5.654 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.221 * * * [progress]: [2/2] Setting up program. 0.226 * [progress]: [Phase 2 of 3] Improving. 0.227 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.227 * * [simplify]: Extracting # 0 : cost 0 0.227 * * [simplify]: Extracting # 1 : cost 0 0.227 * * [simplify]: Extracting # 2 : cost 0 0.227 * * [simplify]: Extracting # 3 : cost 0 0.227 * * [simplify]: Extracting # 4 : cost 0 0.227 * * [simplify]: Extracting # 5 : cost 0 0.227 * * [simplify]: Extracting # 6 : cost 0 0.227 * * [simplify]: Extracting # 7 : cost 0 0.227 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.233 * * [simplify]: Extracting # 0 : cost 0 0.233 * * [simplify]: Extracting # 1 : cost 0 0.233 * * [simplify]: Extracting # 2 : cost 0 0.234 * * [simplify]: Extracting # 3 : cost 0 0.234 * * [simplify]: Extracting # 4 : cost 0 0.234 * * [simplify]: Extracting # 5 : cost 0 0.234 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.245 * * [simplify]: Extracting # 0 : cost 0 0.246 * * [simplify]: Extracting # 1 : cost 0 0.246 * * [simplify]: Extracting # 2 : cost 0 0.246 * * [simplify]: Extracting # 3 : cost 0 0.246 * * [simplify]: Extracting # 4 : cost 0 0.246 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.271 * * [simplify]: Extracting # 0 : cost 0 0.272 * * [simplify]: Extracting # 1 : cost 0 0.272 * * [simplify]: Extracting # 2 : cost 0 0.272 * * [simplify]: Extracting # 3 : cost 0 0.272 * * [simplify]: Extracting # 4 : cost 0 0.273 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.327 * * [simplify]: Extracting # 0 : cost 0 0.328 * * [simplify]: Extracting # 1 : cost 0 0.328 * * [simplify]: Extracting # 2 : cost 0 0.329 * * [simplify]: Extracting # 3 : cost 0 0.329 * * [simplify]: Extracting # 4 : cost 0 0.330 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.631 * * [simplify]: Extracting # 0 : cost 0 0.633 * * [simplify]: Extracting # 1 : cost 0 0.634 * * [simplify]: Extracting # 2 : cost 0 0.636 * * [simplify]: Extracting # 3 : cost 0 0.637 * * [simplify]: Extracting # 4 : cost 0 0.638 * * [simplify]: iteration 5 : 853 enodes (cost 16 ) 2.221 * * [simplify]: Extracting # 0 : cost 0 2.228 * * [simplify]: Extracting # 1 : cost 0 2.233 * * [simplify]: Extracting # 2 : cost 0 2.243 * * [simplify]: Extracting # 3 : cost 0 2.249 * * [simplify]: Extracting # 4 : cost 0 2.254 * * [simplify]: iteration 6 : 3196 enodes (cost 16 ) 3.991 * * [simplify]: Extracting # 0 : cost 0 3.997 * * [simplify]: Extracting # 1 : cost 0 4.003 * * [simplify]: Extracting # 2 : cost 0 4.013 * * [simplify]: Extracting # 3 : cost 0 4.027 * * [simplify]: Extracting # 4 : cost 0 4.036 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 4.036 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 4.037 * * [progress]: iteration 1 / 4 4.037 * * * [progress]: picking best candidate 4.042 * * * * [pick]: Picked # 4.043 * * * [progress]: localizing error 4.075 * * * [progress]: generating rewritten candidates 4.075 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.120 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 4.135 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 4.174 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.229 * * * [progress]: generating series expansions 4.229 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.230 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.230 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.230 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.230 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.230 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.230 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.230 * [taylor]: Taking taylor expansion of 0.5 in k 4.230 * [backup-simplify]: Simplify 0.5 into 0.5 4.230 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.230 * [taylor]: Taking taylor expansion of 1.0 in k 4.230 * [backup-simplify]: Simplify 1.0 into 1.0 4.230 * [taylor]: Taking taylor expansion of k in k 4.230 * [backup-simplify]: Simplify 0 into 0 4.230 * [backup-simplify]: Simplify 1 into 1 4.230 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.230 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.230 * [taylor]: Taking taylor expansion of 2.0 in k 4.230 * [backup-simplify]: Simplify 2.0 into 2.0 4.230 * [taylor]: Taking taylor expansion of (* n PI) in k 4.230 * [taylor]: Taking taylor expansion of n in k 4.230 * [backup-simplify]: Simplify n into n 4.230 * [taylor]: Taking taylor expansion of PI in k 4.230 * [backup-simplify]: Simplify PI into PI 4.231 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.231 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.231 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.231 * [backup-simplify]: Simplify (- 0) into 0 4.231 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.232 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.232 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.232 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.232 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.232 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.232 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.232 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.232 * [taylor]: Taking taylor expansion of 0.5 in n 4.232 * [backup-simplify]: Simplify 0.5 into 0.5 4.232 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.232 * [taylor]: Taking taylor expansion of 1.0 in n 4.232 * [backup-simplify]: Simplify 1.0 into 1.0 4.232 * [taylor]: Taking taylor expansion of k in n 4.232 * [backup-simplify]: Simplify k into k 4.232 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.232 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.232 * [taylor]: Taking taylor expansion of 2.0 in n 4.232 * [backup-simplify]: Simplify 2.0 into 2.0 4.232 * [taylor]: Taking taylor expansion of (* n PI) in n 4.232 * [taylor]: Taking taylor expansion of n in n 4.232 * [backup-simplify]: Simplify 0 into 0 4.232 * [backup-simplify]: Simplify 