53.720 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.193 * * * [progress]: [2/2] Setting up program. 0.197 * [progress]: [Phase 2 of 3] Improving. 0.197 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.198 * * [simplify]: iteration 0: 13 enodes 0.201 * * [simplify]: iteration 1: 29 enodes 0.207 * * [simplify]: iteration 2: 58 enodes 0.219 * * [simplify]: iteration 3: 114 enodes 0.245 * * [simplify]: iteration 4: 285 enodes 0.378 * * [simplify]: iteration 5: 816 enodes 1.417 * * [simplify]: iteration 6: 2792 enodes 2.443 * * [simplify]: iteration complete: 5003 enodes 2.443 * * [simplify]: Extracting #0: cost 1 inf + 0 2.443 * * [simplify]: Extracting #1: cost 108 inf + 0 2.446 * * [simplify]: Extracting #2: cost 443 inf + 1 2.453 * * [simplify]: Extracting #3: cost 1022 inf + 49 2.466 * * [simplify]: Extracting #4: cost 1321 inf + 10849 2.513 * * [simplify]: Extracting #5: cost 617 inf + 94525 2.631 * * [simplify]: Extracting #6: cost 187 inf + 373026 2.799 * * [simplify]: Extracting #7: cost 0 inf + 567203 2.925 * * [simplify]: Extracting #8: cost 0 inf + 562474 3.058 * * [simplify]: Extracting #9: cost 0 inf + 561804 3.189 * [simplify]: Simplified to: (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) 3.189 * * [progress]: iteration 1 / 4 3.189 * * * [progress]: picking best candidate 3.194 * * * * [pick]: Picked # 3.194 * * * [progress]: localizing error 3.226 * * * [progress]: generating rewritten candidates 3.226 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.250 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 3.268 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 3.277 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.326 * * * [progress]: generating series expansions 3.326 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.327 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.327 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.327 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.327 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.327 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.327 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.327 * [taylor]: Taking taylor expansion of 0.5 in k 3.327 * [backup-simplify]: Simplify 0.5 into 0.5 3.327 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.327 * [taylor]: Taking taylor expansion of 1.0 in k 3.327 * [backup-simplify]: Simplify 1.0 into 1.0 3.327 * [taylor]: Taking taylor expansion of k in k 3.327 * [backup-simplify]: Simplify 0 into 0 3.327 * [backup-simplify]: Simplify 1 into 1 3.327 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.327 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.327 * [taylor]: Taking taylor expansion of 2.0 in k 3.327 * [backup-simplify]: Simplify 2.0 into 2.0 3.327 * [taylor]: Taking taylor expansion of (* n PI) in k 3.328 * [taylor]: Taking taylor expansion of n in k 3.328 * [backup-simplify]: Simplify n into n 3.328 * [taylor]: Taking taylor expansion of PI in k 3.328 * [backup-simplify]: Simplify PI into PI 3.328 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.328 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.328 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.328 * [backup-simplify]: Simplify (- 0) into 0 3.329 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.329 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.329 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.330 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.330 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.330 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.330 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.330 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.330 * [taylor]: Taking taylor expansion of 0.5 in n 3.330 * [backup-simplify]: Simplify 0.5 into 0.5 3.330 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.330 * [taylor]: Taking taylor expansion of 1.0 in n 3.330 * [backup-simplify]: Simplify 1.0 into 1.0 3.330 * [taylor]: Taking taylor expansion of k in n 3.330 * [backup-simplify]: Simplify k into k 3.330 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.330 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.330 * [taylor]: Taking taylor expansion of 2.0 in n 3.330 * [backup-simplify]: Simplify 2.0 into 2.0 3.330 * [taylor]: Taking taylor expansion of (* n PI) in n 3.330 * [taylor]: Taking taylor expansion of n in n 3.330 * [backup-simplify]: Simplify 0 into 0 3.330 * [backup-simplify]: Simplify 1 into 1 3.330 * [taylor]: Taking taylor expansion of PI in n 3.330 * [backup-simplify]: Simplify PI into PI 3.331 * [backup-simplify]: Simplify (* 0 PI) into 0 3.331 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.333 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.334 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.336 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.336 * [backup-simplify]: Simplify (- k) into (- k) 3.336 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.336 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.337 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.338 * [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)))) 3.340 * [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))))) 3.340 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.340 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.340 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.340 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.340 * [taylor]: Taking taylor expansion of 0.5 in n 3.340 * [backup-simplify]: Simplify 0.5 into 0.5 3.340 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.340 * [taylor]: Taking taylor expansion of 1.0 in n 3.340 * [backup-simplify]: Simplify 1.0 into 1.0 3.340 * [taylor]: Taking taylor expansion of k in n 3.340 * [backup-simplify]: Simplify k into k 3.340 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.340 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.340 * [taylor]: Taking taylor expansion of 2.0 in n 3.340 * [backup-simplify]: Simplify 2.0 into 2.0 3.340 * [taylor]: Taking taylor expansion of (* n PI) in n 3.340 * [taylor]: Taking taylor expansion of n in n 3.340 * [backup-simplify]: Simplify 0 into 0 3.340 * [backup-simplify]: Simplify 1 into 1 3.340 * [taylor]: Taking taylor expansion of PI in n 3.340 * [backup-simplify]: Simplify PI into PI 3.341 * [backup-simplify]: Simplify (* 0 PI) into 0 3.341 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.343 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.345 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.346 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.346 * [backup-simplify]: Simplify (- k) into (- k) 3.346 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.346 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.347 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.349 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.350 * [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))))) 3.350 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.350 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.350 * [taylor]: Taking taylor expansion of 0.5 in k 3.350 * [backup-simplify]: Simplify 0.5 into 0.5 3.350 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.350 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.350 * [taylor]: Taking taylor expansion of 1.0 in k 3.350 * [backup-simplify]: Simplify 1.0 into 1.0 3.350 * [taylor]: Taking taylor expansion of k in k 3.350 * [backup-simplify]: Simplify 0 into 0 3.350 * [backup-simplify]: Simplify 1 into 1 3.350 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.350 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.350 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.350 * [taylor]: Taking taylor expansion of 2.0 in k 3.350 * [backup-simplify]: Simplify 2.0 into 2.0 3.350 * [taylor]: Taking taylor expansion of PI in k 3.350 * [backup-simplify]: Simplify PI into PI 3.351 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.352 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.352 * [taylor]: Taking taylor expansion of (log n) in k 3.352 * [taylor]: Taking taylor expansion of n in k 3.352 * [backup-simplify]: Simplify n into n 3.352 * [backup-simplify]: Simplify (log n) into (log n) 3.352 * [backup-simplify]: Simplify (- 0) into 0 3.353 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.354 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.355 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.356 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.358 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.359 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.360 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.363 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.363 * [backup-simplify]: Simplify (- 0) into 0 3.367 * [backup-simplify]: Simplify (+ 0 0) into 0 3.368 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.371 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.373 * [taylor]: Taking taylor expansion of 0 in k 3.373 * [backup-simplify]: Simplify 0 into 0 3.373 * [backup-simplify]: Simplify 0 into 0 3.374 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.375 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.376 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.377 * [backup-simplify]: Simplify (+ 0 0) into 0 3.377 * [backup-simplify]: Simplify (- 1) into -1 3.378 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.379 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.381 * [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)))) 3.385 * [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)))))) 3.388 * [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)))))) 3.389 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.394 * [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 3.395 * [backup-simplify]: Simplify (- 0) into 0 3.395 * [backup-simplify]: Simplify (+ 0 0) into 0 3.396 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.397 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.398 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.399 * [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 3.399 * [taylor]: Taking taylor expansion of 0 in k 3.399 * [backup-simplify]: Simplify 0 into 0 3.399 * [backup-simplify]: Simplify 0 into 0 3.399 * [backup-simplify]: Simplify 0 into 0 3.400 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.402 * [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 3.403 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.403 * [backup-simplify]: Simplify (+ 0 0) into 0 3.404 * [backup-simplify]: Simplify (- 0) into 0 3.404 * [backup-simplify]: Simplify (+ 0 0) into 0 3.405 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.407 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.409 * [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)))))) 3.413 * [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)))))) 3.420 * [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))))) 3.420 * [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)))) 3.420 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.420 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.420 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.420 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.420 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.420 * [taylor]: Taking taylor expansion of 0.5 in k 3.420 * [backup-simplify]: Simplify 0.5 into 0.5 3.420 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.420 * [taylor]: Taking taylor expansion of 1.0 in k 3.420 * [backup-simplify]: Simplify 1.0 into 1.0 3.420 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.420 * [taylor]: Taking taylor expansion of k in k 3.420 * [backup-simplify]: Simplify 0 into 0 3.420 * [backup-simplify]: Simplify 1 into 1 3.421 * [backup-simplify]: Simplify (/ 1 1) into 1 3.421 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.421 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.421 * [taylor]: Taking taylor expansion of 2.0 in k 3.421 * [backup-simplify]: Simplify 2.0 into 2.0 3.421 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.421 * [taylor]: Taking taylor expansion of PI in k 3.421 * [backup-simplify]: Simplify PI into PI 3.421 * [taylor]: Taking taylor expansion of n in k 3.421 * [backup-simplify]: Simplify n into n 3.421 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.421 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.421 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.421 * [backup-simplify]: Simplify (- 1) into -1 3.422 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.422 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.422 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.422 * [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)))))) 3.422 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.422 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.422 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.422 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.422 * [taylor]: Taking taylor expansion of 0.5 in n 3.422 * [backup-simplify]: Simplify 0.5 into 0.5 3.422 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.422 * [taylor]: Taking taylor expansion of 1.0 in n 3.422 * [backup-simplify]: Simplify 1.0 into 1.0 3.422 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.422 * [taylor]: Taking taylor expansion of k in n 3.422 * [backup-simplify]: Simplify k into k 3.422 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.422 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.422 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.422 * [taylor]: Taking taylor expansion of 2.0 in n 3.422 * [backup-simplify]: Simplify 2.0 into 2.0 3.422 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.422 * [taylor]: Taking taylor expansion of PI in n 3.422 * [backup-simplify]: Simplify PI into PI 3.422 * [taylor]: Taking taylor expansion of n in n 3.422 * [backup-simplify]: Simplify 0 into 0 3.422 * [backup-simplify]: Simplify 1 into 1 3.423 * [backup-simplify]: Simplify (/ PI 1) into PI 3.423 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.424 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.424 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.424 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.424 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.425 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.427 * [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)))) 3.428 * [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))))) 3.428 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.428 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.428 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.428 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.428 * [taylor]: Taking taylor expansion of 0.5 in n 3.428 * [backup-simplify]: Simplify 0.5 into 0.5 3.428 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.428 * [taylor]: Taking taylor expansion of 1.0 in n 3.428 * [backup-simplify]: Simplify 1.0 into 1.0 3.428 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.428 * [taylor]: Taking taylor expansion of k in n 3.428 * [backup-simplify]: Simplify k into k 3.429 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.429 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.429 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.429 * [taylor]: Taking taylor expansion of 2.0 in n 3.429 * [backup-simplify]: Simplify 2.0 into 2.0 3.429 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.429 * [taylor]: Taking taylor expansion of PI in n 3.429 * [backup-simplify]: Simplify PI into PI 3.429 * [taylor]: Taking taylor expansion of n in n 3.429 * [backup-simplify]: Simplify 0 into 0 3.429 * [backup-simplify]: Simplify 1 into 1 3.429 * [backup-simplify]: Simplify (/ PI 1) into PI 3.430 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.431 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.431 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.431 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.431 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.433 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.434 * [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)))) 3.435 * [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))))) 3.435 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 3.435 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 3.436 * [taylor]: Taking taylor expansion of 0.5 in k 3.436 * [backup-simplify]: Simplify 0.5 into 0.5 3.436 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 3.436 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.436 * [taylor]: Taking taylor expansion of 1.0 in k 3.436 * [backup-simplify]: Simplify 1.0 into 1.0 3.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.436 * [taylor]: Taking taylor expansion of k in k 3.436 * [backup-simplify]: Simplify 0 into 0 3.436 * [backup-simplify]: Simplify 1 into 1 3.436 * [backup-simplify]: Simplify (/ 1 1) into 1 3.436 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.436 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.436 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.436 * [taylor]: Taking taylor expansion of 2.0 in k 3.436 * [backup-simplify]: Simplify 2.0 into 2.0 3.436 * [taylor]: Taking taylor expansion of PI in k 3.436 * [backup-simplify]: Simplify PI into PI 3.437 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.438 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.438 * [taylor]: Taking taylor expansion of (log n) in k 3.438 * [taylor]: Taking taylor expansion of n in k 3.438 * [backup-simplify]: Simplify n into n 3.438 * [backup-simplify]: Simplify (log n) into (log n) 3.439 * [backup-simplify]: Simplify (- 1) into -1 3.439 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.439 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.441 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.442 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.443 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.445 * [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))))) 3.446 * [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))))) 3.447 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.448 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.450 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.451 * [backup-simplify]: Simplify (- 0) into 0 3.451 * [backup-simplify]: Simplify (+ 0 0) into 0 3.452 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.455 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.457 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.457 * [taylor]: Taking taylor expansion of 0 in k 3.457 * [backup-simplify]: Simplify 0 into 0 3.457 * [backup-simplify]: Simplify 0 into 0 3.457 * [backup-simplify]: Simplify 0 into 0 3.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.459 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.463 * [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 3.463 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.465 * [backup-simplify]: Simplify (- 0) into 0 3.465 * [backup-simplify]: Simplify (+ 0 0) into 0 3.466 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.470 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.472 * [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 3.472 * [taylor]: Taking taylor expansion of 0 in k 3.472 * [backup-simplify]: Simplify 0 into 0 3.472 * [backup-simplify]: Simplify 0 into 0 3.472 * [backup-simplify]: Simplify 0 into 0 3.472 * [backup-simplify]: Simplify 0 into 0 3.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.481 * [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 3.481 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.482 * [backup-simplify]: Simplify (- 0) into 0 3.482 * [backup-simplify]: Simplify (+ 0 0) into 0 3.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.485 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.487 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.490 * [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 3.490 * [taylor]: Taking taylor expansion of 0 in k 3.490 * [backup-simplify]: Simplify 0 into 0 3.490 * [backup-simplify]: Simplify 0 into 0 3.491 * [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)))))) 3.492 * [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))) 3.492 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.492 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.492 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.492 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.492 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.492 * [taylor]: Taking taylor expansion of 0.5 in k 3.492 * [backup-simplify]: Simplify 0.5 into 0.5 3.492 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.492 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.492 * [taylor]: Taking taylor expansion of k in k 3.492 * [backup-simplify]: Simplify 0 into 0 3.492 * [backup-simplify]: Simplify 1 into 1 3.493 * [backup-simplify]: Simplify (/ 1 1) into 1 3.493 * [taylor]: Taking taylor expansion of 1.0 in k 3.493 * [backup-simplify]: Simplify 1.0 into 1.0 3.493 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.493 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.493 * [taylor]: Taking taylor expansion of -2.0 in k 3.493 * [backup-simplify]: Simplify -2.0 into -2.0 3.493 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.493 * [taylor]: Taking taylor expansion of PI in k 3.493 * [backup-simplify]: Simplify PI into PI 3.493 * [taylor]: Taking taylor expansion of n in k 3.493 * [backup-simplify]: Simplify n into n 3.493 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.493 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.493 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.494 * [backup-simplify]: Simplify (+ 1 0) into 1 3.494 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.495 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.495 * [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)))) 3.495 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.495 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.495 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.495 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.495 * [taylor]: Taking taylor expansion of 0.5 in n 3.495 * [backup-simplify]: Simplify 0.5 into 0.5 3.495 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.495 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.495 * [taylor]: Taking taylor expansion of k in n 3.495 * [backup-simplify]: Simplify k into k 3.495 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.495 * [taylor]: Taking taylor expansion of 1.0 in n 3.495 * [backup-simplify]: Simplify 1.0 into 1.0 3.496 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.496 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.496 * [taylor]: Taking taylor expansion of -2.0 in n 3.496 * [backup-simplify]: Simplify -2.0 into -2.0 3.496 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.496 * [taylor]: Taking taylor expansion of PI in n 3.496 * [backup-simplify]: Simplify PI into PI 3.496 * [taylor]: Taking taylor expansion of n in n 3.496 * [backup-simplify]: Simplify 0 into 0 3.496 * [backup-simplify]: Simplify 1 into 1 3.496 * [backup-simplify]: Simplify (/ PI 1) into PI 3.497 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.498 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.498 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.498 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.502 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.503 * [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))) 3.505 * [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)))) 3.505 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.505 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.505 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.505 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.505 * [taylor]: Taking taylor expansion of 0.5 in n 3.505 * [backup-simplify]: Simplify 0.5 into 0.5 3.505 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.505 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.505 * [taylor]: Taking taylor expansion of k in n 3.505 * [backup-simplify]: Simplify k into k 3.505 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.505 * [taylor]: Taking taylor expansion of 1.0 in n 3.505 * [backup-simplify]: Simplify 1.0 into 1.0 3.505 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.505 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.505 * [taylor]: Taking taylor expansion of -2.0 in n 3.505 * [backup-simplify]: Simplify -2.0 into -2.0 3.505 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.505 * [taylor]: Taking taylor expansion of PI in n 3.505 * [backup-simplify]: Simplify PI into PI 3.505 * [taylor]: Taking taylor expansion of n in n 3.505 * [backup-simplify]: Simplify 0 into 0 3.506 * [backup-simplify]: Simplify 1 into 1 3.506 * [backup-simplify]: Simplify (/ PI 1) into PI 3.506 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.508 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.508 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.508 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.509 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.511 * [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))) 3.512 * [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)))) 3.512 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 3.512 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 3.512 * [taylor]: Taking taylor expansion of 0.5 in k 3.512 * [backup-simplify]: Simplify 0.5 into 0.5 3.512 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 3.512 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.512 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.512 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.512 * [taylor]: Taking taylor expansion of -2.0 in k 3.512 * [backup-simplify]: Simplify -2.0 into -2.0 3.512 * [taylor]: Taking taylor expansion of PI in k 3.512 * [backup-simplify]: Simplify PI into PI 3.513 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.514 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.514 * [taylor]: Taking taylor expansion of (log n) in k 3.514 * [taylor]: Taking taylor expansion of n in k 3.514 * [backup-simplify]: Simplify n into n 3.514 * [backup-simplify]: Simplify (log n) into (log n) 3.514 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.514 * [taylor]: Taking taylor expansion of k in k 3.514 * [backup-simplify]: Simplify 0 into 0 3.514 * [backup-simplify]: Simplify 1 into 1 3.515 * [backup-simplify]: Simplify (/ 1 1) into 1 3.515 * [taylor]: Taking taylor expansion of 1.0 in k 3.515 * [backup-simplify]: Simplify 1.0 into 1.0 3.515 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.516 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.516 * [backup-simplify]: Simplify (+ 1 0) into 1 3.517 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 3.518 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.520 * [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)))) 3.521 * [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)))) 3.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.522 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.523 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.523 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.523 * [backup-simplify]: Simplify (+ 0 0) into 0 3.523 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.524 * [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 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.526 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.526 * [taylor]: Taking taylor expansion of 0 in k 3.526 * [backup-simplify]: Simplify 0 into 0 3.526 * [backup-simplify]: Simplify 0 into 0 3.526 * [backup-simplify]: Simplify 0 into 0 3.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.527 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.529 * [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 3.530 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.530 * [backup-simplify]: Simplify (+ 0 0) into 0 3.530 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.532 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.534 * [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 3.534 * [taylor]: Taking taylor expansion of 0 in k 3.534 * [backup-simplify]: Simplify 0 into 0 3.534 * [backup-simplify]: Simplify 0 into 0 3.534 * [backup-simplify]: Simplify 0 into 0 3.534 * [backup-simplify]: Simplify 0 into 0 3.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.535 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.538 * [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 3.538 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.539 * [backup-simplify]: Simplify (+ 0 0) into 0 3.539 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.542 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.543 * [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 3.543 * [taylor]: Taking taylor expansion of 0 in k 3.543 * [backup-simplify]: Simplify 0 into 0 3.543 * [backup-simplify]: Simplify 0 into 0 3.544 * [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)))))) 3.544 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 3.544 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.544 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.544 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.545 * [taylor]: Taking taylor expansion of 2.0 in n 3.545 * [backup-simplify]: Simplify 2.0 into 2.0 3.545 * [taylor]: Taking taylor expansion of (* n PI) in n 3.545 * [taylor]: Taking taylor expansion of n in n 3.545 * [backup-simplify]: Simplify 0 into 0 3.545 * [backup-simplify]: Simplify 1 into 1 3.545 * [taylor]: Taking taylor expansion of PI in n 3.545 * [backup-simplify]: Simplify PI into PI 3.545 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.545 * [taylor]: Taking taylor expansion of 2.0 in n 3.545 * [backup-simplify]: Simplify 2.0 into 2.0 3.545 * [taylor]: Taking taylor expansion of (* n PI) in n 3.545 * [taylor]: Taking taylor expansion of n in n 3.545 * [backup-simplify]: Simplify 0 into 0 3.545 * [backup-simplify]: Simplify 1 into 1 3.545 * [taylor]: Taking taylor expansion of PI in n 3.545 * [backup-simplify]: Simplify PI into PI 3.545 * [backup-simplify]: Simplify (* 0 PI) into 0 3.546 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.546 * [backup-simplify]: Simplify 0 into 0 3.547 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.547 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.548 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.548 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.549 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.549 * [backup-simplify]: Simplify 0 into 0 3.550 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.550 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.550 * [backup-simplify]: Simplify 0 into 0 3.551 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.552 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.552 * [backup-simplify]: Simplify 0 into 0 3.553 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.555 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.555 * [backup-simplify]: Simplify 0 into 0 3.557 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.559 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.559 * [backup-simplify]: Simplify 0 into 0 3.561 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.563 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.563 * [backup-simplify]: Simplify 0 into 0 3.563 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.564 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.564 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.564 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.564 * [taylor]: Taking taylor expansion of 2.0 in n 3.564 * [backup-simplify]: Simplify 2.0 into 2.0 3.564 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.564 * [taylor]: Taking taylor expansion of PI in n 3.564 * [backup-simplify]: Simplify PI into PI 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 3.565 * [backup-simplify]: Simplify (/ PI 1) into PI 3.565 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) 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 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.565 * [taylor]: Taking taylor expansion of PI in n 3.565 * [backup-simplify]: Simplify PI into PI 3.565 * [taylor]: Taking taylor expansion of n in n 3.565 * [backup-simplify]: Simplify 0 into 0 3.565 * [backup-simplify]: Simplify 1 into 1 3.566 * [backup-simplify]: Simplify (/ PI 1) into PI 3.566 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.567 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.568 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.568 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.569 * [backup-simplify]: Simplify 0 into 0 3.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.571 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.571 * [backup-simplify]: Simplify 0 into 0 3.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.573 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.573 * [backup-simplify]: Simplify 0 into 0 3.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.576 * [backup-simplify]: Simplify 0 into 0 3.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.579 * [backup-simplify]: Simplify 0 into 0 3.580 * [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 3.582 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.582 * [backup-simplify]: Simplify 0 into 0 3.582 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.583 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.583 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.583 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.583 * [taylor]: Taking taylor expansion of -2.0 in n 3.583 * [backup-simplify]: Simplify -2.0 into -2.0 3.583 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.583 * [taylor]: Taking taylor expansion of PI in n 3.583 * [backup-simplify]: Simplify PI into PI 3.583 * [taylor]: Taking taylor expansion of n in n 3.583 * [backup-simplify]: Simplify 0 into 0 3.583 * [backup-simplify]: Simplify 1 into 1 3.584 * [backup-simplify]: Simplify (/ PI 1) into PI 3.584 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.584 * [taylor]: Taking taylor expansion of -2.0 in n 3.584 * [backup-simplify]: Simplify -2.0 into -2.0 3.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.584 * [taylor]: Taking taylor expansion of PI in n 3.584 * [backup-simplify]: Simplify PI into PI 3.584 * [taylor]: Taking taylor expansion of n in n 3.584 * [backup-simplify]: Simplify 0 into 0 3.584 * [backup-simplify]: Simplify 1 into 1 3.585 * [backup-simplify]: Simplify (/ PI 1) into PI 3.585 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.586 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.587 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.587 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.587 * [backup-simplify]: Simplify 0 into 0 3.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.590 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.590 * [backup-simplify]: Simplify 0 into 0 3.591 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.592 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.592 * [backup-simplify]: Simplify 0 into 0 3.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.594 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.594 * [backup-simplify]: Simplify 0 into 0 3.596 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.597 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.597 * [backup-simplify]: Simplify 0 into 0 3.599 * [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 3.600 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.600 * [backup-simplify]: Simplify 0 into 0 3.601 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.601 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.601 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.601 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.601 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.601 * [taylor]: Taking taylor expansion of 1.0 in k 3.601 * [backup-simplify]: Simplify 1.0 into 1.0 3.601 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.601 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.601 * [taylor]: Taking taylor expansion of k in k 3.601 * [backup-simplify]: Simplify 0 into 0 3.601 * [backup-simplify]: Simplify 1 into 1 3.602 * [backup-simplify]: Simplify (/ 1 1) into 1 3.602 * [backup-simplify]: Simplify (sqrt 0) into 0 3.604 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.604 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.604 * [taylor]: Taking taylor expansion of 1.0 in k 3.604 * [backup-simplify]: Simplify 1.0 into 1.0 3.604 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.604 * [taylor]: Taking taylor expansion of k in k 3.604 * [backup-simplify]: Simplify 0 into 0 3.604 * [backup-simplify]: Simplify 1 into 1 3.604 * [backup-simplify]: Simplify (/ 1 1) into 1 3.605 * [backup-simplify]: Simplify (sqrt 0) into 0 3.606 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.607 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.607 * [backup-simplify]: Simplify 0 into 0 3.608 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.609 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.610 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.613 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.615 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.615 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.616 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.620 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.622 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.623 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.624 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 3.625 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.625 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.625 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.625 * [taylor]: Taking taylor expansion of 1.0 in k 3.625 * [backup-simplify]: Simplify 1.0 into 1.0 3.625 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.625 * [taylor]: Taking taylor expansion of k in k 3.625 * [backup-simplify]: Simplify 0 into 0 3.625 * [backup-simplify]: Simplify 1 into 1 3.625 * [backup-simplify]: Simplify (sqrt 0) into 0 3.627 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.627 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.627 * [taylor]: Taking taylor expansion of 1.0 in k 3.627 * [backup-simplify]: Simplify 1.0 into 1.0 3.627 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.627 * [taylor]: Taking taylor expansion of k in k 3.627 * [backup-simplify]: Simplify 0 into 0 3.627 * [backup-simplify]: Simplify 1 into 1 3.630 * [backup-simplify]: Simplify (sqrt 0) into 0 3.631 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.632 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.632 * [backup-simplify]: Simplify 0 into 0 3.633 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.634 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.637 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.639 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.639 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.644 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.646 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.647 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.648 * [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)))))))) 3.649 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.649 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.649 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.649 * [taylor]: Taking taylor expansion of 1.0 in k 3.649 * [backup-simplify]: Simplify 1.0 into 1.0 3.649 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.649 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.649 * [taylor]: Taking taylor expansion of -1 in k 3.649 * [backup-simplify]: Simplify -1 into -1 3.649 * [taylor]: Taking taylor expansion of k in k 3.649 * [backup-simplify]: Simplify 0 into 0 3.649 * [backup-simplify]: Simplify 1 into 1 3.649 * [backup-simplify]: Simplify (/ -1 1) into -1 3.650 * [backup-simplify]: Simplify (sqrt 0) into 0 3.651 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.652 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.652 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.652 * [taylor]: Taking taylor expansion of 1.0 in k 3.652 * [backup-simplify]: Simplify 1.0 into 1.0 3.652 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.652 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.652 * [taylor]: Taking taylor expansion of -1 in k 3.652 * [backup-simplify]: Simplify -1 into -1 3.652 * [taylor]: Taking taylor expansion of k in k 3.652 * [backup-simplify]: Simplify 0 into 0 3.652 * [backup-simplify]: Simplify 1 into 1 3.653 * [backup-simplify]: Simplify (/ -1 1) into -1 3.653 * [backup-simplify]: Simplify (sqrt 0) into 0 3.654 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.655 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.655 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.656 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.659 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.662 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.662 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.667 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.671 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.672 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.673 * [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))))) 3.673 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.674 * [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)))) 3.674 * [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 3.674 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 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 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 3.674 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.674 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.674 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.674 * [taylor]: Taking taylor expansion of 0.5 in n 3.674 * [backup-simplify]: Simplify 0.5 into 0.5 3.674 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.674 * [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 k in n 3.675 * [backup-simplify]: Simplify k into k 3.675 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.675 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.675 * [taylor]: Taking taylor expansion of 2.0 in n 3.675 * [backup-simplify]: Simplify 2.0 into 2.0 3.675 * [taylor]: Taking taylor expansion of (* n PI) in n 3.675 * [taylor]: Taking taylor expansion of n in n 3.675 * [backup-simplify]: Simplify 0 into 0 3.675 * [backup-simplify]: Simplify 1 into 1 3.675 * [taylor]: Taking taylor expansion of PI in n 3.675 * [backup-simplify]: Simplify PI into PI 3.676 * [backup-simplify]: Simplify (* 0 PI) into 0 3.676 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.678 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.680 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.681 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.681 * [backup-simplify]: Simplify (- k) into (- k) 3.681 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.681 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.683 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.684 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 3.685 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 3.685 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.685 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.685 * [taylor]: Taking taylor expansion of k in n 3.685 * [backup-simplify]: Simplify k into k 3.685 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.685 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.685 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.686 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.686 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.686 * [taylor]: Taking taylor expansion of 1.0 in k 3.686 * [backup-simplify]: Simplify 1.0 into 1.0 3.686 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.686 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.686 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.686 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.686 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.686 * [taylor]: Taking taylor expansion of 0.5 in k 3.686 * [backup-simplify]: Simplify 0.5 into 0.5 3.686 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.686 * [taylor]: Taking taylor expansion of 1.0 in k 3.686 * [backup-simplify]: Simplify 1.0 into 1.0 3.686 * [taylor]: Taking taylor expansion of k in k 3.686 * [backup-simplify]: Simplify 0 into 0 3.686 * [backup-simplify]: Simplify 1 into 1 3.686 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.686 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.686 * [taylor]: Taking taylor expansion of 2.0 in k 3.686 * [backup-simplify]: Simplify 2.0 into 2.0 3.686 * [taylor]: Taking taylor expansion of (* n PI) in k 3.686 * [taylor]: Taking taylor expansion of n in k 3.686 * [backup-simplify]: Simplify n into n 3.686 * [taylor]: Taking taylor expansion of PI in k 3.686 * [backup-simplify]: Simplify PI into PI 3.686 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.686 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.687 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.687 * [backup-simplify]: Simplify (- 0) into 0 3.687 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.688 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.688 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.688 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.688 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.688 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.688 * [taylor]: Taking taylor expansion of k in k 3.688 * [backup-simplify]: Simplify 0 into 0 3.688 * [backup-simplify]: Simplify 1 into 1 3.689 * [backup-simplify]: Simplify (/ 1 1) into 1 3.689 * [backup-simplify]: Simplify (sqrt 0) into 0 3.690 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.691 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.691 * [taylor]: Taking taylor expansion of 1.0 in k 3.691 * [backup-simplify]: Simplify 1.0 into 1.0 3.691 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.691 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.691 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.691 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.691 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.691 * [taylor]: Taking taylor expansion of 0.5 in k 3.691 * [backup-simplify]: Simplify 0.5 into 0.5 3.691 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.691 * [taylor]: Taking taylor expansion of 1.0 in k 3.691 * [backup-simplify]: Simplify 1.0 into 1.0 3.691 * [taylor]: Taking taylor expansion of k in k 3.691 * [backup-simplify]: Simplify 0 into 0 3.691 * [backup-simplify]: Simplify 1 into 1 3.691 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.691 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.691 * [taylor]: Taking taylor expansion of 2.0 in k 3.691 * [backup-simplify]: Simplify 2.0 into 2.0 3.691 * [taylor]: Taking taylor expansion of (* n PI) in k 3.691 * [taylor]: Taking taylor expansion of n in k 3.691 * [backup-simplify]: Simplify n into n 3.691 * [taylor]: Taking taylor expansion of PI in k 3.691 * [backup-simplify]: Simplify PI into PI 3.691 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.692 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.692 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.692 * [backup-simplify]: Simplify (- 0) into 0 3.692 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.693 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.693 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.693 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.693 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.693 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.693 * [taylor]: Taking taylor expansion of k in k 3.693 * [backup-simplify]: Simplify 0 into 0 3.693 * [backup-simplify]: Simplify 1 into 1 3.693 * [backup-simplify]: Simplify (/ 1 1) into 1 3.693 * [backup-simplify]: Simplify (sqrt 0) into 0 3.694 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.694 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 3.695 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.695 * [taylor]: Taking taylor expansion of 0 in n 3.695 * [backup-simplify]: Simplify 0 into 0 3.695 * [backup-simplify]: Simplify 0 into 0 3.695 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 3.695 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 3.696 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 3.696 * [backup-simplify]: Simplify (- 1) into -1 3.697 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.698 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.698 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 3.699 * [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))))) 3.700 * [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))) 3.701 * [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))) 3.701 * [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 3.701 * [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 3.701 * [taylor]: Taking taylor expansion of +nan.0 in n 3.701 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.701 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.701 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.701 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.701 * [taylor]: Taking taylor expansion of 0.5 in n 3.701 * [backup-simplify]: Simplify 0.5 into 0.5 3.701 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.701 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.701 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.701 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.701 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.701 * [taylor]: Taking taylor expansion of 1.0 in n 3.701 * [backup-simplify]: Simplify 1.0 into 1.0 3.701 * [taylor]: Taking taylor expansion of (log PI) in n 3.701 * [taylor]: Taking taylor expansion of PI in n 3.701 * [backup-simplify]: Simplify PI into PI 3.701 * [backup-simplify]: Simplify (log PI) into (log PI) 3.702 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.703 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.703 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.703 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.703 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.703 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.703 * [taylor]: Taking taylor expansion of 1.0 in n 3.703 * [backup-simplify]: Simplify 1.0 into 1.0 3.703 * [taylor]: Taking taylor expansion of (log n) in n 3.703 * [taylor]: Taking taylor expansion of n in n 3.703 * [backup-simplify]: Simplify 0 into 0 3.703 * [backup-simplify]: Simplify 1 into 1 3.703 * [backup-simplify]: Simplify (log 1) into 0 3.704 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.704 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.704 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.704 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.704 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.704 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.704 * [taylor]: Taking taylor expansion of 1.0 in n 3.704 * [backup-simplify]: Simplify 1.0 into 1.0 3.704 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.704 * [taylor]: Taking taylor expansion of 2.0 in n 3.704 * [backup-simplify]: Simplify 2.0 into 2.0 3.704 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.705 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.706 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.706 * [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) 3.707 * [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) 3.708 * [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)) 3.708 * [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))) 3.709 * [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) 3.710 * [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)) 3.711 * [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))) 3.712 * [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))) 3.712 * [backup-simplify]: Simplify 0 into 0 3.712 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.714 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.715 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 3.715 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 3.716 * [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 3.717 * [backup-simplify]: Simplify (- 0) into 0 3.717 * [backup-simplify]: Simplify (+ 0 0) into 0 3.717 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.718 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 3.719 * [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))) 3.721 * [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))))) 3.724 * [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))))) 3.724 * [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 3.724 * [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 3.724 * [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 3.724 * [taylor]: Taking taylor expansion of +nan.0 in n 3.724 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.724 * [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 3.724 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.724 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.724 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.724 * [taylor]: Taking taylor expansion of 0.5 in n 3.724 * [backup-simplify]: Simplify 0.5 into 0.5 3.724 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.724 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.724 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.724 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.724 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.724 * [taylor]: Taking taylor expansion of 1.0 in n 3.724 * [backup-simplify]: Simplify 1.0 into 1.0 3.724 * [taylor]: Taking taylor expansion of (log PI) in n 3.724 * [taylor]: Taking taylor expansion of PI in n 3.724 * [backup-simplify]: Simplify PI into PI 3.725 * [backup-simplify]: Simplify (log PI) into (log PI) 3.725 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.726 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.726 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.726 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.726 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.726 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.726 * [taylor]: Taking taylor expansion of 1.0 in n 3.726 * [backup-simplify]: Simplify 1.0 into 1.0 3.726 * [taylor]: Taking taylor expansion of (log n) in n 3.726 * [taylor]: Taking taylor expansion of n in n 3.726 * [backup-simplify]: Simplify 0 into 0 3.726 * [backup-simplify]: Simplify 1 into 1 3.727 * [backup-simplify]: Simplify (log 1) into 0 3.727 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.727 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.727 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.727 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.727 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.727 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.727 * [taylor]: Taking taylor expansion of 1.0 in n 3.727 * [backup-simplify]: Simplify 1.0 into 1.0 3.727 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.727 * [taylor]: Taking taylor expansion of 2.0 in n 3.727 * [backup-simplify]: Simplify 2.0 into 2.0 3.727 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.728 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.729 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.730 * [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) 3.731 * [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) 3.733 * [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)) 3.734 * [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))) 3.736 * [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) 3.736 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.736 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.736 * [taylor]: Taking taylor expansion of 2.0 in n 3.736 * [backup-simplify]: Simplify 2.0 into 2.0 3.736 * [taylor]: Taking taylor expansion of (* n PI) in n 3.736 * [taylor]: Taking taylor expansion of n in n 3.736 * [backup-simplify]: Simplify 0 into 0 3.736 * [backup-simplify]: Simplify 1 into 1 3.736 * [taylor]: Taking taylor expansion of PI in n 3.736 * [backup-simplify]: Simplify PI into PI 3.737 * [backup-simplify]: Simplify (* 0 PI) into 0 3.737 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.739 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.740 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.741 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.742 * [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 3.742 * [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 3.742 * [taylor]: Taking taylor expansion of +nan.0 in n 3.742 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.742 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.742 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.742 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.742 * [taylor]: Taking taylor expansion of 0.5 in n 3.742 * [backup-simplify]: Simplify 0.5 into 0.5 3.742 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.742 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.742 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.742 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.742 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.742 * [taylor]: Taking taylor expansion of 1.0 in n 3.742 * [backup-simplify]: Simplify 1.0 into 1.0 3.742 * [taylor]: Taking taylor expansion of (log PI) in n 3.742 * [taylor]: Taking taylor expansion of PI in n 3.742 * [backup-simplify]: Simplify PI into PI 3.743 * [backup-simplify]: Simplify (log PI) into (log PI) 3.744 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.745 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.745 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.745 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.745 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.745 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.745 * [taylor]: Taking taylor expansion of 1.0 in n 3.746 * [backup-simplify]: Simplify 1.0 into 1.0 3.746 * [taylor]: Taking taylor expansion of (log n) in n 3.746 * [taylor]: Taking taylor expansion of n in n 3.746 * [backup-simplify]: Simplify 0 into 0 3.746 * [backup-simplify]: Simplify 1 into 1 3.746 * [backup-simplify]: Simplify (log 1) into 0 3.747 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.747 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.747 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.747 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.747 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.747 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.747 * [taylor]: Taking taylor expansion of 1.0 in n 3.747 * [backup-simplify]: Simplify 1.0 into 1.0 3.747 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.747 * [taylor]: Taking taylor expansion of 2.0 in n 3.747 * [backup-simplify]: Simplify 2.0 into 2.0 3.748 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.749 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.750 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.751 * [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) 3.752 * [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) 3.753 * [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)) 3.755 * [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))) 3.756 * [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) 3.757 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.763 * [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))) 3.765 * [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)))) 3.766 * [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)) 3.767 * [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))) 3.769 * [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))))))) 3.773 * [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))))))))) 3.777 * [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))))))) 3.778 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 3.778 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 3.779 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 3.780 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.780 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.780 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 3.781 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.781 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 3.782 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 3.783 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 3.784 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 3.785 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 3.786 * [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 3.787 * [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 3.789 * [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 3.791 * [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 3.791 * [backup-simplify]: Simplify (- 0) into 0 3.791 * [backup-simplify]: Simplify 0 into 0 3.791 * [backup-simplify]: Simplify 0 into 0 3.792 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.796 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.797 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.799 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 3.802 * [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 3.803 * [backup-simplify]: Simplify (- 0) into 0 3.803 * [backup-simplify]: Simplify (+ 0 0) into 0 3.804 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 3.806 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 3.808 * [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))) 3.814 * [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)))))))) 3.825 * [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)))))))) 3.825 * [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 3.825 * [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 3.826 * [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 3.826 * [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 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 3.826 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.826 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.826 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) 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 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.826 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.826 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.826 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.826 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) 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 (log PI) in n 3.826 * [taylor]: Taking taylor expansion of PI in n 3.826 * [backup-simplify]: Simplify PI into PI 3.827 * [backup-simplify]: Simplify (log PI) into (log PI) 3.828 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.829 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.829 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.829 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.830 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.830 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.830 * [taylor]: Taking taylor expansion of 1.0 in n 3.830 * [backup-simplify]: Simplify 1.0 into 1.0 3.830 * [taylor]: Taking taylor expansion of (log n) in n 3.830 * [taylor]: Taking taylor expansion of n in n 3.830 * [backup-simplify]: Simplify 0 into 0 3.830 * [backup-simplify]: Simplify 1 into 1 3.830 * [backup-simplify]: Simplify (log 1) into 0 3.831 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.831 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.831 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.831 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.831 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.831 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.831 * [taylor]: Taking taylor expansion of 1.0 in n 3.831 * [backup-simplify]: Simplify 1.0 into 1.0 3.831 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.831 * [taylor]: Taking taylor expansion of 2.0 in n 3.831 * [backup-simplify]: Simplify 2.0 into 2.0 3.831 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.832 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.834 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.835 * [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) 3.836 * [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) 3.837 * [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)) 3.839 * [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))) 3.840 * [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) 3.840 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.840 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.840 * [taylor]: Taking taylor expansion of 2.0 in n 3.840 * [backup-simplify]: Simplify 2.0 into 2.0 3.840 * [taylor]: Taking taylor expansion of (* n PI) in n 3.840 * [taylor]: Taking taylor expansion of n in n 3.840 * [backup-simplify]: Simplify 0 into 0 3.840 * [backup-simplify]: Simplify 1 into 1 3.840 * [taylor]: Taking taylor expansion of PI in n 3.840 * [backup-simplify]: Simplify PI into PI 3.841 * [backup-simplify]: Simplify (* 0 PI) into 0 3.841 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.843 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.845 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.846 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.846 * [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 3.846 * [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 3.846 * [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 3.846 * [taylor]: Taking taylor expansion of +nan.0 in n 3.846 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.846 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.846 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.846 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.846 * [taylor]: Taking taylor expansion of 0.5 in n 3.846 * [backup-simplify]: Simplify 0.5 into 0.5 3.846 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.846 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.846 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.846 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.846 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.846 * [taylor]: Taking taylor expansion of 1.0 in n 3.846 * [backup-simplify]: Simplify 1.0 into 1.0 3.846 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.846 * [taylor]: Taking taylor expansion of 2.0 in n 3.846 * [backup-simplify]: Simplify 2.0 into 2.0 3.847 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.848 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.849 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.849 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.849 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.849 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.849 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.849 * [taylor]: Taking taylor expansion of 1.0 in n 3.849 * [backup-simplify]: Simplify 1.0 into 1.0 3.849 * [taylor]: Taking taylor expansion of (log n) in n 3.850 * [taylor]: Taking taylor expansion of n in n 3.850 * [backup-simplify]: Simplify 0 into 0 3.850 * [backup-simplify]: Simplify 1 into 1 3.850 * [backup-simplify]: Simplify (log 1) into 0 3.850 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.850 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.851 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.851 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.851 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.851 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.851 * [taylor]: Taking taylor expansion of 1.0 in n 3.851 * [backup-simplify]: Simplify 1.0 into 1.0 3.851 * [taylor]: Taking taylor expansion of (log PI) in n 3.851 * [taylor]: Taking taylor expansion of PI in n 3.851 * [backup-simplify]: Simplify PI into PI 3.851 * [backup-simplify]: Simplify (log PI) into (log PI) 3.852 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.854 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.855 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.856 * [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) 3.858 * [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)) 3.859 * [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))) 3.860 * [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) 3.861 * [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 3.861 * [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 3.861 * [taylor]: Taking taylor expansion of +nan.0 in n 3.861 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.861 * [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 3.861 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.861 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.861 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.861 * [taylor]: Taking taylor expansion of 0.5 in n 3.861 * [backup-simplify]: Simplify 0.5 into 0.5 3.861 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.861 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.861 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.861 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.861 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.861 * [taylor]: Taking taylor expansion of 1.0 in n 3.861 * [backup-simplify]: Simplify 1.0 into 1.0 3.861 * [taylor]: Taking taylor expansion of (log PI) in n 3.861 * [taylor]: Taking taylor expansion of PI in n 3.861 * [backup-simplify]: Simplify PI into PI 3.862 * [backup-simplify]: Simplify (log PI) into (log PI) 3.863 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.864 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.864 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.864 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.865 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.865 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.865 * [taylor]: Taking taylor expansion of 1.0 in n 3.865 * [backup-simplify]: Simplify 1.0 into 1.0 3.865 * [taylor]: Taking taylor expansion of (log n) in n 3.865 * [taylor]: Taking taylor expansion of n in n 3.865 * [backup-simplify]: Simplify 0 into 0 3.865 * [backup-simplify]: Simplify 1 into 1 3.865 * [backup-simplify]: Simplify (log 1) into 0 3.866 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.866 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.866 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.866 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.866 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.866 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.866 * [taylor]: Taking taylor expansion of 1.0 in n 3.866 * [backup-simplify]: Simplify 1.0 into 1.0 3.866 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.866 * [taylor]: Taking taylor expansion of 2.0 in n 3.866 * [backup-simplify]: Simplify 2.0 into 2.0 3.866 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.867 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.869 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.870 * [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) 3.871 * [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) 3.872 * [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)) 3.874 * [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))) 3.875 * [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) 3.875 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.875 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.875 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.875 * [taylor]: Taking taylor expansion of 2.0 in n 3.875 * [backup-simplify]: Simplify 2.0 into 2.0 3.875 * [taylor]: Taking taylor expansion of (* n PI) in n 3.875 * [taylor]: Taking taylor expansion of n in n 3.875 * [backup-simplify]: Simplify 0 into 0 3.875 * [backup-simplify]: Simplify 1 into 1 3.875 * [taylor]: Taking taylor expansion of PI in n 3.875 * [backup-simplify]: Simplify PI into PI 3.876 * [backup-simplify]: Simplify (* 0 PI) into 0 3.876 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.878 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.880 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.882 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.883 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.885 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.887 * [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))) 3.890 * [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)))) 3.892 * [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)) 3.894 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.895 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.897 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.904 * [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)) 3.906 * [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))) 3.910 * [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)))))))) 3.921 * [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))))))))) 3.932 * [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)))))))))) 3.947 * [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))))))))))))) 3.961 * [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))))))))))))) 3.971 * [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))))))))))))))) 3.989 * [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))))))))))))))))))))))) 3.990 * [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))) 3.990 * [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 3.990 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 3.990 * [taylor]: Taking taylor expansion of 1.0 in n 3.990 * [backup-simplify]: Simplify 1.0 into 1.0 3.990 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 3.990 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.990 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.990 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.990 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.990 * [taylor]: Taking taylor expansion of 0.5 in n 3.990 * [backup-simplify]: Simplify 0.5 into 0.5 3.990 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.990 * [taylor]: Taking taylor expansion of 1.0 in n 3.990 * [backup-simplify]: Simplify 1.0 into 1.0 3.991 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.991 * [taylor]: Taking taylor expansion of k in n 3.991 * [backup-simplify]: Simplify k into k 3.991 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.991 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.991 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.991 * [taylor]: Taking taylor expansion of 2.0 in n 3.991 * [backup-simplify]: Simplify 2.0 into 2.0 3.991 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.991 * [taylor]: Taking taylor expansion of PI in n 3.991 * [backup-simplify]: Simplify PI into PI 3.991 * [taylor]: Taking taylor expansion of n in n 3.991 * [backup-simplify]: Simplify 0 into 0 3.991 * [backup-simplify]: Simplify 1 into 1 3.992 * [backup-simplify]: Simplify (/ PI 1) into PI 3.992 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.993 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.993 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.993 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.993 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.996 * [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)))) 3.998 * [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))))) 3.998 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.998 * [taylor]: Taking taylor expansion of k in n 3.998 * [backup-simplify]: Simplify k into k 3.998 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.998 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.998 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.998 * [taylor]: Taking taylor expansion of 1.0 in k 3.998 * [backup-simplify]: Simplify 1.0 into 1.0 3.998 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.998 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.998 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.998 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.998 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.998 * [taylor]: Taking taylor expansion of 0.5 in k 3.998 * [backup-simplify]: Simplify 0.5 into 0.5 3.998 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.998 * [taylor]: Taking taylor expansion of 1.0 in k 3.998 * [backup-simplify]: Simplify 1.0 into 1.0 3.998 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.998 * [taylor]: Taking taylor expansion of k in k 3.999 * [backup-simplify]: Simplify 0 into 0 3.999 * [backup-simplify]: Simplify 1 into 1 3.999 * [backup-simplify]: Simplify (/ 1 1) into 1 3.999 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.999 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.999 * [taylor]: Taking taylor expansion of 2.0 in k 3.999 * [backup-simplify]: Simplify 2.0 into 2.0 3.999 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.999 * [taylor]: Taking taylor expansion of PI in k 3.999 * [backup-simplify]: Simplify PI into PI 3.999 * [taylor]: Taking taylor expansion of n in k 3.999 * [backup-simplify]: Simplify n into n 3.999 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.999 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.000 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.000 * [backup-simplify]: Simplify (- 1) into -1 4.000 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.001 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.001 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.001 * [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)))))) 4.001 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.001 * [taylor]: Taking taylor expansion of k in k 4.001 * [backup-simplify]: Simplify 0 into 0 4.001 * [backup-simplify]: Simplify 1 into 1 4.001 * [backup-simplify]: Simplify (sqrt 0) into 0 4.002 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.002 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 4.002 * [taylor]: Taking taylor expansion of 1.0 in k 4.002 * [backup-simplify]: Simplify 1.0 into 1.0 4.002 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 4.002 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.002 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.002 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.002 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.002 * [taylor]: Taking taylor expansion of 0.5 in k 4.002 * [backup-simplify]: Simplify 0.5 into 0.5 4.002 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.002 * [taylor]: Taking taylor expansion of 1.0 in k 4.002 * [backup-simplify]: Simplify 1.0 into 1.0 4.002 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.002 * [taylor]: Taking taylor expansion of k in k 4.002 * [backup-simplify]: Simplify 0 into 0 4.002 * [backup-simplify]: Simplify 1 into 1 4.003 * [backup-simplify]: Simplify (/ 1 1) into 1 4.003 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.003 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.003 * [taylor]: Taking taylor expansion of 2.0 in k 4.003 * [backup-simplify]: Simplify 2.0 into 2.0 4.003 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.003 * [taylor]: Taking taylor expansion of PI in k 4.003 * [backup-simplify]: Simplify PI into PI 4.003 * [taylor]: Taking taylor expansion of n in k 4.003 * [backup-simplify]: Simplify n into n 4.003 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.003 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.003 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.003 * [backup-simplify]: Simplify (- 1) into -1 4.003 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.004 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.004 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.004 * [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)))))) 4.004 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.004 * [taylor]: Taking taylor expansion of k in k 4.004 * [backup-simplify]: Simplify 0 into 0 4.004 * [backup-simplify]: Simplify 1 into 1 4.004 * [backup-simplify]: Simplify (sqrt 0) into 0 4.005 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.005 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 4.006 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.006 * [taylor]: Taking taylor expansion of 0 in n 4.006 * [backup-simplify]: Simplify 0 into 0 4.006 * [backup-simplify]: Simplify 0 into 0 4.006 * [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)))))))) 4.007 * [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)))))))) 4.007 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 4.007 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 4.007 * [taylor]: Taking taylor expansion of +nan.0 in n 4.007 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.007 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 4.007 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 4.007 * [taylor]: Taking taylor expansion of 0.5 in n 4.007 * [backup-simplify]: Simplify 0.5 into 0.5 4.007 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 4.007 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.007 * [taylor]: Taking taylor expansion of 1.0 in n 4.007 * [backup-simplify]: Simplify 1.0 into 1.0 4.007 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.007 * [taylor]: Taking taylor expansion of k in n 4.007 * [backup-simplify]: Simplify k into k 4.007 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.007 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.007 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.007 * [taylor]: Taking taylor expansion of 2.0 in n 4.007 * [backup-simplify]: Simplify 2.0 into 2.0 4.007 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.007 * [taylor]: Taking taylor expansion of PI in n 4.007 * [backup-simplify]: Simplify PI into PI 4.007 * [taylor]: Taking taylor expansion of n in n 4.007 * [backup-simplify]: Simplify 0 into 0 4.007 * [backup-simplify]: Simplify 1 into 1 4.007 * [backup-simplify]: Simplify (/ PI 1) into PI 4.008 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.008 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.008 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.008 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.009 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.010 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 4.011 * [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)))) 4.012 * [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))))) 4.013 * [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)))))) 4.013 * [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))))))) 4.014 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 4.014 * [backup-simplify]: Simplify 0 into 0 4.016 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.017 * [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)))))))) 4.017 * [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)))))))) 4.017 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 4.017 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 4.017 * [taylor]: Taking taylor expansion of +nan.0 in n 4.017 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.017 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 4.017 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 4.018 * [taylor]: Taking taylor expansion of 0.5 in n 4.018 * [backup-simplify]: Simplify 0.5 into 0.5 4.018 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 4.018 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.018 * [taylor]: Taking taylor expansion of 1.0 in n 4.018 * [backup-simplify]: Simplify 1.0 into 1.0 4.018 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.018 * [taylor]: Taking taylor expansion of k in n 4.018 * [backup-simplify]: Simplify k into k 4.018 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.018 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.018 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.018 * [taylor]: Taking taylor expansion of 2.0 in n 4.018 * [backup-simplify]: Simplify 2.0 into 2.0 4.018 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.018 * [taylor]: Taking taylor expansion of PI in n 4.018 * [backup-simplify]: Simplify PI into PI 4.018 * [taylor]: Taking taylor expansion of n in n 4.018 * [backup-simplify]: Simplify 0 into 0 4.018 * [backup-simplify]: Simplify 1 into 1 4.018 * [backup-simplify]: Simplify (/ PI 1) into PI 4.019 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.019 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.019 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.019 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.020 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.021 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 4.024 * [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)))) 4.025 * [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))))) 4.026 * [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)))))) 4.026 * [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))))))) 4.027 * [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))))))) 4.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.028 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.030 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.030 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.031 * [backup-simplify]: Simplify (- 0) into 0 4.031 * [backup-simplify]: Simplify (+ 0 0) into 0 4.033 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.034 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.036 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 4.038 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.039 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 4.040 * [backup-simplify]: Simplify (- 0) into 0 4.040 * [backup-simplify]: Simplify 0 into 0 4.040 * [backup-simplify]: Simplify 0 into 0 4.044 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.045 * [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)))))))) 4.047 * [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)))))))) 4.047 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 4.047 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 4.047 * [taylor]: Taking taylor expansion of +nan.0 in n 4.047 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.047 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 4.047 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 4.047 * [taylor]: Taking taylor expansion of 0.5 in n 4.047 * [backup-simplify]: Simplify 0.5 into 0.5 4.047 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 4.047 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.047 * [taylor]: Taking taylor expansion of 1.0 in n 4.047 * [backup-simplify]: Simplify 1.0 into 1.0 4.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.047 * [taylor]: Taking taylor expansion of k in n 4.047 * [backup-simplify]: Simplify k into k 4.047 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.047 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.047 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.047 * [taylor]: Taking taylor expansion of 2.0 in n 4.047 * [backup-simplify]: Simplify 2.0 into 2.0 4.047 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.047 * [taylor]: Taking taylor expansion of PI in n 4.047 * [backup-simplify]: Simplify PI into PI 4.047 * [taylor]: Taking taylor expansion of n in n 4.047 * [backup-simplify]: Simplify 0 into 0 4.047 * [backup-simplify]: Simplify 1 into 1 4.048 * [backup-simplify]: Simplify (/ PI 1) into PI 4.049 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.050 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.050 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.050 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.052 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.053 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 4.054 * [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)))) 4.055 * [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))))) 4.057 * [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)))))) 4.058 * [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))))))) 4.060 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 4.064 * [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)))))))) 4.065 * [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)))) 4.065 * [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 4.065 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 4.065 * [taylor]: Taking taylor expansion of 1.0 in n 4.065 * [backup-simplify]: Simplify 1.0 into 1.0 4.065 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 4.065 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.065 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.065 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.065 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.065 * [taylor]: Taking taylor expansion of 0.5 in n 4.065 * [backup-simplify]: Simplify 0.5 into 0.5 4.065 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.065 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.065 * [taylor]: Taking taylor expansion of k in n 4.065 * [backup-simplify]: Simplify k into k 4.065 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.065 * [taylor]: Taking taylor expansion of 1.0 in n 4.065 * [backup-simplify]: Simplify 1.0 into 1.0 4.065 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.065 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.065 * [taylor]: Taking taylor expansion of -2.0 in n 4.065 * [backup-simplify]: Simplify -2.0 into -2.0 4.065 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.066 * [taylor]: Taking taylor expansion of PI in n 4.066 * [backup-simplify]: Simplify PI into PI 4.066 * [taylor]: Taking taylor expansion of n in n 4.066 * [backup-simplify]: Simplify 0 into 0 4.066 * [backup-simplify]: Simplify 1 into 1 4.066 * [backup-simplify]: Simplify (/ PI 1) into PI 4.066 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.067 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.067 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.067 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.068 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.069 * [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))) 4.070 * [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)))) 4.070 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 4.070 * [taylor]: Taking taylor expansion of (/ -1 k) in n 4.070 * [taylor]: Taking taylor expansion of -1 in n 4.070 * [backup-simplify]: Simplify -1 into -1 4.070 * [taylor]: Taking taylor expansion of k in n 4.070 * [backup-simplify]: Simplify k into k 4.070 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 4.070 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 4.070 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 4.070 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 4.071 * [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))) 4.071 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.071 * [taylor]: Taking taylor expansion of 1.0 in k 4.071 * [backup-simplify]: Simplify 1.0 into 1.0 4.071 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.071 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.071 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.071 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.071 * [taylor]: Taking taylor expansion of 0.5 in k 4.071 * [backup-simplify]: Simplify 0.5 into 0.5 4.071 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.071 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.071 * [taylor]: Taking taylor expansion of k in k 4.071 * [backup-simplify]: Simplify 0 into 0 4.071 * [backup-simplify]: Simplify 1 into 1 4.072 * [backup-simplify]: Simplify (/ 1 1) into 1 4.072 * [taylor]: Taking taylor expansion of 1.0 in k 4.072 * [backup-simplify]: Simplify 1.0 into 1.0 4.072 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.072 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.072 * [taylor]: Taking taylor expansion of -2.0 in k 4.072 * [backup-simplify]: Simplify -2.0 into -2.0 4.072 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.072 * [taylor]: Taking taylor expansion of PI in k 4.072 * [backup-simplify]: Simplify PI into PI 4.072 * [taylor]: Taking taylor expansion of n in k 4.072 * [backup-simplify]: Simplify n into n 4.072 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.072 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.072 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.072 * [backup-simplify]: Simplify (+ 1 0) into 1 4.073 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.073 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.073 * [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)))) 4.073 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.073 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.073 * [taylor]: Taking taylor expansion of -1 in k 4.073 * [backup-simplify]: Simplify -1 into -1 4.073 * [taylor]: Taking taylor expansion of k in k 4.073 * [backup-simplify]: Simplify 0 into 0 4.073 * [backup-simplify]: Simplify 1 into 1 4.073 * [backup-simplify]: Simplify (/ -1 1) into -1 4.073 * [backup-simplify]: Simplify (sqrt 0) into 0 4.074 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.074 * [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))))) 4.075 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 4.075 * [taylor]: Taking taylor expansion of 1.0 in k 4.075 * [backup-simplify]: Simplify 1.0 into 1.0 4.075 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 4.075 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.075 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.075 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.075 * [taylor]: Taking taylor expansion of 0.5 in k 4.075 * [backup-simplify]: Simplify 0.5 into 0.5 4.075 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.075 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.075 * [taylor]: Taking taylor expansion of k in k 4.075 * [backup-simplify]: Simplify 0 into 0 4.075 * [backup-simplify]: Simplify 1 into 1 4.075 * [backup-simplify]: Simplify (/ 1 1) into 1 4.075 * [taylor]: Taking taylor expansion of 1.0 in k 4.075 * [backup-simplify]: Simplify 1.0 into 1.0 4.075 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.075 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.075 * [taylor]: Taking taylor expansion of -2.0 in k 4.075 * [backup-simplify]: Simplify -2.0 into -2.0 4.075 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.075 * [taylor]: Taking taylor expansion of PI in k 4.075 * [backup-simplify]: Simplify PI into PI 4.075 * [taylor]: Taking taylor expansion of n in k 4.075 * [backup-simplify]: Simplify n into n 4.075 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.075 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.075 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.076 * [backup-simplify]: Simplify (+ 1 0) into 1 4.076 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.076 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.076 * [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)))) 4.076 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.076 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.076 * [taylor]: Taking taylor expansion of -1 in k 4.076 * [backup-simplify]: Simplify -1 into -1 4.076 * [taylor]: Taking taylor expansion of k in k 4.076 * [backup-simplify]: Simplify 0 into 0 4.076 * [backup-simplify]: Simplify 1 into 1 4.077 * [backup-simplify]: Simplify (/ -1 1) into -1 4.077 * [backup-simplify]: Simplify (sqrt 0) into 0 4.078 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.078 * [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))))) 4.078 * [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))))) 4.078 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 4.078 * [taylor]: Taking taylor expansion of +nan.0 in n 4.078 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.078 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 4.078 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 4.078 * [taylor]: Taking taylor expansion of 0.5 in n 4.078 * [backup-simplify]: Simplify 0.5 into 0.5 4.078 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 4.078 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.078 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.078 * [taylor]: Taking taylor expansion of -2.0 in n 4.078 * [backup-simplify]: Simplify -2.0 into -2.0 4.078 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.078 * [taylor]: Taking taylor expansion of PI in n 4.078 * [backup-simplify]: Simplify PI into PI 4.078 * [taylor]: Taking taylor expansion of n in n 4.078 * [backup-simplify]: Simplify 0 into 0 4.078 * [backup-simplify]: Simplify 1 into 1 4.079 * [backup-simplify]: Simplify (/ PI 1) into PI 4.079 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.080 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.080 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.080 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.080 * [taylor]: Taking taylor expansion of k in n 4.080 * [backup-simplify]: Simplify k into k 4.080 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.080 * [taylor]: Taking taylor expansion of 1.0 in n 4.080 * [backup-simplify]: Simplify 1.0 into 1.0 4.081 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.081 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.081 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 4.082 * [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))) 4.083 * [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)))) 4.084 * [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))))) 4.085 * [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))))) 4.085 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.087 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.088 * [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)))))) 4.088 * [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)))))) 4.088 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 4.088 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 4.088 * [taylor]: Taking taylor expansion of +nan.0 in n 4.088 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.088 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 4.088 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 4.088 * [taylor]: Taking taylor expansion of 0.5 in n 4.088 * [backup-simplify]: Simplify 0.5 into 0.5 4.088 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 4.088 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.088 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.088 * [taylor]: Taking taylor expansion of -2.0 in n 4.088 * [backup-simplify]: Simplify -2.0 into -2.0 4.088 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.088 * [taylor]: Taking taylor expansion of PI in n 4.088 * [backup-simplify]: Simplify PI into PI 4.088 * [taylor]: Taking taylor expansion of n in n 4.088 * [backup-simplify]: Simplify 0 into 0 4.088 * [backup-simplify]: Simplify 1 into 1 4.089 * [backup-simplify]: Simplify (/ PI 1) into PI 4.089 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.090 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.090 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.090 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.090 * [taylor]: Taking taylor expansion of k in n 4.090 * [backup-simplify]: Simplify k into k 4.090 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.090 * [taylor]: Taking taylor expansion of 1.0 in n 4.090 * [backup-simplify]: Simplify 1.0 into 1.0 4.091 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.091 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.092 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 4.092 * [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))) 4.094 * [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)))) 4.095 * [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))))) 4.096 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 4.098 * [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)))))) 4.099 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.099 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.100 * [backup-simplify]: Simplify (+ 0 0) into 0 4.