.0 in n 11.348 * [backup-simplify]: Simplify 1.0 into 1.0 11.348 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 11.348 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 11.348 * [taylor]: Taking taylor expansion of -2.0 in n 11.348 * [backup-simplify]: Simplify -2.0 into -2.0 11.348 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.348 * [taylor]: Taking taylor expansion of PI in n 11.348 * [backup-simplify]: Simplify PI into PI 11.348 * [taylor]: Taking taylor expansion of n in n 11.348 * [backup-simplify]: Simplify 0 into 0 11.348 * [backup-simplify]: Simplify 1 into 1 11.349 * [backup-simplify]: Simplify (/ PI 1) into PI 11.349 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.350 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.350 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 11.350 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 11.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.353 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 11.354 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 11.354 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 11.354 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 11.354 * [taylor]: Taking taylor expansion of 0.5 in k 11.354 * [backup-simplify]: Simplify 0.5 into 0.5 11.354 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 11.354 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 11.354 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 11.354 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 11.354 * [taylor]: Taking taylor expansion of -2.0 in k 11.354 * [backup-simplify]: Simplify -2.0 into -2.0 11.354 * [taylor]: Taking taylor expansion of PI in k 11.354 * [backup-simplify]: Simplify PI into PI 11.355 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 11.356 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 11.356 * [taylor]: Taking taylor expansion of (log n) in k 11.356 * [taylor]: Taking taylor expansion of n in k 11.356 * [backup-simplify]: Simplify n into n 11.356 * [backup-simplify]: Simplify (log n) into (log n) 11.356 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 11.356 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.356 * [taylor]: Taking taylor expansion of k in k 11.356 * [backup-simplify]: Simplify 0 into 0 11.356 * [backup-simplify]: Simplify 1 into 1 11.356 * [backup-simplify]: Simplify (/ 1 1) into 1 11.356 * [taylor]: Taking taylor expansion of 1.0 in k 11.356 * [backup-simplify]: Simplify 1.0 into 1.0 11.357 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 11.358 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 11.358 * [backup-simplify]: Simplify (+ 1 0) into 1 11.359 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 11.360 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 11.362 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 11.363 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 11.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.365 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 11.366 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 11.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.367 * [backup-simplify]: Simplify (+ 0 0) into 0 11.368 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 11.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.371 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 11.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.373 * [taylor]: Taking taylor expansion of 0 in k 11.373 * [backup-simplify]: Simplify 0 into 0 11.373 * [backup-simplify]: Simplify 0 into 0 11.373 * [backup-simplify]: Simplify 0 into 0 11.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.376 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 11.379 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 11.379 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.380 * [backup-simplify]: Simplify (+ 0 0) into 0 11.381 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 11.382 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.384 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 11.387 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.387 * [taylor]: Taking taylor expansion of 0 in k 11.387 * [backup-simplify]: Simplify 0 into 0 11.387 * [backup-simplify]: Simplify 0 into 0 11.387 * [backup-simplify]: Simplify 0 into 0 11.387 * [backup-simplify]: Simplify 0 into 0 11.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.389 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.395 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 11.396 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 11.396 * [backup-simplify]: Simplify (+ 0 0) into 0 11.404 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 11.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 11.407 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 11.409 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.409 * [taylor]: Taking taylor expansion of 0 in k 11.410 * [backup-simplify]: Simplify 0 into 0 11.410 * [backup-simplify]: Simplify 0 into 0 11.411 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 11.411 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1) 11.411 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4)) 11.411 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0 11.411 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 11.411 * [taylor]: Taking taylor expansion of 1.0 in k 11.411 * [backup-simplify]: Simplify 1.0 into 1.0 11.411 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 11.411 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 11.411 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 11.411 * [taylor]: Taking taylor expansion of 1/4 in k 11.411 * [backup-simplify]: Simplify 1/4 into 1/4 11.411 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 11.411 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.411 * [taylor]: Taking taylor expansion of k in k 11.411 * [backup-simplify]: Simplify 0 into 0 11.411 * [backup-simplify]: Simplify 1 into 1 11.412 * [backup-simplify]: Simplify (/ 1 1) into 1 11.412 * [backup-simplify]: Simplify (log 1) into 0 11.412 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.413 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 11.413 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 11.413 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k 11.413 * [taylor]: Taking taylor expansion of 1.0 in k 11.413 * [backup-simplify]: Simplify 1.0 into 1.0 11.413 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 11.413 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 11.413 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 11.413 * [taylor]: Taking taylor expansion of 1/4 in k 11.413 * [backup-simplify]: Simplify 1/4 into 1/4 11.413 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 11.413 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.413 * [taylor]: Taking taylor expansion of k in k 11.413 * [backup-simplify]: Simplify 0 into 0 11.413 * [backup-simplify]: Simplify 1 into 1 11.413 * [backup-simplify]: Simplify (/ 1 1) into 1 11.414 * [backup-simplify]: Simplify (log 1) into 0 11.414 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.414 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 11.414 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 11.414 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 11.415 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 11.415 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.416 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 11.417 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.417 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 11.418 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 11.419 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0 11.419 * [backup-simplify]: Simplify 0 into 0 11.420 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.422 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 11.422 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.424 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 11.425 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.426 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0 11.426 * [backup-simplify]: Simplify 0 into 0 11.426 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.431 * [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 11.432 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.433 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 11.434 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.436 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0 11.436 * [backup-simplify]: Simplify 0 into 0 11.437 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.446 * [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 11.447 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.448 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 11.450 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.451 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0 11.451 * [backup-simplify]: Simplify 0 into 0 11.451 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.461 * [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 11.461 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.462 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 11.464 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.466 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0 11.466 * [backup-simplify]: Simplify 0 into 0 11.466 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.485 * [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 11.486 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 11.488 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 11.494 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.497 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0 11.497 * [backup-simplify]: Simplify 0 into 0 11.497 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 11.497 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4)) 11.497 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0 11.497 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 11.497 * [taylor]: Taking taylor expansion of 1.0 in k 11.497 * [backup-simplify]: Simplify 1.0 into 1.0 11.497 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 11.497 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 11.497 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 11.497 * [taylor]: Taking taylor expansion of 1/4 in k 11.497 * [backup-simplify]: Simplify 1/4 into 1/4 11.497 * [taylor]: Taking taylor expansion of (log k) in k 11.497 * [taylor]: Taking taylor expansion of k in k 11.497 * [backup-simplify]: Simplify 0 into 0 11.497 * [backup-simplify]: Simplify 1 into 1 11.498 * [backup-simplify]: Simplify (log 1) into 0 11.498 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.498 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 11.499 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 11.499 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k 11.499 * [taylor]: Taking taylor expansion of 1.0 in k 11.499 * [backup-simplify]: Simplify 1.0 into 1.0 11.499 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 11.499 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 11.499 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 11.499 * [taylor]: Taking taylor