55.161 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.160 * * * [progress]: [2/2] Setting up program. 0.164 * [progress]: [Phase 2 of 3] Improving. 0.164 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.165 * * [simplify]: iteration 0: 13 enodes 0.168 * * [simplify]: iteration 1: 29 enodes 0.174 * * [simplify]: iteration 2: 58 enodes 0.193 * * [simplify]: iteration 3: 114 enodes 0.219 * * [simplify]: iteration 4: 285 enodes 0.344 * * [simplify]: iteration 5: 816 enodes 1.367 * * [simplify]: iteration 6: 2792 enodes 2.336 * * [simplify]: iteration complete: 5003 enodes 2.336 * * [simplify]: Extracting #0: cost 1 inf + 0 2.336 * * [simplify]: Extracting #1: cost 108 inf + 0 2.338 * * [simplify]: Extracting #2: cost 443 inf + 1 2.341 * * [simplify]: Extracting #3: cost 1022 inf + 49 2.348 * * [simplify]: Extracting #4: cost 1321 inf + 10849 2.383 * * [simplify]: Extracting #5: cost 617 inf + 94525 2.474 * * [simplify]: Extracting #6: cost 187 inf + 373026 2.620 * * [simplify]: Extracting #7: cost 0 inf + 567203 2.764 * * [simplify]: Extracting #8: cost 0 inf + 562474 2.918 * * [simplify]: Extracting #9: cost 0 inf + 561804 3.084 * [simplify]: Simplified to: (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) 3.085 * * [progress]: iteration 1 / 4 3.085 * * * [progress]: picking best candidate 3.094 * * * * [pick]: Picked # 3.094 * * * [progress]: localizing error 3.140 * * * [progress]: generating rewritten candidates 3.140 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 3.173 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 3.196 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 3.201 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 3.249 * * * [progress]: generating series expansions 3.249 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 3.250 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 3.250 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 3.250 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.250 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.250 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.250 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.250 * [taylor]: Taking taylor expansion of 0.5 in k 3.250 * [backup-simplify]: Simplify 0.5 into 0.5 3.250 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.250 * [taylor]: Taking taylor expansion of 1.0 in k 3.250 * [backup-simplify]: Simplify 1.0 into 1.0 3.250 * [taylor]: Taking taylor expansion of k in k 3.250 * [backup-simplify]: Simplify 0 into 0 3.250 * [backup-simplify]: Simplify 1 into 1 3.250 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.250 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.250 * [taylor]: Taking taylor expansion of 2.0 in k 3.250 * [backup-simplify]: Simplify 2.0 into 2.0 3.250 * [taylor]: Taking taylor expansion of (* n PI) in k 3.250 * [taylor]: Taking taylor expansion of n in k 3.250 * [backup-simplify]: Simplify n into n 3.250 * [taylor]: Taking taylor expansion of PI in k 3.250 * [backup-simplify]: Simplify PI into PI 3.250 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.250 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.250 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.251 * [backup-simplify]: Simplify (- 0) into 0 3.251 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.251 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.251 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.252 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.252 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.252 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.252 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.252 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.252 * [taylor]: Taking taylor expansion of 0.5 in n 3.252 * [backup-simplify]: Simplify 0.5 into 0.5 3.252 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.252 * [taylor]: Taking taylor expansion of 1.0 in n 3.252 * [backup-simplify]: Simplify 1.0 into 1.0 3.252 * [taylor]: Taking taylor expansion of k in n 3.252 * [backup-simplify]: Simplify k into k 3.252 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.252 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.252 * [taylor]: Taking taylor expansion of 2.0 in n 3.252 * [backup-simplify]: Simplify 2.0 into 2.0 3.252 * [taylor]: Taking taylor expansion of (* n PI) in n 3.252 * [taylor]: Taking taylor expansion of n in n 3.252 * [backup-simplify]: Simplify 0 into 0 3.252 * [backup-simplify]: Simplify 1 into 1 3.252 * [taylor]: Taking taylor expansion of PI in n 3.252 * [backup-simplify]: Simplify PI into PI 3.252 * [backup-simplify]: Simplify (* 0 PI) into 0 3.253 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.254 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.255 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.255 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.255 * [backup-simplify]: Simplify (- k) into (- k) 3.255 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.256 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.256 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.257 * [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)))) 3.258 * [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))))) 3.258 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.258 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.258 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.258 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.258 * [taylor]: Taking taylor expansion of 0.5 in n 3.258 * [backup-simplify]: Simplify 0.5 into 0.5 3.258 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.258 * [taylor]: Taking taylor expansion of 1.0 in n 3.258 * [backup-simplify]: Simplify 1.0 into 1.0 3.258 * [taylor]: Taking taylor expansion of k in n 3.258 * [backup-simplify]: Simplify k into k 3.258 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.258 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.258 * [taylor]: Taking taylor expansion of 2.0 in n 3.258 * [backup-simplify]: Simplify 2.0 into 2.0 3.258 * [taylor]: Taking taylor expansion of (* n PI) in n 3.258 * [taylor]: Taking taylor expansion of n in n 3.258 * [backup-simplify]: Simplify 0 into 0 3.258 * [backup-simplify]: Simplify 1 into 1 3.258 * [taylor]: Taking taylor expansion of PI in n 3.258 * [backup-simplify]: Simplify PI into PI 3.259 * [backup-simplify]: Simplify (* 0 PI) into 0 3.259 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.260 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.261 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.262 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.262 * [backup-simplify]: Simplify (- k) into (- k) 3.262 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.262 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.263 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.264 * [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)))) 3.265 * [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))))) 3.265 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 3.265 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 3.265 * [taylor]: Taking taylor expansion of 0.5 in k 3.265 * [backup-simplify]: Simplify 0.5 into 0.5 3.265 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 3.265 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.265 * [taylor]: Taking taylor expansion of 1.0 in k 3.265 * [backup-simplify]: Simplify 1.0 into 1.0 3.265 * [taylor]: Taking taylor expansion of k in k 3.265 * [backup-simplify]: Simplify 0 into 0 3.265 * [backup-simplify]: Simplify 1 into 1 3.266 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 3.266 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.266 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.266 * [taylor]: Taking taylor expansion of 2.0 in k 3.266 * [backup-simplify]: Simplify 2.0 into 2.0 3.266 * [taylor]: Taking taylor expansion of PI in k 3.266 * [backup-simplify]: Simplify PI into PI 3.266 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.267 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.268 * [taylor]: Taking taylor expansion of (log n) in k 3.268 * [taylor]: Taking taylor expansion of n in k 3.268 * [backup-simplify]: Simplify n into n 3.268 * [backup-simplify]: Simplify (log n) into (log n) 3.269 * [backup-simplify]: Simplify (- 0) into 0 3.269 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.271 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 3.272 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 3.273 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 3.275 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.276 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 3.277 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.278 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.280 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.281 * [backup-simplify]: Simplify (- 0) into 0 3.281 * [backup-simplify]: Simplify (+ 0 0) into 0 3.282 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 3.287 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.288 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 3.290 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.291 * [taylor]: Taking taylor expansion of 0 in k 3.291 * [backup-simplify]: Simplify 0 into 0 3.291 * [backup-simplify]: Simplify 0 into 0 3.291 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.293 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.294 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.295 * [backup-simplify]: Simplify (+ 0 0) into 0 3.295 * [backup-simplify]: Simplify (- 1) into -1 3.295 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.297 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 3.299 * [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)))) 3.303 * [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)))))) 3.306 * [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)))))) 3.307 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.312 * [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 3.313 * [backup-simplify]: Simplify (- 0) into 0 3.313 * [backup-simplify]: Simplify (+ 0 0) into 0 3.314 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 3.315 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.317 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.320 * [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 3.320 * [taylor]: Taking taylor expansion of 0 in k 3.320 * [backup-simplify]: Simplify 0 into 0 3.320 * [backup-simplify]: Simplify 0 into 0 3.320 * [backup-simplify]: Simplify 0 into 0 3.