4.911 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.188 * * * [progress]: [2/2] Setting up program. 0.191 * [progress]: [Phase 2 of 3] Improving. 0.191 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.191 * * [simplify]: Extracting # 0 : cost 0 0.191 * * [simplify]: Extracting # 1 : cost 0 0.191 * * [simplify]: Extracting # 2 : cost 0 0.191 * * [simplify]: Extracting # 3 : cost 0 0.191 * * [simplify]: Extracting # 4 : cost 0 0.191 * * [simplify]: Extracting # 5 : cost 0 0.191 * * [simplify]: Extracting # 6 : cost 0 0.191 * * [simplify]: Extracting # 7 : cost 0 0.191 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.230 * * [simplify]: Extracting # 0 : cost 0 0.231 * * [simplify]: Extracting # 1 : cost 0 0.231 * * [simplify]: Extracting # 2 : cost 0 0.231 * * [simplify]: Extracting # 3 : cost 0 0.231 * * [simplify]: Extracting # 4 : cost 0 0.231 * * [simplify]: Extracting # 5 : cost 0 0.231 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.247 * * [simplify]: Extracting # 0 : cost 0 0.247 * * [simplify]: Extracting # 1 : cost 0 0.247 * * [simplify]: Extracting # 2 : cost 0 0.248 * * [simplify]: Extracting # 3 : cost 0 0.248 * * [simplify]: Extracting # 4 : cost 0 0.248 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.272 * * [simplify]: Extracting # 0 : cost 0 0.272 * * [simplify]: Extracting # 1 : cost 0 0.272 * * [simplify]: Extracting # 2 : cost 0 0.273 * * [simplify]: Extracting # 3 : cost 0 0.273 * * [simplify]: Extracting # 4 : cost 0 0.273 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.302 * * [simplify]: Extracting # 0 : cost 0 0.302 * * [simplify]: Extracting # 1 : cost 0 0.302 * * [simplify]: Extracting # 2 : cost 0 0.303 * * [simplify]: Extracting # 3 : cost 0 0.303 * * [simplify]: Extracting # 4 : cost 0 0.303 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.564 * * [simplify]: Extracting # 0 : cost 0 0.565 * * [simplify]: Extracting # 1 : cost 0 0.566 * * [simplify]: Extracting # 2 : cost 0 0.567 * * [simplify]: Extracting # 3 : cost 0 0.568 * * [simplify]: Extracting # 4 : cost 0 0.568 * * [simplify]: iteration 5 : 843 enodes (cost 16 ) 2.280 * * [simplify]: Extracting # 0 : cost 0 2.287 * * [simplify]: Extracting # 1 : cost 0 2.292 * * [simplify]: Extracting # 2 : cost 0 2.298 * * [simplify]: Extracting # 3 : cost 0 2.302 * * [simplify]: Extracting # 4 : cost 0 2.304 * * [simplify]: iteration 6 : 3221 enodes (cost 16 ) 4.133 * * [simplify]: Extracting # 0 : cost 0 4.144 * * [simplify]: Extracting # 1 : cost 0 4.154 * * [simplify]: Extracting # 2 : cost 0 4.164 * * [simplify]: Extracting # 3 : cost 0 4.173 * * [simplify]: Extracting # 4 : cost 0 4.182 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 4.182 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 4.183 * * [progress]: iteration 1 / 4 4.183 * * * [progress]: picking best candidate 4.188 * * * * [pick]: Picked # 4.188 * * * [progress]: localizing error 4.216 * * * [progress]: generating rewritten candidates 4.216 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.245 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 4.251 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 4.282 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.348 * * * [progress]: generating series expansions 4.349 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.350 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.350 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.351 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.352 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.352 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.352 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.352 * [taylor]: Taking taylor expansion of 0.5 in k 4.352 * [backup-simplify]: Simplify 0.5 into 0.5 4.352 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.352 * [taylor]: Taking taylor expansion of 1.0 in k 4.352 * [backup-simplify]: Simplify 1.0 into 1.0 4.352 * [taylor]: Taking taylor expansion of k in k 4.352 * [backup-simplify]: Simplify 0 into 0 4.352 * [backup-simplify]: Simplify 1 into 1 4.352 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.352 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.352 * [taylor]: Taking taylor expansion of 2.0 in k 4.352 * [backup-simplify]: Simplify 2.0 into 2.0 4.352 * [taylor]: Taking taylor expansion of (* n PI) in k 4.352 * [taylor]: Taking taylor expansion of n in k 4.352 * [backup-simplify]: Simplify n into n 4.352 * [taylor]: Taking taylor expansion of PI in k 4.352 * [backup-simplify]: Simplify PI into PI 4.353 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.353 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.353 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.354 * [backup-simplify]: Simplify (- 0) into 0 4.354 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.355 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.355 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.355 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.355 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.355 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.355 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.355 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.355 * [taylor]: Taking taylor expansion of 0.5 in n 4.355 * [backup-simplify]: Simplify 0.5 into 0.5 4.355 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.355 * [taylor]: Taking taylor expansion of 1.0 in n 4.355 * [backup-simplify]: Simplify 1.0 into 1.0 4.355 * [taylor]: Taking taylor expansion of k in n 4.355 * [backup-simplify]: Simplify k into k 4.355 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.355 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.355 * [taylor]: Taking taylor expansion of 2.0 in n 4.355 * [backup-simplify]: Simplify 2.0 into 2.0 4.355 * [taylor]: Taking taylor expansion of (* n PI) in n 4.356 * [taylor]: Taking taylor expansion of n in n 4.356 * [backup-simplify]: Simplify 0 into 0 4.356 * [backup-simplify]: Simplify 1 into 1 4.356 * [taylor]: Taking taylor expansion of PI in n 4.356 * [backup-simplify]: Simplify PI into PI 4.356 * [backup-simplify]: Simplify (* 0 PI) into 0 4.357 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.358 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.360 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.361 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.361 * [backup-simplify]: Simplify (- k) into (- k) 4.361 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.361 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.363 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.364 * [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)))) 4.365 * [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))))) 4.365 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.365 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.365 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.365 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.365 * [taylor]: Taking taylor expansion of 0.5 in n 4.366 * [backup-simplify]: Simplify 0.5 into 0.5 4.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.366 * [taylor]: Taking taylor expansion of 1.0 in n 4.366 * [backup-simplify]: Simplify 1.0 into 1.0 4.366 * [taylor]: Taking taylor expansion of k in n 4.366 * [backup-simplify]: Simplify k into k 4.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.366 * [taylor]: Taking taylor expansion of 2.0 in n 4.366 * [backup-simplify]: Simplify 2.0 into 2.0 4.366 * [taylor]: Taking taylor expansion of (* n PI) in n 4.366 * [taylor]: Taking taylor expansion of n in n 4.366 * [backup-simplify]: Simplify 0 into 0 4.366 * [backup-simplify]: Simplify 1 into 1 4.366 * [taylor]: Taking taylor expansion of PI in n 4.366 * [backup-simplify]: Simplify PI into PI 4.366 * [backup-simplify]: Simplify (* 0 PI) into 0 4.367 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.368 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.370 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.371 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.371 * [backup-simplify]: Simplify (- k) into (- k) 4.371 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.371 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.374 * [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)))) 4.375 * [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))))) 4.375 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.375 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.376 * [taylor]: Taking taylor expansion of 0.5 in k 4.376 * [backup-simplify]: Simplify 0.5 into 0.5 4.376 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.376 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.376 * [taylor]: Taking taylor expansion of 1.0 in k 4.376 * [backup-simplify]: Simplify 1.0 into 1.0 4.376 * [taylor]: Taking taylor expansion of k in k 4.376 * [backup-simplify]: Simplify 0 into 0 4.376 * [backup-simplify]: Simplify 1 into 1 4.376 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.376 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.376 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.376 * [taylor]: Taking taylor expansion of 2.0 in k 4.376 * [backup-simplify]: Simplify 2.0 into 2.0 4.376 * [taylor]: Taking taylor expansion of PI in k 4.376 * [backup-simplify]: Simplify PI into PI 4.377 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.378 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.378 * [taylor]: Taking taylor expansion of (log n) in k 4.378 * [taylor]: Taking taylor expansion of n in k 4.378 * [backup-simplify]: Simplify n into n 4.378 * [backup-simplify]: Simplify (log n) into (log n) 4.378 * [backup-simplify]: Simplify (- 0) into 0 4.379 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.380 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.381 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.382 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.383 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.385 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.387 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.391 * [backup-simplify]: Simplify (- 0) into 0 4.391 * [backup-simplify]: Simplify (+ 0 0) into 0 4.392 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.393 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.395 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.397 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.397 * [taylor]: Taking taylor expansion of 0 in k 4.397 * [backup-simplify]: Simplify 0 into 0 4.397 * [backup-simplify]: Simplify 0 into 0 4.398 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.400 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.401 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.401 * [backup-simplify]: Simplify (+ 0 0) into 0 4.401 * [backup-simplify]: Simplify (- 1) into -1 4.402 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.404 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.406 * [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)))) 4.409 * [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)))))) 4.413 * [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)))))) 4.415 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.417 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.420 * [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 4.421 * [backup-simplify]: Simplify (- 0) into 0 4.421 * [backup-simplify]: Simplify (+ 0 0) into 0 4.422 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.424 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.425 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.428 * [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 4.428 * [taylor]: Taking taylor expansion of 0 in k 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 0 into 0 4.428 * [backup-simplify]: Simplify 0 into 0 4.429 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.433 * [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