expansion of 1/4 in k 11.499 * [backup-simplify]: Simplify 1/4 into 1/4 11.499 * [taylor]: Taking taylor expansion of (log k) in k 11.499 * [taylor]: Taking taylor expansion of k in k 11.499 * [backup-simplify]: Simplify 0 into 0 11.499 * [backup-simplify]: Simplify 1 into 1 11.499 * [backup-simplify]: Simplify (log 1) into 0 11.500 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.500 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 11.500 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 11.500 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 11.500 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4)) 11.502 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 11.502 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.503 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 11.504 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 11.504 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0 11.504 * [backup-simplify]: Simplify 0 into 0 11.507 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 11.508 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.509 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 11.510 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.511 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 11.511 * [backup-simplify]: Simplify 0 into 0 11.516 * [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 11.517 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.518 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 11.520 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.529 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 11.529 * [backup-simplify]: Simplify 0 into 0 11.537 * [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 11.538 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.539 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 11.541 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.543 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 11.543 * [backup-simplify]: Simplify 0 into 0 11.554 * [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 11.555 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.556 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 11.558 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 11.559 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 11.559 * [backup-simplify]: Simplify 0 into 0 11.579 * [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 11.579 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 11.581 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 11.587 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.589 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 11.589 * [backup-simplify]: Simplify 0 into 0 11.589 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4)) 11.589 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) 11.589 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0 11.589 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 11.589 * [taylor]: Taking taylor expansion of 1.0 in k 11.589 * [backup-simplify]: Simplify 1.0 into 1.0 11.589 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 11.589 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 11.589 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.589 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.589 * [taylor]: Taking taylor expansion of -1 in k 11.589 * [backup-simplify]: Simplify -1 into -1 11.589 * [taylor]: Taking taylor expansion of k in k 11.589 * [backup-simplify]: Simplify 0 into 0 11.589 * [backup-simplify]: Simplify 1 into 1 11.590 * [backup-simplify]: Simplify (/ -1 1) into -1 11.590 * [backup-simplify]: Simplify (sqrt 0) into 0 11.591 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.592 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 11.592 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 11.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.596 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.598 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.599 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 11.599 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k 11.599 * [taylor]: Taking taylor expansion of 1.0 in k 11.599 * [backup-simplify]: Simplify 1.0 into 1.0 11.600 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 11.600 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 11.600 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.600 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.600 * [taylor]: Taking taylor expansion of -1 in k 11.600 * [backup-simplify]: Simplify -1 into -1 11.600 * [taylor]: Taking taylor expansion of k in k 11.600 * [backup-simplify]: Simplify 0 into 0 11.600 * [backup-simplify]: Simplify 1 into 1 11.600 * [backup-simplify]: Simplify (/ -1 1) into -1 11.600 * [backup-simplify]: Simplify (sqrt 0) into 0 11.602 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.602 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 11.603 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 11.603 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.606 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.608 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.609 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 11.610 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 11.611 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0)) 11.614 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 11.616 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0)))) 11.617 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.620 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.623 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.628 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 11.645 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) 11.653 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) 11.662 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ 1 (sqrt +nan.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) 11.662 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 11.662 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k))) 11.662 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.662 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.662 * [taylor]: Taking taylor expansion of 1.0 in k 11.662 * [backup-simplify]: Simplify 1.0 into 1.0 11.662 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.662 * [taylor]: Taking taylor expansion of k in k 11.662 * [backup-simplify]: Simplify 0 into 0 11.662 * [backup-simplify]: Simplify 1 into 1 11.662 * [backup-simplify]: Simplify (/ 1 1) into 1 11.663 * [backup-simplify]: Simplify (sqrt 0) into 0 11.664 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.664 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.664 * [taylor]: Taking taylor expansion of 1.0 in k 11.664 * [backup-simplify]: Simplify 1.0 into 1.0 11.664 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.664 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.664 * [taylor]: Taking taylor expansion of k in k 11.664 * [backup-simplify]: Simplify 0 into 0 11.664 * [backup-simplify]: Simplify 1 into 1 11.664 * [backup-simplify]: Simplify (/ 1 1) into 1 11.664 * [backup-simplify]: Simplify (sqrt 0) into 0 11.665 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.665 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.665 * [backup-simplify]: Simplify 0 into 0 11.666 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.666 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.667 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.669 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.670 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.670 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.671 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.673 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.675 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.675 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.676 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 11.676 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k)) 11.676 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.676 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.676 * [taylor]: Taking taylor expansion of 1.0 in k 11.676 * [backup-simplify]: Simplify 1.0 into 1.0 11.676 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.676 * [taylor]: Taking taylor expansion of k in k 11.676 * [backup-simplify]: Simplify 0 into 0 11.676 * [backup-simplify]: Simplify 1 into 1 11.676 * [backup-simplify]: Simplify (sqrt 0) into 0 11.677 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.677 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.677 * [taylor]: Taking taylor expansion of 1.0 in k 11.677 * [backup-simplify]: Simplify 1.0 into 1.0 11.677 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.677 * [taylor]: Taking taylor expansion of k in k 11.677 * [backup-simplify]: Simplify 0 into 0 11.677 * [backup-simplify]: Simplify 1 into 1 11.677 * [backup-simplify]: Simplify (sqrt 0) into 0 11.678 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.678 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.679 * [backup-simplify]: Simplify 0 into 0 11.679 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.680 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.681 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.683 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.683 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.685 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.686 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.687 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.688 * [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)))))))) 11.688 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k))) 11.688 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.688 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.688 * [taylor]: Taking taylor expansion of 1.0 in k 11.688 * [backup-simplify]: Simplify 1.0 into 1.0 11.688 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.688 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.688 * [taylor]: Taking taylor expansion of -1 in k 11.688 * [backup-simplify]: Simplify -1 into -1 11.688 * [taylor]: Taking taylor expansion of k in k 11.688 * [backup-simplify]: Simplify 0 into 0 11.688 * [backup-simplify]: Simplify 1 into 1 11.688 * [backup-simplify]: Simplify (/ -1 1) into -1 11.689 * [backup-simplify]: Simplify (sqrt 0) into 0 11.689 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.690 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.690 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.690 * [taylor]: Taking taylor expansion of 1.0 in k 11.690 * [backup-simplify]: Simplify 1.0 into 1.0 11.690 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.690 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.690 * [taylor]: Taking taylor expansion of -1 in k 11.690 * [backup-simplify]: Simplify -1 into -1 11.690 * [taylor]: Taking taylor expansion of k in k 11.690 * [backup-simplify]: Simplify 0 into 0 11.690 * [backup-simplify]: Simplify 1 into 1 11.690 * [backup-simplify]: Simplify (/ -1 1) into -1 11.690 * [backup-simplify]: Simplify (sqrt 0) into 0 11.691 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.691 