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.324 * [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 3.325 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.325 * [backup-simplify]: Simplify (+ 0 0) into 0 3.326 * [backup-simplify]: Simplify (- 0) into 0 3.326 * [backup-simplify]: Simplify (+ 0 0) into 0 3.327 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 3.329 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 3.331 * [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)))))) 3.335 * [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)))))) 3.342 * [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))))) 3.342 * [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)))) 3.342 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 3.342 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.342 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.342 * [taylor]: Taking taylor expansion of 0.5 in k 3.342 * [backup-simplify]: Simplify 0.5 into 0.5 3.342 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.342 * [taylor]: Taking taylor expansion of 1.0 in k 3.342 * [backup-simplify]: Simplify 1.0 into 1.0 3.342 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.342 * [taylor]: Taking taylor expansion of k in k 3.342 * [backup-simplify]: Simplify 0 into 0 3.342 * [backup-simplify]: Simplify 1 into 1 3.343 * [backup-simplify]: Simplify (/ 1 1) into 1 3.343 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.343 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.343 * [taylor]: Taking taylor expansion of 2.0 in k 3.343 * [backup-simplify]: Simplify 2.0 into 2.0 3.343 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.343 * [taylor]: Taking taylor expansion of PI in k 3.343 * [backup-simplify]: Simplify PI into PI 3.343 * [taylor]: Taking taylor expansion of n in k 3.343 * [backup-simplify]: Simplify n into n 3.343 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.343 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.343 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.343 * [backup-simplify]: Simplify (- 1) into -1 3.344 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.344 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.344 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.344 * [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)))))) 3.344 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.344 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.344 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.344 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.344 * [taylor]: Taking taylor expansion of 0.5 in n 3.344 * [backup-simplify]: Simplify 0.5 into 0.5 3.344 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.344 * [taylor]: Taking taylor expansion of 1.0 in n 3.344 * [backup-simplify]: Simplify 1.0 into 1.0 3.344 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.344 * [taylor]: Taking taylor expansion of k in n 3.344 * [backup-simplify]: Simplify k into k 3.344 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.344 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.344 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.344 * [taylor]: Taking taylor expansion of 2.0 in n 3.344 * [backup-simplify]: Simplify 2.0 into 2.0 3.344 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.344 * [taylor]: Taking taylor expansion of PI in n 3.344 * [backup-simplify]: Simplify PI into PI 3.344 * [taylor]: Taking taylor expansion of n in n 3.344 * [backup-simplify]: Simplify 0 into 0 3.344 * [backup-simplify]: Simplify 1 into 1 3.345 * [backup-simplify]: Simplify (/ PI 1) into PI 3.345 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.346 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.346 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.346 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.346 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.347 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.348 * [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)))) 3.349 * [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))))) 3.349 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.349 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.349 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.349 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.349 * [taylor]: Taking taylor expansion of 0.5 in n 3.349 * [backup-simplify]: Simplify 0.5 into 0.5 3.349 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.349 * [taylor]: Taking taylor expansion of 1.0 in n 3.349 * [backup-simplify]: Simplify 1.0 into 1.0 3.349 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.349 * [taylor]: Taking taylor expansion of k in n 3.349 * [backup-simplify]: Simplify k into k 3.349 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.349 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.349 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.349 * [taylor]: Taking taylor expansion of 2.0 in n 3.349 * [backup-simplify]: Simplify 2.0 into 2.0 3.349 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.349 * [taylor]: Taking taylor expansion of PI in n 3.349 * [backup-simplify]: Simplify PI into PI 3.349 * [taylor]: Taking taylor expansion of n in n 3.349 * [backup-simplify]: Simplify 0 into 0 3.349 * [backup-simplify]: Simplify 1 into 1 3.349 * [backup-simplify]: Simplify (/ PI 1) into PI 3.350 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.350 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.350 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.350 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.350 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.351 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.352 * [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)))) 3.353 * [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))))) 3.353 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 3.353 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 3.353 * [taylor]: Taking taylor expansion of 0.5 in k 3.353 * [backup-simplify]: Simplify 0.5 into 0.5 3.353 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 3.353 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.353 * [taylor]: Taking taylor expansion of 1.0 in k 3.353 * [backup-simplify]: Simplify 1.0 into 1.0 3.353 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.353 * [taylor]: Taking taylor expansion of k in k 3.353 * [backup-simplify]: Simplify 0 into 0 3.353 * [backup-simplify]: Simplify 1 into 1 3.353 * [backup-simplify]: Simplify (/ 1 1) into 1 3.353 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 3.353 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 3.353 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 3.353 * [taylor]: Taking taylor expansion of 2.0 in k 3.354 * [backup-simplify]: Simplify 2.0 into 2.0 3.354 * [taylor]: Taking taylor expansion of PI in k 3.354 * [backup-simplify]: Simplify PI into PI 3.354 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.354 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.355 * [taylor]: Taking taylor expansion of (log n) in k 3.355 * [taylor]: Taking taylor expansion of n in k 3.355 * [backup-simplify]: Simplify n into n 3.355 * [backup-simplify]: Simplify (log n) into (log n) 3.355 * [backup-simplify]: Simplify (- 1) into -1 3.355 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.355 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.356 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 3.357 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 3.358 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 3.360 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.360 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 3.361 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.362 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.363 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.363 * [backup-simplify]: Simplify (- 0) into 0 3.363 * [backup-simplify]: Simplify (+ 0 0) into 0 3.363 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.365 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.366 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.366 * [taylor]: Taking taylor expansion of 0 in k 3.366 * [backup-simplify]: Simplify 0 into 0 3.366 * [backup-simplify]: Simplify 0 into 0 3.366 * [backup-simplify]: Simplify 0 into 0 3.367 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.368 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.369 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 3.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.370 * [backup-simplify]: Simplify (- 0) into 0 3.370 * [backup-simplify]: Simplify (+ 0 0) into 0 3.371 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 3.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.373 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 3.374 * [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 3.374 * [taylor]: Taking taylor expansion of 0 in k 3.374 * [backup-simplify]: Simplify 0 into 0 3.374 * [backup-simplify]: Simplify 0 into 0 3.374 * [backup-simplify]: Simplify 0 into 0 3.374 * [backup-simplify]: Simplify 0 into 0 3.