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.102 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.104 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.105 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.107 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 4.109 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.110 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 4.111 * [backup-simplify]: Simplify 0 into 0 4.112 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.116 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.118 * [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)))))) 4.119 * [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)))))) 4.119 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 4.119 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 4.119 * [taylor]: Taking taylor expansion of +nan.0 in n 4.119 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.119 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 4.119 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 4.119 * [taylor]: Taking taylor expansion of 0.5 in n 4.119 * [backup-simplify]: Simplify 0.5 into 0.5 4.119 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 4.119 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.119 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.119 * [taylor]: Taking taylor expansion of -2.0 in n 4.119 * [backup-simplify]: Simplify -2.0 into -2.0 4.119 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.120 * [taylor]: Taking taylor expansion of PI in n 4.120 * [backup-simplify]: Simplify PI into PI 4.120 * [taylor]: Taking taylor expansion of n in n 4.120 * [backup-simplify]: Simplify 0 into 0 4.120 * [backup-simplify]: Simplify 1 into 1 4.120 * [backup-simplify]: Simplify (/ PI 1) into PI 4.121 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.121 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.121 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.121 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.121 * [taylor]: Taking taylor expansion of k in n 4.121 * [backup-simplify]: Simplify k into k 4.121 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.121 * [taylor]: Taking taylor expansion of 1.0 in n 4.121 * [backup-simplify]: Simplify 1.0 into 1.0 4.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.122 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.123 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 4.124 * [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))) 4.125 * [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)))) 4.126 * [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))))) 4.126 * [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)))))) 4.127 * [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)))))) 4.130 * [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)))))))) 4.130 * * * [progress]: simplifying candidates 4.133 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (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 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k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 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k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +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 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 4.136 * * [simplify]: iteration 0: 361 enodes 4.241 * * [simplify]: iteration 1: 1004 enodes 4.768 * * [simplify]: iteration 2: 3445 enodes 6.101 * * [simplify]: iteration complete: 5004 enodes 6.101 * * [simplify]: Extracting #0: cost 125 inf + 0 6.102 * * [simplify]: Extracting #1: cost 635 inf + 2 6.106 * * [simplify]: Extracting #2: cost 1123 inf + 2802 6.115 * * [simplify]: Extracting #3: cost 1125 inf + 37571 6.164 * * [simplify]: Extracting #4: cost 740 inf + 164402 6.223 * * [simplify]: Extracting #5: cost 432 inf + 325779 6.352 * * [simplify]: Extracting #6: cost 266 inf + 428235 6.505 * * [simplify]: Extracting #7: cost 69 inf + 606033 6.685 * * [simplify]: Extracting #8: cost 12 inf + 681945 6.900 * * [simplify]: Extracting #9: cost 1 inf + 696348 7.087 * * [simplify]: Extracting #10: cost 0 inf + 694281 7.290 * * [simplify]: Extracting #11: cost 0 inf + 693991 7.452 * * [simplify]: Extracting #12: cost 0 inf + 693801 7.623 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (pow (* (* PI 2.0) n) (/ k 2.0)) (pow (* (* PI 2.0) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* PI 2.0) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* PI 2.0) n) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* (* PI 2.0) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* PI 2.0) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI 2.0) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* PI 2.0) n) (sqrt (- 1.0 k))) (pow (* (* PI 2.0) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ 1 (sqrt 2.0))) 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(cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* PI 2.0) n) (/ k 2.0))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (sqrt 1.0) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (sqrt 1.0) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (- (fma (* (* (* (log n) (* k k)) (exp (* 0.5 (log (* (* PI 2.0) n))))) (log (* PI 2.0))) 0.25 (fma 0.125 (* (* (log n) (log n)) (* (* k k) (exp (* 0.5 (log (* (* PI 2.0) n)))))) (fma (* (* (log (* PI 2.0)) (log (* PI 2.0))) 0.125) (* (* k k) (exp (* 0.5 (log (* (* PI 2.0) n))))) (exp (* 0.5 (log (* (* PI 2.0) n))))))) (* 0.5 (* k (fma (log n) (exp (* 0.5 (log (* (* PI 2.0) n)))) (* (log (* PI 2.0)) (exp (* 0.5 (log (* (* PI 2.0) n))))))))) (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* PI 2.0) n) (* (* PI 2.0) n) (* (* PI 2.0) n) (- (* (- +nan.0) (* k k)) (fma k +nan.0 (- +nan.0))) (+ (/ (- +nan.0) (* k k)) (fma +nan.0 (/ 1 k) (* (/ (- +nan.0) (* k k)) (/ 1 k)))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) +nan.0)) (fma (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) k (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* k k) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log n) (* k k))) (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (fma (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (log (* PI 2.0)) (log (* PI 2.0)))) (* k k) (* (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (* (* (log n) (* k k)) (log (* PI 2.0))))) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log (* PI 2.0)) k)) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (log n) k) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (* (log n) k) (* (log n) k)) (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log (* PI 2.0)) (* k k)))))))))))) (fma (- (/ (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) (* k k))) +nan.0 (* +nan.0 (+ (/ (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) k) (- (/ (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) (* k (* k k))))))) (fma (- +nan.0) (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)))))) k) +nan.0) (* (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (/ +nan.0 k)))) 7.635 * * * [progress]: adding candidates to table 8.635 * * [progress]: iteration 2 / 4 8.635 * * * [progress]: picking best candidate 8.695 * * * * [pick]: Picked # 8.695 * * * [progress]: localizing error 8.742 * * * [progress]: generating rewritten candidates 8.742 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 8.764 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 8.782 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 8.791 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 8.854 * * * [progress]: generating series expansions 8.854 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 8.855 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 8.855 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 8.855 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 8.855 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.855 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.855 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 8.855 * [taylor]: Taking taylor expansion of 0.5 in k 8.855 * [backup-simplify]: Simplify 0.5 into 0.5 8.855 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.855 * [taylor]: Taking taylor expansion of 1.0 in k 8.855 * [backup-simplify]: Simplify 1.0 into 1.0 8.855 * [taylor]: Taking taylor expansion of k in k 8.855 * [backup-simplify]: Simplify 0 into 0 8.855 * [backup-simplify]: Simplify 1 into 1 8.855 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.855 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.855 * [taylor]: Taking taylor expansion of 2.0 in k 8.855 * [backup-simplify]: Simplify 2.0 into 2.0 8.855 * [taylor]: Taking taylor expansion of (* n PI) in k 8.855 * [taylor]: Taking taylor expansion of n in k 8.855 * [backup-simplify]: Simplify n into n 8.855 * [taylor]: Taking taylor expansion of PI in k 8.856 * [backup-simplify]: Simplify PI into PI 8.856 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.856 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.856 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.856 * [backup-simplify]: Simplify (- 0) into 0 8.857 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.857 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 8.857 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 8.857 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 8.857 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.858 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.858 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.858 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.858 * [taylor]: Taking taylor expansion of 0.5 in n 8.858 * [backup-simplify]: Simplify 0.5 into 0.5 8.858 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.858 * [taylor]: Taking taylor expansion of 1.0 in n 8.858 * [backup-simplify]: Simplify 1.0 into 1.0 8.858 * [taylor]: Taking taylor expansion of k in n 8.858 * [backup-simplify]: Simplify k into k 8.858 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.858 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.858 * [taylor]: Taking taylor expansion of 2.0 in n 8.858 * [backup-simplify]: Simplify 2.0 into 2.0 8.858 * [taylor]: Taking taylor expansion of (* n PI) in n 8.858 * [taylor]: Taking taylor expansion of n in n 8.858 * [backup-simplify]: Simplify 0 into 0 8.858 * [backup-simplify]: Simplify 1 into 1 8.858 * [taylor]: Taking taylor expansion of PI in n 8.858 * [backup-simplify]: Simplify PI into PI 8.859 * [backup-simplify]: Simplify (* 0 PI) into 0 8.859 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.861 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.862 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.863 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.863 * [backup-simplify]: Simplify (- k) into (- k) 8.863 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.863 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.865 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.866 * [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)))) 8.867 * [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))))) 8.867 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 8.867 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.867 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.867 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 8.867 * [taylor]: Taking taylor expansion of 0.5 in n 8.867 * [backup-simplify]: Simplify 0.5 into 0.5 8.867 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.867 * [taylor]: Taking taylor expansion of 1.0 in n 8.867 * [backup-simplify]: Simplify 1.0 into 1.0 8.867 * [taylor]: Taking taylor expansion of k in n 8.867 * [backup-simplify]: Simplify k into k 8.867 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.868 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.868 * [taylor]: Taking taylor expansion of 2.0 in n 8.868 * [backup-simplify]: Simplify 2.0 into 2.0 8.868 * [taylor]: Taking taylor expansion of (* n PI) in n 8.868 * [taylor]: Taking taylor expansion of n in n 8.868 * [backup-simplify]: Simplify 0 into 0 8.868 * [backup-simplify]: Simplify 1 into 1 8.868 * [taylor]: Taking taylor expansion of PI in n 8.868 * [backup-simplify]: Simplify PI into PI 8.868 * [backup-simplify]: Simplify (* 0 PI) into 0 8.869 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.870 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.872 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.873 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.873 * [backup-simplify]: Simplify (- k) into (- k) 8.873 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.873 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 8.874 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.875 * [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)))) 8.877 * [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))))) 8.877 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.877 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.877 * [taylor]: Taking taylor expansion of 0.5 in k 8.877 * [backup-simplify]: Simplify 0.5 into 0.5 8.877 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.877 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.877 * [taylor]: Taking taylor expansion of 1.0 in k 8.877 * [backup-simplify]: Simplify 1.0 into 1.0 8.877 * [taylor]: Taking taylor expansion of k in k 8.877 * [backup-simplify]: Simplify 0 into 0 8.877 * [backup-simplify]: Simplify 1 into 1 8.877 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.877 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.877 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.877 * [taylor]: Taking taylor expansion of 2.0 in k 8.877 * [backup-simplify]: Simplify 2.0 into 2.0 8.877 * [taylor]: Taking taylor expansion of PI in k 8.877 * [backup-simplify]: Simplify PI into PI 8.878 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.879 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.879 * [taylor]: Taking taylor expansion of (log n) in k 8.879 * [taylor]: Taking taylor expansion of n in k 8.879 * [backup-simplify]: Simplify n into n 8.879 * [backup-simplify]: Simplify (log n) into (log n) 8.879 * [backup-simplify]: Simplify (- 0) into 0 8.880 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.881 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.882 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.883 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 8.884 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.885 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 8.886 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.887 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.889 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.890 * [backup-simplify]: Simplify (- 0) into 0 8.890 * [backup-simplify]: Simplify (+ 0 0) into 0 8.890 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 8.892 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.898 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.900 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.900 * [taylor]: Taking taylor expansion of 0 in k 8.900 * [backup-simplify]: Simplify 0 into 0 8.900 * [backup-simplify]: Simplify 0 into 0 8.901 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.903 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.904 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.904 * [backup-simplify]: Simplify (+ 0 0) into 0 8.904 * [backup-simplify]: Simplify (- 1) into -1 8.905 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.905 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.907 * [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)))) 8.909 * [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)))))) 8.911 * [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)))))) 8.911 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.912 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.914 * [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 8.915 * [backup-simplify]: Simplify (- 0) into 0 8.915 * [backup-simplify]: Simplify (+ 0 0) into 0 8.915 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.916 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.917 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.919 * [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 8.919 * [taylor]: Taking taylor expansion of 0 in k 8.919 * [backup-simplify]: Simplify 0 into 0 8.919 * [backup-simplify]: Simplify 0 into 0 8.919 * [backup-simplify]: Simplify 0 into 0 8.920 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.922 * [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 8.923 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.923 * [backup-simplify]: Simplify (+ 0 0) into 0 8.923 * [backup-simplify]: Simplify (- 0) into 0 8.924 * [backup-simplify]: Simplify (+ 0 0) into 0 8.925 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.926 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.929 * [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)))))) 8.932 * [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)))))) 8.938 * [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))))) 8.939 * [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)))) 8.939 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 8.939 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 8.939 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.939 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.939 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 8.939 * [taylor]: Taking taylor expansion of 0.5 in k 8.939 * [backup-simplify]: Simplify 0.5 into 0.5 8.939 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.939 * [taylor]: Taking taylor expansion of 1.0 in k 8.939 * [backup-simplify]: Simplify 1.0 into 1.0 8.939 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.939 * [taylor]: Taking taylor expansion of k in k 8.939 * [backup-simplify]: Simplify 0 into 0 8.939 * [backup-simplify]: Simplify 1 into 1 8.939 * [backup-simplify]: Simplify (/ 1 1) into 1 8.939 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.939 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.939 * [taylor]: Taking taylor expansion of 2.0 in k 8.939 * [backup-simplify]: Simplify 2.0 into 2.0 8.939 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.939 * [taylor]: Taking taylor expansion of PI in k 8.939 * [backup-simplify]: Simplify PI into PI 8.939 * [taylor]: Taking taylor expansion of n in k 8.939 * [backup-simplify]: Simplify n into n 8.939 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.939 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.940 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.940 * [backup-simplify]: Simplify (- 1) into -1 8.940 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.940 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 8.940 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 8.941 * [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)))))) 8.941 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.941 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.941 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.941 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.941 * [taylor]: Taking taylor expansion of 0.5 in n 8.941 * [backup-simplify]: Simplify 0.5 into 0.5 8.941 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.941 * [taylor]: Taking taylor expansion of 1.0 in n 8.941 * [backup-simplify]: Simplify 1.0 into 1.0 8.941 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.941 * [taylor]: Taking taylor expansion of k in n 8.941 * [backup-simplify]: Simplify k into k 8.941 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.941 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.941 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.941 * [taylor]: Taking taylor expansion of 2.0 in n 8.941 * [backup-simplify]: Simplify 2.0 into 2.0 8.941 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.941 * [taylor]: Taking taylor expansion of PI in n 8.941 * [backup-simplify]: Simplify PI into PI 8.941 * [taylor]: Taking taylor expansion of n in n 8.941 * [backup-simplify]: Simplify 0 into 0 8.941 * [backup-simplify]: Simplify 1 into 1 8.941 * [backup-simplify]: Simplify (/ PI 1) into PI 8.942 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.942 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.942 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.942 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.942 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.944 * [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)))) 8.945 * [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))))) 8.945 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 8.945 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.945 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.945 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 8.945 * [taylor]: Taking taylor expansion of 0.5 in n 8.945 * [backup-simplify]: Simplify 0.5 into 0.5 8.945 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.945 * [taylor]: Taking taylor expansion of 1.0 in n 8.945 * [backup-simplify]: Simplify 1.0 into 1.0 8.945 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.945 * [taylor]: Taking taylor expansion of k in n 8.945 * [backup-simplify]: Simplify k into k 8.945 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.945 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.945 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.945 * [taylor]: Taking taylor expansion of 2.0 in n 8.945 * [backup-simplify]: Simplify 2.0 into 2.0 8.945 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.945 * [taylor]: Taking taylor expansion of PI in n 8.945 * [backup-simplify]: Simplify PI into PI 8.945 * [taylor]: Taking taylor expansion of n in n 8.945 * [backup-simplify]: Simplify 0 into 0 8.945 * [backup-simplify]: Simplify 1 into 1 8.945 * [backup-simplify]: Simplify (/ PI 1) into PI 8.946 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.946 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.946 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.947 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.947 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 8.948 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.948 * [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)))) 8.949 * [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))))) 8.949 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 8.949 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 8.949 * [taylor]: Taking taylor expansion of 0.5 in k 8.949 * [backup-simplify]: Simplify 0.5 into 0.5 8.949 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 8.949 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.949 * [taylor]: Taking taylor expansion of 1.0 in k 8.949 * [backup-simplify]: Simplify 1.0 into 1.0 8.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.949 * [taylor]: Taking taylor expansion of k in k 8.949 * [backup-simplify]: Simplify 0 into 0 8.949 * [backup-simplify]: Simplify 1 into 1 8.950 * [backup-simplify]: Simplify (/ 1 1) into 1 8.950 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.950 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.950 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.950 * [taylor]: Taking taylor expansion of 2.0 in k 8.950 * [backup-simplify]: Simplify 2.0 into 2.0 8.950 * [taylor]: Taking taylor expansion of PI in k 8.950 * [backup-simplify]: Simplify PI into PI 8.950 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.951 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.951 * [taylor]: Taking taylor expansion of (log n) in k 8.951 * [taylor]: Taking taylor expansion of n in k 8.951 * [backup-simplify]: Simplify n into n 8.951 * [backup-simplify]: Simplify (log n) into (log n) 8.951 * [backup-simplify]: Simplify (- 1) into -1 8.951 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.951 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.952 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.953 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.953 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 8.954 * [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))))) 8.955 * [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))))) 8.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.956 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.957 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.957 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.958 * [backup-simplify]: Simplify (- 0) into 0 8.958 * [backup-simplify]: Simplify (+ 0 0) into 0 8.958 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.960 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.961 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.961 * [taylor]: Taking taylor expansion of 0 in k 8.961 * [backup-simplify]: Simplify 0 into 0 8.961 * [backup-simplify]: Simplify 0 into 0 8.961 * [backup-simplify]: Simplify 0 into 0 8.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.964 * [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 8.964 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.965 * [backup-simplify]: Simplify (- 0) into 0 8.965 * [backup-simplify]: Simplify (+ 0 0) into 0 8.965 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.966 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.967 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.969 * [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 8.969 * [taylor]: Taking taylor expansion of 0 in k 8.969 * [backup-simplify]: Simplify 0 into 0 8.969 * [backup-simplify]: Simplify 0 into 0 8.969 * [backup-simplify]: Simplify 0 into 0 8.969 * [backup-simplify]: Simplify 0 into 0 8.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.973 * [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 8.974 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.974 * [backup-simplify]: Simplify (- 0) into 0 8.974 * [backup-simplify]: Simplify (+ 0 0) into 0 8.975 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.976 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.977 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.979 * [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 8.979 * [taylor]: Taking taylor expansion of 0 in k 8.979 * [backup-simplify]: Simplify 0 into 0 8.979 * [backup-simplify]: Simplify 0 into 0 8.980 * [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)))))) 8.980 * [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))) 8.980 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 8.980 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 8.980 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.980 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.980 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 8.980 * [taylor]: Taking taylor expansion of 0.5 in k 8.980 * [backup-simplify]: Simplify 0.5 into 0.5 8.980 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.980 * [taylor]: Taking taylor expansion of k in k 8.980 * [backup-simplify]: Simplify 0 into 0 8.980 * [backup-simplify]: Simplify 1 into 1 8.981 * [backup-simplify]: Simplify (/ 1 1) into 1 8.981 * [taylor]: Taking taylor expansion of 1.0 in k 8.981 * [backup-simplify]: Simplify 1.0 into 1.0 8.981 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.981 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.981 * [taylor]: Taking taylor expansion of -2.0 in k 8.981 * [backup-simplify]: Simplify -2.0 into -2.0 8.981 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.981 * [taylor]: Taking taylor expansion of PI in k 8.981 * [backup-simplify]: Simplify PI into PI 8.981 * [taylor]: Taking taylor expansion of n in k 8.981 * [backup-simplify]: Simplify n into n 8.981 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.981 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.981 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.981 * [backup-simplify]: Simplify (+ 1 0) into 1 8.982 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 8.982 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 8.982 * [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)))) 8.982 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.982 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.982 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.982 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.982 * [taylor]: Taking taylor expansion of 0.5 in n 8.982 * [backup-simplify]: Simplify 0.5 into 0.5 8.982 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.982 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.982 * [taylor]: Taking taylor expansion of k in n 8.982 * [backup-simplify]: Simplify k into k 8.982 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.982 * [taylor]: Taking taylor expansion of 1.0 in n 8.982 * [backup-simplify]: Simplify 1.0 into 1.0 8.982 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.982 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.982 * [taylor]: Taking taylor expansion of -2.0 in n 8.982 * [backup-simplify]: Simplify -2.0 into -2.0 8.982 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.982 * [taylor]: Taking taylor expansion of PI in n 8.982 * [backup-simplify]: Simplify PI into PI 8.982 * [taylor]: Taking taylor expansion of n in n 8.982 * [backup-simplify]: Simplify 0 into 0 8.982 * [backup-simplify]: Simplify 1 into 1 8.982 * [backup-simplify]: Simplify (/ PI 1) into PI 8.983 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.983 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.983 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.984 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.984 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.985 * [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))) 8.986 * [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)))) 8.986 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 8.986 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.986 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.986 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 8.986 * [taylor]: Taking taylor expansion of 0.5 in n 8.986 * [backup-simplify]: Simplify 0.5 into 0.5 8.986 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.986 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.986 * [taylor]: Taking taylor expansion of k in n 8.986 * [backup-simplify]: Simplify k into k 8.986 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.986 * [taylor]: Taking taylor expansion of 1.0 in n 8.986 * [backup-simplify]: Simplify 1.0 into 1.0 8.986 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.986 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.986 * [taylor]: Taking taylor expansion of -2.0 in n 8.986 * [backup-simplify]: Simplify -2.0 into -2.0 8.986 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.986 * [taylor]: Taking taylor expansion of PI in n 8.986 * [backup-simplify]: Simplify PI into PI 8.986 * [taylor]: Taking taylor expansion of n in n 8.986 * [backup-simplify]: Simplify 0 into 0 8.986 * [backup-simplify]: Simplify 1 into 1 8.987 * [backup-simplify]: Simplify (/ PI 1) into PI 8.991 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.992 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.992 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.993 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 8.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.994 * [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))) 8.995 * [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)))) 8.995 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 8.995 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 8.995 * [taylor]: Taking taylor expansion of 0.5 in k 8.995 * [backup-simplify]: Simplify 0.5 into 0.5 8.995 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 8.995 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.995 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.995 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.995 * [taylor]: Taking taylor expansion of -2.0 in k 8.995 * [backup-simplify]: Simplify -2.0 into -2.0 8.995 * [taylor]: Taking taylor expansion of PI in k 8.995 * [backup-simplify]: Simplify PI into PI 8.995 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.996 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.996 * [taylor]: Taking taylor expansion of (log n) in k 8.996 * [taylor]: Taking taylor expansion of n in k 8.996 * [backup-simplify]: Simplify n into n 8.996 * [backup-simplify]: Simplify (log n) into (log n) 8.996 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.996 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.996 * [taylor]: Taking taylor expansion of k in k 8.996 * [backup-simplify]: Simplify 0 into 0 8.996 * [backup-simplify]: Simplify 1 into 1 8.997 * [backup-simplify]: Simplify (/ 1 1) into 1 8.997 * [taylor]: Taking taylor expansion of 1.0 in k 8.997 * [backup-simplify]: Simplify 1.0 into 1.0 8.997 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.997 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.998 * [backup-simplify]: Simplify (+ 1 0) into 1 8.998 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 8.999 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 9.000 * [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)))) 9.001 * [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)))) 9.001 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.002 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.003 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.003 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.003 * [backup-simplify]: Simplify (+ 0 0) into 0 9.003 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.005 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.006 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.006 * [taylor]: Taking taylor expansion of 0 in k 9.006 * [backup-simplify]: Simplify 0 into 0 9.006 * [backup-simplify]: Simplify 0 into 0 9.006 * [backup-simplify]: Simplify 0 into 0 9.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.008 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.010 * [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 9.010 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.010 * [backup-simplify]: Simplify (+ 0 0) into 0 9.011 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.012 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.013 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.014 * [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 9.014 * [taylor]: Taking taylor expansion of 0 in k 9.014 * [backup-simplify]: Simplify 0 into 0 9.014 * [backup-simplify]: Simplify 0 into 0 9.014 * [backup-simplify]: Simplify 0 into 0 9.014 * [backup-simplify]: Simplify 0 into 0 9.015 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.016 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.019 * [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 9.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.019 * [backup-simplify]: Simplify (+ 0 0) into 0 9.020 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.021 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.022 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.024 * [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 9.024 * [taylor]: Taking taylor expansion of 0 in k 9.024 * [backup-simplify]: Simplify 0 into 0 9.024 * [backup-simplify]: Simplify 0 into 0 9.025 * [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)))))) 9.025 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 9.025 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.025 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.025 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.025 * [taylor]: Taking taylor expansion of 2.0 in n 9.025 * [backup-simplify]: Simplify 2.0 into 2.0 9.025 * [taylor]: Taking taylor expansion of (* n PI) in n 9.025 * [taylor]: Taking taylor expansion of n in n 9.025 * [backup-simplify]: Simplify 0 into 0 9.025 * [backup-simplify]: Simplify 1 into 1 9.025 * [taylor]: Taking taylor expansion of PI in n 9.025 * [backup-simplify]: Simplify PI into PI 9.025 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.025 * [taylor]: Taking taylor expansion of 2.0 in n 9.025 * [backup-simplify]: Simplify 2.0 into 2.0 9.025 * [taylor]: Taking taylor expansion of (* n PI) in n 9.025 * [taylor]: Taking taylor expansion of n in n 9.025 * [backup-simplify]: Simplify 0 into 0 9.025 * [backup-simplify]: Simplify 1 into 1 9.025 * [taylor]: Taking taylor expansion of PI in n 9.025 * [backup-simplify]: Simplify PI into PI 9.026 * [backup-simplify]: Simplify (* 0 PI) into 0 9.026 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.026 * [backup-simplify]: Simplify 0 into 0 9.027 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.028 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.028 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.029 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.029 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.029 * [backup-simplify]: Simplify 0 into 0 9.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.031 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.031 * [backup-simplify]: Simplify 0 into 0 9.032 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.032 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.032 * [backup-simplify]: Simplify 0 into 0 9.033 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.034 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.034 * [backup-simplify]: Simplify 0 into 0 9.035 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.036 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.036 * [backup-simplify]: Simplify 0 into 0 9.038 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.040 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.040 * [backup-simplify]: Simplify 0 into 0 9.040 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.041 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.041 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.041 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.041 * [taylor]: Taking taylor expansion of 2.0 in n 9.041 * [backup-simplify]: Simplify 2.0 into 2.0 9.041 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.041 * [taylor]: Taking taylor expansion of PI in n 9.041 * [backup-simplify]: Simplify PI into PI 9.041 * [taylor]: Taking taylor expansion of n in n 9.041 * [backup-simplify]: Simplify 0 into 0 9.041 * [backup-simplify]: Simplify 1 into 1 9.042 * [backup-simplify]: Simplify (/ PI 1) into PI 9.042 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.042 * [taylor]: Taking taylor expansion of 2.0 in n 9.042 * [backup-simplify]: Simplify 2.0 into 2.0 9.042 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.042 * [taylor]: Taking taylor expansion of PI in n 9.042 * [backup-simplify]: Simplify PI into PI 9.042 * [taylor]: Taking taylor expansion of n in n 9.042 * [backup-simplify]: Simplify 0 into 0 9.042 * [backup-simplify]: Simplify 1 into 1 9.043 * [backup-simplify]: Simplify (/ PI 1) into PI 9.043 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.044 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.045 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.045 * [backup-simplify]: Simplify 0 into 0 9.046 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.047 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.047 * [backup-simplify]: Simplify 0 into 0 9.048 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.049 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.050 * [backup-simplify]: Simplify 0 into 0 9.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.052 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.052 * [backup-simplify]: Simplify 0 into 0 9.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.053 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.054 * [backup-simplify]: Simplify 0 into 0 9.054 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.055 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.055 * [backup-simplify]: Simplify 0 into 0 9.055 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.056 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.056 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.056 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.056 * [taylor]: Taking taylor expansion of -2.0 in n 9.056 * [backup-simplify]: Simplify -2.0 into -2.0 9.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.056 * [taylor]: Taking taylor expansion of PI in n 9.056 * [backup-simplify]: Simplify PI into PI 9.056 * [taylor]: Taking taylor expansion of n in n 9.056 * [backup-simplify]: Simplify 0 into 0 9.056 * [backup-simplify]: Simplify 1 into 1 9.056 * [backup-simplify]: Simplify (/ PI 1) into PI 9.056 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.056 * [taylor]: Taking taylor expansion of -2.0 in n 9.056 * [backup-simplify]: Simplify -2.0 into -2.0 9.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.056 * [taylor]: Taking taylor expansion of PI in n 9.056 * [backup-simplify]: Simplify PI into PI 9.056 * [taylor]: Taking taylor expansion of n in n 9.056 * [backup-simplify]: Simplify 0 into 0 9.057 * [backup-simplify]: Simplify 1 into 1 9.057 * [backup-simplify]: Simplify (/ PI 1) into PI 9.057 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.058 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.059 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.059 * [backup-simplify]: Simplify 0 into 0 9.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.060 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.060 * [backup-simplify]: Simplify 0 into 0 9.