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.691 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.694 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.696 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.696 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.701 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.705 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.705 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.707 * [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))))) 11.707 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 11.707 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 11.707 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 11.707 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.707 * [taylor]: Taking taylor expansion of 1.0 in k 11.707 * [backup-simplify]: Simplify 1.0 into 1.0 11.707 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.707 * [taylor]: Taking taylor expansion of k in k 11.707 * [backup-simplify]: Simplify 0 into 0 11.707 * [backup-simplify]: Simplify 1 into 1 11.708 * [backup-simplify]: Simplify (/ 1 1) into 1 11.708 * [backup-simplify]: Simplify (sqrt 0) into 0 11.709 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.710 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 11.710 * [taylor]: Taking taylor expansion of 1.0 in k 11.710 * [backup-simplify]: Simplify 1.0 into 1.0 11.710 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.710 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.710 * [taylor]: Taking taylor expansion of k in k 11.710 * [backup-simplify]: Simplify 0 into 0 11.710 * [backup-simplify]: Simplify 1 into 1 11.710 * [backup-simplify]: Simplify (/ 1 1) into 1 11.710 * [backup-simplify]: Simplify (sqrt 0) into 0 11.712 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.712 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.712 * [backup-simplify]: Simplify 0 into 0 11.714 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.715 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.715 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.719 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.721 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.721 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.722 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.726 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.728 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.729 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.730 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 11.730 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 11.730 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 11.730 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.730 * [taylor]: Taking taylor expansion of 1.0 in k 11.730 * [backup-simplify]: Simplify 1.0 into 1.0 11.730 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.730 * [taylor]: Taking taylor expansion of k in k 11.730 * [backup-simplify]: Simplify 0 into 0 11.730 * [backup-simplify]: Simplify 1 into 1 11.731 * [backup-simplify]: Simplify (sqrt 0) into 0 11.732 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.732 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 11.732 * [taylor]: Taking taylor expansion of 1.0 in k 11.732 * [backup-simplify]: Simplify 1.0 into 1.0 11.732 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.732 * [taylor]: Taking taylor expansion of k in k 11.732 * [backup-simplify]: Simplify 0 into 0 11.732 * [backup-simplify]: Simplify 1 into 1 11.733 * [backup-simplify]: Simplify (sqrt 0) into 0 11.734 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.735 * [backup-simplify]: Simplify (* 1.0 0) into 0 11.735 * [backup-simplify]: Simplify 0 into 0 11.736 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 11.737 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.740 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.741 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 11.741 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.743 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.745 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 11.745 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.746 * [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)))))))) 11.746 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 11.746 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 11.746 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.746 * [taylor]: Taking taylor expansion of 1.0 in k 11.746 * [backup-simplify]: Simplify 1.0 into 1.0 11.746 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.746 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.746 * [taylor]: Taking taylor expansion of -1 in k 11.746 * [backup-simplify]: Simplify -1 into -1 11.746 * [taylor]: Taking taylor expansion of k in k 11.746 * [backup-simplify]: Simplify 0 into 0 11.746 * [backup-simplify]: Simplify 1 into 1 11.747 * [backup-simplify]: Simplify (/ -1 1) into -1 11.747 * [backup-simplify]: Simplify (sqrt 0) into 0 11.748 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.748 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.748 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 11.748 * [taylor]: Taking taylor expansion of 1.0 in k 11.748 * [backup-simplify]: Simplify 1.0 into 1.0 11.748 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.748 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.748 * [taylor]: Taking taylor expansion of -1 in k 11.748 * [backup-simplify]: Simplify -1 into -1 11.748 * [taylor]: Taking taylor expansion of k in k 11.748 * [backup-simplify]: Simplify 0 into 0 11.748 * [backup-simplify]: Simplify 1 into 1 11.748 * [backup-simplify]: Simplify (/ -1 1) into -1 11.749 * [backup-simplify]: Simplify (sqrt 0) into 0 11.749 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.750 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 11.750 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.757 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.758 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 11.758 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.762 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.766 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 11.767 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 11.768 * [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))))) 11.768 * * * [progress]: simplifying candidates 11.779 * [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 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(sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 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(/ (/ 1 (sqrt (sqrt (sqrt k)))) 1) (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k))) (/ (/ 1 (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt 1))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) (sqrt 1)) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))) (/ (/ 1 (sqrt 1)) 1) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt 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(cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k))))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt 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(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) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 1.0 (pow (/ 1 k) 1/4)) (* 1.0 (pow (/ 1 k) 1/4)) (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 11.789 * * [simplify]: iteration 0: 569 enodes 12.065 * * [simplify]: iteration 1: 1370 enodes 12.579 * * [simplify]: iteration 2: 3261 enodes 13.294 * * [simplify]: iteration complete: 5084 enodes 13.295 * * [simplify]: Extracting #0: cost 250 inf + 0 13.297 * * [simplify]: Extracting #1: cost 1265 inf + 2 13.303 * * [simplify]: Extracting #2: cost 2012 inf + 3313 13.328 * * [simplify]: Extracting #3: cost 1539 inf + 110615 13.397 * * [simplify]: Extracting #4: cost 706 inf + 325406 13.490 * * [simplify]: Extracting #5: cost 194 inf + 494948 13.616 * * [simplify]: Extracting #6: cost 10 inf + 562559 13.743 * * [simplify]: Extracting #7: cost 1 inf + 567001 13.843 * * [simplify]: Extracting #8: cost 0 inf + 567213 13.932 * [simplify]: Simplified to: (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* PI n)) (/ 1.0 2.0)) (pow (* 2.0 (* PI n)) (/ k 2.0)) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* PI n)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* 2.0 (* PI n)) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* 2.0 (* PI n)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (* 2.0 (* PI n)) (pow (* 2.0 (* PI n)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* 2.0 (* PI n)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (* 2.0 (* PI n)) (* 2.0 (* PI n)) (pow (* 2.0 (* PI n)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* PI n)))) (exp (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (* (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* PI n)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 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(sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (+ (* (* (* (log (* 2.0 PI)) 0.25) (* (* k k) (log n))) (exp (* 0.5 (log (* 2.0 (* PI n)))))) (* (* (* (log n) (log n)) (exp (* 0.5 (log (* 2.0 (* PI n)))))) (* (* k k) 0.125))) (- (+ (exp (* 0.5 (log (* 2.0 (* PI n))))) (* (* (* 0.125 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (exp (* 0.5 (log (* 2.0 (* PI n)))))) (* k k))) (* 0.5 (* k (+ (* (log n) (exp (* 0.5 (log (* 2.0 (* PI n)))))) (* (exp (* 0.5 (log (* 2.0 (* PI n))))) (log (* 2.0 PI)))))))) (exp (* (- 1.0 k) (* (log (* 2.0 (* PI n))) 0.5))) (exp (* (* (- (log (* PI -2.0)) (log (/ -1 n))) (- 1.0 k)) 0.5)) (* (pow (/ 1 k) 1/4) 1.0) (* (pow (/ 1 k) 1/4) 1.0) (- (* 1.0 (sqrt +nan.0)) (+ (- (/ (/ +nan.0 k) (sqrt +nan.0)) (/ (/ +nan.0 (* k k)) (* (sqrt +nan.0) +nan.0))) (/ +nan.0 (* (sqrt +nan.0) (* k k))))) (- (- (* (* k k) +nan.0) (- +nan.0 (* +nan.0 k)))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k))))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0)) (- (- (* (* k k) +nan.0) (- +nan.0 (* +nan.0 k)))) (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k))))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0)) 14.054 * * * [progress]: adding candidates to table 16.631 * * [progress]: iteration 4 / 4 16.631 * * * [progress]: picking best candidate 16.684 * * * * [pick]: Picked # 16.684 * * * [progress]: localizing error 16.749 * * * [progress]: generating rewritten candidates 16.749 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 16.792 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 16.844 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1) 16.854 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 17.253 * * * [progress]: generating series expansions 17.253 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 17.254 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 17.254 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 17.254 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 17.254 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 17.254 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 17.254 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 17.254 * [taylor]: Taking taylor expansion of 0.5 in k 17.254 * [backup-simplify]: Simplify 