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.376 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.379 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 3.379 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.379 * [backup-simplify]: Simplify (- 0) into 0 3.380 * [backup-simplify]: Simplify (+ 0 0) into 0 3.381 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 3.382 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.383 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 3.384 * [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 3.385 * [taylor]: Taking taylor expansion of 0 in k 3.385 * [backup-simplify]: Simplify 0 into 0 3.385 * [backup-simplify]: Simplify 0 into 0 3.385 * [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)))))) 3.386 * [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))) 3.386 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 3.386 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.386 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.386 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.386 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.386 * [taylor]: Taking taylor expansion of 0.5 in k 3.386 * [backup-simplify]: Simplify 0.5 into 0.5 3.386 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.386 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.386 * [taylor]: Taking taylor expansion of k in k 3.386 * [backup-simplify]: Simplify 0 into 0 3.386 * [backup-simplify]: Simplify 1 into 1 3.386 * [backup-simplify]: Simplify (/ 1 1) into 1 3.386 * [taylor]: Taking taylor expansion of 1.0 in k 3.386 * [backup-simplify]: Simplify 1.0 into 1.0 3.386 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.386 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.386 * [taylor]: Taking taylor expansion of -2.0 in k 3.386 * [backup-simplify]: Simplify -2.0 into -2.0 3.386 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.386 * [taylor]: Taking taylor expansion of PI in k 3.386 * [backup-simplify]: Simplify PI into PI 3.386 * [taylor]: Taking taylor expansion of n in k 3.386 * [backup-simplify]: Simplify n into n 3.387 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.387 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.387 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.387 * [backup-simplify]: Simplify (+ 1 0) into 1 3.387 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.387 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.388 * [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)))) 3.388 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.388 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.388 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.388 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.388 * [taylor]: Taking taylor expansion of 0.5 in n 3.388 * [backup-simplify]: Simplify 0.5 into 0.5 3.388 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.388 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.388 * [taylor]: Taking taylor expansion of k in n 3.388 * [backup-simplify]: Simplify k into k 3.388 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.388 * [taylor]: Taking taylor expansion of 1.0 in n 3.388 * [backup-simplify]: Simplify 1.0 into 1.0 3.388 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.388 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.388 * [taylor]: Taking taylor expansion of -2.0 in n 3.388 * [backup-simplify]: Simplify -2.0 into -2.0 3.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.388 * [taylor]: Taking taylor expansion of PI in n 3.388 * [backup-simplify]: Simplify PI into PI 3.388 * [taylor]: Taking taylor expansion of n in n 3.388 * [backup-simplify]: Simplify 0 into 0 3.388 * [backup-simplify]: Simplify 1 into 1 3.389 * [backup-simplify]: Simplify (/ PI 1) into PI 3.389 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.391 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.391 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.391 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.397 * [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))) 3.398 * [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)))) 3.398 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.398 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.398 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.398 * [taylor]: Taking taylor expansion of 0.5 in n 3.398 * [backup-simplify]: Simplify 0.5 into 0.5 3.399 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.399 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.399 * [taylor]: Taking taylor expansion of k in n 3.399 * [backup-simplify]: Simplify k into k 3.399 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.399 * [taylor]: Taking taylor expansion of 1.0 in n 3.399 * [backup-simplify]: Simplify 1.0 into 1.0 3.399 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.399 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.399 * [taylor]: Taking taylor expansion of -2.0 in n 3.399 * [backup-simplify]: Simplify -2.0 into -2.0 3.399 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.399 * [taylor]: Taking taylor expansion of PI in n 3.399 * [backup-simplify]: Simplify PI into PI 3.399 * [taylor]: Taking taylor expansion of n in n 3.399 * [backup-simplify]: Simplify 0 into 0 3.399 * [backup-simplify]: Simplify 1 into 1 3.400 * [backup-simplify]: Simplify (/ PI 1) into PI 3.400 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.401 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.401 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.401 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.404 * [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))) 3.406 * [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)))) 3.406 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 3.406 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 3.406 * [taylor]: Taking taylor expansion of 0.5 in k 3.406 * [backup-simplify]: Simplify 0.5 into 0.5 3.406 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 3.406 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 3.406 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 3.406 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 3.406 * [taylor]: Taking taylor expansion of -2.0 in k 3.406 * [backup-simplify]: Simplify -2.0 into -2.0 3.406 * [taylor]: Taking taylor expansion of PI in k 3.406 * [backup-simplify]: Simplify PI into PI 3.407 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.408 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.408 * [taylor]: Taking taylor expansion of (log n) in k 3.408 * [taylor]: Taking taylor expansion of n in k 3.408 * [backup-simplify]: Simplify n into n 3.408 * [backup-simplify]: Simplify (log n) into (log n) 3.408 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.408 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.408 * [taylor]: Taking taylor expansion of k in k 3.408 * [backup-simplify]: Simplify 0 into 0 3.408 * [backup-simplify]: Simplify 1 into 1 3.408 * [backup-simplify]: Simplify (/ 1 1) into 1 3.409 * [taylor]: Taking taylor expansion of 1.0 in k 3.409 * [backup-simplify]: Simplify 1.0 into 1.0 3.409 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.410 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 3.410 * [backup-simplify]: Simplify (+ 1 0) into 1 3.412 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 3.413 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 3.414 * [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)))) 3.415 * [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)))) 3.416 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.416 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.417 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.418 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.418 * [backup-simplify]: Simplify (+ 0 0) into 0 3.418 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.419 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.420 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.421 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.421 * [taylor]: Taking taylor expansion of 0 in k 3.421 * [backup-simplify]: Simplify 0 into 0 3.421 * [backup-simplify]: Simplify 0 into 0 3.421 * [backup-simplify]: Simplify 0 into 0 3.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.422 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.424 * [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 3.425 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.425 * [backup-simplify]: Simplify (+ 0 0) into 0 3.425 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 3.426 * [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 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 3.429 * [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 3.429 * [taylor]: Taking taylor expansion of 0 in k 3.429 * [backup-simplify]: Simplify 0 into 0 3.429 * [backup-simplify]: Simplify 0 into 0 3.429 * [backup-simplify]: Simplify 0 into 0 3.429 * [backup-simplify]: Simplify 0 into 0 3.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.430 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.434 * [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 3.434 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.434 * [backup-simplify]: Simplify (+ 0 0) into 0 3.435 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 3.436 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.437 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 3.439 * [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 3.439 * [taylor]: Taking taylor expansion of 0 in k 3.439 * [backup-simplify]: Simplify 0 into 0 3.439 * [backup-simplify]: Simplify 0 into 0 3.440 * [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)))))) 3.440 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 3.440 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.440 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 3.440 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.440 * [taylor]: Taking taylor expansion of 2.0 in n 3.440 * [backup-simplify]: Simplify 2.0 into 2.0 3.440 * [taylor]: Taking taylor expansion of (* n PI) in n 3.440 * [taylor]: Taking taylor expansion of n in n 3.440 * [backup-simplify]: Simplify 0 into 0 3.440 * [backup-simplify]: Simplify 1 into 1 3.440 * [taylor]: Taking taylor expansion of PI in n 3.440 * [backup-simplify]: Simplify PI into PI 3.440 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.440 * [taylor]: Taking taylor expansion of 2.0 in n 3.440 * [backup-simplify]: Simplify 2.0 into 2.0 3.440 * [taylor]: Taking taylor expansion of (* n PI) in n 3.440 * [taylor]: Taking taylor expansion of n in n 3.440 * [backup-simplify]: Simplify 0 into 0 3.440 * [backup-simplify]: Simplify 1 into 1 3.440 * [taylor]: Taking taylor expansion of PI in n 3.441 * [backup-simplify]: Simplify PI into PI 3.441 * [backup-simplify]: Simplify (* 0 PI) into 0 3.441 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.441 * [backup-simplify]: Simplify 0 into 0 3.442 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.443 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.443 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.444 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 3.445 * [backup-simplify]: Simplify 0 into 0 3.445 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.446 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.446 * [backup-simplify]: Simplify 0 into 0 3.447 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.449 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.449 * [backup-simplify]: Simplify 0 into 0 3.450 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.452 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.452 * [backup-simplify]: Simplify 0 into 0 3.454 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.456 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.456 * [backup-simplify]: Simplify 0 into 0 3.