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.061 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.061 * [backup-simplify]: Simplify 0 into 0 9.062 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.063 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.063 * [backup-simplify]: Simplify 0 into 0 9.063 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.064 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.064 * [backup-simplify]: Simplify 0 into 0 9.065 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.066 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.066 * [backup-simplify]: Simplify 0 into 0 9.066 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.066 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 9.066 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 9.066 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 9.066 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.066 * [taylor]: Taking taylor expansion of 1.0 in k 9.066 * [backup-simplify]: Simplify 1.0 into 1.0 9.066 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.066 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.067 * [taylor]: Taking taylor expansion of k in k 9.067 * [backup-simplify]: Simplify 0 into 0 9.067 * [backup-simplify]: Simplify 1 into 1 9.067 * [backup-simplify]: Simplify (/ 1 1) into 1 9.067 * [backup-simplify]: Simplify (sqrt 0) into 0 9.068 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.068 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.068 * [taylor]: Taking taylor expansion of 1.0 in k 9.068 * [backup-simplify]: Simplify 1.0 into 1.0 9.068 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.068 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.068 * [taylor]: Taking taylor expansion of k in k 9.068 * [backup-simplify]: Simplify 0 into 0 9.068 * [backup-simplify]: Simplify 1 into 1 9.068 * [backup-simplify]: Simplify (/ 1 1) into 1 9.068 * [backup-simplify]: Simplify (sqrt 0) into 0 9.069 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.070 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.070 * [backup-simplify]: Simplify 0 into 0 9.070 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.071 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.071 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.073 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.074 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.074 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.075 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.077 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.079 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.079 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.080 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 9.080 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.080 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.080 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.080 * [taylor]: Taking taylor expansion of 1.0 in k 9.080 * [backup-simplify]: Simplify 1.0 into 1.0 9.080 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.080 * [taylor]: Taking taylor expansion of k in k 9.080 * [backup-simplify]: Simplify 0 into 0 9.080 * [backup-simplify]: Simplify 1 into 1 9.080 * [backup-simplify]: Simplify (sqrt 0) into 0 9.081 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.081 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.081 * [taylor]: Taking taylor expansion of 1.0 in k 9.081 * [backup-simplify]: Simplify 1.0 into 1.0 9.081 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.082 * [taylor]: Taking taylor expansion of k in k 9.082 * [backup-simplify]: Simplify 0 into 0 9.082 * [backup-simplify]: Simplify 1 into 1 9.082 * [backup-simplify]: Simplify (sqrt 0) into 0 9.083 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.084 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.084 * [backup-simplify]: Simplify 0 into 0 9.085 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.085 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.095 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.097 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.098 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.102 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.105 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.105 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.107 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 9.108 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.108 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.108 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.108 * [taylor]: Taking taylor expansion of 1.0 in k 9.108 * [backup-simplify]: Simplify 1.0 into 1.0 9.108 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.108 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.108 * [taylor]: Taking taylor expansion of -1 in k 9.108 * [backup-simplify]: Simplify -1 into -1 9.108 * [taylor]: Taking taylor expansion of k in k 9.108 * [backup-simplify]: Simplify 0 into 0 9.108 * [backup-simplify]: Simplify 1 into 1 9.109 * [backup-simplify]: Simplify (/ -1 1) into -1 9.109 * [backup-simplify]: Simplify (sqrt 0) into 0 9.111 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.111 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.111 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.111 * [taylor]: Taking taylor expansion of 1.0 in k 9.111 * [backup-simplify]: Simplify 1.0 into 1.0 9.111 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.111 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.111 * [taylor]: Taking taylor expansion of -1 in k 9.111 * [backup-simplify]: Simplify -1 into -1 9.111 * [taylor]: Taking taylor expansion of k in k 9.111 * [backup-simplify]: Simplify 0 into 0 9.111 * [backup-simplify]: Simplify 1 into 1 9.112 * [backup-simplify]: Simplify (/ -1 1) into -1 9.112 * [backup-simplify]: Simplify (sqrt 0) into 0 9.114 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.115 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.115 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.119 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.122 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.122 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.127 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.131 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.131 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.133 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 9.133 * * * * [progress]: [ 4 / 4 ] generating series at (2) 9.134 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 9.134 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0 9.134 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 9.134 * [taylor]: Taking taylor expansion of 1.0 in k 9.134 * [backup-simplify]: Simplify 1.0 into 1.0 9.134 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 9.134 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 9.134 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.134 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.134 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 9.134 * [taylor]: Taking taylor expansion of 0.5 in k 9.134 * [backup-simplify]: Simplify 0.5 into 0.5 9.134 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.134 * [taylor]: Taking taylor expansion of 1.0 in k 9.134 * [backup-simplify]: Simplify 1.0 into 1.0 9.134 * [taylor]: Taking taylor expansion of k in k 9.134 * [backup-simplify]: Simplify 0 into 0 9.134 * [backup-simplify]: Simplify 1 into 1 9.134 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.134 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.134 * [taylor]: Taking taylor expansion of 2.0 in k 9.134 * [backup-simplify]: Simplify 2.0 into 2.0 9.134 * [taylor]: Taking taylor expansion of (* n PI) in k 9.134 * [taylor]: Taking taylor expansion of n in k 9.134 * [backup-simplify]: Simplify n into n 9.134 * [taylor]: Taking taylor expansion of PI in k 9.134 * [backup-simplify]: Simplify PI into PI 9.134 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.135 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.135 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.135 * [backup-simplify]: Simplify (- 0) into 0 9.136 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.136 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 9.136 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 9.136 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 9.136 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.136 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.136 * [taylor]: Taking taylor expansion of k in k 9.136 * [backup-simplify]: Simplify 0 into 0 9.136 * [backup-simplify]: Simplify 1 into 1 9.137 * [backup-simplify]: Simplify (/ 1 1) into 1 9.137 * [backup-simplify]: Simplify (sqrt 0) into 0 9.139 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.139 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 9.139 * [taylor]: Taking taylor expansion of 1.0 in n 9.139 * [backup-simplify]: Simplify 1.0 into 1.0 9.139 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 9.139 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 9.139 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.139 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.139 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 9.139 * [taylor]: Taking taylor expansion of 0.5 in n 9.139 * [backup-simplify]: Simplify 0.5 into 0.5 9.139 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.139 * [taylor]: Taking taylor expansion of 1.0 in n 9.139 * [backup-simplify]: Simplify 1.0 into 1.0 9.139 * [taylor]: Taking taylor expansion of k in n 9.139 * [backup-simplify]: Simplify k into k 9.139 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.139 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.139 * [taylor]: Taking taylor expansion of 2.0 in n 9.139 * [backup-simplify]: Simplify 2.0 into 2.0 9.139 * [taylor]: Taking taylor expansion of (* n PI) in n 9.139 * [taylor]: Taking taylor expansion of n in n 9.139 * [backup-simplify]: Simplify 0 into 0 9.139 * [backup-simplify]: Simplify 1 into 1 9.139 * [taylor]: Taking taylor expansion of PI in n 9.139 * [backup-simplify]: Simplify PI into PI 9.140 * [backup-simplify]: Simplify (* 0 PI) into 0 9.140 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.143 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.144 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.144 * [backup-simplify]: Simplify (- k) into (- k) 9.145 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.145 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 9.146 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.147 * [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)))) 9.148 * [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))))) 9.148 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 9.149 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.149 * [taylor]: Taking taylor expansion of k in n 9.149 * [backup-simplify]: Simplify k into k 9.149 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.149 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 9.149 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.149 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 9.149 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 9.149 * [taylor]: Taking taylor expansion of 1.0 in n 9.149 * [backup-simplify]: Simplify 1.0 into 1.0 9.149 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 9.149 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 9.149 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.149 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.149 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 9.149 * [taylor]: Taking taylor expansion of 0.5 in n 9.149 * [backup-simplify]: Simplify 0.5 into 0.5 9.149 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.149 * [taylor]: Taking taylor expansion of 1.0 in n 9.149 * [backup-simplify]: Simplify 1.0 into 1.0 9.149 * [taylor]: Taking taylor expansion of k in n 9.149 * [backup-simplify]: Simplify k into k 9.149 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.150 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.150 * [taylor]: Taking taylor expansion of 2.0 in n 9.150 * [backup-simplify]: Simplify 2.0 into 2.0 9.150 * [taylor]: Taking taylor expansion of (* n PI) in n 9.150 * [taylor]: Taking taylor expansion of n in n 9.150 * [backup-simplify]: Simplify 0 into 0 9.150 * [backup-simplify]: Simplify 1 into 1 9.150 * [taylor]: Taking taylor expansion of PI in n 9.150 * [backup-simplify]: Simplify PI into PI 9.150 * [backup-simplify]: Simplify (* 0 PI) into 0 9.151 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.152 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.154 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.155 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.155 * [backup-simplify]: Simplify (- k) into (- k) 9.155 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.155 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 9.157 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.158 * [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)))) 9.159 * [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))))) 9.159 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 9.159 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.159 * [taylor]: Taking taylor expansion of k in n 9.159 * [backup-simplify]: Simplify k into k 9.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.160 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 9.160 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.160 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 9.161 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) 9.163 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) 9.163 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k 9.163 * [taylor]: Taking taylor expansion of 1.0 in k 9.163 * [backup-simplify]: Simplify 1.0 into 1.0 9.163 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k 9.163 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.163 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.163 * [taylor]: Taking taylor expansion of 0.5 in k 9.163 * [backup-simplify]: Simplify 0.5 into 0.5 9.163 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.163 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.163 * [taylor]: Taking taylor expansion of 1.0 in k 9.163 * [backup-simplify]: Simplify 1.0 into 1.0 9.163 * [taylor]: Taking taylor expansion of k in k 9.163 * [backup-simplify]: Simplify 0 into 0 9.163 * [backup-simplify]: Simplify 1 into 1 9.163 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.163 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.163 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.163 * [taylor]: Taking taylor expansion of 2.0 in k 9.163 * [backup-simplify]: Simplify 2.0 into 2.0 9.163 * [taylor]: Taking taylor expansion of PI in k 9.163 * [backup-simplify]: Simplify PI into PI 9.164 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.165 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.165 * [taylor]: Taking taylor expansion of (log n) in k 9.165 * [taylor]: Taking taylor expansion of n in k 9.165 * [backup-simplify]: Simplify n into n 9.165 * [backup-simplify]: Simplify (log n) into (log n) 9.166 * [backup-simplify]: Simplify (- 0) into 0 9.166 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.167 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.168 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.169 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 9.171 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 9.171 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.171 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.171 * [taylor]: Taking taylor expansion of k in k 9.171 * [backup-simplify]: Simplify 0 into 0 9.171 * [backup-simplify]: Simplify 1 into 1 9.171 * [backup-simplify]: Simplify (/ 1 1) into 1 9.172 * [backup-simplify]: Simplify (sqrt 0) into 0 9.173 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.174 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0 9.175 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.175 * [backup-simplify]: Simplify 0 into 0 9.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.176 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.177 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.178 * [backup-simplify]: Simplify (- 0) into 0 9.178 * [backup-simplify]: Simplify (+ 0 0) into 0 9.178 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 9.179 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.180 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.181 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.182 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 9.183 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0 9.183 * [taylor]: Taking taylor expansion of 0 in k 9.183 * [backup-simplify]: Simplify 0 into 0 9.183 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.184 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.185 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.185 * [backup-simplify]: Simplify (+ 0 0) into 0 9.185 * [backup-simplify]: Simplify (- 1) into -1 9.186 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.187 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.188 * [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)))) 9.190 * [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)))))) 9.192 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 9.193 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 9.194 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 9.194 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.195 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 9.195 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.196 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.200 * [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 9.201 * [backup-simplify]: Simplify (- 0) into 0 9.201 * [backup-simplify]: Simplify (+ 0 0) into 0 9.202 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.203 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.205 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.207 * [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 9.209 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 9.212 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0 9.212 * [taylor]: Taking taylor expansion of 0 in k 9.212 * [backup-simplify]: Simplify 0 into 0 9.212 * [backup-simplify]: Simplify 0 into 0 9.213 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.216 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.217 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.220 * [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 9.222 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.223 * [backup-simplify]: Simplify (+ 0 0) into 0 9.223 * [backup-simplify]: Simplify (- 0) into 0 9.223 * [backup-simplify]: Simplify (+ 0 0) into 0 9.225 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.228 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.235 * [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)))))) 9.240 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 9.244 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 9.247 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 9.248 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.248 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 9.249 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.250 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.253 * [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 9.253 * [backup-simplify]: Simplify (- 0) into 0 9.253 * [backup-simplify]: Simplify (+ 0 0) into 0 9.254 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 9.255 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.256 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.258 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.259 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 9.261 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0 9.261 * [taylor]: Taking taylor expansion of 0 in k 9.261 * [backup-simplify]: Simplify 0 into 0 9.261 * [backup-simplify]: Simplify 0 into 0 9.261 * [backup-simplify]: Simplify 0 into 0 9.261 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.264 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.264 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.268 * [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 9.269 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 9.270 * [backup-simplify]: Simplify (+ 0 0) into 0 9.270 * [backup-simplify]: Simplify (- 0) into 0 9.270 * [backup-simplify]: Simplify (+ 0 0) into 0 9.272 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.274 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0 9.278 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 9.292 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) 9.312 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) 9.328 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) 9.345 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))))))))))))))))))) 9.346 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) (/ 1.0 (sqrt (/ 1 k)))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) 9.346 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0 9.346 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 9.346 * [taylor]: Taking taylor expansion of 1.0 in k 9.346 * [backup-simplify]: Simplify 1.0 into 1.0 9.346 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 9.346 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 9.346 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.346 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.346 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 9.346 * [taylor]: Taking taylor expansion of 0.5 in k 9.346 * [backup-simplify]: Simplify 0.5 into 0.5 9.346 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.346 * [taylor]: Taking taylor expansion of 1.0 in k 9.346 * [backup-simplify]: Simplify 1.0 into 1.0 9.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.346 * [taylor]: Taking taylor expansion of k in k 9.346 * [backup-simplify]: Simplify 0 into 0 9.346 * [backup-simplify]: Simplify 1 into 1 9.347 * [backup-simplify]: Simplify (/ 1 1) into 1 9.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.347 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.347 * [taylor]: Taking taylor expansion of 2.0 in k 9.347 * [backup-simplify]: Simplify 2.0 into 2.0 9.347 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.347 * [taylor]: Taking taylor expansion of PI in k 9.347 * [backup-simplify]: Simplify PI into PI 9.347 * [taylor]: Taking taylor expansion of n in k 9.347 * [backup-simplify]: Simplify n into n 9.347 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.347 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.347 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.347 * [backup-simplify]: Simplify (- 1) into -1 9.348 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.348 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 9.348 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 9.348 * [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)))))) 9.348 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.348 * [taylor]: Taking taylor expansion of k in k 9.348 * [backup-simplify]: Simplify 0 into 0 9.348 * [backup-simplify]: Simplify 1 into 1 9.348 * [backup-simplify]: Simplify (sqrt 0) into 0 9.349 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.349 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 9.349 * [taylor]: Taking taylor expansion of 1.0 in n 9.349 * [backup-simplify]: Simplify 1.0 into 1.0 9.349 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 9.349 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 9.349 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.349 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.349 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 9.349 * [taylor]: Taking taylor expansion of 0.5 in n 9.349 * [backup-simplify]: Simplify 0.5 into 0.5 9.349 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.350 * [taylor]: Taking taylor expansion of 1.0 in n 9.350 * [backup-simplify]: Simplify 1.0 into 1.0 9.350 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.350 * [taylor]: Taking taylor expansion of k in n 9.350 * [backup-simplify]: Simplify k into k 9.350 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.350 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.350 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.350 * [taylor]: Taking taylor expansion of 2.0 in n 9.350 * [backup-simplify]: Simplify 2.0 into 2.0 9.350 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.350 * [taylor]: Taking taylor expansion of PI in n 9.350 * [backup-simplify]: Simplify PI into PI 9.350 * [taylor]: Taking taylor expansion of n in n 9.350 * [backup-simplify]: Simplify 0 into 0 9.350 * [backup-simplify]: Simplify 1 into 1 9.350 * [backup-simplify]: Simplify (/ PI 1) into PI 9.350 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.351 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.351 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.351 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 9.352 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.353 * [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)))) 9.354 * [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))))) 9.354 * [taylor]: Taking taylor expansion of (sqrt k) in n 9.354 * [taylor]: Taking taylor expansion of k in n 9.354 * [backup-simplify]: Simplify k into k 9.354 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 9.354 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 9.354 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 9.354 * [taylor]: Taking taylor expansion of 1.0 in n 9.354 * [backup-simplify]: Simplify 1.0 into 1.0 9.354 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 9.354 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 9.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.354 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 9.354 * [taylor]: Taking taylor expansion of 0.5 in n 9.354 * [backup-simplify]: Simplify 0.5 into 0.5 9.354 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.354 * [taylor]: Taking taylor expansion of 1.0 in n 9.354 * [backup-simplify]: Simplify 1.0 into 1.0 9.354 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.354 * [taylor]: Taking taylor expansion of k in n 9.354 * [backup-simplify]: Simplify k into k 9.354 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.354 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.354 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.354 * [taylor]: Taking taylor expansion of 2.0 in n 9.354 * [backup-simplify]: Simplify 2.0 into 2.0 9.354 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.354 * [taylor]: Taking taylor expansion of PI in n 9.354 * [backup-simplify]: Simplify PI into PI 9.354 * [taylor]: Taking taylor expansion of n in n 9.354 * [backup-simplify]: Simplify 0 into 0 9.354 * [backup-simplify]: Simplify 1 into 1 9.354 * [backup-simplify]: Simplify (/ PI 1) into PI 9.355 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.355 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.356 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.356 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.356 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 9.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.358 * [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)))) 9.358 * [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))))) 9.358 * [taylor]: Taking taylor expansion of (sqrt k) in n 9.358 * [taylor]: Taking taylor expansion of k in n 9.358 * [backup-simplify]: Simplify k into k 9.358 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 9.358 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 9.360 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) 9.360 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) 9.360 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k 9.360 * [taylor]: Taking taylor expansion of 1.0 in k 9.360 * [backup-simplify]: Simplify 1.0 into 1.0 9.360 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k 9.360 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 9.361 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 9.361 * [taylor]: Taking taylor expansion of 0.5 in k 9.361 * [backup-simplify]: Simplify 0.5 into 0.5 9.361 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 9.361 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.361 * [taylor]: Taking taylor expansion of 1.0 in k 9.361 * [backup-simplify]: Simplify 1.0 into 1.0 9.361 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.361 * [taylor]: Taking taylor expansion of k in k 9.361 * [backup-simplify]: Simplify 0 into 0 9.361 * [backup-simplify]: Simplify 1 into 1 9.361 * [backup-simplify]: Simplify (/ 1 1) into 1 9.361 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.361 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.361 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.361 * [taylor]: Taking taylor expansion of 2.0 in k 9.361 * [backup-simplify]: Simplify 2.0 into 2.0 9.361 * [taylor]: Taking taylor expansion of PI in k 9.361 * [backup-simplify]: Simplify PI into PI 9.361 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.362 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.362 * [taylor]: Taking taylor expansion of (log n) in k 9.362 * [taylor]: Taking taylor expansion of n in k 9.362 * [backup-simplify]: Simplify n into n 9.362 * [backup-simplify]: Simplify (log n) into (log n) 9.362 * [backup-simplify]: Simplify (- 1) into -1 9.363 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.363 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.363 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.364 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.365 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 9.365 * [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))))) 9.365 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.365 * [taylor]: Taking taylor expansion of k in k 9.365 * [backup-simplify]: Simplify 0 into 0 9.366 * [backup-simplify]: Simplify 1 into 1 9.366 * [backup-simplify]: Simplify (sqrt 0) into 0 9.367 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.367 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0 9.368 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.368 * [backup-simplify]: Simplify 0 into 0 9.368 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.369 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.370 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.370 * [backup-simplify]: Simplify (- 0) into 0 9.370 * [backup-simplify]: Simplify (+ 0 0) into 0 9.371 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.372 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.374 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0 9.375 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0 9.375 * [taylor]: Taking taylor expansion of 0 in k 9.375 * [backup-simplify]: Simplify 0 into 0 9.375 * [backup-simplify]: Simplify 0 into 0 9.376 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 9.377 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 9.378 * [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))))))) 9.379 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 9.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.382 * [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 9.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.382 * [backup-simplify]: Simplify (- 0) into 0 9.382 * [backup-simplify]: Simplify (+ 0 0) into 0 9.383 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.385 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.386 * [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 9.387 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 9.389 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0 9.389 * [taylor]: Taking taylor expansion of 0 in k 9.389 * [backup-simplify]: Simplify 0 into 0 9.389 * [backup-simplify]: Simplify 0 into 0 9.389 * [backup-simplify]: Simplify 0 into 0 9.390 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.392 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 9.393 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 9.394 * [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))))))) 9.395 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 9.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.396 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.402 * [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 9.402 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.403 * [backup-simplify]: Simplify (- 0) into 0 9.403 * [backup-simplify]: Simplify (+ 0 0) into 0 9.404 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.406 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.408 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.411 * [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 9.413 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 9.415 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0 9.415 * [taylor]: Taking taylor expansion of 0 in k 9.415 * [backup-simplify]: Simplify 0 into 0 9.415 * [backup-simplify]: Simplify 0 into 0 9.415 * [backup-simplify]: Simplify 0 into 0 9.415 * [backup-simplify]: Simplify 0 into 0 9.419 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.422 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 9.426 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 9.428 * [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))))))) 9.432 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 9.433 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) (/ 1.0 (sqrt (/ 1 (- k))))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 9.433 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0 9.433 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 9.434 * [taylor]: Taking taylor expansion of 1.0 in k 9.434 * [backup-simplify]: Simplify 1.0 into 1.0 9.434 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 9.434 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 9.434 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.434 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.434 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 9.434 * [taylor]: Taking taylor expansion of 0.5 in k 9.434 * [backup-simplify]: Simplify 0.5 into 0.5 9.434 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.434 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.434 * [taylor]: Taking taylor expansion of k in k 9.434 * [backup-simplify]: Simplify 0 into 0 9.434 * [backup-simplify]: Simplify 1 into 1 9.434 * [backup-simplify]: Simplify (/ 1 1) into 1 9.434 * [taylor]: Taking taylor expansion of 1.0 in k 9.434 * [backup-simplify]: Simplify 1.0 into 1.0 9.434 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.434 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.434 * [taylor]: Taking taylor expansion of -2.0 in k 9.435 * [backup-simplify]: Simplify -2.0 into -2.0 9.435 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.435 * [taylor]: Taking taylor expansion of PI in k 9.435 * [backup-simplify]: Simplify PI into PI 9.435 * [taylor]: Taking taylor expansion of n in k 9.435 * [backup-simplify]: Simplify n into n 9.435 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.435 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.435 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.435 * [backup-simplify]: Simplify (+ 1 0) into 1 9.436 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 9.436 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 9.436 * [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)))) 9.436 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.436 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.436 * [taylor]: Taking taylor expansion of -1 in k 9.436 * [backup-simplify]: Simplify -1 into -1 9.436 * [taylor]: Taking taylor expansion of k in k 9.436 * [backup-simplify]: Simplify 0 into 0 9.436 * [backup-simplify]: Simplify 1 into 1 9.437 * [backup-simplify]: Simplify (/ -1 1) into -1 9.437 * [backup-simplify]: Simplify (sqrt 0) into 0 9.439 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.439 * [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))))) 9.439 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 9.439 * [taylor]: Taking taylor expansion of 1.0 in n 9.439 * [backup-simplify]: Simplify 1.0 into 1.0 9.439 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 9.439 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 9.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.439 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.439 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 9.439 * [taylor]: Taking taylor expansion of 0.5 in n 9.439 * [backup-simplify]: Simplify 0.5 into 0.5 9.439 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.439 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.439 * [taylor]: Taking taylor expansion of k in n 9.439 * [backup-simplify]: Simplify k into k 9.439 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.439 * [taylor]: Taking taylor expansion of 1.0 in n 9.439 * [backup-simplify]: Simplify 1.0 into 1.0 9.439 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.439 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.439 * [taylor]: Taking taylor expansion of -2.0 in n 9.440 * [backup-simplify]: Simplify -2.0 into -2.0 9.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.440 * [taylor]: Taking taylor expansion of PI in n 9.440 * [backup-simplify]: Simplify PI into PI 9.440 * [taylor]: Taking taylor expansion of n in n 9.440 * [backup-simplify]: Simplify 0 into 0 9.440 * [backup-simplify]: Simplify 1 into 1 9.440 * [backup-simplify]: Simplify (/ PI 1) into PI 9.441 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.442 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.442 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.442 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 9.443 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.449 * [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))) 9.451 * [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)))) 9.451 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 9.451 * [taylor]: Taking taylor expansion of (/ -1 k) in n 9.451 * [taylor]: Taking taylor expansion of -1 in n 9.451 * [backup-simplify]: Simplify -1 into -1 9.451 * [taylor]: Taking taylor expansion of k in n 9.451 * [backup-simplify]: Simplify k into k 9.451 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 9.452 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 9.452 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 9.452 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 9.453 * [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))) 9.453 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 9.453 * [taylor]: Taking taylor expansion of 1.0 in n 9.453 * [backup-simplify]: Simplify 1.0 into 1.0 9.453 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 9.453 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 9.453 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.453 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.453 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 9.453 * [taylor]: Taking taylor expansion of 0.5 in n 9.454 * [backup-simplify]: Simplify 0.5 into 0.5 9.454 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.454 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.454 * [taylor]: Taking taylor expansion of k in n 9.454 * [backup-simplify]: Simplify k into k 9.454 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.454 * [taylor]: Taking taylor expansion of 1.0 in n 9.454 * [backup-simplify]: Simplify 1.0 into 1.0 9.454 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.454 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.454 * [taylor]: Taking taylor expansion of -2.0 in n 9.454 * [backup-simplify]: Simplify -2.0 into -2.0 9.454 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.454 * [taylor]: Taking taylor expansion of PI in n 9.454 * [backup-simplify]: Simplify PI into PI 9.454 * [taylor]: Taking taylor expansion of n in n 9.454 * [backup-simplify]: Simplify 0 into 0 9.454 * [backup-simplify]: Simplify 1 into 1 9.455 * [backup-simplify]: Simplify (/ PI 1) into PI 9.455 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.456 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.457 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.457 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 9.458 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.459 * [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))) 9.461 * [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)))) 9.461 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 9.461 * [taylor]: Taking taylor expansion of (/ -1 k) in n 9.461 * [taylor]: Taking taylor expansion of -1 in n 9.461 * [backup-simplify]: Simplify -1 into -1 9.461 * [taylor]: Taking taylor expansion of k in n 9.461 * [backup-simplify]: Simplify k into k 9.461 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 9.461 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 9.461 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 9.462 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 9.463 * [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))) 9.464 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) 9.465 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k 9.465 * [taylor]: Taking taylor expansion of 1.0 in k 9.465 * [backup-simplify]: Simplify 1.0 into 1.0 9.465 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k 9.465 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 9.465 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 9.465 * [taylor]: Taking taylor expansion of 0.5 in k 9.465 * [backup-simplify]: Simplify 0.5 into 0.5 9.465 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 9.465 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.465 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.465 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.465 * [taylor]: Taking taylor expansion of -2.0 in k 9.465 * [backup-simplify]: Simplify -2.0 into -2.0 9.465 * [taylor]: Taking taylor expansion of PI in k 9.465 * [backup-simplify]: Simplify PI into PI 9.466 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.467 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.467 * [taylor]: Taking taylor expansion of (log n) in k 9.467 * [taylor]: Taking taylor expansion of n in k 9.467 * [backup-simplify]: Simplify n into n 9.467 * [backup-simplify]: Simplify (log n) into (log n) 9.467 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.467 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.467 * [taylor]: Taking taylor expansion of k in k 9.467 * [backup-simplify]: Simplify 0 into 0 9.467 * [backup-simplify]: Simplify 1 into 1 9.468 * [backup-simplify]: Simplify (/ 1 1) into 1 9.468 * [taylor]: Taking taylor expansion of 1.0 in k 9.468 * [backup-simplify]: Simplify 1.0 into 1.0 9.468 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.469 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.469 * [backup-simplify]: Simplify (+ 1 0) into 1 9.470 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 9.471 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 9.473 * [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)))) 9.473 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.473 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.473 * [taylor]: Taking taylor expansion of -1 in k 9.473 * [backup-simplify]: Simplify -1 into -1 9.473 * [taylor]: Taking taylor expansion of k in k 9.473 * [backup-simplify]: Simplify 0 into 0 9.473 * [backup-simplify]: Simplify 1 into 1 9.473 * [backup-simplify]: Simplify (/ -1 1) into -1 9.474 * [backup-simplify]: Simplify (sqrt 0) into 0 9.475 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.477 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 9.479 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 9.480 * [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))))) 9.481 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.482 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.484 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.484 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.485 * [backup-simplify]: Simplify (+ 0 0) into 0 9.485 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.488 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.490 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.492 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 9.494 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0 9.494 * [taylor]: Taking taylor expansion of 0 in k 9.494 * [backup-simplify]: Simplify 0 into 0 9.494 * [backup-simplify]: Simplify 0 into 0 9.495 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.498 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.500 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 9.502 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 9.504 * [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)))))) 9.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.506 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.510 * [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 9.510 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.511 * [backup-simplify]: Simplify (+ 0 0) into 0 9.512 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.514 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.515 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.518 * [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 9.518 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.519 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 9.520 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 9.522 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0 9.522 * [taylor]: Taking taylor expansion of 0 in k 9.522 * [backup-simplify]: Simplify 0 into 0 9.522 * [backup-simplify]: Simplify 0 into 0 9.522 * [backup-simplify]: Simplify 0 into 0 9.