0.5 into 0.5 17.254 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.254 * [taylor]: Taking taylor expansion of 1.0 in k 17.254 * [backup-simplify]: Simplify 1.0 into 1.0 17.254 * [taylor]: Taking taylor expansion of k in k 17.254 * [backup-simplify]: Simplify 0 into 0 17.254 * [backup-simplify]: Simplify 1 into 1 17.254 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 17.254 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 17.254 * [taylor]: Taking taylor expansion of 2.0 in k 17.256 * [backup-simplify]: Simplify 2.0 into 2.0 17.256 * [taylor]: Taking taylor expansion of (* n PI) in k 17.256 * [taylor]: Taking taylor expansion of n in k 17.256 * [backup-simplify]: Simplify n into n 17.256 * [taylor]: Taking taylor expansion of PI in k 17.256 * [backup-simplify]: Simplify PI into PI 17.256 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.256 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 17.256 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 17.257 * [backup-simplify]: Simplify (- 0) into 0 17.257 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.257 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 17.257 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 17.257 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 17.258 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.258 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.258 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.258 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.258 * [taylor]: Taking taylor expansion of 0.5 in n 17.258 * [backup-simplify]: Simplify 0.5 into 0.5 17.258 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.258 * [taylor]: Taking taylor expansion of 1.0 in n 17.258 * [backup-simplify]: Simplify 1.0 into 1.0 17.258 * [taylor]: Taking taylor expansion of k in n 17.258 * [backup-simplify]: Simplify k into k 17.258 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.258 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.258 * [taylor]: Taking taylor expansion of 2.0 in n 17.258 * [backup-simplify]: Simplify 2.0 into 2.0 17.258 * [taylor]: Taking taylor expansion of (* n PI) in n 17.258 * [taylor]: Taking taylor expansion of n in n 17.258 * [backup-simplify]: Simplify 0 into 0 17.258 * [backup-simplify]: Simplify 1 into 1 17.258 * [taylor]: Taking taylor expansion of PI in n 17.258 * [backup-simplify]: Simplify PI into PI 17.258 * [backup-simplify]: Simplify (* 0 PI) into 0 17.258 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.259 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.260 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.261 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.261 * [backup-simplify]: Simplify (- k) into (- k) 17.261 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.261 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.262 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.263 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.263 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.263 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 17.263 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 17.263 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 17.264 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 17.264 * [taylor]: Taking taylor expansion of 0.5 in n 17.264 * [backup-simplify]: Simplify 0.5 into 0.5 17.264 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 17.264 * [taylor]: Taking taylor expansion of 1.0 in n 17.264 * [backup-simplify]: Simplify 1.0 into 1.0 17.264 * [taylor]: Taking taylor expansion of k in n 17.264 * [backup-simplify]: Simplify k into k 17.264 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 17.264 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 17.264 * [taylor]: Taking taylor expansion of 2.0 in n 17.264 * [backup-simplify]: Simplify 2.0 into 2.0 17.264 * [taylor]: Taking taylor expansion of (* n PI) in n 17.264 * [taylor]: Taking taylor expansion of n in n 17.264 * [backup-simplify]: Simplify 0 into 0 17.264 * [backup-simplify]: Simplify 1 into 1 17.264 * [taylor]: Taking taylor expansion of PI in n 17.264 * [backup-simplify]: Simplify PI into PI 17.264 * [backup-simplify]: Simplify (* 0 PI) into 0 17.264 * [backup-simplify]: Simplify (* 2.0 0) into 0 17.265 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.266 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 17.267 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.267 * [backup-simplify]: Simplify (- k) into (- k) 17.267 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 17.267 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 17.268 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.269 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 17.269 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 17.269 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 17.269 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 17.269 * [taylor]: Taking taylor expansion of 0.5 in k 17.269 * [backup-simplify]: Simplify 0.5 into 0.5 17.269 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 17.269 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 17.269 * [taylor]: Taking taylor expansion of 1.0 in k 17.270 * [backup-simplify]: Simplify 1.0 into 1.0 17.270 * [taylor]: Taking taylor expansion of k in k 17.270 * [backup-simplify]: Simplify 0 into 0 17.270 * [backup-simplify]: Simplify 1 into 1 17.270 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 17.270 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.270 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.270 * [taylor]: Taking taylor expansion of 2.0 in k 17.270 * [backup-simplify]: Simplify 2.0 into 2.0 17.270 * [taylor]: Taking taylor expansion of PI in k 17.270 * [backup-simplify]: Simplify PI into PI 17.270 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.271 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.271 * [taylor]: Taking taylor expansion of (log n) in k 17.271 * [taylor]: Taking taylor expansion of n in k 17.271 * [backup-simplify]: Simplify n into n 17.271 * [backup-simplify]: Simplify (log n) into (log n) 17.271 * [backup-simplify]: Simplify (- 0) into 0 17.271 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 17.272 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 17.273 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 17.273 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 17.274 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.275 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 17.275 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.276 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 17.278 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.278 * [backup-simplify]: Simplify (- 0) into 0 17.279 * [backup-simplify]: Simplify (+ 0 0) into 0 17.279 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 17.281 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.282 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 17.284 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.284 * [taylor]: Taking taylor expansion of 0 in k 17.284 * [backup-simplify]: Simplify 0 into 0 17.284 * [backup-simplify]: Simplify 0 into 0 17.285 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.287 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.288 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 17.288 * [backup-simplify]: Simplify (+ 0 0) into 0 17.288 * [backup-simplify]: Simplify (- 1) into -1 17.289 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.290 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 17.293 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 17.296 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 17.300 * [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)))))) 17.301 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.302 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 17.306 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.306 * [backup-simplify]: Simplify (- 0) into 0 17.307 * [backup-simplify]: Simplify (+ 0 0) into 0 17.308 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 17.309 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 17.311 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.313 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.313 * [taylor]: Taking taylor expansion of 0 in k 17.313 * [backup-simplify]: Simplify 0 into 0 17.313 * [backup-simplify]: Simplify 0 into 0 17.313 * [backup-simplify]: Simplify 0 into 0 17.313 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.315 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.316 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 17.317 * [backup-simplify]: Simplify (+ 0 0) into 0 17.317 * [backup-simplify]: Simplify (- 0) into 0 17.317 * [backup-simplify]: Simplify (+ 0 0) into 0 17.318 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 17.320 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 17.322 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 17.326 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 17.332 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) 17.333 * [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)))) 17.333 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 17.333 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 17.333 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 17.333 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 17.333 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 17.333 * [taylor]: Taking taylor expansion of 0.5 in k 17.333 * [backup-simplify]: Simplify 0.5 into 0.5 17.333 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.333 * [taylor]: Taking taylor expansion of 1.0 in k 17.333 * [backup-simplify]: Simplify 1.0 into 1.0 17.333 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.333 * [taylor]: Taking taylor expansion of k in k 17.333 * [backup-simplify]: Simplify 0 into 0 17.333 * [backup-simplify]: Simplify 1 into 1 17.333 * [backup-simplify]: Simplify (/ 1 1) into 1 17.333 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 17.333 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 17.333 * [taylor]: Taking taylor expansion of 2.0 in k 17.333 * [backup-simplify]: Simplify 2.0 into 2.0 17.333 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.333 * [taylor]: Taking taylor expansion of PI in k 17.333 * [backup-simplify]: Simplify PI into PI 17.333 * [taylor]: Taking taylor expansion of n in k 17.333 * [backup-simplify]: Simplify n into n 17.333 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.333 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 17.333 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 17.334 * [backup-simplify]: Simplify (- 1) into -1 17.334 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.334 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 17.334 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 17.334 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 17.334 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.335 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.335 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.335 * [taylor]: Taking taylor expansion of 0.5 in n 17.335 * [backup-simplify]: Simplify 0.5 into 0.5 17.335 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.335 * [taylor]: Taking taylor expansion of 1.0 in n 17.335 * [backup-simplify]: Simplify 1.0 into 1.0 17.335 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.335 * [taylor]: Taking taylor expansion of k in n 17.335 * [backup-simplify]: Simplify k into k 17.335 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.335 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.335 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.335 * [taylor]: Taking taylor expansion of 2.0 in n 17.335 * [backup-simplify]: Simplify 2.0 into 2.0 17.335 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.335 * [taylor]: Taking taylor expansion of PI in n 17.335 * [backup-simplify]: Simplify PI into PI 17.335 * [taylor]: Taking taylor expansion of n in n 17.335 * [backup-simplify]: Simplify 0 into 0 17.335 * [backup-simplify]: Simplify 1 into 1 17.335 * [backup-simplify]: Simplify (/ PI 1) into PI 17.336 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.336 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.336 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.336 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.336 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.337 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.338 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 17.339 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.339 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 17.