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.460 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.460 * [backup-simplify]: Simplify 0 into 0 3.461 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 3.461 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 3.461 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 3.461 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.461 * [taylor]: Taking taylor expansion of 2.0 in n 3.461 * [backup-simplify]: Simplify 2.0 into 2.0 3.461 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.461 * [taylor]: Taking taylor expansion of PI in n 3.461 * [backup-simplify]: Simplify PI into PI 3.461 * [taylor]: Taking taylor expansion of n in n 3.461 * [backup-simplify]: Simplify 0 into 0 3.461 * [backup-simplify]: Simplify 1 into 1 3.462 * [backup-simplify]: Simplify (/ PI 1) into PI 3.462 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.462 * [taylor]: Taking taylor expansion of 2.0 in n 3.462 * [backup-simplify]: Simplify 2.0 into 2.0 3.462 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.462 * [taylor]: Taking taylor expansion of PI in n 3.462 * [backup-simplify]: Simplify PI into PI 3.462 * [taylor]: Taking taylor expansion of n in n 3.462 * [backup-simplify]: Simplify 0 into 0 3.462 * [backup-simplify]: Simplify 1 into 1 3.463 * [backup-simplify]: Simplify (/ PI 1) into PI 3.463 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.464 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.465 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.465 * [backup-simplify]: Simplify 0 into 0 3.466 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.467 * [backup-simplify]: Simplify 0 into 0 3.468 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.470 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.470 * [backup-simplify]: Simplify 0 into 0 3.471 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.472 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.472 * [backup-simplify]: Simplify 0 into 0 3.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.475 * [backup-simplify]: Simplify 0 into 0 3.476 * [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 3.477 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.477 * [backup-simplify]: Simplify 0 into 0 3.477 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 3.478 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 3.478 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 3.478 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.478 * [taylor]: Taking taylor expansion of -2.0 in n 3.478 * [backup-simplify]: Simplify -2.0 into -2.0 3.478 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.478 * [taylor]: Taking taylor expansion of PI in n 3.478 * [backup-simplify]: Simplify PI into PI 3.478 * [taylor]: Taking taylor expansion of n in n 3.478 * [backup-simplify]: Simplify 0 into 0 3.478 * [backup-simplify]: Simplify 1 into 1 3.478 * [backup-simplify]: Simplify (/ PI 1) into PI 3.478 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.478 * [taylor]: Taking taylor expansion of -2.0 in n 3.478 * [backup-simplify]: Simplify -2.0 into -2.0 3.478 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.478 * [taylor]: Taking taylor expansion of PI in n 3.478 * [backup-simplify]: Simplify PI into PI 3.478 * [taylor]: Taking taylor expansion of n in n 3.478 * [backup-simplify]: Simplify 0 into 0 3.478 * [backup-simplify]: Simplify 1 into 1 3.478 * [backup-simplify]: Simplify (/ PI 1) into PI 3.479 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.479 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.480 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.480 * [backup-simplify]: Simplify 0 into 0 3.481 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.482 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 3.482 * [backup-simplify]: Simplify 0 into 0 3.482 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.483 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.483 * [backup-simplify]: Simplify 0 into 0 3.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.485 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.485 * [backup-simplify]: Simplify 0 into 0 3.485 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.486 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.486 * [backup-simplify]: Simplify 0 into 0 3.487 * [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 3.488 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.488 * [backup-simplify]: Simplify 0 into 0 3.489 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 3.489 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 3.489 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 3.489 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 3.489 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.489 * [taylor]: Taking taylor expansion of 1.0 in k 3.489 * [backup-simplify]: Simplify 1.0 into 1.0 3.489 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.489 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.489 * [taylor]: Taking taylor expansion of k in k 3.489 * [backup-simplify]: Simplify 0 into 0 3.489 * [backup-simplify]: Simplify 1 into 1 3.489 * [backup-simplify]: Simplify (/ 1 1) into 1 3.489 * [backup-simplify]: Simplify (sqrt 0) into 0 3.490 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.491 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 3.491 * [taylor]: Taking taylor expansion of 1.0 in k 3.491 * [backup-simplify]: Simplify 1.0 into 1.0 3.491 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.491 * [taylor]: Taking taylor expansion of k in k 3.491 * [backup-simplify]: Simplify 0 into 0 3.491 * [backup-simplify]: Simplify 1 into 1 3.491 * [backup-simplify]: Simplify (/ 1 1) into 1 3.491 * [backup-simplify]: Simplify (sqrt 0) into 0 3.492 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.492 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.492 * [backup-simplify]: Simplify 0 into 0 3.493 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.494 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.495 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.497 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.499 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.499 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.500 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.502 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.504 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.504 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.505 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 3.505 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 3.505 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 3.505 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.505 * [taylor]: Taking taylor expansion of 1.0 in k 3.505 * [backup-simplify]: Simplify 1.0 into 1.0 3.505 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.506 * [taylor]: Taking taylor expansion of k in k 3.506 * [backup-simplify]: Simplify 0 into 0 3.506 * [backup-simplify]: Simplify 1 into 1 3.506 * [backup-simplify]: Simplify (sqrt 0) into 0 3.507 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.507 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 3.507 * [taylor]: Taking taylor expansion of 1.0 in k 3.507 * [backup-simplify]: Simplify 1.0 into 1.0 3.507 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.507 * [taylor]: Taking taylor expansion of k in k 3.507 * [backup-simplify]: Simplify 0 into 0 3.507 * [backup-simplify]: Simplify 1 into 1 3.507 * [backup-simplify]: Simplify (sqrt 0) into 0 3.510 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.510 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.510 * [backup-simplify]: Simplify 0 into 0 3.511 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 3.512 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.513 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.515 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 3.515 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.517 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.518 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 3.519 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.520 * [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)))))))) 3.520 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 3.520 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 3.520 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.520 * [taylor]: Taking taylor expansion of 1.0 in k 3.520 * [backup-simplify]: Simplify 1.0 into 1.0 3.520 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.520 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.520 * [taylor]: Taking taylor expansion of -1 in k 3.520 * [backup-simplify]: Simplify -1 into -1 3.520 * [taylor]: Taking taylor expansion of k in k 3.520 * [backup-simplify]: Simplify 0 into 0 3.520 * [backup-simplify]: Simplify 1 into 1 3.520 * [backup-simplify]: Simplify (/ -1 1) into -1 3.521 * [backup-simplify]: Simplify (sqrt 0) into 0 3.521 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.522 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.522 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 3.522 * [taylor]: Taking taylor expansion of 1.0 in k 3.522 * [backup-simplify]: Simplify 1.0 into 1.0 3.522 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.522 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.522 * [taylor]: Taking taylor expansion of -1 in k 3.522 * [backup-simplify]: Simplify -1 into -1 3.522 * [taylor]: Taking taylor expansion of k in k 3.522 * [backup-simplify]: Simplify 0 into 0 3.522 * [backup-simplify]: Simplify 1 into 1 3.522 * [backup-simplify]: Simplify (/ -1 1) into -1 3.522 * [backup-simplify]: Simplify (sqrt 0) into 0 