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.525 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.527 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 9.529 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 9.530 * [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)))))) 9.533 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 9.533 * * * [progress]: simplifying candidates 9.535 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 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(* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +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 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 9.539 * * [simplify]: iteration 0: 343 enodes 9.680 * * [simplify]: iteration 1: 952 enodes 10.241 * * [simplify]: iteration 2: 3248 enodes 11.635 * * [simplify]: iteration complete: 5006 enodes 11.635 * * [simplify]: Extracting #0: cost 127 inf + 0 11.638 * * [simplify]: Extracting #1: cost 649 inf + 43 11.645 * * [simplify]: Extracting #2: cost 1087 inf + 2170 11.664 * * [simplify]: Extracting #3: cost 1035 inf + 42202 11.724 * * [simplify]: Extracting #4: cost 602 inf + 189427 11.801 * * [simplify]: Extracting #5: cost 235 inf + 374211 11.966 * * [simplify]: Extracting #6: cost 64 inf + 464767 12.190 * * [simplify]: Extracting #7: cost 4 inf + 494921 12.374 * * [simplify]: Extracting #8: cost 0 inf + 498450 12.521 * * [simplify]: Extracting #9: cost 0 inf + 496270 12.727 * * [simplify]: Extracting #10: cost 0 inf + 495310 12.926 * * [simplify]: Extracting #11: cost 0 inf + 495080 13.051 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* (* PI 2.0) n))) (* (/ (- 1.0 k) 2.0) (log (* (* PI 2.0) n))) (* (/ (- 1.0 k) 2.0) (log (* (* PI 2.0) n))) (* (/ (- 1.0 k) 2.0) (log (* (* PI 2.0) n))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (pow (* (* PI 2.0) n) (/ k 2.0)) (pow (* (* PI 2.0) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* PI 2.0) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* PI 2.0) n) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow (* (* PI 2.0) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* PI 2.0) n) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* PI 2.0) n) (sqrt (- 1.0 k))) (pow (* (* PI 2.0) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ 1 (sqrt 2.0))) (* (* PI 2.0) n) (pow (* (* PI 2.0) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI 2.0) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* PI 2.0) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI 2.0) n) (/ 1 (sqrt 2.0))) (* (* PI 2.0) n) (* (* PI 2.0) n) (pow (* (* PI 2.0) n) (- 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 2.0) n))) (exp (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0))) (expm1 (* (* PI 2.0) n)) (log1p (* (* PI 2.0) n)) (* (* PI 2.0) n) (* (* PI 2.0) n) (log (* (* PI 2.0) n)) (log (* (* PI 2.0) n)) (log (* (* PI 2.0) n)) (exp (* (* PI 2.0) n)) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* (* PI 2.0) n)) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* (* PI 2.0) n)) (* (cbrt (* (* PI 2.0) n)) (cbrt (* (* PI 2.0) n))) (cbrt (* (* PI 2.0) n)) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* (* PI 2.0) n)) (sqrt (* (* PI 2.0) n)) (sqrt (* (* PI 2.0) n)) (* (* (cbrt n) (cbrt n)) (* PI 2.0)) (* (* PI 2.0) (sqrt n)) (* PI 2.0) (* n PI) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) 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) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (log1p (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (fma (log (* (* PI 2.0) n)) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k)))) (exp (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (/ (* 1.0 1.0) k)))) (* (* (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (cbrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* PI 2.0) n) (/ k 2.0))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (cbrt (/ 1.0 (sqrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))) (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt (sqrt k)) (* (cbrt 1.0) (cbrt 1.0)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* (cbrt 1.0) (cbrt 1.0))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt (sqrt k)) (* (cbrt 1.0) (cbrt 1.0)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* (cbrt 1.0) (cbrt 1.0))) (* (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (fabs (cbrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (fabs (cbrt k))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (* 1.0 (pow n (/ (- 1.0 k) 2.0))) (sqrt k)) (* (/ 1.0 (sqrt k)) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) 1.0) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (/ (pow (* (* PI 2.0) n) (* 1/2 (/ (- 1.0 k) 2.0))) (/ (sqrt k) 1.0)) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (fma (* 0.25 (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (log (* PI 2.0)))) (* (log n) (* k k)) (- (fma (* (* (* (log (* PI 2.0)) k) (* (log (* PI 2.0)) k)) (exp (* (log (* (* PI 2.0) n)) 0.5))) 0.125 (fma (* 0.125 (* (* (log n) k) (* (log n) k))) (exp (* (log (* (* PI 2.0) n)) 0.5)) (exp (* (log (* (* PI 2.0) n)) 0.5)))) (* 0.5 (* k (fma (exp (* (log (* (* PI 2.0) n)) 0.5)) (log n) (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (log (* PI 2.0)))))))) (exp (* (* 0.5 (- 1.0 k)) (log (* (* PI 2.0) n)))) (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (* (* PI 2.0) n) (* (* PI 2.0) n) (* (* PI 2.0) n) (fma (* k k) (- +nan.0) (- +nan.0 (* k +nan.0))) (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) (/ +nan.0 (* k (* k k))))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0)) (fma (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (* (* (log n) (* k k)) (log (* PI 2.0)))) (- +nan.0) (- (* +nan.0 (exp (* (log (* (* PI 2.0) n)) 0.5))) (fma (* +nan.0 (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (* k k))) (* (log (* PI 2.0)) (log (* PI 2.0))) (fma (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (- +nan.0)) (* k k) (fma (* +nan.0 (exp (* (log (* (* PI 2.0) n)) 0.5))) (* (* (log n) k) (* (log n) k)) (fma (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (- +nan.0)) (* (log n) (* k k)) (fma (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (* (log n) k)) (- +nan.0) (fma (* (exp (* (log (* (* PI 2.0) n)) 0.5)) k) (fma (log (* PI 2.0)) +nan.0 (- +nan.0)) (* (* +nan.0 (* (exp (* (log (* (* PI 2.0) n)) 0.5)) (* k k))) (log (* PI 2.0))))))))))) (fma (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* PI 2.0) n)))) (* k k)) (- +nan.0) (- (/ +nan.0 (/ k (exp (* (* 0.5 (- 1.0 k)) (log (* (* PI 2.0) n)))))) (* +nan.0 (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* PI 2.0) n)))) (* k (* k k)))))) (fma (- (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))) +nan.0 (* +nan.0 (+ (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) k) (/ (- (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))) (* k k))))) 13.071 * * * [progress]: adding candidates to table 14.104 * * [progress]: iteration 3 / 4 14.104 * * * [progress]: picking best candidate 14.167 * * * * [pick]: Picked # 14.167 * * * [progress]: localizing error 14.207 * * * [progress]: generating rewritten candidates 14.208 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 14.228 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 14.248 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 14.257 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 14.301 * * * [progress]: generating series expansions 14.301 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 14.302 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 14.302 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 14.302 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.302 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.302 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.302 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.302 * [taylor]: Taking taylor expansion of 0.5 in k 14.302 * [backup-simplify]: Simplify 0.5 into 0.5 14.302 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.302 * [taylor]: Taking taylor expansion of 1.0 in k 14.302 * [backup-simplify]: Simplify 1.0 into 1.0 14.302 * [taylor]: Taking taylor expansion of k in k 14.302 * [backup-simplify]: Simplify 0 into 0 14.302 * [backup-simplify]: Simplify 1 into 1 14.302 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.302 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.302 * [taylor]: Taking taylor expansion of 2.0 in k 14.302 * [backup-simplify]: Simplify 2.0 into 2.0 14.302 * [taylor]: Taking taylor expansion of (* n PI) in k 14.302 * [taylor]: Taking taylor expansion of n in k 14.302 * [backup-simplify]: Simplify n into n 14.302 * [taylor]: Taking taylor expansion of PI in k 14.302 * [backup-simplify]: Simplify PI into PI 14.302 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.302 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.302 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.303 * [backup-simplify]: Simplify (- 0) into 0 14.303 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.303 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.303 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.303 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.303 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.303 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.303 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.303 * [taylor]: Taking taylor expansion of 0.5 in n 14.304 * [backup-simplify]: Simplify 0.5 into 0.5 14.304 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.304 * [taylor]: Taking taylor expansion of 1.0 in n 14.304 * [backup-simplify]: Simplify 1.0 into 1.0 14.304 * [taylor]: Taking taylor expansion of k in n 14.304 * [backup-simplify]: Simplify k into k 14.304 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.304 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.304 * [taylor]: Taking taylor expansion of 2.0 in n 14.304 * [backup-simplify]: Simplify 2.0 into 2.0 14.304 * [taylor]: Taking taylor expansion of (* n PI) in n 14.304 * [taylor]: Taking taylor expansion of n in n 14.304 * [backup-simplify]: Simplify 0 into 0 14.304 * [backup-simplify]: Simplify 1 into 1 14.304 * [taylor]: Taking taylor expansion of PI in n 14.304 * [backup-simplify]: Simplify PI into PI 14.304 * [backup-simplify]: Simplify (* 0 PI) into 0 14.305 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.306 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.308 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.309 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.309 * [backup-simplify]: Simplify (- k) into (- k) 14.309 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.309 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.310 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.310 * [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)))) 14.311 * [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))))) 14.311 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.311 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.311 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.311 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.311 * [taylor]: Taking taylor expansion of 0.5 in n 14.311 * [backup-simplify]: Simplify 0.5 into 0.5 14.311 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.311 * [taylor]: Taking taylor expansion of 1.0 in n 14.311 * [backup-simplify]: Simplify 1.0 into 1.0 14.311 * [taylor]: Taking taylor expansion of k in n 14.311 * [backup-simplify]: Simplify k into k 14.311 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.311 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.311 * [taylor]: Taking taylor expansion of 2.0 in n 14.311 * [backup-simplify]: Simplify 2.0 into 2.0 14.311 * [taylor]: Taking taylor expansion of (* n PI) in n 14.311 * [taylor]: Taking taylor expansion of n in n 14.311 * [backup-simplify]: Simplify 0 into 0 14.311 * [backup-simplify]: Simplify 1 into 1 14.311 * [taylor]: Taking taylor expansion of PI in n 14.311 * [backup-simplify]: Simplify PI into PI 14.312 * [backup-simplify]: Simplify (* 0 PI) into 0 14.312 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.313 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.314 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.315 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.315 * [backup-simplify]: Simplify (- k) into (- k) 14.315 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.315 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.316 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.316 * [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)))) 14.317 * [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))))) 14.317 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 14.317 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 14.317 * [taylor]: Taking taylor expansion of 0.5 in k 14.317 * [backup-simplify]: Simplify 0.5 into 0.5 14.317 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 14.317 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.317 * [taylor]: Taking taylor expansion of 1.0 in k 14.317 * [backup-simplify]: Simplify 1.0 into 1.0 14.317 * [taylor]: Taking taylor expansion of k in k 14.317 * [backup-simplify]: Simplify 0 into 0 14.317 * [backup-simplify]: Simplify 1 into 1 14.317 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 14.317 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.317 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.317 * [taylor]: Taking taylor expansion of 2.0 in k 14.317 * [backup-simplify]: Simplify 2.0 into 2.0 14.317 * [taylor]: Taking taylor expansion of PI in k 14.317 * [backup-simplify]: Simplify PI into PI 14.318 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.318 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.318 * [taylor]: Taking taylor expansion of (log n) in k 14.318 * [taylor]: Taking taylor expansion of n in k 14.318 * [backup-simplify]: Simplify n into n 14.319 * [backup-simplify]: Simplify (log n) into (log n) 14.319 * [backup-simplify]: Simplify (- 0) into 0 14.319 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.323 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 14.324 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 14.324 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 14.325 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.326 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.326 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.327 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.328 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.328 * [backup-simplify]: Simplify (- 0) into 0 14.329 * [backup-simplify]: Simplify (+ 0 0) into 0 14.329 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 14.330 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.330 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 14.332 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.332 * [taylor]: Taking taylor expansion of 0 in k 14.332 * [backup-simplify]: Simplify 0 into 0 14.332 * [backup-simplify]: Simplify 0 into 0 14.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.333 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.334 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 14.334 * [backup-simplify]: Simplify (+ 0 0) into 0 14.334 * [backup-simplify]: Simplify (- 1) into -1 14.335 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.335 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 14.337 * [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)))) 14.339 * [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)))))) 14.342 * [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)))))) 14.343 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.344 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.348 * [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 14.348 * [backup-simplify]: Simplify (- 0) into 0 14.349 * [backup-simplify]: Simplify (+ 0 0) into 0 14.350 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 14.351 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.353 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.356 * [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 14.356 * [taylor]: Taking taylor expansion of 0 in k 14.356 * [backup-simplify]: Simplify 0 into 0 14.356 * [backup-simplify]: Simplify 0 into 0 14.356 * [backup-simplify]: Simplify 0 into 0 14.357 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.361 * [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 14.363 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 14.364 * [backup-simplify]: Simplify (+ 0 0) into 0 14.364 * [backup-simplify]: Simplify (- 0) into 0 14.365 * [backup-simplify]: Simplify (+ 0 0) into 0 14.367 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.369 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.374 * [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)))))) 14.380 * [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)))))) 14.391 * [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))))) 14.391 * [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)))) 14.392 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 14.392 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.392 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.392 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.392 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.392 * [taylor]: Taking taylor expansion of 0.5 in k 14.392 * [backup-simplify]: Simplify 0.5 into 0.5 14.392 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.392 * [taylor]: Taking taylor expansion of 1.0 in k 14.392 * [backup-simplify]: Simplify 1.0 into 1.0 14.392 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.392 * [taylor]: Taking taylor expansion of k in k 14.392 * [backup-simplify]: Simplify 0 into 0 14.392 * [backup-simplify]: Simplify 1 into 1 14.392 * [backup-simplify]: Simplify (/ 1 1) into 1 14.392 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.392 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.392 * [taylor]: Taking taylor expansion of 2.0 in k 14.393 * [backup-simplify]: Simplify 2.0 into 2.0 14.393 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.393 * [taylor]: Taking taylor expansion of PI in k 14.393 * [backup-simplify]: Simplify PI into PI 14.393 * [taylor]: Taking taylor expansion of n in k 14.393 * [backup-simplify]: Simplify n into n 14.393 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.393 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.393 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.393 * [backup-simplify]: Simplify (- 1) into -1 14.394 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.394 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.394 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.395 * [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)))))) 14.395 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.395 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.395 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.395 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.395 * [taylor]: Taking taylor expansion of 0.5 in n 14.395 * [backup-simplify]: Simplify 0.5 into 0.5 14.395 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.395 * [taylor]: Taking taylor expansion of 1.0 in n 14.395 * [backup-simplify]: Simplify 1.0 into 1.0 14.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.395 * [taylor]: Taking taylor expansion of k in n 14.395 * [backup-simplify]: Simplify k into k 14.395 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.395 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.395 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.395 * [taylor]: Taking taylor expansion of 2.0 in n 14.395 * [backup-simplify]: Simplify 2.0 into 2.0 14.395 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.395 * [taylor]: Taking taylor expansion of PI in n 14.395 * [backup-simplify]: Simplify PI into PI 14.395 * [taylor]: Taking taylor expansion of n in n 14.395 * [backup-simplify]: Simplify 0 into 0 14.395 * [backup-simplify]: Simplify 1 into 1 14.396 * [backup-simplify]: Simplify (/ PI 1) into PI 14.396 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.398 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.398 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.398 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.398 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.399 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.401 * [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)))) 14.402 * [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))))) 14.402 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.402 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.402 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.402 * [taylor]: Taking taylor expansion of 0.5 in n 14.403 * [backup-simplify]: Simplify 0.5 into 0.5 14.403 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.403 * [taylor]: Taking taylor expansion of 1.0 in n 14.403 * [backup-simplify]: Simplify 1.0 into 1.0 14.403 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.403 * [taylor]: Taking taylor expansion of k in n 14.403 * [backup-simplify]: Simplify k into k 14.403 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.403 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.403 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.403 * [taylor]: Taking taylor expansion of 2.0 in n 14.403 * [backup-simplify]: Simplify 2.0 into 2.0 14.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.403 * [taylor]: Taking taylor expansion of PI in n 14.403 * [backup-simplify]: Simplify PI into PI 14.403 * [taylor]: Taking taylor expansion of n in n 14.403 * [backup-simplify]: Simplify 0 into 0 14.403 * [backup-simplify]: Simplify 1 into 1 14.404 * [backup-simplify]: Simplify (/ PI 1) into PI 14.404 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.405 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.405 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.405 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.406 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.408 * [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)))) 14.410 * [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))))) 14.410 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 14.410 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 14.410 * [taylor]: Taking taylor expansion of 0.5 in k 14.410 * [backup-simplify]: Simplify 0.5 into 0.5 14.410 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 14.410 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.410 * [taylor]: Taking taylor expansion of 1.0 in k 14.410 * [backup-simplify]: Simplify 1.0 into 1.0 14.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.410 * [taylor]: Taking taylor expansion of k in k 14.410 * [backup-simplify]: Simplify 0 into 0 14.410 * [backup-simplify]: Simplify 1 into 1 14.410 * [backup-simplify]: Simplify (/ 1 1) into 1 14.411 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 14.411 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.411 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.411 * [taylor]: Taking taylor expansion of 2.0 in k 14.411 * [backup-simplify]: Simplify 2.0 into 2.0 14.411 * [taylor]: Taking taylor expansion of PI in k 14.411 * [backup-simplify]: Simplify PI into PI 14.411 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.412 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.412 * [taylor]: Taking taylor expansion of (log n) in k 14.412 * [taylor]: Taking taylor expansion of n in k 14.412 * [backup-simplify]: Simplify n into n 14.413 * [backup-simplify]: Simplify (log n) into (log n) 14.413 * [backup-simplify]: Simplify (- 1) into -1 14.413 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.414 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.415 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 14.416 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 14.417 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 14.418 * [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))))) 14.420 * [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))))) 14.421 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.421 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.423 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.424 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.424 * [backup-simplify]: Simplify (- 0) into 0 14.424 * [backup-simplify]: Simplify (+ 0 0) into 0 14.425 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 14.426 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.428 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 14.430 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.430 * [taylor]: Taking taylor expansion of 0 in k 14.430 * [backup-simplify]: Simplify 0 into 0 14.430 * [backup-simplify]: Simplify 0 into 0 14.430 * [backup-simplify]: Simplify 0 into 0 14.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.436 * [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 14.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.437 * [backup-simplify]: Simplify (- 0) into 0 14.437 * [backup-simplify]: Simplify (+ 0 0) into 0 14.438 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 14.440 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.441 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 14.444 * [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 14.444 * [taylor]: Taking taylor expansion of 0 in k 14.444 * [backup-simplify]: Simplify 0 into 0 14.444 * [backup-simplify]: Simplify 0 into 0 14.444 * [backup-simplify]: Simplify 0 into 0 14.444 * [backup-simplify]: Simplify 0 into 0 14.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.454 * [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 14.454 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.455 * [backup-simplify]: Simplify (- 0) into 0 14.455 * [backup-simplify]: Simplify (+ 0 0) into 0 14.456 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 14.458 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.460 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 14.469 * [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 14.469 * [taylor]: Taking taylor expansion of 0 in k 14.469 * [backup-simplify]: Simplify 0 into 0 14.469 * [backup-simplify]: Simplify 0 into 0 14.471 * [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)))))) 14.471 * [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))) 14.471 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 14.471 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 14.471 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 14.472 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 14.472 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 14.472 * [taylor]: Taking taylor expansion of 0.5 in k 14.472 * [backup-simplify]: Simplify 0.5 into 0.5 14.472 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.472 * [taylor]: Taking taylor expansion of k in k 14.472 * [backup-simplify]: Simplify 0 into 0 14.472 * [backup-simplify]: Simplify 1 into 1 14.472 * [backup-simplify]: Simplify (/ 1 1) into 1 14.472 * [taylor]: Taking taylor expansion of 1.0 in k 14.472 * [backup-simplify]: Simplify 1.0 into 1.0 14.472 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 14.472 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 14.472 * [taylor]: Taking taylor expansion of -2.0 in k 14.472 * [backup-simplify]: Simplify -2.0 into -2.0 14.472 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.472 * [taylor]: Taking taylor expansion of PI in k 14.472 * [backup-simplify]: Simplify PI into PI 14.472 * [taylor]: Taking taylor expansion of n in k 14.473 * [backup-simplify]: Simplify n into n 14.473 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.473 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 14.473 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 14.473 * [backup-simplify]: Simplify (+ 1 0) into 1 14.474 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 14.474 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 14.474 * [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)))) 14.474 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.474 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.474 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.474 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.474 * [taylor]: Taking taylor expansion of 0.5 in n 14.474 * [backup-simplify]: Simplify 0.5 into 0.5 14.474 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.474 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.474 * [taylor]: Taking taylor expansion of k in n 14.474 * [backup-simplify]: Simplify k into k 14.475 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.475 * [taylor]: Taking taylor expansion of 1.0 in n 14.475 * [backup-simplify]: Simplify 1.0 into 1.0 14.475 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.475 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.475 * [taylor]: Taking taylor expansion of -2.0 in n 14.475 * [backup-simplify]: Simplify -2.0 into -2.0 14.475 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.475 * [taylor]: Taking taylor expansion of PI in n 14.475 * [backup-simplify]: Simplify PI into PI 14.475 * [taylor]: Taking taylor expansion of n in n 14.475 * [backup-simplify]: Simplify 0 into 0 14.475 * [backup-simplify]: Simplify 1 into 1 14.475 * [backup-simplify]: Simplify (/ PI 1) into PI 14.476 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.477 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.477 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.477 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.481 * [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))) 14.482 * [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)))) 14.482 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.482 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.482 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.482 * [taylor]: Taking taylor expansion of 0.5 in n 14.482 * [backup-simplify]: Simplify 0.5 into 0.5 14.482 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.482 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.482 * [taylor]: Taking taylor expansion of k in n 14.482 * [backup-simplify]: Simplify k into k 14.482 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.482 * [taylor]: Taking taylor expansion of 1.0 in n 14.482 * [backup-simplify]: Simplify 1.0 into 1.0 14.482 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.482 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.483 * [taylor]: Taking taylor expansion of -2.0 in n 14.483 * [backup-simplify]: Simplify -2.0 into -2.0 14.483 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.483 * [taylor]: Taking taylor expansion of PI in n 14.483 * [backup-simplify]: Simplify PI into PI 14.483 * [taylor]: Taking taylor expansion of n in n 14.483 * [backup-simplify]: Simplify 0 into 0 14.483 * [backup-simplify]: Simplify 1 into 1 14.483 * [backup-simplify]: Simplify (/ PI 1) into PI 14.484 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.485 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.485 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.485 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.488 * [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))) 14.489 * [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)))) 14.489 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 14.489 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 14.489 * [taylor]: Taking taylor expansion of 0.5 in k 14.489 * [backup-simplify]: Simplify 0.5 into 0.5 14.489 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 14.489 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 14.489 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 14.489 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 14.489 * [taylor]: Taking taylor expansion of -2.0 in k 14.489 * [backup-simplify]: Simplify -2.0 into -2.0 14.489 * [taylor]: Taking taylor expansion of PI in k 14.489 * [backup-simplify]: Simplify PI into PI 14.490 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.491 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.491 * [taylor]: Taking taylor expansion of (log n) in k 14.491 * [taylor]: Taking taylor expansion of n in k 14.491 * [backup-simplify]: Simplify n into n 14.491 * [backup-simplify]: Simplify (log n) into (log n) 14.491 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.491 * [taylor]: Taking taylor expansion of k in k 14.491 * [backup-simplify]: Simplify 0 into 0 14.491 * [backup-simplify]: Simplify 1 into 1 14.491 * [backup-simplify]: Simplify (/ 1 1) into 1 14.491 * [taylor]: Taking taylor expansion of 1.0 in k 14.491 * [backup-simplify]: Simplify 1.0 into 1.0 14.492 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.493 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 14.493 * [backup-simplify]: Simplify (+ 1 0) into 1 14.494 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 14.495 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 14.496 * [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)))) 14.498 * [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)))) 14.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.499 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.501 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 14.501 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.502 * [backup-simplify]: Simplify (+ 0 0) into 0 14.503 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 14.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.505 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 14.507 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 14.507 * [taylor]: Taking taylor expansion of 0 in k 14.507 * [backup-simplify]: Simplify 0 into 0 14.507 * [backup-simplify]: Simplify 0 into 0 14.507 * [backup-simplify]: Simplify 0 into 0 14.508 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.509 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.513 * [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 14.513 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.514 * [backup-simplify]: Simplify (+ 0 0) into 0 14.514 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 14.516 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.517 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 14.520 * [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 14.520 * [taylor]: Taking taylor expansion of 0 in k 14.520 * [backup-simplify]: Simplify 0 into 0 14.520 * [backup-simplify]: Simplify 0 into 0 14.520 * [backup-simplify]: Simplify 0 into 0 14.520 * [backup-simplify]: Simplify 0 into 0 14.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.522 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.528 * [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 14.529 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.529 * [backup-simplify]: Simplify (+ 0 0) into 0 14.530 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 14.533 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.535 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 14.537 * [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 14.538 * [taylor]: Taking taylor expansion of 0 in k 14.538 * [backup-simplify]: Simplify 0 into 0 14.538 * [backup-simplify]: Simplify 0 into 0 14.539 * [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)))))) 14.539 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 14.540 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.540 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 14.540 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.540 * [taylor]: Taking taylor expansion of 2.0 in n 14.540 * [backup-simplify]: Simplify 2.0 into 2.0 14.540 * [taylor]: Taking taylor expansion of (* n PI) in n 14.540 * [taylor]: Taking taylor expansion of n in n 14.540 * [backup-simplify]: Simplify 0 into 0 14.540 * [backup-simplify]: Simplify 1 into 1 14.540 * [taylor]: Taking taylor expansion of PI in n 14.540 * [backup-simplify]: Simplify PI into PI 14.540 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.540 * [taylor]: Taking taylor expansion of 2.0 in n 14.540 * [backup-simplify]: Simplify 2.0 into 2.0 14.540 * [taylor]: Taking taylor expansion of (* n PI) in n 14.540 * [taylor]: Taking taylor expansion of n in n 14.540 * [backup-simplify]: Simplify 0 into 0 14.540 * [backup-simplify]: Simplify 1 into 1 14.540 * [taylor]: Taking taylor expansion of PI in n 14.540 * [backup-simplify]: Simplify PI into PI 14.541 * [backup-simplify]: Simplify (* 0 PI) into 0 14.541 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.542 * [backup-simplify]: Simplify 0 into 0 14.543 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.545 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.545 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.547 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.548 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.548 * [backup-simplify]: Simplify 0 into 0 14.549 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.550 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.550 * [backup-simplify]: Simplify 0 into 0 14.551 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.553 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 14.553 * [backup-simplify]: Simplify 0 into 0 14.554 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 14.556 * [backup-simplify]: Simplify 0 into 0 14.558 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.560 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 14.560 * [backup-simplify]: Simplify 0 into 0 14.562 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 14.564 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 14.564 * [backup-simplify]: Simplify 0 into 0 14.565 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 14.565 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 14.565 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 14.565 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.565 * [taylor]: Taking taylor expansion of 2.0 in n 14.565 * [backup-simplify]: Simplify 2.0 into 2.0 14.565 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.565 * [taylor]: Taking taylor expansion of PI in n 14.565 * [backup-simplify]: Simplify PI into PI 14.565 * [taylor]: Taking taylor expansion of n in n 14.566 * [backup-simplify]: Simplify 0 into 0 14.566 * [backup-simplify]: Simplify 1 into 1 14.566 * [backup-simplify]: Simplify (/ PI 1) into PI 14.566 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.566 * [taylor]: Taking taylor expansion of 2.0 in n 14.566 * [backup-simplify]: Simplify 2.0 into 2.0 14.566 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.566 * [taylor]: Taking taylor expansion of PI in n 14.566 * [backup-simplify]: Simplify PI into PI 14.566 * [taylor]: Taking taylor expansion of n in n 14.566 * [backup-simplify]: Simplify 0 into 0 14.566 * [backup-simplify]: Simplify 1 into 1 14.567 * [backup-simplify]: Simplify (/ PI 1) into PI 14.567 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.568 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.569 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.570 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.570 * [backup-simplify]: Simplify 0 into 0 14.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.572 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.572 * [backup-simplify]: Simplify 0 into 0 14.573 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.574 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.575 * [backup-simplify]: Simplify 0 into 0 14.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.577 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.577 * [backup-simplify]: Simplify 0 into 0 14.578 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.580 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.580 * [backup-simplify]: Simplify 0 into 0 14.581 * [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 14.583 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.583 * [backup-simplify]: Simplify 0 into 0 14.584 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 14.584 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 14.584 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 14.584 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.584 * [taylor]: Taking taylor expansion of -2.0 in n 14.584 * [backup-simplify]: Simplify -2.0 into -2.0 14.584 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.584 * [taylor]: Taking taylor expansion of PI in n 14.584 * [backup-simplify]: Simplify PI into PI 14.585 * [taylor]: Taking taylor expansion of n in n 14.585 * [backup-simplify]: Simplify 0 into 0 14.585 * [backup-simplify]: Simplify 1 into 1 14.585 * [backup-simplify]: Simplify (/ PI 1) into PI 14.585 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.585 * [taylor]: Taking taylor expansion of -2.0 in n 14.585 * [backup-simplify]: Simplify -2.0 into -2.0 14.585 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.585 * [taylor]: Taking taylor expansion of PI in n 14.585 * [backup-simplify]: Simplify PI into PI 14.585 * [taylor]: Taking taylor expansion of n in n 14.585 * [backup-simplify]: Simplify 0 into 0 14.585 * [backup-simplify]: Simplify 1 into 1 14.586 * [backup-simplify]: Simplify (/ PI 1) into PI 14.586 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.587 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.589 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.589 * [backup-simplify]: Simplify 0 into 0 14.590 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.591 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.591 * [backup-simplify]: Simplify 0 into 0 14.592 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.594 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.594 * [backup-simplify]: Simplify 0 into 0 14.595 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.596 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.596 * [backup-simplify]: Simplify 0 into 0 14.597 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.599 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.599 * [backup-simplify]: Simplify 0 into 0 14.600 * [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 14.602 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.602 * [backup-simplify]: Simplify 0 into 0 14.603 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 14.603 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 14.603 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 14.603 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 14.603 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.603 * [taylor]: Taking taylor expansion of 1.0 in k 14.603 * [backup-simplify]: Simplify 1.0 into 1.0 14.603 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.603 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.603 * [taylor]: Taking taylor expansion of k in k 14.603 * [backup-simplify]: Simplify 0 into 0 14.603 * [backup-simplify]: Simplify 1 into 1 14.604 * [backup-simplify]: Simplify (/ 1 1) into 1 14.604 * [backup-simplify]: Simplify (sqrt 0) into 0 14.605 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.606 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.606 * [taylor]: Taking taylor expansion of 1.0 in k 14.606 * [backup-simplify]: Simplify 1.0 into 1.0 14.606 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.606 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.606 * [taylor]: Taking taylor expansion of k in k 14.606 * [backup-simplify]: Simplify 0 into 0 14.606 * [backup-simplify]: Simplify 1 into 1 14.606 * [backup-simplify]: Simplify (/ 1 1) into 1 14.606 * [backup-simplify]: Simplify (sqrt 0) into 0 14.608 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.608 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.608 * [backup-simplify]: Simplify 0 into 0 14.610 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.610 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.611 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.614 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.616 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.616 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.617 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.627 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.628 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.628 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.629 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 14.629 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 14.629 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 14.629 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.629 * [taylor]: Taking taylor expansion of 1.0 in k 14.629 * [backup-simplify]: Simplify 1.0 into 1.0 14.629 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.629 * [taylor]: Taking taylor expansion of k in k 14.629 * [backup-simplify]: Simplify 0 into 0 14.629 * [backup-simplify]: Simplify 1 into 1 14.630 * [backup-simplify]: Simplify (sqrt 0) into 0 14.630 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.631 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.631 * [taylor]: Taking taylor expansion of 1.0 in k 14.631 * [backup-simplify]: Simplify 1.0 into 1.0 14.631 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.631 * [taylor]: Taking taylor expansion of k in k 14.631 * [backup-simplify]: Simplify 0 into 0 14.631 * [backup-simplify]: Simplify 1 into 1 14.631 * [backup-simplify]: Simplify (sqrt 0) into 0 14.632 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.632 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.632 * [backup-simplify]: Simplify 0 into 0 14.633 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.633 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.635 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.636 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.636 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.639 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.640 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.640 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.641 * [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)))))))) 14.641 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 14.641 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 14.641 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.641 * [taylor]: Taking taylor expansion of 1.0 in k 14.641 * [backup-simplify]: Simplify 1.0 into 1.0 14.641 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.641 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.641 * [taylor]: Taking taylor expansion of -1 in k 14.641 * [backup-simplify]: Simplify -1 into -1 14.642 * [taylor]: Taking taylor expansion of k in k 14.642 * [backup-simplify]: Simplify 0 into 0 14.642 * [backup-simplify]: Simplify 1 into 1 14.642 * [backup-simplify]: Simplify (/ -1 1) into -1 14.642 * [backup-simplify]: Simplify (sqrt 0) into 0 14.643 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.643 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.643 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.643 * [taylor]: Taking taylor expansion of 1.0 in k 14.643 * [backup-simplify]: Simplify 1.0 into 1.0 14.643 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.643 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.643 * [taylor]: Taking taylor expansion of -1 in k 14.643 * [backup-simplify]: Simplify -1 into -1 14.643 * [taylor]: Taking taylor expansion of k in k 14.643 * [backup-simplify]: Simplify 0 into 0 14.643 * [backup-simplify]: Simplify 1 into 1 14.644 * [backup-simplify]: Simplify (/ -1 1) into -1 14.644 * [backup-simplify]: Simplify (sqrt 0) into 0 14.645 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.645 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.645 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.647 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.649 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.649 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.650 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.652 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.655 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.655 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.656 * [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))))) 14.656 * * * * [progress]: [ 4 / 4 ] generating series at (2) 14.656 * [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)))) 14.656 * [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 14.656 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 14.656 * [taylor]: Taking taylor expansion of 1.0 in n 14.656 * [backup-simplify]: Simplify 1.0 into 1.0 14.656 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 14.656 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.656 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.656 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.656 * [taylor]: Taking taylor expansion of 0.5 in n 14.656 * [backup-simplify]: Simplify 0.5 into 0.5 14.656 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.656 * [taylor]: Taking taylor expansion of 1.0 in n 14.656 * [backup-simplify]: Simplify 1.0 into 1.0 14.656 * [taylor]: Taking taylor expansion of k in n 14.656 * [backup-simplify]: Simplify k into k 14.