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 17.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 17.339 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 17.339 * [taylor]: Taking taylor expansion of 0.5 in n 17.339 * [backup-simplify]: Simplify 0.5 into 0.5 17.339 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 17.339 * [taylor]: Taking taylor expansion of 1.0 in n 17.339 * [backup-simplify]: Simplify 1.0 into 1.0 17.339 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.339 * [taylor]: Taking taylor expansion of k in n 17.339 * [backup-simplify]: Simplify k into k 17.339 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.339 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 17.339 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 17.339 * [taylor]: Taking taylor expansion of 2.0 in n 17.339 * [backup-simplify]: Simplify 2.0 into 2.0 17.339 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.339 * [taylor]: Taking taylor expansion of PI in n 17.339 * [backup-simplify]: Simplify PI into PI 17.339 * [taylor]: Taking taylor expansion of n in n 17.339 * [backup-simplify]: Simplify 0 into 0 17.339 * [backup-simplify]: Simplify 1 into 1 17.339 * [backup-simplify]: Simplify (/ PI 1) into PI 17.340 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.341 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.341 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 17.341 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 17.341 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 17.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.344 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) 17.345 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.345 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 17.346 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 17.346 * [taylor]: Taking taylor expansion of 0.5 in k 17.346 * [backup-simplify]: Simplify 0.5 into 0.5 17.346 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 17.346 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 17.346 * [taylor]: Taking taylor expansion of 1.0 in k 17.346 * [backup-simplify]: Simplify 1.0 into 1.0 17.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.346 * [taylor]: Taking taylor expansion of k in k 17.346 * [backup-simplify]: Simplify 0 into 0 17.346 * [backup-simplify]: Simplify 1 into 1 17.346 * [backup-simplify]: Simplify (/ 1 1) into 1 17.346 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 17.346 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 17.346 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 17.346 * [taylor]: Taking taylor expansion of 2.0 in k 17.346 * [backup-simplify]: Simplify 2.0 into 2.0 17.346 * [taylor]: Taking taylor expansion of PI in k 17.346 * [backup-simplify]: Simplify PI into PI 17.347 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 17.348 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 17.348 * [taylor]: Taking taylor expansion of (log n) in k 17.348 * [taylor]: Taking taylor expansion of n in k 17.348 * [backup-simplify]: Simplify n into n 17.348 * [backup-simplify]: Simplify (log n) into (log n) 17.348 * [backup-simplify]: Simplify (- 1) into -1 17.349 * [backup-simplify]: Simplify (+ 0 -1) into -1 17.349 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.350 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 17.351 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 17.359 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 17.360 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.361 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 17.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.363 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 17.365 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 17.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.366 * [backup-simplify]: Simplify (- 0) into 0 17.366 * [backup-simplify]: Simplify (+ 0 0) into 0 17.366 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 17.368 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.369 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 17.371 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.371 * [taylor]: Taking taylor expansion of 0 in k 17.371 * [backup-simplify]: Simplify 0 into 0 17.371 * [backup-simplify]: Simplify 0 into 0 17.371 * [backup-simplify]: Simplify 0 into 0 17.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.373 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.377 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 17.377 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.378 * [backup-simplify]: Simplify (- 0) into 0 17.378 * [backup-simplify]: Simplify (+ 0 0) into 0 17.379 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 17.380 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.382 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 17.385 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.385 * [taylor]: Taking taylor expansion of 0 in k 17.385 * [backup-simplify]: Simplify 0 into 0 17.385 * [backup-simplify]: Simplify 0 into 0 17.385 * [backup-simplify]: Simplify 0 into 0 17.385 * [backup-simplify]: Simplify 0 into 0 17.386 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.393 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 17.394 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.394 * [backup-simplify]: Simplify (- 0) into 0 17.394 * [backup-simplify]: Simplify (+ 0 0) into 0 17.396 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 17.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 17.398 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 17.400 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.400 * [taylor]: Taking taylor expansion of 0 in k 17.400 * [backup-simplify]: Simplify 0 into 0 17.400 * [backup-simplify]: Simplify 0 into 0 17.401 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) 17.401 * [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))) 17.401 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 17.401 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 17.401 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 17.401 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 17.401 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 17.401 * [taylor]: Taking taylor expansion of 0.5 in k 17.401 * [backup-simplify]: Simplify 0.5 into 0.5 17.401 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.401 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.401 * [taylor]: Taking taylor expansion of k in k 17.401 * [backup-simplify]: Simplify 0 into 0 17.401 * [backup-simplify]: Simplify 1 into 1 17.401 * [backup-simplify]: Simplify (/ 1 1) into 1 17.402 * [taylor]: Taking taylor expansion of 1.0 in k 17.402 * [backup-simplify]: Simplify 1.0 into 1.0 17.402 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 17.402 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 17.402 * [taylor]: Taking taylor expansion of -2.0 in k 17.402 * [backup-simplify]: Simplify -2.0 into -2.0 17.402 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.402 * [taylor]: Taking taylor expansion of PI in k 17.402 * [backup-simplify]: Simplify PI into PI 17.402 * [taylor]: Taking taylor expansion of n in k 17.402 * [backup-simplify]: Simplify n into n 17.402 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.402 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 17.402 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.402 * [backup-simplify]: Simplify (+ 1 0) into 1 17.402 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 17.402 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 17.403 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) 17.403 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.403 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.403 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.403 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.403 * [taylor]: Taking taylor expansion of 0.5 in n 17.403 * [backup-simplify]: Simplify 0.5 into 0.5 17.403 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.403 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.403 * [taylor]: Taking taylor expansion of k in n 17.403 * [backup-simplify]: Simplify k into k 17.403 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.403 * [taylor]: Taking taylor expansion of 1.0 in n 17.403 * [backup-simplify]: Simplify 1.0 into 1.0 17.403 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.403 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.403 * [taylor]: Taking taylor expansion of -2.0 in n 17.403 * [backup-simplify]: Simplify -2.0 into -2.0 17.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.403 * [taylor]: Taking taylor expansion of PI in n 17.403 * [backup-simplify]: Simplify PI into PI 17.403 * [taylor]: Taking taylor expansion of n in n 17.403 * [backup-simplify]: Simplify 0 into 0 17.403 * [backup-simplify]: Simplify 1 into 1 17.403 * [backup-simplify]: Simplify (/ PI 1) into PI 17.404 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.404 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.404 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.404 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.406 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 17.407 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.407 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 17.407 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.407 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.407 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 17.407 * [taylor]: Taking taylor expansion of 0.5 in n 17.407 * [backup-simplify]: Simplify 0.5 into 0.5 17.407 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.407 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.407 * [taylor]: Taking taylor expansion of k in n 17.407 * [backup-simplify]: Simplify k into k 17.407 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.407 * [taylor]: Taking taylor expansion of 1.0 in n 17.407 * [backup-simplify]: Simplify 1.0 into 1.0 17.407 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.407 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.407 * [taylor]: Taking taylor expansion of -2.0 in n 17.407 * [backup-simplify]: Simplify -2.0 into -2.0 17.407 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.407 * [taylor]: Taking taylor expansion of PI in n 17.407 * [backup-simplify]: Simplify PI into PI 17.407 * [taylor]: Taking taylor expansion of n in n 17.407 * [backup-simplify]: Simplify 0 into 0 17.407 * [backup-simplify]: Simplify 1 into 1 17.407 * [backup-simplify]: Simplify (/ PI 1) into PI 17.408 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.408 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.409 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.409 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 17.