3.523 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.523 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 3.523 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.526 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.527 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 3.528 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.530 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.533 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 3.533 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 3.534 * [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))))) 3.534 * * * * [progress]: [ 4 / 4 ] generating series at (2) 3.535 * [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)))) 3.535 * [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 3.535 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 3.535 * [taylor]: Taking taylor expansion of 1.0 in n 3.535 * [backup-simplify]: Simplify 1.0 into 1.0 3.535 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 3.535 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 3.535 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 3.535 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 3.535 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 3.535 * [taylor]: Taking taylor expansion of 0.5 in n 3.535 * [backup-simplify]: Simplify 0.5 into 0.5 3.535 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 3.535 * [taylor]: Taking taylor expansion of 1.0 in n 3.535 * [backup-simplify]: Simplify 1.0 into 1.0 3.535 * [taylor]: Taking taylor expansion of k in n 3.535 * [backup-simplify]: Simplify k into k 3.535 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.535 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.535 * [taylor]: Taking taylor expansion of 2.0 in n 3.535 * [backup-simplify]: Simplify 2.0 into 2.0 3.535 * [taylor]: Taking taylor expansion of (* n PI) in n 3.535 * [taylor]: Taking taylor expansion of n in n 3.535 * [backup-simplify]: Simplify 0 into 0 3.535 * [backup-simplify]: Simplify 1 into 1 3.535 * [taylor]: Taking taylor expansion of PI in n 3.535 * [backup-simplify]: Simplify PI into PI 3.535 * [backup-simplify]: Simplify (* 0 PI) into 0 3.536 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.537 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.538 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.538 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.538 * [backup-simplify]: Simplify (- k) into (- k) 3.538 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 3.539 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 3.540 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.541 * [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)))) 3.542 * [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))))) 3.542 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.542 * [taylor]: Taking taylor expansion of k in n 3.542 * [backup-simplify]: Simplify k into k 3.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.542 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.542 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.542 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.543 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.543 * [taylor]: Taking taylor expansion of 1.0 in k 3.543 * [backup-simplify]: Simplify 1.0 into 1.0 3.543 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.543 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.543 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.543 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.543 * [taylor]: Taking taylor expansion of 0.5 in k 3.543 * [backup-simplify]: Simplify 0.5 into 0.5 3.543 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.543 * [taylor]: Taking taylor expansion of 1.0 in k 3.543 * [backup-simplify]: Simplify 1.0 into 1.0 3.543 * [taylor]: Taking taylor expansion of k in k 3.543 * [backup-simplify]: Simplify 0 into 0 3.543 * [backup-simplify]: Simplify 1 into 1 3.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.543 * [taylor]: Taking taylor expansion of 2.0 in k 3.543 * [backup-simplify]: Simplify 2.0 into 2.0 3.543 * [taylor]: Taking taylor expansion of (* n PI) in k 3.543 * [taylor]: Taking taylor expansion of n in k 3.543 * [backup-simplify]: Simplify n into n 3.543 * [taylor]: Taking taylor expansion of PI in k 3.543 * [backup-simplify]: Simplify PI into PI 3.543 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.543 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.543 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.544 * [backup-simplify]: Simplify (- 0) into 0 3.544 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.545 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.545 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.545 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.545 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.545 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.545 * [taylor]: Taking taylor expansion of k in k 3.545 * [backup-simplify]: Simplify 0 into 0 3.545 * [backup-simplify]: Simplify 1 into 1 3.546 * [backup-simplify]: Simplify (/ 1 1) into 1 3.546 * [backup-simplify]: Simplify (sqrt 0) into 0 3.547 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.548 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 3.548 * [taylor]: Taking taylor expansion of 1.0 in k 3.548 * [backup-simplify]: Simplify 1.0 into 1.0 3.548 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 3.548 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 3.548 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 3.548 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 3.548 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 3.548 * [taylor]: Taking taylor expansion of 0.5 in k 3.548 * [backup-simplify]: Simplify 0.5 into 0.5 3.548 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 3.548 * [taylor]: Taking taylor expansion of 1.0 in k 3.548 * [backup-simplify]: Simplify 1.0 into 1.0 3.548 * [taylor]: Taking taylor expansion of k in k 3.548 * [backup-simplify]: Simplify 0 into 0 3.548 * [backup-simplify]: Simplify 1 into 1 3.548 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 3.548 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 3.548 * [taylor]: Taking taylor expansion of 2.0 in k 3.548 * [backup-simplify]: Simplify 2.0 into 2.0 3.548 * [taylor]: Taking taylor expansion of (* n PI) in k 3.548 * [taylor]: Taking taylor expansion of n in k 3.548 * [backup-simplify]: Simplify n into n 3.548 * [taylor]: Taking taylor expansion of PI in k 3.548 * [backup-simplify]: Simplify PI into PI 3.548 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.548 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 3.549 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 3.549 * [backup-simplify]: Simplify (- 0) into 0 3.549 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 3.550 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 3.550 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 3.550 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 3.550 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.550 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.550 * [taylor]: Taking taylor expansion of k in k 3.550 * [backup-simplify]: Simplify 0 into 0 3.550 * [backup-simplify]: Simplify 1 into 1 3.551 * [backup-simplify]: Simplify (/ 1 1) into 1 3.551 * [backup-simplify]: Simplify (sqrt 0) into 0 3.553 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.553 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0 3.553 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.553 * [taylor]: Taking taylor expansion of 0 in n 3.554 * [backup-simplify]: Simplify 0 into 0 3.554 * [backup-simplify]: Simplify 0 into 0 3.554 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 3.555 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 3.555 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 3.556 * [backup-simplify]: Simplify (- 1) into -1 3.556 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.558 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 3.559 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 3.559 * [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))))) 3.561 * [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))) 3.563 * [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))) 3.563 * [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 3.563 * [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 3.563 * [taylor]: Taking taylor expansion of +nan.0 in n 3.563 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.563 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.563 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.563 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.563 * [taylor]: Taking taylor expansion of 0.5 in n 3.563 * [backup-simplify]: Simplify 0.5 into 0.5 3.563 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.563 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.563 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.563 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.563 * [taylor]: Taking taylor expansion of 1.0 in n 3.563 * [backup-simplify]: Simplify 1.0 into 1.0 3.563 * [taylor]: Taking taylor expansion of (log PI) in n 3.563 * [taylor]: Taking taylor expansion of PI in n 3.564 * [backup-simplify]: Simplify PI into PI 3.564 * [backup-simplify]: Simplify (log PI) into (log PI) 3.565 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.567 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.567 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.567 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.567 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.567 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.567 * [taylor]: Taking taylor expansion of 1.0 in n 3.567 * [backup-simplify]: Simplify 1.0 into 1.0 3.567 * [taylor]: Taking taylor expansion of (log n) in n 3.567 * [taylor]: Taking taylor expansion of n in n 3.567 * [backup-simplify]: Simplify 0 into 0 3.567 * [backup-simplify]: Simplify 1 into 1 3.567 * [backup-simplify]: Simplify (log 1) into 0 3.568 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.568 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.568 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.568 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.568 