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.656 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.656 * [taylor]: Taking taylor expansion of 2.0 in n 14.656 * [backup-simplify]: Simplify 2.0 into 2.0 14.656 * [taylor]: Taking taylor expansion of (* n PI) in n 14.656 * [taylor]: Taking taylor expansion of n in n 14.656 * [backup-simplify]: Simplify 0 into 0 14.657 * [backup-simplify]: Simplify 1 into 1 14.657 * [taylor]: Taking taylor expansion of PI in n 14.657 * [backup-simplify]: Simplify PI into PI 14.657 * [backup-simplify]: Simplify (* 0 PI) into 0 14.657 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.658 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.659 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.660 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.660 * [backup-simplify]: Simplify (- k) into (- k) 14.660 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.660 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.661 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.662 * [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)))) 14.664 * [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))))) 14.664 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 14.664 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.664 * [taylor]: Taking taylor expansion of k in n 14.664 * [backup-simplify]: Simplify k into k 14.664 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.664 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 14.664 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.664 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 14.664 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 14.664 * [taylor]: Taking taylor expansion of 1.0 in k 14.664 * [backup-simplify]: Simplify 1.0 into 1.0 14.664 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 14.664 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.664 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.664 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.664 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.664 * [taylor]: Taking taylor expansion of 0.5 in k 14.665 * [backup-simplify]: Simplify 0.5 into 0.5 14.665 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.665 * [taylor]: Taking taylor expansion of 1.0 in k 14.665 * [backup-simplify]: Simplify 1.0 into 1.0 14.665 * [taylor]: Taking taylor expansion of k in k 14.665 * [backup-simplify]: Simplify 0 into 0 14.665 * [backup-simplify]: Simplify 1 into 1 14.665 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.665 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.665 * [taylor]: Taking taylor expansion of 2.0 in k 14.665 * [backup-simplify]: Simplify 2.0 into 2.0 14.665 * [taylor]: Taking taylor expansion of (* n PI) in k 14.665 * [taylor]: Taking taylor expansion of n in k 14.665 * [backup-simplify]: Simplify n into n 14.665 * [taylor]: Taking taylor expansion of PI in k 14.665 * [backup-simplify]: Simplify PI into PI 14.665 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.665 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.665 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.666 * [backup-simplify]: Simplify (- 0) into 0 14.666 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.667 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.667 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.667 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.667 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.667 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.667 * [taylor]: Taking taylor expansion of k in k 14.667 * [backup-simplify]: Simplify 0 into 0 14.667 * [backup-simplify]: Simplify 1 into 1 14.667 * [backup-simplify]: Simplify (/ 1 1) into 1 14.668 * [backup-simplify]: Simplify (sqrt 0) into 0 14.669 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.669 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 14.669 * [taylor]: Taking taylor expansion of 1.0 in k 14.669 * [backup-simplify]: Simplify 1.0 into 1.0 14.669 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 14.669 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.669 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.670 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.670 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.670 * [taylor]: Taking taylor expansion of 0.5 in k 14.670 * [backup-simplify]: Simplify 0.5 into 0.5 14.670 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.670 * [taylor]: Taking taylor expansion of 1.0 in k 14.670 * [backup-simplify]: Simplify 1.0 into 1.0 14.670 * [taylor]: Taking taylor expansion of k in k 14.670 * [backup-simplify]: Simplify 0 into 0 14.670 * [backup-simplify]: Simplify 1 into 1 14.670 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.670 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.670 * [taylor]: Taking taylor expansion of 2.0 in k 14.670 * [backup-simplify]: Simplify 2.0 into 2.0 14.670 * [taylor]: Taking taylor expansion of (* n PI) in k 14.670 * [taylor]: Taking taylor expansion of n in k 14.670 * [backup-simplify]: Simplify n into n 14.670 * [taylor]: Taking taylor expansion of PI in k 14.670 * [backup-simplify]: Simplify PI into PI 14.670 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.670 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.670 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.671 * [backup-simplify]: Simplify (- 0) into 0 14.671 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.672 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.672 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.672 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.672 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.672 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.672 * [taylor]: Taking taylor expansion of k in k 14.672 * [backup-simplify]: Simplify 0 into 0 14.672 * [backup-simplify]: Simplify 1 into 1 14.672 * [backup-simplify]: Simplify (/ 1 1) into 1 14.673 * [backup-simplify]: Simplify (sqrt 0) into 0 14.674 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.675 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 14.675 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.675 * [taylor]: Taking taylor expansion of 0 in n 14.675 * [backup-simplify]: Simplify 0 into 0 14.675 * [backup-simplify]: Simplify 0 into 0 14.676 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 14.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 14.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 14.677 * [backup-simplify]: Simplify (- 1) into -1 14.678 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.679 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 14.680 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 14.681 * [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))))) 14.683 * [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))) 14.684 * [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))) 14.685 * [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 14.685 * [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 14.685 * [taylor]: Taking taylor expansion of +nan.0 in n 14.685 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.685 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 14.685 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 14.685 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 14.685 * [taylor]: Taking taylor expansion of 0.5 in n 14.685 * [backup-simplify]: Simplify 0.5 into 0.5 14.685 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 14.685 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 14.685 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 14.685 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 14.685 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 14.685 * [taylor]: Taking taylor expansion of 1.0 in n 14.685 * [backup-simplify]: Simplify 1.0 into 1.0 14.685 * [taylor]: Taking taylor expansion of (log PI) in n 14.685 * [taylor]: Taking taylor expansion of PI in n 14.685 * [backup-simplify]: Simplify PI into PI 14.686 * [backup-simplify]: Simplify (log PI) into (log PI) 14.687 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 14.688 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 14.688 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 14.689 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 14.689 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 14.689 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 14.689 * [taylor]: Taking taylor expansion of 1.0 in n 14.689 * [backup-simplify]: Simplify 1.0 into 1.0 14.689 * [taylor]: Taking taylor expansion of (log n) in n 14.689 * [taylor]: Taking taylor expansion of n in n 14.689 * [backup-simplify]: Simplify 0 into 0 14.689 * [backup-simplify]: Simplify 1 into 1 14.689 * [backup-simplify]: Simplify (log 1) into 0 14.690 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.690 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 14.690 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 14.690 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 14.690 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 14.690 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 14.690 * [taylor]: Taking taylor expansion of 1.0 in n 14.690 * [backup-simplify]: Simplify 1.0 into 1.0 14.690 * [taylor]: Taking taylor expansion of (log 2.0) in n 14.690 * [taylor]: Taking taylor expansion of 2.0 in n 14.690 * [backup-simplify]: Simplify 2.0 into 2.0 14.690 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 14.691 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 14.693 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 14.694 * [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) 14.695 * [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) 14.696 * [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)) 14.698 * [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))) 14.699 * [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) 14.701 * [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)) 14.702 * [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))) 14.704 * [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))) 14.704 * [backup-simplify]: Simplify 0 into 0 14.704 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.707 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.708 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 14.709 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 14.711 * [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 14.712 * [backup-simplify]: Simplify (- 0) into 0 14.712 * [backup-simplify]: Simplify (+ 0 0) into 0 14.713 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 14.715 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 14.716 * [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))) 14.719 * [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))))) 14.725 * [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))))) 14.725 * [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 14.725 * [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 14.725 * [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 14.725 * [taylor]: Taking taylor expansion of +nan.0 in n 14.725 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.725 * [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 14.725 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 14.725 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 14.725 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 14.725 * [taylor]: Taking taylor expansion of 0.5 in n 14.725 * [backup-simplify]: Simplify 0.5 into 0.5 14.725 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 14.725 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 14.726 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 14.726 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 14.726 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 14.726 * [taylor]: Taking taylor expansion of 1.0 in n 14.726 * [backup-simplify]: Simplify 1.0 into 1.0 14.726 * [taylor]: Taking taylor expansion of (log PI) in n 14.726 * [taylor]: Taking taylor expansion of PI in n 14.726 * [backup-simplify]: Simplify PI into PI 14.726 * [backup-simplify]: Simplify (log PI) into (log PI) 14.728 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 14.729 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 14.729 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 14.729 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 14.729 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 14.729 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 14.729 * [taylor]: Taking taylor expansion of 1.0 in n 14.729 * [backup-simplify]: Simplify 1.0 into 1.0 14.729 * [taylor]: Taking taylor expansion of (log n) in n 14.729 * [taylor]: Taking taylor expansion of n in n 14.729 * [backup-simplify]: Simplify 0 into 0 14.729 * [backup-simplify]: Simplify 1 into 1 14.729 * [backup-simplify]: Simplify (log 1) into 0 14.730 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.730 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 14.730 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 14.730 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 14.730 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 14.730 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 14.730 * [taylor]: Taking taylor expansion of 1.0 in n 14.730 * [backup-simplify]: Simplify 1.0 into 1.0 14.730 * [taylor]: Taking taylor expansion of (log 2.0) in n 14.730 * [taylor]: Taking taylor expansion of 2.0 in n 14.730 * [backup-simplify]: Simplify 2.0 into 2.0 14.730 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 14.731 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 14.732 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 14.732 * [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) 14.733 * [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) 14.734 * [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)) 14.734 * [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))) 14.735 * [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) 14.735 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.735 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.735 * [taylor]: Taking taylor expansion of 2.0 in n 14.735 * [backup-simplify]: Simplify 2.0 into 2.0 14.735 * [taylor]: Taking taylor expansion of (* n PI) in n 14.736 * [taylor]: Taking taylor expansion of n in n 14.736 * [backup-simplify]: Simplify 0 into 0 14.736 * [backup-simplify]: Simplify 1 into 1 14.736 * [taylor]: Taking taylor expansion of PI in n 14.736 * [backup-simplify]: Simplify PI into PI 14.736 * [backup-simplify]: Simplify (* 0 PI) into 0 14.736 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.737 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.738 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.739 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.739 * [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 14.739 * [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 14.739 * [taylor]: Taking taylor expansion of +nan.0 in n 14.739 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.739 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 14.739 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 14.739 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 14.739 * [taylor]: Taking taylor expansion of 0.5 in n 14.739 * [backup-simplify]: Simplify 0.5 into 0.5 14.739 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 14.739 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 14.739 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 14.739 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 14.739 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 14.739 * [taylor]: Taking taylor expansion of 1.0 in n 14.739 * [backup-simplify]: Simplify 1.0 into 1.0 14.739 * [taylor]: Taking taylor expansion of (log PI) in n 14.739 * [taylor]: Taking taylor expansion of PI in n 14.739 * [backup-simplify]: Simplify PI into PI 14.739 * [backup-simplify]: Simplify (log PI) into (log PI) 14.740 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 14.741 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 14.741 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 14.741 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 14.741 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 14.741 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 14.741 * [taylor]: Taking taylor expansion of 1.0 in n 14.741 * [backup-simplify]: Simplify 1.0 into 1.0 14.741 * [taylor]: Taking taylor expansion of (log n) in n 14.741 * [taylor]: Taking taylor expansion of n in n 14.741 * [backup-simplify]: Simplify 0 into 0 14.741 * [backup-simplify]: Simplify 1 into 1 14.741 * [backup-simplify]: Simplify (log 1) into 0 14.742 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.742 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 14.742 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 14.742 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 14.742 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 14.742 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 14.742 * [taylor]: Taking taylor expansion of 1.0 in n 14.742 * [backup-simplify]: Simplify 1.0 into 1.0 14.742 * [taylor]: Taking taylor expansion of (log 2.0) in n 14.742 * [taylor]: Taking taylor expansion of 2.0 in n 14.742 * [backup-simplify]: Simplify 2.0 into 2.0 14.742 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 14.743 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 14.748 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 14.749 * [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) 14.749 * [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) 14.750 * [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)) 14.751 * [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))) 14.752 * [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) 14.753 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.755 * [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))) 14.756 * [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)))) 14.757 * [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)) 14.758 * [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))) 14.760 * [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))))))) 14.764 * [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))))))))) 14.768 * [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))))))) 14.769 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 14.769 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 14.770 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 14.771 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.771 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.772 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 14.772 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 14.773 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 14.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 14.774 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 14.775 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 14.776 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 14.777 * [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 14.778 * [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 14.780 * [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 14.781 * [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 14.781 * [backup-simplify]: Simplify (- 0) into 0 14.781 * [backup-simplify]: Simplify 0 into 0 14.781 * [backup-simplify]: Simplify 0 into 0 14.782 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.784 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.785 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.785 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 14.787 * [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 14.788 * [backup-simplify]: Simplify (- 0) into 0 14.788 * [backup-simplify]: Simplify (+ 0 0) into 0 14.789 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 14.789 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 14.791 * [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))) 14.794 * [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)))))))) 14.800 * [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)))))))) 14.800 * [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 14.800 * [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 14.800 * [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 14.800 * [taylor]: Taking taylor expansion of +nan.0 in n 14.800 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.801 * [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 14.801 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 14.801 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 14.801 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 14.801 * [taylor]: Taking taylor expansion of 0.5 in n 14.801 * [backup-simplify]: Simplify 0.5 into 0.5 14.801 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 14.801 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 14.801 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 14.801 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 14.801 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 14.801 * [taylor]: Taking taylor expansion of 1.0 in n 14.801 * [backup-simplify]: Simplify 1.0 into 1.0 14.801 * [taylor]: Taking taylor expansion of (log PI) in n 14.801 * [taylor]: Taking taylor expansion of PI in n 14.801 * [backup-simplify]: Simplify PI into PI 14.801 * [backup-simplify]: Simplify (log PI) into (log PI) 14.802 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 14.803 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 14.803 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 14.803 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 14.803 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 14.803 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 14.803 * [taylor]: Taking taylor expansion of 1.0 in n 14.803 * [backup-simplify]: Simplify 1.0 into 1.0 14.803 * [taylor]: Taking taylor expansion of (log n) in n 14.803 * [taylor]: Taking taylor expansion of n in n 14.803 * [backup-simplify]: Simplify 0 into 0 14.803 * [backup-simplify]: Simplify 1 into 1 14.803 * [backup-simplify]: Simplify (log 1) into 0 14.804 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.804 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 14.804 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 14.804 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 14.804 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 14.804 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 14.804 * [taylor]: Taking taylor expansion of 1.0 in n 14.804 * [backup-simplify]: Simplify 1.0 into 1.0 14.804 * [taylor]: Taking taylor expansion of (log 2.0) in n 14.804 * [taylor]: Taking taylor expansion of 2.0 in n 14.804 * [backup-simplify]: Simplify 2.0 into 2.0 14.805 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 14.805 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 14.806 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 14.806 * [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) 14.807 * [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) 14.808 * [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)) 14.809 * [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))) 14.810 * [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) 14.810 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.811 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.811 * [taylor]: Taking taylor expansion of 2.0 in n 14.811 * [backup-simplify]: Simplify 2.0 into 2.0 14.811 * [taylor]: Taking taylor expansion of (* n PI) in n 14.811 * [taylor]: Taking taylor expansion of n in n 14.811 * [backup-simplify]: Simplify 0 into 0 14.811 * [backup-simplify]: Simplify 1 into 1 14.811 * [taylor]: Taking taylor expansion of PI in n 14.811 * [backup-simplify]: Simplify PI into PI 14.811 * [backup-simplify]: Simplify (* 0 PI) into 0 14.812 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.813 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.815 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.816 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.816 * [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 14.816 * [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 14.816 * [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 14.816 * [taylor]: Taking taylor expansion of +nan.0 in n 14.816 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.816 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 14.816 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 14.816 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 14.816 * [taylor]: Taking taylor expansion of 0.5 in n 14.816 * [backup-simplify]: Simplify 0.5 into 0.5 14.816 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 14.816 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 14.816 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 14.816 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 14.816 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 14.816 * [taylor]: Taking taylor expansion of 1.0 in n 14.816 * [backup-simplify]: Simplify 1.0 into 1.0 14.816 * [taylor]: Taking taylor expansion of (log 2.0) in n 14.816 * [taylor]: Taking taylor expansion of 2.0 in n 14.816 * [backup-simplify]: Simplify 2.0 into 2.0 14.817 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 14.817 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 14.819 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 14.819 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 14.819 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 14.819 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 14.819 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 14.819 * [taylor]: Taking taylor expansion of 1.0 in n 14.819 * [backup-simplify]: Simplify 1.0 into 1.0 14.819 * [taylor]: Taking taylor expansion of (log n) in n 14.819 * [taylor]: Taking taylor expansion of n in n 14.819 * [backup-simplify]: Simplify 0 into 0 14.819 * [backup-simplify]: Simplify 1 into 1 14.819 * [backup-simplify]: Simplify (log 1) into 0 14.820 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.820 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 14.820 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 14.820 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 14.820 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 14.820 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 14.820 * [taylor]: Taking taylor expansion of 1.0 in n 14.820 * [backup-simplify]: Simplify 1.0 into 1.0 14.820 * [taylor]: Taking taylor expansion of (log PI) in n 14.820 * [taylor]: Taking taylor expansion of PI in n 14.820 * [backup-simplify]: Simplify PI into PI 14.821 * [backup-simplify]: Simplify (log PI) into (log PI) 14.821 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 14.823 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 14.824 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 14.825 * [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) 14.826 * [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)) 14.827 * [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))) 14.828 * [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) 14.828 * [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 14.828 * [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 14.828 * [taylor]: Taking taylor expansion of +nan.0 in n 14.829 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.829 * [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 14.829 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 14.829 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 14.829 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 14.829 * [taylor]: Taking taylor expansion of 0.5 in n 14.829 * [backup-simplify]: Simplify 0.5 into 0.5 14.829 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 14.829 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 14.829 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 14.829 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 14.829 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 14.829 * [taylor]: Taking taylor expansion of 1.0 in n 14.829 * [backup-simplify]: Simplify 1.0 into 1.0 14.829 * [taylor]: Taking taylor expansion of (log PI) in n 14.829 * [taylor]: Taking taylor expansion of PI in n 14.829 * [backup-simplify]: Simplify PI into PI 14.829 * [backup-simplify]: Simplify (log PI) into (log PI) 14.830 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 14.832 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 14.832 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 14.832 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 14.832 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 14.832 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 14.832 * [taylor]: Taking taylor expansion of 1.0 in n 14.832 * [backup-simplify]: Simplify 1.0 into 1.0 14.832 * [taylor]: Taking taylor expansion of (log n) in n 14.832 * [taylor]: Taking taylor expansion of n in n 14.832 * [backup-simplify]: Simplify 0 into 0 14.832 * [backup-simplify]: Simplify 1 into 1 14.832 * [backup-simplify]: Simplify (log 1) into 0 14.833 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 14.833 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 14.833 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 14.833 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 14.833 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 14.833 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 14.833 * [taylor]: Taking taylor expansion of 1.0 in n 14.833 * [backup-simplify]: Simplify 1.0 into 1.0 14.833 * [taylor]: Taking taylor expansion of (log 2.0) in n 14.833 * [taylor]: Taking taylor expansion of 2.0 in n 14.833 * [backup-simplify]: Simplify 2.0 into 2.0 14.833 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 14.834 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 14.836 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 14.836 * [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) 14.837 * [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) 14.839 * [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)) 14.840 * [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))) 14.841 * [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) 14.841 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 14.841 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.841 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.841 * [taylor]: Taking taylor expansion of 2.0 in n 14.841 * [backup-simplify]: Simplify 2.0 into 2.0 14.841 * [taylor]: Taking taylor expansion of (* n PI) in n 14.841 * [taylor]: Taking taylor expansion of n in n 14.841 * [backup-simplify]: Simplify 0 into 0 14.841 * [backup-simplify]: Simplify 1 into 1 14.841 * [taylor]: Taking taylor expansion of PI in n 14.841 * [backup-simplify]: Simplify PI into PI 14.842 * [backup-simplify]: Simplify (* 0 PI) into 0 14.842 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.844 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.845 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.846 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.847 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.849 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.851 * [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))) 14.859 * [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)))) 14.861 * [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)) 14.862 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.863 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.866 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 14.869 * [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)) 14.871 * [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))) 14.874 * [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)))))))) 14.885 * [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))))))))) 14.897 * [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)))))))))) 14.911 * [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))))))))))))) 14.930 * [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))))))))))))) 14.948 * [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))))))))))))))) 14.976 * [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))))))))))))))))))))))) 14.978 * [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))) 14.978 * [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 14.978 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 14.978 * [taylor]: Taking taylor expansion of 1.0 in n 14.978 * [backup-simplify]: Simplify 1.0 into 1.0 14.978 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 14.978 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.978 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.978 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.978 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.978 * [taylor]: Taking taylor expansion of 0.5 in n 14.978 * [backup-simplify]: Simplify 0.5 into 0.5 14.978 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.978 * [taylor]: Taking taylor expansion of 1.0 in n 14.978 * [backup-simplify]: Simplify 1.0 into 1.0 14.978 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.978 * [taylor]: Taking taylor expansion of k in n 14.978 * [backup-simplify]: Simplify k into k 14.978 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.978 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.978 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.978 * [taylor]: Taking taylor expansion of 2.0 in n 14.978 * [backup-simplify]: Simplify 2.0 into 2.0 14.978 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.978 * [taylor]: Taking taylor expansion of PI in n 14.978 * [backup-simplify]: Simplify PI into PI 14.978 * [taylor]: Taking taylor expansion of n in n 14.978 * [backup-simplify]: Simplify 0 into 0 14.979 * [backup-simplify]: Simplify 1 into 1 14.979 * [backup-simplify]: Simplify (/ PI 1) into PI 14.980 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.981 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.981 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.981 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.981 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.984 * [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)))) 14.985 * [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))))) 14.985 * [taylor]: Taking taylor expansion of (sqrt k) in n 14.985 * [taylor]: Taking taylor expansion of k in n 14.985 * [backup-simplify]: Simplify k into k 14.985 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 14.986 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 14.986 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 14.986 * [taylor]: Taking taylor expansion of 1.0 in k 14.986 * [backup-simplify]: Simplify 1.0 into 1.0 14.986 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 14.986 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.986 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.986 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.986 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.986 * [taylor]: Taking taylor expansion of 0.5 in k 14.986 * [backup-simplify]: Simplify 0.5 into 0.5 14.986 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.986 * [taylor]: Taking taylor expansion of 1.0 in k 14.986 * [backup-simplify]: Simplify 1.0 into 1.0 14.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.986 * [taylor]: Taking taylor expansion of k in k 14.986 * [backup-simplify]: Simplify 0 into 0 14.986 * [backup-simplify]: Simplify 1 into 1 14.987 * [backup-simplify]: Simplify (/ 1 1) into 1 14.987 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.987 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.987 * [taylor]: Taking taylor expansion of 2.0 in k 14.987 * [backup-simplify]: Simplify 2.0 into 2.0 14.987 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.987 * [taylor]: Taking taylor expansion of PI in k 14.987 * [backup-simplify]: Simplify PI into PI 14.987 * [taylor]: Taking taylor expansion of n in k 14.987 * [backup-simplify]: Simplify n into n 14.987 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.987 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.987 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.987 * [backup-simplify]: Simplify (- 1) into -1 14.988 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.988 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.989 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.989 * [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)))))) 14.989 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.989 * [taylor]: Taking taylor expansion of k in k 14.989 * [backup-simplify]: Simplify 0 into 0 14.989 * [backup-simplify]: Simplify 1 into 1 14.989 * [backup-simplify]: Simplify (sqrt 0) into 0 14.991 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.991 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 14.991 * [taylor]: Taking taylor expansion of 1.0 in k 14.991 * [backup-simplify]: Simplify 1.0 into 1.0 14.991 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 14.991 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.991 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.991 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.991 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.991 * [taylor]: Taking taylor expansion of 0.5 in k 14.991 * [backup-simplify]: Simplify 0.5 into 0.5 14.991 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.991 * [taylor]: Taking taylor expansion of 1.0 in k 14.991 * [backup-simplify]: Simplify 1.0 into 1.0 14.991 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.991 * [taylor]: Taking taylor expansion of k in k 14.991 * [backup-simplify]: Simplify 0 into 0 14.992 * [backup-simplify]: Simplify 1 into 1 14.992 * [backup-simplify]: Simplify (/ 1 1) into 1 14.992 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.992 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.992 * [taylor]: Taking taylor expansion of 2.0 in k 14.992 * [backup-simplify]: Simplify 2.0 into 2.0 14.992 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.992 * [taylor]: Taking taylor expansion of PI in k 14.992 * [backup-simplify]: Simplify PI into PI 14.992 * [taylor]: Taking taylor expansion of n in k 14.992 * [backup-simplify]: Simplify n into n 14.992 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.992 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.992 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.993 * [backup-simplify]: Simplify (- 1) into -1 14.993 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.993 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.993 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.993 * [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)))))) 14.993 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.993 * [taylor]: Taking taylor expansion of k in k 14.993 * [backup-simplify]: Simplify 0 into 0 14.993 * [backup-simplify]: Simplify 1 into 1 14.994 * [backup-simplify]: Simplify (sqrt 0) into 0 14.994 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.995 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 14.995 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.995 * [taylor]: Taking taylor expansion of 0 in n 14.995 * [backup-simplify]: Simplify 0 into 0 14.995 * [backup-simplify]: Simplify 0 into 0 14.995 * [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)))))))) 14.996 * [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)))))))) 14.996 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 14.996 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 14.996 * [taylor]: Taking taylor expansion of +nan.0 in n 14.996 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.996 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 14.996 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 14.996 * [taylor]: Taking taylor expansion of 0.5 in n 14.996 * [backup-simplify]: Simplify 0.5 into 0.5 14.996 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 14.996 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.996 * [taylor]: Taking taylor expansion of 1.0 in n 14.996 * [backup-simplify]: Simplify 1.0 into 1.0 14.996 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.996 * [taylor]: Taking taylor expansion of k in n 14.996 * [backup-simplify]: Simplify k into k 14.996 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.996 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.996 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.996 * [taylor]: Taking taylor expansion of 2.0 in n 14.996 * [backup-simplify]: Simplify 2.0 into 2.0 14.996 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.996 * [taylor]: Taking taylor expansion of PI in n 14.996 * [backup-simplify]: Simplify PI into PI 14.996 * [taylor]: Taking taylor expansion of n in n 14.996 * [backup-simplify]: Simplify 0 into 0 14.996 * [backup-simplify]: Simplify 1 into 1 14.997 * [backup-simplify]: Simplify (/ PI 1) into PI 14.997 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.998 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.998 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.998 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.999 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 15.000 * [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)))) 15.001 * [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))))) 15.002 * [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)))))) 15.003 * [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))))))) 15.003 * [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))))))) 15.003 * [backup-simplify]: Simplify 0 into 0 15.009 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.010 * [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)))))))) 15.010 * [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)))))))) 15.010 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 15.010 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 15.010 * [taylor]: Taking taylor expansion of +nan.0 in n 15.010 * [backup-simplify]: Simplify +nan.0 into +nan.0 15.010 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 15.011 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 15.011 * [taylor]: Taking taylor expansion of 0.5 in n 15.011 * [backup-simplify]: Simplify 0.5 into 0.5 15.011 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 15.011 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.011 * [taylor]: Taking taylor expansion of 1.0 in n 15.011 * [backup-simplify]: Simplify 1.0 into 1.0 15.011 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.011 * [taylor]: Taking taylor expansion of k in n 15.011 * [backup-simplify]: Simplify k into k 15.011 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.011 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 15.011 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 15.011 * [taylor]: Taking taylor expansion of 2.0 in n 15.011 * [backup-simplify]: Simplify 2.0 into 2.0 15.011 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.011 * [taylor]: Taking taylor expansion of PI in n 15.011 * [backup-simplify]: Simplify PI into PI 15.011 * [taylor]: Taking taylor expansion of n in n 15.011 * [backup-simplify]: Simplify 0 into 0 15.011 * [backup-simplify]: Simplify 1 into 1 15.011 * [backup-simplify]: Simplify (/ PI 1) into PI 15.012 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.012 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.012 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.012 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.013 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.014 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 15.015 * [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)))) 15.015 * [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))))) 15.016 * [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)))))) 15.017 * [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))))))) 15.018 * [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))))))) 15.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.019 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 15.020 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 15.020 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.021 * [backup-simplify]: Simplify (- 0) into 0 15.021 * [backup-simplify]: Simplify (+ 0 0) into 0 15.022 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.024 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 15.026 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 15.028 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.030 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 15.030 * [backup-simplify]: Simplify (- 0) into 0 15.030 * [backup-simplify]: Simplify 0 into 0 15.030 * [backup-simplify]: Simplify 0 into 0 15.035 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.036 * [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)))))))) 15.037 * [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)))))))) 15.037 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 15.038 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 15.038 * [taylor]: Taking taylor expansion of +nan.0 in n 15.038 * [backup-simplify]: Simplify +nan.0 into +nan.0 15.038 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 15.038 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 15.038 * [taylor]: Taking taylor expansion of 0.5 in n 15.038 * [backup-simplify]: Simplify 0.5 into 0.5 15.038 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 15.038 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 15.038 * [taylor]: Taking taylor expansion of 1.0 in n 15.038 * [backup-simplify]: Simplify 1.0 into 1.0 15.038 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.038 * [taylor]: Taking taylor expansion of k in n 15.038 * [backup-simplify]: Simplify k into k 15.038 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.038 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 15.038 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 15.038 * [taylor]: Taking taylor expansion of 2.0 in n 15.038 * [backup-simplify]: Simplify 2.0 into 2.0 15.038 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.038 * [taylor]: Taking taylor expansion of PI in n 15.038 * [backup-simplify]: Simplify PI into PI 15.038 * [taylor]: Taking taylor expansion of n in n 15.038 * [backup-simplify]: Simplify 0 into 0 15.038 * [backup-simplify]: Simplify 1 into 1 15.039 * [backup-simplify]: Simplify (/ PI 1) into PI 15.040 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 15.041 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 15.041 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 15.041 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 15.042 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.044 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 15.045 * [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)))) 15.045 * [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))))) 15.046 * [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)))))) 15.047 * [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))))))) 15.048 * [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))))))) 15.051 * [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)))))))) 15.051 * [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)))) 15.052 * [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 15.052 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 15.052 * [taylor]: Taking taylor expansion of 1.0 in n 15.052 * [backup-simplify]: Simplify 1.0 into 1.0 15.052 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 15.052 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 15.