1 into 1 4.232 * [taylor]: Taking taylor expansion of PI in n 4.232 * [backup-simplify]: Simplify PI into PI 4.233 * [backup-simplify]: Simplify (* 0 PI) into 0 4.233 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.234 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.235 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.236 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.236 * [backup-simplify]: Simplify (- k) into (- k) 4.236 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.236 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.237 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.237 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.238 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.238 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.239 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.239 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.239 * [taylor]: Taking taylor expansion of 0.5 in n 4.239 * [backup-simplify]: Simplify 0.5 into 0.5 4.239 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.239 * [taylor]: Taking taylor expansion of 1.0 in n 4.239 * [backup-simplify]: Simplify 1.0 into 1.0 4.239 * [taylor]: Taking taylor expansion of k in n 4.239 * [backup-simplify]: Simplify k into k 4.239 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.239 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.239 * [taylor]: Taking taylor expansion of 2.0 in n 4.239 * [backup-simplify]: Simplify 2.0 into 2.0 4.239 * [taylor]: Taking taylor expansion of (* n PI) in n 4.239 * [taylor]: Taking taylor expansion of n in n 4.239 * [backup-simplify]: Simplify 0 into 0 4.239 * [backup-simplify]: Simplify 1 into 1 4.239 * [taylor]: Taking taylor expansion of PI in n 4.239 * [backup-simplify]: Simplify PI into PI 4.240 * [backup-simplify]: Simplify (* 0 PI) into 0 4.240 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.242 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.243 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.244 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.244 * [backup-simplify]: Simplify (- k) into (- k) 4.244 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.245 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.247 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.248 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.249 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.249 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.249 * [taylor]: Taking taylor expansion of 0.5 in k 4.249 * [backup-simplify]: Simplify 0.5 into 0.5 4.249 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.249 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.249 * [taylor]: Taking taylor expansion of 1.0 in k 4.249 * [backup-simplify]: Simplify 1.0 into 1.0 4.249 * [taylor]: Taking taylor expansion of k in k 4.249 * [backup-simplify]: Simplify 0 into 0 4.255 * [backup-simplify]: Simplify 1 into 1 4.255 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.255 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.255 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.255 * [taylor]: Taking taylor expansion of 2.0 in k 4.255 * [backup-simplify]: Simplify 2.0 into 2.0 4.255 * [taylor]: Taking taylor expansion of PI in k 4.255 * [backup-simplify]: Simplify PI into PI 4.256 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.257 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.257 * [taylor]: Taking taylor expansion of (log n) in k 4.257 * [taylor]: Taking taylor expansion of n in k 4.257 * [backup-simplify]: Simplify n into n 4.257 * [backup-simplify]: Simplify (log n) into (log n) 4.258 * [backup-simplify]: Simplify (- 0) into 0 4.258 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.260 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.261 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.262 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.264 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.265 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.268 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.270 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.270 * [backup-simplify]: Simplify (- 0) into 0 4.271 * [backup-simplify]: Simplify (+ 0 0) into 0 4.271 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.273 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.274 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.276 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.276 * [taylor]: Taking taylor expansion of 0 in k 4.276 * [backup-simplify]: Simplify 0 into 0 4.276 * [backup-simplify]: Simplify 0 into 0 4.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.279 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.280 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.280 * [backup-simplify]: Simplify (+ 0 0) into 0 4.280 * [backup-simplify]: Simplify (- 1) into -1 4.281 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.282 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.284 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 4.288 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.291 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.293 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.295 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.298 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.299 * [backup-simplify]: Simplify (- 0) into 0 4.299 * [backup-simplify]: Simplify (+ 0 0) into 0 4.300 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.302 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.303 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.306 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.306 * [taylor]: Taking taylor expansion of 0 in k 4.306 * [backup-simplify]: Simplify 0 into 0 4.306 * [backup-simplify]: Simplify 0 into 0 4.306 * [backup-simplify]: Simplify 0 into 0 4.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.311 * [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