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.410 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 17.411 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.411 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 17.411 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 17.411 * [taylor]: Taking taylor expansion of 0.5 in k 17.411 * [backup-simplify]: Simplify 0.5 into 0.5 17.411 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 17.411 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.411 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.411 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.411 * [taylor]: Taking taylor expansion of -2.0 in k 17.411 * [backup-simplify]: Simplify -2.0 into -2.0 17.411 * [taylor]: Taking taylor expansion of PI in k 17.411 * [backup-simplify]: Simplify PI into PI 17.412 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.412 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.412 * [taylor]: Taking taylor expansion of (log n) in k 17.412 * [taylor]: Taking taylor expansion of n in k 17.412 * [backup-simplify]: Simplify n into n 17.412 * [backup-simplify]: Simplify (log n) into (log n) 17.412 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.412 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.412 * [taylor]: Taking taylor expansion of k in k 17.412 * [backup-simplify]: Simplify 0 into 0 17.412 * [backup-simplify]: Simplify 1 into 1 17.413 * [backup-simplify]: Simplify (/ 1 1) into 1 17.413 * [taylor]: Taking taylor expansion of 1.0 in k 17.413 * [backup-simplify]: Simplify 1.0 into 1.0 17.413 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.413 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.414 * [backup-simplify]: Simplify (+ 1 0) into 1 17.414 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 17.415 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 17.416 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.416 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) 17.417 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.418 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.419 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.419 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.419 * [backup-simplify]: Simplify (+ 0 0) into 0 17.419 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.420 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.421 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.422 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 17.422 * [taylor]: Taking taylor expansion of 0 in k 17.422 * [backup-simplify]: Simplify 0 into 0 17.422 * [backup-simplify]: Simplify 0 into 0 17.422 * [backup-simplify]: Simplify 0 into 0 17.423 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.424 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.425 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 17.426 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.426 * [backup-simplify]: Simplify (+ 0 0) into 0 17.426 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.428 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.431 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.431 * [taylor]: Taking taylor expansion of 0 in k 17.431 * [backup-simplify]: Simplify 0 into 0 17.431 * [backup-simplify]: Simplify 0 into 0 17.431 * [backup-simplify]: Simplify 0 into 0 17.431 * [backup-simplify]: Simplify 0 into 0 17.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.434 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.440 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 17.440 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.441 * [backup-simplify]: Simplify (+ 0 0) into 0 17.442 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.445 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.449 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.449 * [taylor]: Taking taylor expansion of 0 in k 17.449 * [backup-simplify]: Simplify 0 into 0 17.449 * [backup-simplify]: Simplify 0 into 0 17.450 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 17.450 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 17.451 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) into (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) 17.451 * [approximate]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in (k) around 0 17.451 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in k 17.451 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 17.451 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 17.451 * [taylor]: Taking taylor expansion of 1.0 in k 17.451 * [backup-simplify]: Simplify 1.0 into 1.0 17.451 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 17.452 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 17.452 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.452 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.452 * [taylor]: Taking taylor expansion of k in k 17.452 * [backup-simplify]: Simplify 0 into 0 17.452 * [backup-simplify]: Simplify 1 into 1 17.452 * [backup-simplify]: Simplify (/ 1 1) into 1 17.453 * [backup-simplify]: Simplify (sqrt 0) into 0 17.454 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.454 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in k 17.454 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 17.454 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 17.454 * [taylor]: Taking taylor expansion of 1.0 in k 17.454 * [backup-simplify]: Simplify 1.0 into 1.0 17.455 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 17.456 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 17.456 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.456 * [taylor]: Taking taylor expansion of k in k 17.456 * [backup-simplify]: Simplify 0 into 0 17.456 * [backup-simplify]: Simplify 1 into 1 17.456 * [backup-simplify]: Simplify (/ 1 1) into 1 17.456 * [backup-simplify]: Simplify (sqrt 0) into 0 17.458 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.459 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 17.460 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) 0) into 0 17.460 * [backup-simplify]: Simplify 0 into 0 17.460 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 17.462 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.464 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.464 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.466 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.467 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 17.467 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 17.469 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.471 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.471 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.476 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.477 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 17.478 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 17.480 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.481 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.486 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow k 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) k) (- (* +nan.0 (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) k))))))) 17.486 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 k)))) (sqrt (/ 1.0 (sqrt (/ 1 k))))) into (* (pow (sqrt 1.0) 2) (sqrt k)) 17.486 * [approximate]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in (k) around 0 17.486 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in k 17.486 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 17.486 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 17.486 * [taylor]: Taking taylor expansion of 1.0 in k 17.486 * [backup-simplify]: Simplify 1.0 into 1.0 17.487 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 17.487 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 17.487 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.487 * [taylor]: Taking taylor expansion of k in k 17.487 * [backup-simplify]: Simplify 0 into 0 17.487 * [backup-simplify]: Simplify 1 into 1 17.487 * [backup-simplify]: Simplify (sqrt 0) into 0 17.488 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.488 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in k 17.488 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 17.488 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 17.488 * [taylor]: Taking taylor expansion of 1.0 in k 17.488 * [backup-simplify]: Simplify 1.0 into 1.0 17.489 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 17.490 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 17.490 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.490 * [taylor]: Taking taylor expansion of k in k 17.490 * [backup-simplify]: Simplify 0 into 0 17.490 * [backup-simplify]: Simplify 1 into 1 17.490 * [backup-simplify]: Simplify (sqrt 0) into 0 17.491 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.493 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 17.493 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) 0) into 0 17.493 * [backup-simplify]: Simplify 0 into 0 17.494 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 17.497 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.500 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.503 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.504 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 17.505 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 17.509 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.511 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.516 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.516 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 17.517 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 17.519 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.521 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.526 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k))))))) 17.526 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 (- k))))) (sqrt (/ 1.0 (sqrt (/ 1 (- k)))))) into (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) 17.526 * [approximate]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in (k) around 0 17.526 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k 17.526 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 17.526 