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 15.052 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 15.052 * [taylor]: Taking taylor expansion of 0.5 in n 15.052 * [backup-simplify]: Simplify 0.5 into 0.5 15.052 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.052 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.052 * [taylor]: Taking taylor expansion of k in n 15.052 * [backup-simplify]: Simplify k into k 15.052 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.052 * [taylor]: Taking taylor expansion of 1.0 in n 15.052 * [backup-simplify]: Simplify 1.0 into 1.0 15.052 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.052 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.052 * [taylor]: Taking taylor expansion of -2.0 in n 15.052 * [backup-simplify]: Simplify -2.0 into -2.0 15.052 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.052 * [taylor]: Taking taylor expansion of PI in n 15.052 * [backup-simplify]: Simplify PI into PI 15.052 * [taylor]: Taking taylor expansion of n in n 15.052 * [backup-simplify]: Simplify 0 into 0 15.052 * [backup-simplify]: Simplify 1 into 1 15.053 * [backup-simplify]: Simplify (/ PI 1) into PI 15.053 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.054 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.054 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.054 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.056 * [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))) 15.057 * [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)))) 15.057 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 15.057 * [taylor]: Taking taylor expansion of (/ -1 k) in n 15.057 * [taylor]: Taking taylor expansion of -1 in n 15.057 * [backup-simplify]: Simplify -1 into -1 15.057 * [taylor]: Taking taylor expansion of k in n 15.057 * [backup-simplify]: Simplify k into k 15.057 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 15.057 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 15.058 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 15.058 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 15.059 * [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))) 15.059 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 15.059 * [taylor]: Taking taylor expansion of 1.0 in k 15.059 * [backup-simplify]: Simplify 1.0 into 1.0 15.059 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 15.059 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.059 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 15.059 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 15.059 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.059 * [taylor]: Taking taylor expansion of 0.5 in k 15.059 * [backup-simplify]: Simplify 0.5 into 0.5 15.059 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.059 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.059 * [taylor]: Taking taylor expansion of k in k 15.059 * [backup-simplify]: Simplify 0 into 0 15.059 * [backup-simplify]: Simplify 1 into 1 15.059 * [backup-simplify]: Simplify (/ 1 1) into 1 15.059 * [taylor]: Taking taylor expansion of 1.0 in k 15.059 * [backup-simplify]: Simplify 1.0 into 1.0 15.059 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 15.059 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 15.059 * [taylor]: Taking taylor expansion of -2.0 in k 15.059 * [backup-simplify]: Simplify -2.0 into -2.0 15.060 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.060 * [taylor]: Taking taylor expansion of PI in k 15.060 * [backup-simplify]: Simplify PI into PI 15.060 * [taylor]: Taking taylor expansion of n in k 15.060 * [backup-simplify]: Simplify n into n 15.060 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.060 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 15.060 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 15.060 * [backup-simplify]: Simplify (+ 1 0) into 1 15.061 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.061 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 15.061 * [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)))) 15.061 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.061 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.061 * [taylor]: Taking taylor expansion of -1 in k 15.061 * [backup-simplify]: Simplify -1 into -1 15.061 * [taylor]: Taking taylor expansion of k in k 15.061 * [backup-simplify]: Simplify 0 into 0 15.061 * [backup-simplify]: Simplify 1 into 1 15.062 * [backup-simplify]: Simplify (/ -1 1) into -1 15.062 * [backup-simplify]: Simplify (sqrt 0) into 0 15.063 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.063 * [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))))) 15.063 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 15.063 * [taylor]: Taking taylor expansion of 1.0 in k 15.063 * [backup-simplify]: Simplify 1.0 into 1.0 15.063 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 15.063 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 15.063 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 15.063 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.063 * [taylor]: Taking taylor expansion of 0.5 in k 15.063 * [backup-simplify]: Simplify 0.5 into 0.5 15.063 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.063 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.063 * [taylor]: Taking taylor expansion of k in k 15.063 * [backup-simplify]: Simplify 0 into 0 15.063 * [backup-simplify]: Simplify 1 into 1 15.063 * [backup-simplify]: Simplify (/ 1 1) into 1 15.064 * [taylor]: Taking taylor expansion of 1.0 in k 15.064 * [backup-simplify]: Simplify 1.0 into 1.0 15.064 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 15.064 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 15.064 * [taylor]: Taking taylor expansion of -2.0 in k 15.064 * [backup-simplify]: Simplify -2.0 into -2.0 15.064 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.064 * [taylor]: Taking taylor expansion of PI in k 15.064 * [backup-simplify]: Simplify PI into PI 15.064 * [taylor]: Taking taylor expansion of n in k 15.064 * [backup-simplify]: Simplify n into n 15.064 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.064 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 15.064 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 15.066 * [backup-simplify]: Simplify (+ 1 0) into 1 15.067 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.067 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 15.067 * [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)))) 15.067 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.067 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.067 * [taylor]: Taking taylor expansion of -1 in k 15.067 * [backup-simplify]: Simplify -1 into -1 15.067 * [taylor]: Taking taylor expansion of k in k 15.067 * [backup-simplify]: Simplify 0 into 0 15.067 * [backup-simplify]: Simplify 1 into 1 15.067 * [backup-simplify]: Simplify (/ -1 1) into -1 15.068 * [backup-simplify]: Simplify (sqrt 0) into 0 15.068 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.069 * [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))))) 15.069 * [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))))) 15.069 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 15.069 * [taylor]: Taking taylor expansion of +nan.0 in n 15.069 * [backup-simplify]: Simplify +nan.0 into +nan.0 15.069 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 15.069 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 15.069 * [taylor]: Taking taylor expansion of 0.5 in n 15.069 * [backup-simplify]: Simplify 0.5 into 0.5 15.069 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 15.069 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.069 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.069 * [taylor]: Taking taylor expansion of -2.0 in n 15.069 * [backup-simplify]: Simplify -2.0 into -2.0 15.069 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.069 * [taylor]: Taking taylor expansion of PI in n 15.069 * [backup-simplify]: Simplify PI into PI 15.069 * [taylor]: Taking taylor expansion of n in n 15.069 * [backup-simplify]: Simplify 0 into 0 15.069 * [backup-simplify]: Simplify 1 into 1 15.070 * [backup-simplify]: Simplify (/ PI 1) into PI 15.070 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.071 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.071 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.071 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.071 * [taylor]: Taking taylor expansion of k in n 15.071 * [backup-simplify]: Simplify k into k 15.071 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.071 * [taylor]: Taking taylor expansion of 1.0 in n 15.071 * [backup-simplify]: Simplify 1.0 into 1.0 15.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.072 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.073 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 15.074 * [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))) 15.076 * [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)))) 15.077 * [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))))) 15.078 * [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))))) 15.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 15.082 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.084 * [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)))))) 15.084 * [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)))))) 15.084 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 15.084 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 15.084 * [taylor]: Taking taylor expansion of +nan.0 in n 15.084 * [backup-simplify]: Simplify +nan.0 into +nan.0 15.084 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 15.084 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 15.084 * [taylor]: Taking taylor expansion of 0.5 in n 15.085 * [backup-simplify]: Simplify 0.5 into 0.5 15.085 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 15.085 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.085 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.085 * [taylor]: Taking taylor expansion of -2.0 in n 15.085 * [backup-simplify]: Simplify -2.0 into -2.0 15.085 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.085 * [taylor]: Taking taylor expansion of PI in n 15.085 * [backup-simplify]: Simplify PI into PI 15.085 * [taylor]: Taking taylor expansion of n in n 15.085 * [backup-simplify]: Simplify 0 into 0 15.085 * [backup-simplify]: Simplify 1 into 1 15.085 * [backup-simplify]: Simplify (/ PI 1) into PI 15.086 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.087 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.087 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.087 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.087 * [taylor]: Taking taylor expansion of k in n 15.087 * [backup-simplify]: Simplify k into k 15.087 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.087 * [taylor]: Taking taylor expansion of 1.0 in n 15.087 * [backup-simplify]: Simplify 1.0 into 1.0 15.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.089 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.090 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 15.091 * [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))) 15.093 * [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)))) 15.094 * [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))))) 15.095 * [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)))))) 15.097 * [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)))))) 15.098 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.098 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.099 * [backup-simplify]: Simplify (+ 0 0) into 0 15.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.100 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 15.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 15.103 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 15.105 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 15.107 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 15.109 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 15.109 * [backup-simplify]: Simplify 0 into 0 15.110 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.114 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.116 * [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)))))) 15.117 * [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)))))) 15.117 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 15.117 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 15.117 * [taylor]: Taking taylor expansion of +nan.0 in n 15.117 * [backup-simplify]: Simplify +nan.0 into +nan.0 15.117 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 15.117 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 15.117 * [taylor]: Taking taylor expansion of 0.5 in n 15.117 * [backup-simplify]: Simplify 0.5 into 0.5 15.117 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 15.117 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.117 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.117 * [taylor]: Taking taylor expansion of -2.0 in n 15.117 * [backup-simplify]: Simplify -2.0 into -2.0 15.117 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.117 * [taylor]: Taking taylor expansion of PI in n 15.117 * [backup-simplify]: Simplify PI into PI 15.117 * [taylor]: Taking taylor expansion of n in n 15.117 * [backup-simplify]: Simplify 0 into 0 15.117 * [backup-simplify]: Simplify 1 into 1 15.118 * [backup-simplify]: Simplify (/ PI 1) into PI 15.118 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.119 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.120 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.120 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.120 * [taylor]: Taking taylor expansion of k in n 15.120 * [backup-simplify]: Simplify k into k 15.120 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.120 * [taylor]: Taking taylor expansion of 1.0 in n 15.120 * [backup-simplify]: Simplify 1.0 into 1.0 15.121 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.121 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.123 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 15.124 * [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))) 15.125 * [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)))) 15.127 * [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))))) 15.128 * [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)))))) 15.129 * [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)))))) 15.134 * [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)))))))) 15.135 * * * [progress]: simplifying candidates 15.145 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (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) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) 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(- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 15.152 * * [simplify]: iteration 0: 361 enodes 15.270 * * [simplify]: iteration 1: 1004 enodes 15.841 * * [simplify]: iteration 2: 3445 enodes 17.570 * * [simplify]: iteration complete: 5004 enodes 17.570 * * [simplify]: Extracting #0: cost 125 inf + 0 17.571 * * [simplify]: Extracting #1: cost 635 inf + 2 17.575 * * [simplify]: Extracting #2: cost 1123 inf + 2802 17.585 * * [simplify]: Extracting #3: cost 1125 inf + 37571 17.616 * * [simplify]: Extracting #4: cost 740 inf + 164402 17.685 * * [simplify]: Extracting #5: cost 432 inf + 325779 17.824 * * [simplify]: Extracting #6: cost 266 inf + 428235 17.957 * * [simplify]: Extracting #7: cost 69 inf + 606033 18.139 * * [simplify]: Extracting #8: cost 12 inf + 681945 18.358 * * [simplify]: Extracting #9: cost 1 inf + 696348 18.589 * * [simplify]: Extracting #10: cost 0 inf + 694281 18.821 * * [simplify]: Extracting #11: cost 0 inf + 693991 19.016 * * [simplify]: Extracting #12: cost 0 inf + 693801 19.200 * [simplify]: Simplified to: (expm1 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (pow (* (* PI 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(* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* PI 2.0) n) (/ k 2.0))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (* (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (cbrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k)))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k))) (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (sqrt 1.0) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (/ (* (sqrt 1.0) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k)))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (pow (* (* PI 2.0) n) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (* 1.0 (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))) (- (fma (* (* (* (log n) (* k k)) (exp (* 0.5 (log (* (* PI 2.0) n))))) (log (* PI 2.0))) 0.25 (fma 0.125 (* (* (log n) (log n)) (* (* k k) (exp (* 0.5 (log (* (* PI 2.0) n)))))) (fma (* (* (log (* PI 2.0)) (log (* PI 2.0))) 0.125) (* (* k k) (exp (* 0.5 (log (* (* PI 2.0) n))))) (exp (* 0.5 (log (* (* PI 2.0) n))))))) (* 0.5 (* k (fma (log n) (exp (* 0.5 (log (* (* PI 2.0) n)))) (* (log (* PI 2.0)) (exp (* 0.5 (log (* (* PI 2.0) n))))))))) (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* PI 2.0) n) (* (* PI 2.0) n) (* (* PI 2.0) n) (- (* (- +nan.0) (* k k)) (fma k +nan.0 (- +nan.0))) (+ (/ (- +nan.0) (* k k)) (fma +nan.0 (/ 1 k) (* (/ (- +nan.0) (* k k)) (/ 1 k)))) (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) +nan.0)) (fma (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) k (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* k k) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log n) (* k k))) (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (fma (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (log (* PI 2.0)) (log (* PI 2.0)))) (* k k) (* (- (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5))) (* (* (log n) (* k k)) (log (* PI 2.0))))) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log (* PI 2.0)) k)) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (log n) k) (fma (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (* (* (log n) k) (* (log n) k)) (* (* +nan.0 (pow (* (* (pow n 1.0) (pow 2.0 1.0)) (pow PI 1.0)) 0.5)) (- (* (log (* PI 2.0)) (* k k)))))))))))) (fma (- (/ (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) (* k k))) +nan.0 (* +nan.0 (+ (/ (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) k) (- (/ (exp (* (log (* (* PI 2.0) n)) (* 0.5 (- 1.0 k)))) (* k (* k k))))))) (fma (- +nan.0) (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)))))) k) +nan.0) (* (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (/ +nan.0 k)))) 19.213 * * * [progress]: adding candidates to table 20.196 * * [progress]: iteration 4 / 4 20.197 * * * [progress]: picking best candidate 20.239 * * * * [pick]: Picked # 20.239 * * * [progress]: localizing error 20.276 * * * [progress]: generating rewritten candidates 20.276 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 20.293 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 20.310 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 2 1) 20.326 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 2 1) 20.344 * * * [progress]: generating series expansions 20.344 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 20.345 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 20.345 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 20.345 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 20.345 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 20.345 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 20.345 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 20.345 * [taylor]: Taking taylor expansion of 0.5 in k 20.345 * [backup-simplify]: Simplify 0.5 into 0.5 20.345 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 20.345 * [taylor]: Taking taylor expansion of 1.0 in k 20.345 * [backup-simplify]: Simplify 1.0 into 1.0 20.345 * [taylor]: Taking taylor expansion of k in k 20.345 * [backup-simplify]: Simplify 0 into 0 20.345 * [backup-simplify]: Simplify 1 into 1 20.345 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 20.345 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 20.345 * [taylor]: Taking taylor expansion of 2.0 in k 20.345 * [backup-simplify]: Simplify 2.0 into 2.0 20.345 * [taylor]: Taking taylor expansion of (* n PI) in k 20.345 * [taylor]: Taking taylor expansion of n in k 20.345 * [backup-simplify]: Simplify n into n 20.345 * [taylor]: Taking taylor expansion of PI in k 20.345 * [backup-simplify]: Simplify PI into PI 20.345 * [backup-simplify]: Simplify (* n PI) into (* n PI) 20.345 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 20.345 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 20.346 * [backup-simplify]: Simplify (- 0) into 0 20.346 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 20.347 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 20.347 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 20.347 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 20.347 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 20.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 20.347 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 20.347 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 20.347 * [taylor]: Taking taylor expansion of 0.5 in n 20.347 * [backup-simplify]: Simplify 0.5 into 0.5 20.347 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 20.347 * [taylor]: Taking taylor expansion of 1.0 in n 20.347 * [backup-simplify]: Simplify 1.0 into 1.0 20.347 * [taylor]: Taking taylor expansion of k in n 20.347 * [backup-simplify]: Simplify k into k 20.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 20.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.347 * [taylor]: Taking taylor expansion of 2.0 in n 20.347 * [backup-simplify]: Simplify 2.0 into 2.0 20.347 * [taylor]: Taking taylor expansion of (* n PI) in n 20.347 * [taylor]: Taking taylor expansion of n in n 20.347 * [backup-simplify]: Simplify 0 into 0 20.347 * [backup-simplify]: Simplify 1 into 1 20.347 * [taylor]: Taking taylor expansion of PI in n 20.347 * [backup-simplify]: Simplify PI into PI 20.348 * [backup-simplify]: Simplify (* 0 PI) into 0 20.348 * [backup-simplify]: Simplify (* 2.0 0) into 0 20.350 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.351 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 20.352 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.352 * [backup-simplify]: Simplify (- k) into (- k) 20.353 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 20.353 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 20.354 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.355 * [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)))) 20.357 * [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))))) 20.357 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 20.357 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 20.357 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 20.357 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 20.357 * [taylor]: Taking taylor expansion of 0.5 in n 20.357 * [backup-simplify]: Simplify 0.5 into 0.5 20.357 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 20.357 * [taylor]: Taking taylor expansion of 1.0 in n 20.357 * [backup-simplify]: Simplify 1.0 into 1.0 20.357 * [taylor]: Taking taylor expansion of k in n 20.357 * [backup-simplify]: Simplify k into k 20.357 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 20.357 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.357 * [taylor]: Taking taylor expansion of 2.0 in n 20.357 * [backup-simplify]: Simplify 2.0 into 2.0 20.357 * [taylor]: Taking taylor expansion of (* n PI) in n 20.357 * [taylor]: Taking taylor expansion of n in n 20.357 * [backup-simplify]: Simplify 0 into 0 20.357 * [backup-simplify]: Simplify 1 into 1 20.357 * [taylor]: Taking taylor expansion of PI in n 20.357 * [backup-simplify]: Simplify PI into PI 20.358 * [backup-simplify]: Simplify (* 0 PI) into 0 20.358 * [backup-simplify]: Simplify (* 2.0 0) into 0 20.360 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.361 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 20.362 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.363 * [backup-simplify]: Simplify (- k) into (- k) 20.363 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 20.363 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 20.364 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.365 * [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)))) 20.367 * [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))))) 20.367 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 20.367 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 20.367 * [taylor]: Taking taylor expansion of 0.5 in k 20.367 * [backup-simplify]: Simplify 0.5 into 0.5 20.367 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 20.367 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 20.367 * [taylor]: Taking taylor expansion of 1.0 in k 20.367 * [backup-simplify]: Simplify 1.0 into 1.0 20.367 * [taylor]: Taking taylor expansion of k in k 20.367 * [backup-simplify]: Simplify 0 into 0 20.367 * [backup-simplify]: Simplify 1 into 1 20.367 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 20.367 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 20.367 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 20.367 * [taylor]: Taking taylor expansion of 2.0 in k 20.367 * [backup-simplify]: Simplify 2.0 into 2.0 20.367 * [taylor]: Taking taylor expansion of PI in k 20.367 * [backup-simplify]: Simplify PI into PI 20.368 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.369 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.369 * [taylor]: Taking taylor expansion of (log n) in k 20.369 * [taylor]: Taking taylor expansion of n in k 20.369 * [backup-simplify]: Simplify n into n 20.369 * [backup-simplify]: Simplify (log n) into (log n) 20.369 * [backup-simplify]: Simplify (- 0) into 0 20.370 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 20.371 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 20.372 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 20.373 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 20.375 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 20.376 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 20.377 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 20.380 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 20.381 * [backup-simplify]: Simplify (- 0) into 0 20.381 * [backup-simplify]: Simplify (+ 0 0) into 0 20.382 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 20.383 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.384 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 20.386 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.386 * [taylor]: Taking taylor expansion of 0 in k 20.386 * [backup-simplify]: Simplify 0 into 0 20.386 * [backup-simplify]: Simplify 0 into 0 20.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 20.389 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 20.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 20.391 * [backup-simplify]: Simplify (+ 0 0) into 0 20.391 * [backup-simplify]: Simplify (- 1) into -1 20.392 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.393 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 20.395 * [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)))) 20.398 * [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)))))) 20.401 * [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)))))) 20.403 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.407 * [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 20.408 * [backup-simplify]: Simplify (- 0) into 0 20.408 * [backup-simplify]: Simplify (+ 0 0) into 0 20.409 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 20.410 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.412 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 20.414 * [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 20.414 * [taylor]: Taking taylor expansion of 0 in k 20.414 * [backup-simplify]: Simplify 0 into 0 20.414 * [backup-simplify]: Simplify 0 into 0 20.414 * [backup-simplify]: Simplify 0 into 0 20.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.418 * [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 20.420 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 20.420 * [backup-simplify]: Simplify (+ 0 0) into 0 20.421 * [backup-simplify]: Simplify (- 0) into 0 20.421 * [backup-simplify]: Simplify (+ 0 0) into 0 20.423 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 20.431 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 20.435 * [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)))))) 20.439 * [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)))))) 20.445 * [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))))) 20.446 * [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)))) 20.446 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 20.446 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 20.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 20.446 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 20.446 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 20.446 * [taylor]: Taking taylor expansion of 0.5 in k 20.446 * [backup-simplify]: Simplify 0.5 into 0.5 20.446 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.446 * [taylor]: Taking taylor expansion of 1.0 in k 20.446 * [backup-simplify]: Simplify 1.0 into 1.0 20.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.446 * [taylor]: Taking taylor expansion of k in k 20.446 * [backup-simplify]: Simplify 0 into 0 20.446 * [backup-simplify]: Simplify 1 into 1 20.446 * [backup-simplify]: Simplify (/ 1 1) into 1 20.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 20.447 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 20.447 * [taylor]: Taking taylor expansion of 2.0 in k 20.447 * [backup-simplify]: Simplify 2.0 into 2.0 20.447 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.447 * [taylor]: Taking taylor expansion of PI in k 20.447 * [backup-simplify]: Simplify PI into PI 20.447 * [taylor]: Taking taylor expansion of n in k 20.447 * [backup-simplify]: Simplify n into n 20.447 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.447 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 20.447 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 20.447 * [backup-simplify]: Simplify (- 1) into -1 20.447 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.448 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 20.448 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 20.448 * [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)))))) 20.448 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 20.448 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 20.448 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 20.448 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 20.448 * [taylor]: Taking taylor expansion of 0.5 in n 20.448 * [backup-simplify]: Simplify 0.5 into 0.5 20.448 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.448 * [taylor]: Taking taylor expansion of 1.0 in n 20.448 * [backup-simplify]: Simplify 1.0 into 1.0 20.448 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.448 * [taylor]: Taking taylor expansion of k in n 20.448 * [backup-simplify]: Simplify k into k 20.448 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.448 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 20.448 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.448 * [taylor]: Taking taylor expansion of 2.0 in n 20.448 * [backup-simplify]: Simplify 2.0 into 2.0 20.448 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.448 * [taylor]: Taking taylor expansion of PI in n 20.448 * [backup-simplify]: Simplify PI into PI 20.448 * [taylor]: Taking taylor expansion of n in n 20.448 * [backup-simplify]: Simplify 0 into 0 20.448 * [backup-simplify]: Simplify 1 into 1 20.449 * [backup-simplify]: Simplify (/ PI 1) into PI 20.449 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.449 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.450 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.450 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.450 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 20.451 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.451 * [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)))) 20.452 * [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))))) 20.452 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 20.452 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 20.452 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 20.452 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 20.452 * [taylor]: Taking taylor expansion of 0.5 in n 20.452 * [backup-simplify]: Simplify 0.5 into 0.5 20.452 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.452 * [taylor]: Taking taylor expansion of 1.0 in n 20.452 * [backup-simplify]: Simplify 1.0 into 1.0 20.452 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.452 * [taylor]: Taking taylor expansion of k in n 20.452 * [backup-simplify]: Simplify k into k 20.452 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.452 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 20.452 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.452 * [taylor]: Taking taylor expansion of 2.0 in n 20.452 * [backup-simplify]: Simplify 2.0 into 2.0 20.452 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.452 * [taylor]: Taking taylor expansion of PI in n 20.452 * [backup-simplify]: Simplify PI into PI 20.452 * [taylor]: Taking taylor expansion of n in n 20.452 * [backup-simplify]: Simplify 0 into 0 20.452 * [backup-simplify]: Simplify 1 into 1 20.453 * [backup-simplify]: Simplify (/ PI 1) into PI 20.453 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.454 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.454 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.454 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.454 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 20.455 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.455 * [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)))) 20.456 * [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))))) 20.456 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 20.456 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 20.456 * [taylor]: Taking taylor expansion of 0.5 in k 20.456 * [backup-simplify]: Simplify 0.5 into 0.5 20.456 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 20.456 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.456 * [taylor]: Taking taylor expansion of 1.0 in k 20.456 * [backup-simplify]: Simplify 1.0 into 1.0 20.457 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.457 * [taylor]: Taking taylor expansion of k in k 20.457 * [backup-simplify]: Simplify 0 into 0 20.457 * [backup-simplify]: Simplify 1 into 1 20.457 * [backup-simplify]: Simplify (/ 1 1) into 1 20.457 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 20.457 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 20.457 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 20.457 * [taylor]: Taking taylor expansion of 2.0 in k 20.457 * [backup-simplify]: Simplify 2.0 into 2.0 20.457 * [taylor]: Taking taylor expansion of PI in k 20.457 * [backup-simplify]: Simplify PI into PI 20.457 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.458 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.458 * [taylor]: Taking taylor expansion of (log n) in k 20.458 * [taylor]: Taking taylor expansion of n in k 20.458 * [backup-simplify]: Simplify n into n 20.458 * [backup-simplify]: Simplify (log n) into (log n) 20.458 * [backup-simplify]: Simplify (- 1) into -1 20.458 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.459 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.459 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 20.460 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 20.461 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 20.461 * [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))))) 20.462 * [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))))) 20.463 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.463 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 20.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 20.464 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.464 * [backup-simplify]: Simplify (- 0) into 0 20.465 * [backup-simplify]: Simplify (+ 0 0) into 0 20.465 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 20.466 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.467 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 20.468 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.468 * [taylor]: Taking taylor expansion of 0 in k 20.468 * [backup-simplify]: Simplify 0 into 0 20.468 * [backup-simplify]: Simplify 0 into 0 20.468 * [backup-simplify]: Simplify 0 into 0 20.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.471 * [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 20.471 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.471 * [backup-simplify]: Simplify (- 0) into 0 20.472 * [backup-simplify]: Simplify (+ 0 0) into 0 20.472 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 20.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.474 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 20.476 * [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 20.476 * [taylor]: Taking taylor expansion of 0 in k 20.476 * [backup-simplify]: Simplify 0 into 0 20.476 * [backup-simplify]: Simplify 0 into 0 20.476 * [backup-simplify]: Simplify 0 into 0 20.476 * [backup-simplify]: Simplify 0 into 0 20.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.478 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.484 * [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 20.484 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.485 * [backup-simplify]: Simplify (- 0) into 0 20.485 * [backup-simplify]: Simplify (+ 0 0) into 0 20.487 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 20.488 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.490 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 20.493 * [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 20.493 * [taylor]: Taking taylor expansion of 0 in k 20.493 * [backup-simplify]: Simplify 0 into 0 20.493 * [backup-simplify]: Simplify 0 into 0 20.495 * [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)))))) 20.496 * [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))) 20.496 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 20.496 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 20.496 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 20.496 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 20.496 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 20.496 * [taylor]: Taking taylor expansion of 0.5 in k 20.496 * [backup-simplify]: Simplify 0.5 into 0.5 20.496 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.496 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.496 * [taylor]: Taking taylor expansion of k in k 20.496 * [backup-simplify]: Simplify 0 into 0 20.496 * [backup-simplify]: Simplify 1 into 1 20.496 * [backup-simplify]: Simplify (/ 1 1) into 1 20.497 * [taylor]: Taking taylor expansion of 1.0 in k 20.497 * [backup-simplify]: Simplify 1.0 into 1.0 20.497 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 20.497 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 20.497 * [taylor]: Taking taylor expansion of -2.0 in k 20.497 * [backup-simplify]: Simplify -2.0 into -2.0 20.497 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.497 * [taylor]: Taking taylor expansion of PI in k 20.497 * [backup-simplify]: Simplify PI into PI 20.497 * [taylor]: Taking taylor expansion of n in k 20.497 * [backup-simplify]: Simplify n into n 20.497 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.497 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 20.497 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 20.498 * [backup-simplify]: Simplify (+ 1 0) into 1 20.498 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 20.498 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 20.499 * [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)))) 20.499 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 20.499 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 20.499 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 20.499 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 20.499 * [taylor]: Taking taylor expansion of 0.5 in n 20.499 * [backup-simplify]: Simplify 0.5 into 0.5 20.499 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.499 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.499 * [taylor]: Taking taylor expansion of k in n 20.499 * [backup-simplify]: Simplify k into k 20.499 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.499 * [taylor]: Taking taylor expansion of 1.0 in n 20.499 * [backup-simplify]: Simplify 1.0 into 1.0 20.499 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 20.499 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.499 * [taylor]: Taking taylor expansion of -2.0 in n 20.499 * [backup-simplify]: Simplify -2.0 into -2.0 20.499 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.499 * [taylor]: Taking taylor expansion of PI in n 20.499 * [backup-simplify]: Simplify PI into PI 20.499 * [taylor]: Taking taylor expansion of n in n 20.499 * [backup-simplify]: Simplify 0 into 0 20.499 * [backup-simplify]: Simplify 1 into 1 20.500 * [backup-simplify]: Simplify (/ PI 1) into PI 20.500 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.502 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 20.502 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.502 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 20.503 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.505 * [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))) 20.506 * [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)))) 20.506 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 20.506 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 20.506 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 20.506 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 20.506 * [taylor]: Taking taylor expansion of 0.5 in n 20.506 * [backup-simplify]: Simplify 0.5 into 0.5 20.506 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.506 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.506 * [taylor]: Taking taylor expansion of k in n 20.506 * [backup-simplify]: Simplify k into k 20.506 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.506 * [taylor]: Taking taylor expansion of 1.0 in n 20.506 * [backup-simplify]: Simplify 1.0 into 1.0 20.506 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 20.506 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.506 * [taylor]: Taking taylor expansion of -2.0 in n 20.507 * [backup-simplify]: Simplify -2.0 into -2.0 20.507 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.507 * [taylor]: Taking taylor expansion of PI in n 20.507 * [backup-simplify]: Simplify PI into PI 20.507 * [taylor]: Taking taylor expansion of n in n 20.507 * [backup-simplify]: Simplify 0 into 0 20.507 * [backup-simplify]: Simplify 1 into 1 20.507 * [backup-simplify]: Simplify (/ PI 1) into PI 20.508 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.509 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 20.509 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.509 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 20.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.512 * [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))) 20.513 * [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)))) 20.514 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 20.514 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 20.514 * [taylor]: Taking taylor expansion of 0.5 in k 20.514 * [backup-simplify]: Simplify 0.5 into 0.5 20.514 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 20.514 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 20.514 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 20.514 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 20.514 * [taylor]: Taking taylor expansion of -2.0 in k 20.514 * [backup-simplify]: Simplify -2.0 into -2.0 20.514 * [taylor]: Taking taylor expansion of PI in k 20.514 * [backup-simplify]: Simplify PI into PI 20.515 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.516 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 20.516 * [taylor]: Taking taylor expansion of (log n) in k 20.516 * [taylor]: Taking taylor expansion of n in k 20.516 * [backup-simplify]: Simplify n into n 20.516 * [backup-simplify]: Simplify (log n) into (log n) 20.516 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.516 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.516 * [taylor]: Taking taylor expansion of k in k 20.516 * [backup-simplify]: Simplify 0 into 0 20.516 * [backup-simplify]: Simplify 1 into 1 20.517 * [backup-simplify]: Simplify (/ 1 1) into 1 20.517 * [taylor]: Taking taylor expansion of 1.0 in k 20.517 * [backup-simplify]: Simplify 1.0 into 1.0 20.517 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.518 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 20.518 * [backup-simplify]: Simplify (+ 1 0) into 1 20.520 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 20.521 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 20.522 * [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)))) 20.523 * [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)))) 20.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.526 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 20.527 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 20.528 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.528 * [backup-simplify]: Simplify (+ 0 0) into 0 20.529 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 20.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.531 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 20.534 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.534 * [taylor]: Taking taylor expansion of 0 in k 20.534 * [backup-simplify]: Simplify 0 into 0 20.534 * [backup-simplify]: Simplify 0 into 0 20.534 * [backup-simplify]: Simplify 0 into 0 20.535 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.536 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.541 * [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 20.541 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.541 * [backup-simplify]: Simplify (+ 0 0) into 0 20.542 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 20.544 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.545 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 20.548 * [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 20.548 * [taylor]: Taking taylor expansion of 0 in k 20.548 * [backup-simplify]: Simplify 0 into 0 20.548 * [backup-simplify]: Simplify 0 into 0 20.548 * [backup-simplify]: Simplify 0 into 0 20.548 * [backup-simplify]: Simplify 0 into 0 20.550 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.551 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.562 * [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 20.563 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.563 * [backup-simplify]: Simplify (+ 0 0) into 0 20.565 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 20.