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.568 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.568 * [taylor]: Taking taylor expansion of 1.0 in n 3.568 * [backup-simplify]: Simplify 1.0 into 1.0 3.568 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.568 * [taylor]: Taking taylor expansion of 2.0 in n 3.568 * [backup-simplify]: Simplify 2.0 into 2.0 3.569 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.570 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.571 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.572 * [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) 3.573 * [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) 3.574 * [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)) 3.575 * [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))) 3.576 * [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) 3.577 * [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)) 3.578 * [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))) 3.579 * [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))) 3.579 * [backup-simplify]: Simplify 0 into 0 3.579 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.581 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.582 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 3.582 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 3.584 * [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 3.584 * [backup-simplify]: Simplify (- 0) into 0 3.584 * [backup-simplify]: Simplify (+ 0 0) into 0 3.585 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 3.585 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 3.586 * [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))) 3.588 * [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))))) 3.591 * [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))))) 3.591 * [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 3.591 * [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 3.591 * [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 3.591 * [taylor]: Taking taylor expansion of +nan.0 in n 3.591 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.591 * [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 3.591 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.591 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.591 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.591 * [taylor]: Taking taylor expansion of 0.5 in n 3.591 * [backup-simplify]: Simplify 0.5 into 0.5 3.591 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.591 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.592 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.592 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.592 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.592 * [taylor]: Taking taylor expansion of 1.0 in n 3.592 * [backup-simplify]: Simplify 1.0 into 1.0 3.592 * [taylor]: Taking taylor expansion of (log PI) in n 3.592 * [taylor]: Taking taylor expansion of PI in n 3.592 * [backup-simplify]: Simplify PI into PI 3.592 * [backup-simplify]: Simplify (log PI) into (log PI) 3.593 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.593 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.594 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.594 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.594 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.594 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.594 * [taylor]: Taking taylor expansion of 1.0 in n 3.594 * [backup-simplify]: Simplify 1.0 into 1.0 3.594 * [taylor]: Taking taylor expansion of (log n) in n 3.594 * [taylor]: Taking taylor expansion of n in n 3.594 * [backup-simplify]: Simplify 0 into 0 3.594 * [backup-simplify]: Simplify 1 into 1 3.594 * [backup-simplify]: Simplify (log 1) into 0 3.594 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.594 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.594 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.594 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.594 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.594 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.594 * [taylor]: Taking taylor expansion of 1.0 in n 3.594 * [backup-simplify]: Simplify 1.0 into 1.0 3.594 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.594 * [taylor]: Taking taylor expansion of 2.0 in n 3.594 * [backup-simplify]: Simplify 2.0 into 2.0 3.595 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.595 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.596 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.597 * [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) 3.597 * [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) 3.598 * [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)) 3.599 * [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))) 3.600 * [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) 3.600 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.600 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.600 * [taylor]: Taking taylor expansion of 2.0 in n 3.600 * [backup-simplify]: Simplify 2.0 into 2.0 3.600 * [taylor]: Taking taylor expansion of (* n PI) in n 3.600 * [taylor]: Taking taylor expansion of n in n 3.600 * [backup-simplify]: Simplify 0 into 0 3.600 * [backup-simplify]: Simplify 1 into 1 3.600 * [taylor]: Taking taylor expansion of PI in n 3.600 * [backup-simplify]: Simplify PI into PI 3.600 * [backup-simplify]: Simplify (* 0 PI) into 0 3.601 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.602 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.603 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.603 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.603 * [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 3.603 * [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 3.603 * [taylor]: Taking taylor expansion of +nan.0 in n 3.603 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.603 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.603 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.604 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.604 * [taylor]: Taking taylor expansion of 0.5 in n 3.604 * [backup-simplify]: Simplify 0.5 into 0.5 3.604 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.604 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.604 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.604 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.604 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.604 * [taylor]: Taking taylor expansion of 1.0 in n 3.604 * [backup-simplify]: Simplify 1.0 into 1.0 3.604 * [taylor]: Taking taylor expansion of (log PI) in n 3.604 * [taylor]: Taking taylor expansion of PI in n 3.604 * [backup-simplify]: Simplify PI into PI 3.604 * [backup-simplify]: Simplify (log PI) into (log PI) 3.605 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.607 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.607 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.607 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.607 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.607 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.607 * [taylor]: Taking taylor expansion of 1.0 in n 3.607 * [backup-simplify]: Simplify 1.0 into 1.0 3.607 * [taylor]: Taking taylor expansion of (log n) in n 3.607 * [taylor]: Taking taylor expansion of n in n 3.607 * [backup-simplify]: Simplify 0 into 0 3.607 * [backup-simplify]: Simplify 1 into 1 3.608 * [backup-simplify]: Simplify (log 1) into 0 3.608 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.608 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.608 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.608 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.609 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.609 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.609 * [taylor]: Taking taylor expansion of 1.0 in n 3.609 * [backup-simplify]: Simplify 1.0 into 1.0 3.609 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.609 * [taylor]: Taking taylor expansion of 2.0 in n 3.609 * [backup-simplify]: Simplify 2.0 into 2.0 3.609 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.610 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.612 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.612 * [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) 3.614 * [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) 3.615 * [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)) 3.616 * [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))) 3.618 * [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) 3.619 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.622 * [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))) 3.629 * [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)))) 3.630 * [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)) 3.633 * [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))) 3.637 * [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))))))) 3.643 * [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))))))))) 3.648 * [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))))))) 3.649 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 3.650 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 3.651 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 3.651 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 3.652 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.652 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 3.653 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 3.653 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 3.654 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 3.655 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 3.655 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 3.656 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 3.658 * [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 3.659 * [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 3.660 * [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 3.661 * [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 3.661 * [backup-simplify]: Simplify (- 0) into 0 3.662 * [backup-simplify]: Simplify 0 into 0 3.662 * [backup-simplify]: Simplify 0 into 0 3.662 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.665 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.665 