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 17.526 * [taylor]: Taking taylor expansion of 1.0 in k 17.526 * [backup-simplify]: Simplify 1.0 into 1.0 17.526 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 17.527 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 17.527 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.527 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.527 * [taylor]: Taking taylor expansion of -1 in k 17.527 * [backup-simplify]: Simplify -1 into -1 17.527 * [taylor]: Taking taylor expansion of k in k 17.527 * [backup-simplify]: Simplify 0 into 0 17.527 * [backup-simplify]: Simplify 1 into 1 17.527 * [backup-simplify]: Simplify (/ -1 1) into -1 17.527 * [backup-simplify]: Simplify (sqrt 0) into 0 17.528 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.529 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 17.530 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2)) 17.530 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k 17.530 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 17.530 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 17.530 * [taylor]: Taking taylor expansion of 1.0 in k 17.530 * [backup-simplify]: Simplify 1.0 into 1.0 17.530 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 17.530 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 17.530 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.530 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.531 * [taylor]: Taking taylor expansion of -1 in k 17.531 * [backup-simplify]: Simplify -1 into -1 17.531 * [taylor]: Taking taylor expansion of k in k 17.531 * [backup-simplify]: Simplify 0 into 0 17.531 * [backup-simplify]: Simplify 1 into 1 17.531 * [backup-simplify]: Simplify (/ -1 1) into -1 17.531 * [backup-simplify]: Simplify (sqrt 0) into 0 17.532 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.533 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 17.534 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2)) 17.535 * [backup-simplify]: Simplify (* +nan.0 (pow (sqrt 1.0) 2)) into (* +nan.0 (pow (sqrt 1.0) 2)) 17.535 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 17.536 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 17.538 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.541 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.542 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.543 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 17.544 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 17.544 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.547 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.553 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.556 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2))) 17.563 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 (- k))) (* +nan.0 (pow (sqrt 1.0) 2)))) into (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k))))))) 17.563 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1) 17.563 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 17.563 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 17.563 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 17.564 * [taylor]: Taking taylor expansion of 1.0 in k 17.564 * [backup-simplify]: Simplify 1.0 into 1.0 17.564 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.564 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.564 * [taylor]: Taking taylor expansion of k in k 17.564 * [backup-simplify]: Simplify 0 into 0 17.564 * [backup-simplify]: Simplify 1 into 1 17.564 * [backup-simplify]: Simplify (/ 1 1) into 1 17.564 * [backup-simplify]: Simplify (sqrt 0) into 0 17.566 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.566 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 17.566 * [taylor]: Taking taylor expansion of 1.0 in k 17.566 * [backup-simplify]: Simplify 1.0 into 1.0 17.566 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.566 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.566 * [taylor]: Taking taylor expansion of k in k 17.566 * [backup-simplify]: Simplify 0 into 0 17.566 * [backup-simplify]: Simplify 1 into 1 17.566 * [backup-simplify]: Simplify (/ 1 1) into 1 17.567 * [backup-simplify]: Simplify (sqrt 0) into 0 17.568 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.569 * [backup-simplify]: Simplify (* 1.0 0) into 0 17.569 * [backup-simplify]: Simplify 0 into 0 17.570 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 17.570 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.571 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.574 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.576 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 17.577 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.578 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.584 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.587 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 17.587 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.588 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 17.588 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 17.588 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 17.588 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 17.588 * [taylor]: Taking taylor expansion of 1.0 in k 17.588 * [backup-simplify]: Simplify 1.0 into 1.0 17.588 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.588 * [taylor]: Taking taylor expansion of k in k 17.588 * [backup-simplify]: Simplify 0 into 0 17.588 * [backup-simplify]: Simplify 1 into 1 17.589 * [backup-simplify]: Simplify (sqrt 0) into 0 17.589 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.589 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 17.589 * [taylor]: Taking taylor expansion of 1.0 in k 17.590 * [backup-simplify]: Simplify 1.0 into 1.0 17.590 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.590 * [taylor]: Taking taylor expansion of k in k 17.590 * [backup-simplify]: Simplify 0 into 0 17.590 * [backup-simplify]: Simplify 1 into 1 17.590 * [backup-simplify]: Simplify (sqrt 0) into 0 17.591 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.591 * [backup-simplify]: Simplify (* 1.0 0) into 0 17.591 * [backup-simplify]: Simplify 0 into 0 17.592 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 17.592 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.594 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.595 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 17.596 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.598 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.600 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 17.600 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.601 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 17.601 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 17.601 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 17.601 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 17.601 * [taylor]: Taking taylor expansion of 1.0 in k 17.601 * [backup-simplify]: Simplify 1.0 into 1.0 17.601 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.601 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.601 * [taylor]: Taking taylor expansion of -1 in k 17.601 * [backup-simplify]: Simplify -1 into -1 17.601 * [taylor]: Taking taylor expansion of k in k 17.601 * [backup-simplify]: Simplify 0 into 0 17.601 * [backup-simplify]: Simplify 1 into 1 17.601 * [backup-simplify]: Simplify (/ -1 1) into -1 17.602 * [backup-simplify]: Simplify (sqrt 0) into 0 17.603 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.603 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 17.603 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 17.603 * [taylor]: Taking taylor expansion of 1.0 in k 17.603 * [backup-simplify]: Simplify 1.0 into 1.0 17.603 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.603 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.603 * [taylor]: Taking taylor expansion of -1 in k 17.603 * [backup-simplify]: Simplify -1 into -1 17.603 * [taylor]: Taking taylor expansion of k in k 17.603 * [backup-simplify]: Simplify 0 into 0 17.603 * [backup-simplify]: Simplify 1 into 1 17.603 * [backup-simplify]: Simplify (/ -1 1) into -1 17.604 * [backup-simplify]: Simplify (sqrt 0) into 0 17.604 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.605 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 17.605 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 17.607 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.609 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 17.609 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.609 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.612 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.614 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 17.614 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.615 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 17.615 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 17.615 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 17.615 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 17.615 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 17.615 * [taylor]: Taking taylor expansion of 1.0 in k 17.615 * [backup-simplify]: Simplify 1.0 into 1.0 17.615 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.615 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.615 * [taylor]: Taking taylor expansion of k in k 17.615 * [backup-simplify]: Simplify 0 into 0 17.615 * [backup-simplify]: Simplify 1 into 1 17.616 * [backup-simplify]: Simplify (/ 1 1) into 1 17.616 * [backup-simplify]: Simplify (sqrt 0) into 0 17.617 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.617 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 17.617 * [taylor]: Taking taylor expansion of 1.0 in k 17.617 * [backup-simplify]: Simplify 1.0 into 1.0 17.617 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.617 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.617 * [taylor]: Taking taylor expansion of k in k 17.617 * [backup-simplify]: Simplify 0 into 0 17.617 * [backup-simplify]: Simplify 1 into 1 17.617 * [backup-simplify]: Simplify (/ 1 1) into 1 17.617 * [backup-simplify]: Simplify (sqrt 0) into 0 17.618 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.618 * [backup-simplify]: Simplify (* 1.0 0) into 0 17.618 * [backup-simplify]: Simplify 0 into 0 17.619 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 17.619 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.620 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.622 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.623 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 17.623 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.624 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.628 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.630 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 17.630 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.632 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 17.632 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 17.632 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 17.632 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 17.632 * [taylor]: Taking taylor expansion of 1.0 in k 17.632 * [backup-simplify]: Simplify 1.0 into 1.0 17.632 