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.568 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 20.571 * [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 20.571 * [taylor]: Taking taylor expansion of 0 in k 20.571 * [backup-simplify]: Simplify 0 into 0 20.571 * [backup-simplify]: Simplify 0 into 0 20.572 * [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)))))) 20.573 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 20.573 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 20.573 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 20.573 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 20.573 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 20.573 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 20.574 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 20.574 * [taylor]: Taking taylor expansion of 0.5 in k 20.574 * [backup-simplify]: Simplify 0.5 into 0.5 20.574 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 20.574 * [taylor]: Taking taylor expansion of 1.0 in k 20.574 * [backup-simplify]: Simplify 1.0 into 1.0 20.574 * [taylor]: Taking taylor expansion of k in k 20.574 * [backup-simplify]: Simplify 0 into 0 20.574 * [backup-simplify]: Simplify 1 into 1 20.574 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 20.574 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 20.574 * [taylor]: Taking taylor expansion of 2.0 in k 20.574 * [backup-simplify]: Simplify 2.0 into 2.0 20.574 * [taylor]: Taking taylor expansion of (* n PI) in k 20.574 * [taylor]: Taking taylor expansion of n in k 20.574 * [backup-simplify]: Simplify n into n 20.574 * [taylor]: Taking taylor expansion of PI in k 20.574 * [backup-simplify]: Simplify PI into PI 20.574 * [backup-simplify]: Simplify (* n PI) into (* n PI) 20.574 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 20.574 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 20.575 * [backup-simplify]: Simplify (- 0) into 0 20.575 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 20.576 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 20.576 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 20.576 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 20.576 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 20.576 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 20.576 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 20.576 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 20.576 * [taylor]: Taking taylor expansion of 0.5 in n 20.576 * [backup-simplify]: Simplify 0.5 into 0.5 20.576 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 20.576 * [taylor]: Taking taylor expansion of 1.0 in n 20.576 * [backup-simplify]: Simplify 1.0 into 1.0 20.576 * [taylor]: Taking taylor expansion of k in n 20.576 * [backup-simplify]: Simplify k into k 20.576 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 20.576 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.576 * [taylor]: Taking taylor expansion of 2.0 in n 20.576 * [backup-simplify]: Simplify 2.0 into 2.0 20.576 * [taylor]: Taking taylor expansion of (* n PI) in n 20.576 * [taylor]: Taking taylor expansion of n in n 20.576 * [backup-simplify]: Simplify 0 into 0 20.576 * [backup-simplify]: Simplify 1 into 1 20.576 * [taylor]: Taking taylor expansion of PI in n 20.576 * [backup-simplify]: Simplify PI into PI 20.577 * [backup-simplify]: Simplify (* 0 PI) into 0 20.577 * [backup-simplify]: Simplify (* 2.0 0) into 0 20.578 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.579 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 20.580 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.580 * [backup-simplify]: Simplify (- k) into (- k) 20.580 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 20.580 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 20.581 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.581 * [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)))) 20.582 * [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))))) 20.582 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 20.582 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 20.582 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 20.582 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 20.582 * [taylor]: Taking taylor expansion of 0.5 in n 20.582 * [backup-simplify]: Simplify 0.5 into 0.5 20.582 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 20.582 * [taylor]: Taking taylor expansion of 1.0 in n 20.582 * [backup-simplify]: Simplify 1.0 into 1.0 20.582 * [taylor]: Taking taylor expansion of k in n 20.582 * [backup-simplify]: Simplify k into k 20.582 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 20.582 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.582 * [taylor]: Taking taylor expansion of 2.0 in n 20.582 * [backup-simplify]: Simplify 2.0 into 2.0 20.582 * [taylor]: Taking taylor expansion of (* n PI) in n 20.582 * [taylor]: Taking taylor expansion of n in n 20.582 * [backup-simplify]: Simplify 0 into 0 20.582 * [backup-simplify]: Simplify 1 into 1 20.582 * [taylor]: Taking taylor expansion of PI in n 20.582 * [backup-simplify]: Simplify PI into PI 20.583 * [backup-simplify]: Simplify (* 0 PI) into 0 20.583 * [backup-simplify]: Simplify (* 2.0 0) into 0 20.584 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.585 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 20.585 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.586 * [backup-simplify]: Simplify (- k) into (- k) 20.586 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 20.586 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 20.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.587 * [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)))) 20.588 * [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))))) 20.588 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 20.588 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 20.588 * [taylor]: Taking taylor expansion of 0.5 in k 20.588 * [backup-simplify]: Simplify 0.5 into 0.5 20.588 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 20.588 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 20.588 * [taylor]: Taking taylor expansion of 1.0 in k 20.588 * [backup-simplify]: Simplify 1.0 into 1.0 20.588 * [taylor]: Taking taylor expansion of k in k 20.588 * [backup-simplify]: Simplify 0 into 0 20.588 * [backup-simplify]: Simplify 1 into 1 20.588 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 20.588 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 20.588 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 20.588 * [taylor]: Taking taylor expansion of 2.0 in k 20.588 * [backup-simplify]: Simplify 2.0 into 2.0 20.589 * [taylor]: Taking taylor expansion of PI in k 20.589 * [backup-simplify]: Simplify PI into PI 20.589 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.589 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.590 * [taylor]: Taking taylor expansion of (log n) in k 20.590 * [taylor]: Taking taylor expansion of n in k 20.590 * [backup-simplify]: Simplify n into n 20.590 * [backup-simplify]: Simplify (log n) into (log n) 20.590 * [backup-simplify]: Simplify (- 0) into 0 20.590 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 20.591 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 20.591 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 20.592 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 20.593 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 20.594 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 20.594 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.595 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 20.596 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 20.596 * [backup-simplify]: Simplify (- 0) into 0 20.596 * [backup-simplify]: Simplify (+ 0 0) into 0 20.597 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 20.598 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.598 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 20.600 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.600 * [taylor]: Taking taylor expansion of 0 in k 20.600 * [backup-simplify]: Simplify 0 into 0 20.600 * [backup-simplify]: Simplify 0 into 0 20.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 20.601 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 20.602 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 20.602 * [backup-simplify]: Simplify (+ 0 0) into 0 20.602 * [backup-simplify]: Simplify (- 1) into -1 20.603 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.604 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 20.605 * [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)))) 20.607 * [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)))))) 20.609 * [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)))))) 20.611 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.612 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.615 * [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 20.616 * [backup-simplify]: Simplify (- 0) into 0 20.616 * [backup-simplify]: Simplify (+ 0 0) into 0 20.617 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 20.619 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 20.620 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 20.622 * [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 20.622 * [taylor]: Taking taylor expansion of 0 in k 20.622 * [backup-simplify]: Simplify 0 into 0 20.622 * [backup-simplify]: Simplify 0 into 0 20.622 * [backup-simplify]: Simplify 0 into 0 20.623 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.625 * [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 20.626 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 20.626 * [backup-simplify]: Simplify (+ 0 0) into 0 20.626 * [backup-simplify]: Simplify (- 0) into 0 20.627 * [backup-simplify]: Simplify (+ 0 0) into 0 20.628 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 20.629 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 20.632 * [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)))))) 20.635 * [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)))))) 20.642 * [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))))) 20.642 * [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)))) 20.642 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 20.642 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 20.642 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 20.643 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 20.643 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 20.643 * [taylor]: Taking taylor expansion of 0.5 in k 20.643 * [backup-simplify]: Simplify 0.5 into 0.5 20.643 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.643 * [taylor]: Taking taylor expansion of 1.0 in k 20.643 * [backup-simplify]: Simplify 1.0 into 1.0 20.643 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.643 * [taylor]: Taking taylor expansion of k in k 20.643 * [backup-simplify]: Simplify 0 into 0 20.643 * [backup-simplify]: Simplify 1 into 1 20.643 * [backup-simplify]: Simplify (/ 1 1) into 1 20.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 20.643 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 20.643 * [taylor]: Taking taylor expansion of 2.0 in k 20.643 * [backup-simplify]: Simplify 2.0 into 2.0 20.643 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.643 * [taylor]: Taking taylor expansion of PI in k 20.643 * [backup-simplify]: Simplify PI into PI 20.643 * [taylor]: Taking taylor expansion of n in k 20.643 * [backup-simplify]: Simplify n into n 20.643 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.643 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 20.643 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 20.643 * [backup-simplify]: Simplify (- 1) into -1 20.644 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.644 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 20.644 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 20.644 * [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)))))) 20.644 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 20.644 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 20.644 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 20.644 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 20.644 * [taylor]: Taking taylor expansion of 0.5 in n 20.644 * [backup-simplify]: Simplify 0.5 into 0.5 20.644 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.644 * [taylor]: Taking taylor expansion of 1.0 in n 20.644 * [backup-simplify]: Simplify 1.0 into 1.0 20.644 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.644 * [taylor]: Taking taylor expansion of k in n 20.644 * [backup-simplify]: Simplify k into k 20.645 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.645 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 20.645 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.645 * [taylor]: Taking taylor expansion of 2.0 in n 20.645 * [backup-simplify]: Simplify 2.0 into 2.0 20.645 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.645 * [taylor]: Taking taylor expansion of PI in n 20.645 * [backup-simplify]: Simplify PI into PI 20.645 * [taylor]: Taking taylor expansion of n in n 20.645 * [backup-simplify]: Simplify 0 into 0 20.645 * [backup-simplify]: Simplify 1 into 1 20.645 * [backup-simplify]: Simplify (/ PI 1) into PI 20.645 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.646 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.646 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.646 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.646 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 20.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.648 * [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)))) 20.649 * [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))))) 20.649 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 20.649 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 20.649 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 20.649 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 20.649 * [taylor]: Taking taylor expansion of 0.5 in n 20.649 * [backup-simplify]: Simplify 0.5 into 0.5 20.649 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.649 * [taylor]: Taking taylor expansion of 1.0 in n 20.649 * [backup-simplify]: Simplify 1.0 into 1.0 20.649 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.649 * [taylor]: Taking taylor expansion of k in n 20.649 * [backup-simplify]: Simplify k into k 20.649 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.649 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 20.649 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.649 * [taylor]: Taking taylor expansion of 2.0 in n 20.649 * [backup-simplify]: Simplify 2.0 into 2.0 20.649 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.649 * [taylor]: Taking taylor expansion of PI in n 20.649 * [backup-simplify]: Simplify PI into PI 20.649 * [taylor]: Taking taylor expansion of n in n 20.649 * [backup-simplify]: Simplify 0 into 0 20.649 * [backup-simplify]: Simplify 1 into 1 20.650 * [backup-simplify]: Simplify (/ PI 1) into PI 20.650 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.651 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.651 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.651 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.651 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 20.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.653 * [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)))) 20.653 * [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))))) 20.653 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 20.653 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 20.653 * [taylor]: Taking taylor expansion of 0.5 in k 20.653 * [backup-simplify]: Simplify 0.5 into 0.5 20.654 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 20.654 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.654 * [taylor]: Taking taylor expansion of 1.0 in k 20.654 * [backup-simplify]: Simplify 1.0 into 1.0 20.654 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.654 * [taylor]: Taking taylor expansion of k in k 20.654 * [backup-simplify]: Simplify 0 into 0 20.654 * [backup-simplify]: Simplify 1 into 1 20.654 * [backup-simplify]: Simplify (/ 1 1) into 1 20.654 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 20.654 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 20.654 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 20.654 * [taylor]: Taking taylor expansion of 2.0 in k 20.654 * [backup-simplify]: Simplify 2.0 into 2.0 20.654 * [taylor]: Taking taylor expansion of PI in k 20.654 * [backup-simplify]: Simplify PI into PI 20.654 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.655 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 20.655 * [taylor]: Taking taylor expansion of (log n) in k 20.655 * [taylor]: Taking taylor expansion of n in k 20.655 * [backup-simplify]: Simplify n into n 20.655 * [backup-simplify]: Simplify (log n) into (log n) 20.655 * [backup-simplify]: Simplify (- 1) into -1 20.656 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.656 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.656 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 20.657 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 20.659 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 20.660 * [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))))) 20.661 * [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))))) 20.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 20.665 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 20.665 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.665 * [backup-simplify]: Simplify (- 0) into 0 20.666 * [backup-simplify]: Simplify (+ 0 0) into 0 20.666 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 20.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.673 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 20.674 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.674 * [taylor]: Taking taylor expansion of 0 in k 20.674 * [backup-simplify]: Simplify 0 into 0 20.674 * [backup-simplify]: Simplify 0 into 0 20.674 * [backup-simplify]: Simplify 0 into 0 20.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.675 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.677 * [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 20.677 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.677 * [backup-simplify]: Simplify (- 0) into 0 20.678 * [backup-simplify]: Simplify (+ 0 0) into 0 20.678 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 20.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.680 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 20.682 * [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 20.682 * [taylor]: Taking taylor expansion of 0 in k 20.682 * [backup-simplify]: Simplify 0 into 0 20.682 * [backup-simplify]: Simplify 0 into 0 20.682 * [backup-simplify]: Simplify 0 into 0 20.682 * [backup-simplify]: Simplify 0 into 0 20.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.683 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.686 * [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 20.686 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.687 * [backup-simplify]: Simplify (- 0) into 0 20.687 * [backup-simplify]: Simplify (+ 0 0) into 0 20.688 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 20.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 20.690 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 20.691 * [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 20.691 * [taylor]: Taking taylor expansion of 0 in k 20.691 * [backup-simplify]: Simplify 0 into 0 20.691 * [backup-simplify]: Simplify 0 into 0 20.692 * [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)))))) 20.693 * [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))) 20.693 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 20.693 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 20.693 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 20.693 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 20.693 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 20.693 * [taylor]: Taking taylor expansion of 0.5 in k 20.693 * [backup-simplify]: Simplify 0.5 into 0.5 20.693 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.693 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.693 * [taylor]: Taking taylor expansion of k in k 20.693 * [backup-simplify]: Simplify 0 into 0 20.693 * [backup-simplify]: Simplify 1 into 1 20.693 * [backup-simplify]: Simplify (/ 1 1) into 1 20.693 * [taylor]: Taking taylor expansion of 1.0 in k 20.693 * [backup-simplify]: Simplify 1.0 into 1.0 20.693 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 20.693 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 20.693 * [taylor]: Taking taylor expansion of -2.0 in k 20.693 * [backup-simplify]: Simplify -2.0 into -2.0 20.693 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.693 * [taylor]: Taking taylor expansion of PI in k 20.693 * [backup-simplify]: Simplify PI into PI 20.693 * [taylor]: Taking taylor expansion of n in k 20.693 * [backup-simplify]: Simplify n into n 20.693 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.693 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 20.694 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 20.694 * [backup-simplify]: Simplify (+ 1 0) into 1 20.694 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 20.694 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 20.694 * [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)))) 20.694 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 20.694 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 20.694 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 20.694 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 20.694 * [taylor]: Taking taylor expansion of 0.5 in n 20.694 * [backup-simplify]: Simplify 0.5 into 0.5 20.694 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.694 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.694 * [taylor]: Taking taylor expansion of k in n 20.695 * [backup-simplify]: Simplify k into k 20.695 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.695 * [taylor]: Taking taylor expansion of 1.0 in n 20.695 * [backup-simplify]: Simplify 1.0 into 1.0 20.695 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 20.695 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.695 * [taylor]: Taking taylor expansion of -2.0 in n 20.695 * [backup-simplify]: Simplify -2.0 into -2.0 20.695 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.695 * [taylor]: Taking taylor expansion of PI in n 20.695 * [backup-simplify]: Simplify PI into PI 20.695 * [taylor]: Taking taylor expansion of n in n 20.695 * [backup-simplify]: Simplify 0 into 0 20.695 * [backup-simplify]: Simplify 1 into 1 20.695 * [backup-simplify]: Simplify (/ PI 1) into PI 20.695 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.696 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 20.696 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.696 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 20.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.698 * [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))) 20.699 * [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)))) 20.699 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 20.699 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 20.699 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 20.699 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 20.699 * [taylor]: Taking taylor expansion of 0.5 in n 20.699 * [backup-simplify]: Simplify 0.5 into 0.5 20.699 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.699 * [taylor]: Taking taylor expansion of k in n 20.699 * [backup-simplify]: Simplify k into k 20.699 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.699 * [taylor]: Taking taylor expansion of 1.0 in n 20.699 * [backup-simplify]: Simplify 1.0 into 1.0 20.699 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 20.699 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.699 * [taylor]: Taking taylor expansion of -2.0 in n 20.699 * [backup-simplify]: Simplify -2.0 into -2.0 20.699 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.699 * [taylor]: Taking taylor expansion of PI in n 20.699 * [backup-simplify]: Simplify PI into PI 20.699 * [taylor]: Taking taylor expansion of n in n 20.699 * [backup-simplify]: Simplify 0 into 0 20.699 * [backup-simplify]: Simplify 1 into 1 20.699 * [backup-simplify]: Simplify (/ PI 1) into PI 20.700 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.701 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 20.701 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.701 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 20.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.704 * [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))) 20.705 * [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)))) 20.705 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 20.705 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 20.705 * [taylor]: Taking taylor expansion of 0.5 in k 20.705 * [backup-simplify]: Simplify 0.5 into 0.5 20.705 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 20.705 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 20.705 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 20.705 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 20.705 * [taylor]: Taking taylor expansion of -2.0 in k 20.705 * [backup-simplify]: Simplify -2.0 into -2.0 20.705 * [taylor]: Taking taylor expansion of PI in k 20.705 * [backup-simplify]: Simplify PI into PI 20.706 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.707 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 20.707 * [taylor]: Taking taylor expansion of (log n) in k 20.707 * [taylor]: Taking taylor expansion of n in k 20.707 * [backup-simplify]: Simplify n into n 20.707 * [backup-simplify]: Simplify (log n) into (log n) 20.707 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.707 * [taylor]: Taking taylor expansion of k in k 20.707 * [backup-simplify]: Simplify 0 into 0 20.707 * [backup-simplify]: Simplify 1 into 1 20.708 * [backup-simplify]: Simplify (/ 1 1) into 1 20.708 * [taylor]: Taking taylor expansion of 1.0 in k 20.708 * [backup-simplify]: Simplify 1.0 into 1.0 20.708 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.709 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 20.709 * [backup-simplify]: Simplify (+ 1 0) into 1 20.711 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 20.712 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 20.713 * [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)))) 20.714 * [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)))) 20.716 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.716 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 20.718 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 20.718 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.719 * [backup-simplify]: Simplify (+ 0 0) into 0 20.719 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 20.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.722 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 20.724 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.724 * [taylor]: Taking taylor expansion of 0 in k 20.724 * [backup-simplify]: Simplify 0 into 0 20.724 * [backup-simplify]: Simplify 0 into 0 20.724 * [backup-simplify]: Simplify 0 into 0 20.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.726 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.729 * [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 20.729 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.729 * [backup-simplify]: Simplify (+ 0 0) into 0 20.730 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 20.731 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.732 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 20.733 * [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 20.733 * [taylor]: Taking taylor expansion of 0 in k 20.733 * [backup-simplify]: Simplify 0 into 0 20.733 * [backup-simplify]: Simplify 0 into 0 20.733 * [backup-simplify]: Simplify 0 into 0 20.733 * [backup-simplify]: Simplify 0 into 0 20.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.735 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.738 * [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 20.738 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.738 * [backup-simplify]: Simplify (+ 0 0) into 0 20.739 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 20.740 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 20.741 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 20.743 * [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 20.743 * [taylor]: Taking taylor expansion of 0 in k 20.743 * [backup-simplify]: Simplify 0 into 0 20.743 * [backup-simplify]: Simplify 0 into 0 20.744 * [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)))))) 20.744 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 2 1) 20.744 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 20.744 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 20.744 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.744 * [taylor]: Taking taylor expansion of 2.0 in n 20.744 * [backup-simplify]: Simplify 2.0 into 2.0 20.744 * [taylor]: Taking taylor expansion of (* n PI) in n 20.744 * [taylor]: Taking taylor expansion of n in n 20.744 * [backup-simplify]: Simplify 0 into 0 20.744 * [backup-simplify]: Simplify 1 into 1 20.744 * [taylor]: Taking taylor expansion of PI in n 20.744 * [backup-simplify]: Simplify PI into PI 20.744 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.744 * [taylor]: Taking taylor expansion of 2.0 in n 20.744 * [backup-simplify]: Simplify 2.0 into 2.0 20.744 * [taylor]: Taking taylor expansion of (* n PI) in n 20.744 * [taylor]: Taking taylor expansion of n in n 20.745 * [backup-simplify]: Simplify 0 into 0 20.745 * [backup-simplify]: Simplify 1 into 1 20.745 * [taylor]: Taking taylor expansion of PI in n 20.745 * [backup-simplify]: Simplify PI into PI 20.745 * [backup-simplify]: Simplify (* 0 PI) into 0 20.745 * [backup-simplify]: Simplify (* 2.0 0) into 0 20.745 * [backup-simplify]: Simplify 0 into 0 20.746 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.747 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 20.747 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.748 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.749 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 20.749 * [backup-simplify]: Simplify 0 into 0 20.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.750 * [backup-simplify]: Simplify 0 into 0 20.751 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.752 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 20.752 * [backup-simplify]: Simplify 0 into 0 20.753 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.753 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 20.754 * [backup-simplify]: Simplify 0 into 0 20.754 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 20.755 * [backup-simplify]: Simplify 0 into 0 20.757 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 20.758 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 20.758 * [backup-simplify]: Simplify 0 into 0 20.758 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 20.758 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 20.758 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 20.758 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.759 * [taylor]: Taking taylor expansion of 2.0 in n 20.759 * [backup-simplify]: Simplify 2.0 into 2.0 20.759 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.759 * [taylor]: Taking taylor expansion of PI in n 20.759 * [backup-simplify]: Simplify PI into PI 20.759 * [taylor]: Taking taylor expansion of n in n 20.759 * [backup-simplify]: Simplify 0 into 0 20.759 * [backup-simplify]: Simplify 1 into 1 20.759 * [backup-simplify]: Simplify (/ PI 1) into PI 20.759 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.759 * [taylor]: Taking taylor expansion of 2.0 in n 20.759 * [backup-simplify]: Simplify 2.0 into 2.0 20.759 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.759 * [taylor]: Taking taylor expansion of PI in n 20.759 * [backup-simplify]: Simplify PI into PI 20.759 * [taylor]: Taking taylor expansion of n in n 20.759 * [backup-simplify]: Simplify 0 into 0 20.759 * [backup-simplify]: Simplify 1 into 1 20.759 * [backup-simplify]: Simplify (/ PI 1) into PI 20.760 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.760 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.762 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 20.762 * [backup-simplify]: Simplify 0 into 0 20.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.764 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.764 * [backup-simplify]: Simplify 0 into 0 20.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.766 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.766 * [backup-simplify]: Simplify 0 into 0 20.768 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.769 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.769 * [backup-simplify]: Simplify 0 into 0 20.770 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.772 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.772 * [backup-simplify]: Simplify 0 into 0 20.773 * [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 20.775 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.775 * [backup-simplify]: Simplify 0 into 0 20.775 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 20.776 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 20.776 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 20.776 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.776 * [taylor]: Taking taylor expansion of -2.0 in n 20.776 * [backup-simplify]: Simplify -2.0 into -2.0 20.776 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.776 * [taylor]: Taking taylor expansion of PI in n 20.776 * [backup-simplify]: Simplify PI into PI 20.776 * [taylor]: Taking taylor expansion of n in n 20.776 * [backup-simplify]: Simplify 0 into 0 20.776 * [backup-simplify]: Simplify 1 into 1 20.777 * [backup-simplify]: Simplify (/ PI 1) into PI 20.777 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.777 * [taylor]: Taking taylor expansion of -2.0 in n 20.777 * [backup-simplify]: Simplify -2.0 into -2.0 20.777 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.777 * [taylor]: Taking taylor expansion of PI in n 20.777 * [backup-simplify]: Simplify PI into PI 20.777 * [taylor]: Taking taylor expansion of n in n 20.777 * [backup-simplify]: Simplify 0 into 0 20.777 * [backup-simplify]: Simplify 1 into 1 20.783 * [backup-simplify]: Simplify (/ PI 1) into PI 20.784 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.785 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.786 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 20.786 * [backup-simplify]: Simplify 0 into 0 20.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.787 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.787 * [backup-simplify]: Simplify 0 into 0 20.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.788 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.788 * [backup-simplify]: Simplify 0 into 0 20.789 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.790 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.790 * [backup-simplify]: Simplify 0 into 0 20.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.791 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.791 * [backup-simplify]: Simplify 0 into 0 20.792 * [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 20.793 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.793 * [backup-simplify]: Simplify 0 into 0 20.793 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 20.793 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 2 1) 20.794 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 20.794 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 20.794 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.794 * [taylor]: Taking taylor expansion of 2.0 in n 20.794 * [backup-simplify]: Simplify 2.0 into 2.0 20.794 * [taylor]: Taking taylor expansion of (* n PI) in n 20.794 * [taylor]: Taking taylor expansion of n in n 20.794 * [backup-simplify]: Simplify 0 into 0 20.794 * [backup-simplify]: Simplify 1 into 1 20.794 * [taylor]: Taking taylor expansion of PI in n 20.794 * [backup-simplify]: Simplify PI into PI 20.794 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 20.794 * [taylor]: Taking taylor expansion of 2.0 in n 20.794 * [backup-simplify]: Simplify 2.0 into 2.0 20.794 * [taylor]: Taking taylor expansion of (* n PI) in n 20.794 * [taylor]: Taking taylor expansion of n in n 20.794 * [backup-simplify]: Simplify 0 into 0 20.794 * [backup-simplify]: Simplify 1 into 1 20.794 * [taylor]: Taking taylor expansion of PI in n 20.794 * [backup-simplify]: Simplify PI into PI 20.794 * [backup-simplify]: Simplify (* 0 PI) into 0 20.795 * [backup-simplify]: Simplify (* 2.0 0) into 0 20.795 * [backup-simplify]: Simplify 0 into 0 20.796 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.797 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 20.797 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.797 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 20.798 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 20.798 * [backup-simplify]: Simplify 0 into 0 20.799 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 20.799 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 20.799 * [backup-simplify]: Simplify 0 into 0 20.801 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.801 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 20.801 * [backup-simplify]: Simplify 0 into 0 20.802 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.803 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 20.803 * [backup-simplify]: Simplify 0 into 0 20.804 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 20.806 * [backup-simplify]: Simplify 0 into 0 20.807 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 20.808 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 20.808 * [backup-simplify]: Simplify 0 into 0 20.808 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 20.809 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 20.809 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 20.809 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.809 * [taylor]: Taking taylor expansion of 2.0 in n 20.809 * [backup-simplify]: Simplify 2.0 into 2.0 20.809 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.809 * [taylor]: Taking taylor expansion of PI in n 20.809 * [backup-simplify]: Simplify PI into PI 20.809 * [taylor]: Taking taylor expansion of n in n 20.809 * [backup-simplify]: Simplify 0 into 0 20.809 * [backup-simplify]: Simplify 1 into 1 20.809 * [backup-simplify]: Simplify (/ PI 1) into PI 20.809 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 20.809 * [taylor]: Taking taylor expansion of 2.0 in n 20.809 * [backup-simplify]: Simplify 2.0 into 2.0 20.809 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.809 * [taylor]: Taking taylor expansion of PI in n 20.809 * [backup-simplify]: Simplify PI into PI 20.809 * [taylor]: Taking taylor expansion of n in n 20.809 * [backup-simplify]: Simplify 0 into 0 20.809 * [backup-simplify]: Simplify 1 into 1 20.810 * [backup-simplify]: Simplify (/ PI 1) into PI 20.810 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.810 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 20.811 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.811 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 20.811 * [backup-simplify]: Simplify 0 into 0 20.812 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.813 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.813 * [backup-simplify]: Simplify 0 into 0 20.813 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.814 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.814 * [backup-simplify]: Simplify 0 into 0 20.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.815 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.815 * [backup-simplify]: Simplify 0 into 0 20.816 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.818 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.818 * [backup-simplify]: Simplify 0 into 0 20.819 * [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 20.821 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.821 * [backup-simplify]: Simplify 0 into 0 20.822 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 20.822 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 20.822 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 20.822 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.822 * [taylor]: Taking taylor expansion of -2.0 in n 20.822 * [backup-simplify]: Simplify -2.0 into -2.0 20.822 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.822 * [taylor]: Taking taylor expansion of PI in n 20.822 * [backup-simplify]: Simplify PI into PI 20.822 * [taylor]: Taking taylor expansion of n in n 20.822 * [backup-simplify]: Simplify 0 into 0 20.822 * [backup-simplify]: Simplify 1 into 1 20.823 * [backup-simplify]: Simplify (/ PI 1) into PI 20.823 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 20.823 * [taylor]: Taking taylor expansion of -2.0 in n 20.823 * [backup-simplify]: Simplify -2.0 into -2.0 20.823 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.823 * [taylor]: Taking taylor expansion of PI in n 20.823 * [backup-simplify]: Simplify PI into PI 20.823 * [taylor]: Taking taylor expansion of n in n 20.823 * [backup-simplify]: Simplify 0 into 0 20.823 * [backup-simplify]: Simplify 1 into 1 20.824 * [backup-simplify]: Simplify (/ PI 1) into PI 20.824 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.825 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 20.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.827 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 20.827 * [backup-simplify]: Simplify 0 into 0 20.828 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.829 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 20.829 * [backup-simplify]: Simplify 0 into 0 20.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.831 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 20.831 * [backup-simplify]: Simplify 0 into 0 20.832 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.834 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 20.834 * [backup-simplify]: Simplify 0 into 0 20.835 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.837 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 20.837 * [backup-simplify]: Simplify 0 into 0 20.838 * [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 20.840 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 20.840 * [backup-simplify]: Simplify 0 into 0 20.840 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 20.840 * * * [progress]: simplifying candidates 20.844 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 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)))))) (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 20.847 * * [simplify]: iteration 0: 154 enodes 20.910 * * [simplify]: iteration 1: 430 enodes 21.096 * * [simplify]: iteration 2: 1340 enodes 21.688 * * [simplify]: iteration complete: 5000 enodes 21.688 * * [simplify]: Extracting #0: cost 44 inf + 0 21.690 * * [simplify]: Extracting #1: cost 566 inf + 0 21.700 * * [simplify]: Extracting #2: cost 1549 inf + 1434 21.718 * * [simplify]: Extracting #3: cost 1577 inf + 50817 21.771 * * [simplify]: Extracting #4: cost 705 inf + 243770 21.867 * * [simplify]: Extracting #5: cost 280 inf + 432795 22.027 * * [simplify]: Extracting #6: cost 121 inf + 510681 22.222 * * [simplify]: Extracting #7: cost 19 inf + 544118 22.331 * * [simplify]: Extracting #8: cost 1 inf + 551507 22.497 * * [simplify]: Extracting #9: cost 0 inf + 552215 22.646 * [simplify]: Simplified to: (expm1 (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (log1p (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n (* PI 2.0)) (/ 1.0 2.0)) (pow (* n (* PI 2.0)) (/ k 2.0)) (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (sqrt (- 1.0 k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (+ (sqrt k) (sqrt 1.0))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (pow (* n (* PI 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 (* n (* PI 2.0)))) (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (log1p (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n (* PI 2.0)) (/ 1.0 2.0)) (pow (* n (* PI 2.0)) (/ k 2.0)) (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (sqrt (- 1.0 k))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (pow (* n (* PI 2.0)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* n (* PI 2.0)) (+ (sqrt k) (sqrt 1.0))) (pow (* n (* PI 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0))) (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (pow (* n (* PI 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 (* n (* PI 2.0)))) (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* n (* PI 2.0))) (log1p (* n (* PI 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (exp (* n (* PI 2.0))) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* n (* PI 2.0))) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* n (* PI 2.0))) (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0)))) (cbrt (* n (* PI 2.0))) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (* (* (* 2.0 PI) (cbrt n)) (cbrt n)) (* (* 2.0 PI) (sqrt n)) (* PI 2.0) (* n PI) (expm1 (* n (* PI 2.0))) (log1p (* n (* PI 2.0))) (* n (* PI 2.0)) (* n (* PI 2.0)) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (log (* n (* PI 2.0))) (exp (* n (* PI 2.0))) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* n (* PI 2.0))) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* n (* PI 2.0))) (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0)))) (cbrt (* n (* PI 2.0))) (* (* (* n (* PI 2.0)) (* n (* PI 2.0))) (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (sqrt (* n (* PI 2.0))) (* (* (* 2.0 PI) (cbrt n)) (cbrt n)) (* (* 2.0 PI) (sqrt n)) (* PI 2.0) (* n PI) (fma (* (log (* PI 2.0)) 0.25) (* (* (exp (* (log (* n (* PI 2.0))) 0.5)) (* k k)) (log n)) (- (+ (* (* (exp (* (log (* n (* PI 2.0))) 0.5)) 0.125) (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0))))) (fma (* (exp (* (log (* n (* PI 2.0))) 0.5)) 0.125) (* (* (log n) k) (* (log n) k)) (exp (* (log (* n (* PI 2.0))) 0.5)))) (* (* k (* (exp (* (log (* n (* PI 2.0))) 0.5)) (+ (log n) (log (* PI 2.0))))) 0.5))) (exp (* 0.5 (* (log (* n (* PI 2.0))) (- 1.0 k)))) (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) (fma (* (log (* PI 2.0)) 0.25) (* (* (exp (* (log (* n (* PI 2.0))) 0.5)) (* k k)) (log n)) (- (+ (* (* (exp (* (log (* n (* PI 2.0))) 0.5)) 0.125) (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0))))) (fma (* (exp (* (log (* n (* PI 2.0))) 0.5)) 0.125) (* (* (log n) k) (* (log n) k)) (exp (* (log (* n (* PI 2.0))) 0.5)))) (* (* k (* (exp (* (log (* n (* PI 2.0))) 0.5)) (+ (log n) (log (* PI 2.0))))) 0.5))) (exp (* 0.5 (* (log (* n (* PI 2.0))) (- 1.0 k)))) (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) (* n (* PI 2.0)) 22.669 * * * [progress]: adding candidates to table 23.755 * [progress]: [Phase 3 of 3] Extracting. 23.755 * * [regime]: Finding splitpoints for: (# # # # # # # #) 23.756 * * * [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) 23.756 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 23.833 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # #) 23.966 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 24.088 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 24.210 * * * [regime]: Found split indices: #