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.666 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 3.668 * [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 3.668 * [backup-simplify]: Simplify (- 0) into 0 3.668 * [backup-simplify]: Simplify (+ 0 0) into 0 3.669 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 3.670 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 3.671 * [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))) 3.675 * [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)))))))) 3.685 * [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)))))))) 3.686 * [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 3.686 * [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 3.686 * [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 3.686 * [taylor]: Taking taylor expansion of +nan.0 in n 3.686 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.686 * [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 3.686 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.686 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.686 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.686 * [taylor]: Taking taylor expansion of 0.5 in n 3.686 * [backup-simplify]: Simplify 0.5 into 0.5 3.686 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.686 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.686 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.686 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.686 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.686 * [taylor]: Taking taylor expansion of 1.0 in n 3.686 * [backup-simplify]: Simplify 1.0 into 1.0 3.686 * [taylor]: Taking taylor expansion of (log PI) in n 3.686 * [taylor]: Taking taylor expansion of PI in n 3.686 * [backup-simplify]: Simplify PI into PI 3.687 * [backup-simplify]: Simplify (log PI) into (log PI) 3.688 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.689 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.689 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.689 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.689 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.689 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.690 * [taylor]: Taking taylor expansion of 1.0 in n 3.690 * [backup-simplify]: Simplify 1.0 into 1.0 3.690 * [taylor]: Taking taylor expansion of (log n) in n 3.690 * [taylor]: Taking taylor expansion of n in n 3.690 * [backup-simplify]: Simplify 0 into 0 3.690 * [backup-simplify]: Simplify 1 into 1 3.690 * [backup-simplify]: Simplify (log 1) into 0 3.690 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.691 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.691 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.691 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.691 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.691 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.691 * [taylor]: Taking taylor expansion of 1.0 in n 3.691 * [backup-simplify]: Simplify 1.0 into 1.0 3.691 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.691 * [taylor]: Taking taylor expansion of 2.0 in n 3.691 * [backup-simplify]: Simplify 2.0 into 2.0 3.691 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.693 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.694 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.695 * [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) 3.696 * [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) 3.697 * [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)) 3.699 * [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))) 3.700 * [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) 3.700 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.700 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.700 * [taylor]: Taking taylor expansion of 2.0 in n 3.700 * [backup-simplify]: Simplify 2.0 into 2.0 3.700 * [taylor]: Taking taylor expansion of (* n PI) in n 3.700 * [taylor]: Taking taylor expansion of n in n 3.701 * [backup-simplify]: Simplify 0 into 0 3.701 * [backup-simplify]: Simplify 1 into 1 3.701 * [taylor]: Taking taylor expansion of PI in n 3.701 * [backup-simplify]: Simplify PI into PI 3.701 * [backup-simplify]: Simplify (* 0 PI) into 0 3.702 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.703 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.705 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.706 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.706 * [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 3.706 * [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 3.706 * [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 3.706 * [taylor]: Taking taylor expansion of +nan.0 in n 3.706 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.706 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.706 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.706 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.706 * [taylor]: Taking taylor expansion of 0.5 in n 3.706 * [backup-simplify]: Simplify 0.5 into 0.5 3.706 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.706 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.706 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.706 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.706 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.706 * [taylor]: Taking taylor expansion of 1.0 in n 3.706 * [backup-simplify]: Simplify 1.0 into 1.0 3.706 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.706 * [taylor]: Taking taylor expansion of 2.0 in n 3.706 * [backup-simplify]: Simplify 2.0 into 2.0 3.707 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.708 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.709 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.709 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.709 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.709 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.709 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.709 * [taylor]: Taking taylor expansion of 1.0 in n 3.709 * [backup-simplify]: Simplify 1.0 into 1.0 3.709 * [taylor]: Taking taylor expansion of (log n) in n 3.709 * [taylor]: Taking taylor expansion of n in n 3.709 * [backup-simplify]: Simplify 0 into 0 3.709 * [backup-simplify]: Simplify 1 into 1 3.710 * [backup-simplify]: Simplify (log 1) into 0 3.710 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.710 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.710 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.710 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.710 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.711 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.711 * [taylor]: Taking taylor expansion of 1.0 in n 3.711 * [backup-simplify]: Simplify 1.0 into 1.0 3.711 * [taylor]: Taking taylor expansion of (log PI) in n 3.711 * [taylor]: Taking taylor expansion of PI in n 3.711 * [backup-simplify]: Simplify PI into PI 3.711 * [backup-simplify]: Simplify (log PI) into (log PI) 3.712 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.714 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.715 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.716 * [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) 3.717 * [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)) 3.719 * [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))) 3.720 * [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) 3.720 * [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 3.720 * [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 3.720 * [taylor]: Taking taylor expansion of +nan.0 in n 3.720 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.720 * [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 3.720 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 3.720 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 3.720 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 3.720 * [taylor]: Taking taylor expansion of 0.5 in n 3.720 * [backup-simplify]: Simplify 0.5 into 0.5 3.720 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 3.720 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 3.720 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.720 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.720 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.720 * [taylor]: Taking taylor expansion of 1.0 in n 3.720 * [backup-simplify]: Simplify 1.0 into 1.0 3.720 * [taylor]: Taking taylor expansion of (log PI) in n 3.720 * [taylor]: Taking taylor expansion of PI in n 3.720 * [backup-simplify]: Simplify PI into PI 3.721 * [backup-simplify]: Simplify (log PI) into (log PI) 3.721 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.722 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.722 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 3.722 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.722 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.722 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.723 * [taylor]: Taking taylor expansion of 1.0 in n 3.723 * [backup-simplify]: Simplify 1.0 into 1.0 3.723 * [taylor]: Taking taylor expansion of (log n) in n 3.723 * [taylor]: Taking taylor expansion of n in n 3.723 * [backup-simplify]: Simplify 0 into 0 3.723 * [backup-simplify]: Simplify 1 into 1 3.723 * [backup-simplify]: Simplify (log 1) into 0 3.723 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.723 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.723 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.723 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.723 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.723 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.723 * [taylor]: Taking taylor expansion of 1.0 in n 3.723 * [backup-simplify]: Simplify 1.0 into 1.0 3.723 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.723 * [taylor]: Taking taylor expansion of 2.0 in n 3.723 * [backup-simplify]: Simplify 2.0 into 2.0 3.724 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.724 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.725 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.726 * [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) 3.726 * [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) 3.727 * [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)) 3.728 * [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))) 