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.632 * [taylor]: Taking taylor expansion of k in k 17.632 * [backup-simplify]: Simplify 0 into 0 17.632 * [backup-simplify]: Simplify 1 into 1 17.632 * [backup-simplify]: Simplify (sqrt 0) into 0 17.634 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.634 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 17.634 * [taylor]: Taking taylor expansion of 1.0 in k 17.634 * [backup-simplify]: Simplify 1.0 into 1.0 17.634 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.634 * [taylor]: Taking taylor expansion of k in k 17.634 * [backup-simplify]: Simplify 0 into 0 17.634 * [backup-simplify]: Simplify 1 into 1 17.634 * [backup-simplify]: Simplify (sqrt 0) into 0 17.636 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.636 * [backup-simplify]: Simplify (* 1.0 0) into 0 17.636 * [backup-simplify]: Simplify 0 into 0 17.638 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 17.638 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.641 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.643 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 17.643 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.648 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.650 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 17.650 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.652 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 17.652 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 17.652 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 17.652 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 17.652 * [taylor]: Taking taylor expansion of 1.0 in k 17.652 * [backup-simplify]: Simplify 1.0 into 1.0 17.652 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.652 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.652 * [taylor]: Taking taylor expansion of -1 in k 17.652 * [backup-simplify]: Simplify -1 into -1 17.652 * [taylor]: Taking taylor expansion of k in k 17.652 * [backup-simplify]: Simplify 0 into 0 17.652 * [backup-simplify]: Simplify 1 into 1 17.653 * [backup-simplify]: Simplify (/ -1 1) into -1 17.653 * [backup-simplify]: Simplify (sqrt 0) into 0 17.655 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.655 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 17.655 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 17.655 * [taylor]: Taking taylor expansion of 1.0 in k 17.655 * [backup-simplify]: Simplify 1.0 into 1.0 17.655 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.655 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.655 * [taylor]: Taking taylor expansion of -1 in k 17.655 * [backup-simplify]: Simplify -1 into -1 17.655 * [taylor]: Taking taylor expansion of k in k 17.655 * [backup-simplify]: Simplify 0 into 0 17.655 * [backup-simplify]: Simplify 1 into 1 17.656 * [backup-simplify]: Simplify (/ -1 1) into -1 17.656 * [backup-simplify]: Simplify (sqrt 0) into 0 17.657 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.658 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 17.658 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.659 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 17.662 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.664 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 17.665 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.666 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.670 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.674 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 17.675 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.676 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 17.676 * * * [progress]: simplifying candidates 17.683 * [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)) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (+ 1 1) (+ (log (sqrt (/ 1.0 (sqrt k)))) (log (sqrt (/ 1.0 (sqrt k))))) (log (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (exp (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))) (* (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))) (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (sqrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (sqrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt 1.0) (sqrt 1.0)) (* (sqrt (sqrt k)) (sqrt (sqrt k))) (* (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k)))))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))))) (* (sqrt (cbrt (/ 1.0 (sqrt k)))) (sqrt (cbrt (/ 1.0 (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (cbrt (sqrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)))) (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k)))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1))) (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k)))) (* (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt 1))) (sqrt (/ (sqrt 1.0) (sqrt 1)))) (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k)))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) 1)) (sqrt (/ (sqrt 1.0) 1))) (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k)))) (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ 1.0 (cbrt (sqrt k)))) (sqrt (/ 1.0 (cbrt (sqrt k))))) (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt (cbrt k))))) (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k))))) (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k))))) (* (sqrt (/ 1 (sqrt 1))) (sqrt (/ 1 (sqrt 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(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) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) k))))))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k))))))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k))))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 17.692 * * [simplify]: iteration 0: 362 enodes 17.883 * * [simplify]: iteration 1: 815 enodes 18.195 * * [simplify]: iteration 2: 2196 enodes 18.880 * * [simplify]: iteration complete: 5003 enodes 18.880 * * [simplify]: Extracting #0: cost 107 inf + 0 18.883 * * [simplify]: Extracting #1: cost 693 inf + 3 18.900 * * [simplify]: Extracting #2: cost 1542 inf + 1705 18.918 * * [simplify]: Extracting #3: cost 1772 inf + 35146 18.983 * * [simplify]: Extracting #4: cost 932 inf + 227902 19.102 * * [simplify]: Extracting #5: cost 261 inf + 487253 19.229 * * [simplify]: Extracting #6: cost 26 inf + 593497 19.357 * * [simplify]: Extracting #7: cost 0 inf + 606745 19.525 * * [simplify]: Extracting #8: cost 0 inf + 606705 19.722 * [simplify]: Simplified to: (* (log (* (* PI n) 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* (* PI n) 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* (* PI n) 2.0)) (/ (- 1.0 k) 2.0)) (* (log (* (* PI n) 2.0)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI n) 2.0) (/ 1.0 2.0)) (pow (* (* PI n) 2.0) (/ k 2.0)) (pow (* (* PI n) 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* PI n) 2.0) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* PI n) 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* (* PI n) 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* PI n) 2.0) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* PI n) 2.0) (sqrt (- 1.0 k))) (pow (* (* PI n) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ 1 (sqrt 2.0))) (* (* PI n) 2.0) (pow (* (* PI n) 2.0) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI n) 2.0) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* (* PI n) 2.0) (+ (sqrt k) (sqrt 1.0))) (pow (* (* PI n) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ 1 (sqrt 2.0))) (* (* PI n) 2.0) (* (* PI n) 2.0) (pow (* (* PI n) 2.0) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* PI n) 2.0)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (pow (* (* PI n) 2.0) (* (/ (- 1.0 k) 2.0) 1/2)) (pow (* (* PI n) 2.0) (* (/ (- 1.0 k) 2.0) 1/2)) 1 1 2 1 1 (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) 2 (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) 1.0 (sqrt k) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) 1 (/ 1.0 (sqrt k)) 1.0 (/ 1 (sqrt k)) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) 1 (/ 1.0 (sqrt k)) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) 1 2 1 (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (fabs (cbrt (/ 1.0 (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (* (fabs (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)))) (* (sqrt (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0))) (sqrt (/ 1.0 (sqrt k)))) (* (fabs (cbrt 1.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0))) (sqrt (/ 1.0 (sqrt k)))) (* (fabs (cbrt 1.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (fabs (cbrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt 1.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (sqrt 1.0)) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (fabs (cbrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0)) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (sqrt (/ 1.0 (sqrt k))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (cbrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (cbrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt (cbrt k))))) (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k)))) (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (cbrt (sqrt k))))) (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k))))) (/ 1.0 (sqrt k)) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k))))) (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k))))) (/ 1.0 (sqrt k)) (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0)) (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0)) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (* (* 0.125 (exp (* (log (* (* PI n) 2.0)) 0.5))) (* (* k (log n)) (* k (log n)))) (- (+ (exp (* (log (* (* PI n) 2.0)) 0.5)) (* (exp (* (log (* (* PI n) 2.0)) 0.5)) (+ (* (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) 0.125) (* k k)) (* (* 0.25 (log (* 2.0 PI))) (* (* k k) (log n)))))) (* 0.5 (* (exp (* (log (* (* PI n) 2.0)) 0.5)) (+ (* k (log (* 2.0 PI))) (* k (log n))))))) (exp (* (- 1.0 k) (* (log (* (* PI n) 2.0)) 0.5))) (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) (- (* (- +nan.0) (* 1.0 (* k k))) (* 1.0 (- (- +nan.0) (* (- +nan.0) k)))) (+ (+ (* (/ 1.0 k) (- +nan.0)) (* (/ +nan.0 (* k k)) (/ 1.0 k))) (* (- +nan.0) (/ 1.0 (* k k)))) (+ (- (* 1.0 +nan.0)) (- (* (/ +nan.0 k) (/ 1.0 k)) (/ (* 1.0 +nan.0) k))) (- (* (- +nan.0) (* k k)) (+ (- +nan.0) (* +nan.0 k))) (+ (- (/ +nan.0 k) (/ +nan.0 (* k (* k k)))) (/ (- +nan.0) (* k k))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) (- (* (- +nan.0) (* k k)) (+ (- +nan.0) (* +nan.0 k))) (+ (- (/ +nan.0 k) (/ +nan.0 (* k (* k k)))) (/ (- +nan.0) (* k k))) (+ (- (/ +nan.0 k) +nan.0) (/ (- +nan.0) (* k k))) 19.769 * * * [progress]: adding candidates to table 21.280 * [progress]: [Phase 3 of 3] Extracting. 21.280 * * [regime]: Finding splitpoints for: (# # # # # # # # # #) 21.285 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 21.285 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # # #) 21.406 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # # # #) 21.566 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# #) 21.629 * * * * [regimes]: Trying to branch on n from (# # # # # # # # # #) 21.759 * * * * [regimes]: Trying to branch on k from (# # # # # # # # # #) 21.883 * * * [regime]: Found split indices: #