3.729 * [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) 3.729 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.729 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.729 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.729 * [taylor]: Taking taylor expansion of 2.0 in n 3.729 * [backup-simplify]: Simplify 2.0 into 2.0 3.729 * [taylor]: Taking taylor expansion of (* n PI) in n 3.729 * [taylor]: Taking taylor expansion of n in n 3.729 * [backup-simplify]: Simplify 0 into 0 3.729 * [backup-simplify]: Simplify 1 into 1 3.729 * [taylor]: Taking taylor expansion of PI in n 3.729 * [backup-simplify]: Simplify PI into PI 3.730 * [backup-simplify]: Simplify (* 0 PI) into 0 3.730 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.731 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.732 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.732 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.733 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.734 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.736 * [backup-simplify]: Simplify (* (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))) 3.738 * [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)))) 3.739 * [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)) 3.740 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.741 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.743 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.745 * [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)) 3.749 * [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))) 3.751 * [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)))))))) 3.761 * [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))))))))) 3.772 * [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)))))))))) 3.787 * [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))))))))))))) 3.804 * [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))))))))))))) 3.814 * [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))))))))))))))) 3.830 * [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))))))))))))))))))))))) 3.830 * [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))) 3.830 * [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 3.830 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 3.830 * [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 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 3.831 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.831 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.831 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.831 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.831 * [taylor]: Taking taylor expansion of 0.5 in n 3.831 * [backup-simplify]: Simplify 0.5 into 0.5 3.831 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) 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 (/ 1 k) in n 3.831 * [taylor]: Taking taylor expansion of k in n 3.831 * [backup-simplify]: Simplify k into k 3.831 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.831 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.831 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) 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 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.831 * [taylor]: Taking taylor expansion of PI in n 3.831 * [backup-simplify]: Simplify PI into PI 3.831 * [taylor]: Taking taylor expansion of n in n 3.831 * [backup-simplify]: Simplify 0 into 0 3.831 * [backup-simplify]: Simplify 1 into 1 3.831 * [backup-simplify]: Simplify (/ PI 1) into PI 3.832 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.833 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.833 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.833 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.833 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.836 * [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)))) 3.837 * [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))))) 3.837 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.837 * [taylor]: Taking taylor expansion of k in n 3.837 * [backup-simplify]: Simplify k into k 3.837 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.837 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.837 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.837 * [taylor]: Taking taylor expansion of 1.0 in k 3.838 * [backup-simplify]: Simplify 1.0 into 1.0 3.838 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.838 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.838 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.838 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.838 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.838 * [taylor]: Taking taylor expansion of 0.5 in k 3.838 * [backup-simplify]: Simplify 0.5 into 0.5 3.838 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.838 * [taylor]: Taking taylor expansion of 1.0 in k 3.838 * [backup-simplify]: Simplify 1.0 into 1.0 3.838 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.838 * [taylor]: Taking taylor expansion of k in k 3.838 * [backup-simplify]: Simplify 0 into 0 3.838 * [backup-simplify]: Simplify 1 into 1 3.838 * [backup-simplify]: Simplify (/ 1 1) into 1 3.838 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.838 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.838 * [taylor]: Taking taylor expansion of 2.0 in k 3.838 * [backup-simplify]: Simplify 2.0 into 2.0 3.838 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.838 * [taylor]: Taking taylor expansion of PI in k 3.839 * [backup-simplify]: Simplify PI into PI 3.839 * [taylor]: Taking taylor expansion of n in k 3.839 * [backup-simplify]: Simplify n into n 3.839 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.839 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.839 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.839 * [backup-simplify]: Simplify (- 1) into -1 3.840 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.840 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.840 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.840 * [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)))))) 3.841 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.841 * [taylor]: Taking taylor expansion of k in k 3.841 * [backup-simplify]: Simplify 0 into 0 3.841 * [backup-simplify]: Simplify 1 into 1 3.841 * [backup-simplify]: Simplify (sqrt 0) into 0 3.843 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.843 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 3.843 * [taylor]: Taking taylor expansion of 1.0 in k 3.843 * [backup-simplify]: Simplify 1.0 into 1.0 3.843 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 3.843 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.843 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.843 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.843 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.843 * [taylor]: Taking taylor expansion of 0.5 in k 3.843 * [backup-simplify]: Simplify 0.5 into 0.5 3.843 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.843 * [taylor]: Taking taylor expansion of 1.0 in k 3.843 * [backup-simplify]: Simplify 1.0 into 1.0 3.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.843 * [taylor]: Taking taylor expansion of k in k 3.843 * [backup-simplify]: Simplify 0 into 0 3.843 * [backup-simplify]: Simplify 1 into 1 3.844 * [backup-simplify]: Simplify (/ 1 1) into 1 3.844 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.844 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.844 * [taylor]: Taking taylor expansion of 2.0 in k 3.844 * [backup-simplify]: Simplify 2.0 into 2.0 3.844 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.844 * [taylor]: Taking taylor expansion of PI in k 3.844 * [backup-simplify]: Simplify PI into PI 3.844 * [taylor]: Taking taylor expansion of n in k 3.844 * [backup-simplify]: Simplify n into n 3.844 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.844 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.844 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.845 * [backup-simplify]: Simplify (- 1) into -1 3.845 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.845 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.846 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.846 * [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)))))) 3.846 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.846 * [taylor]: Taking taylor expansion of k in k 3.846 * [backup-simplify]: Simplify 0 into 0 3.846 * [backup-simplify]: Simplify 1 into 1 3.846 * [backup-simplify]: Simplify (sqrt 0) into 0 3.848 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.848 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0 3.849 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.849 * [taylor]: Taking taylor expansion of 0 in n 3.849 * [backup-simplify]: Simplify 0 into 0 3.849 * [backup-simplify]: Simplify 0 into 0 3.850 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.850 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.850 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.850 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.850 * [taylor]: Taking taylor expansion of +nan.0 in n 3.851 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.851 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.851 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.851 * [taylor]: Taking taylor expansion of 0.5 in n 3.851 * [backup-simplify]: Simplify 0.5 into 0.5 3.851 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.851 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) 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 (/ 1 k) in n 3.851 * [taylor]: Taking taylor expansion of k in n 3.851 * [backup-simplify]: Simplify k into k 3.851 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.851 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.851 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.851 * [taylor]: Taking taylor expansion of 2.0 in n 3.851 * [backup-simplify]: Simplify 2.0 into 2.0 3.851 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.851 * [taylor]: Taking taylor expansion of PI in n 3.851 * [backup-simplify]: Simplify PI into PI 3.851 * [taylor]: Taking taylor expansion of n in n 3.851 * [backup-simplify]: Simplify 0 into 0 3.851 * [backup-simplify]: Simplify 1 into 1 3.852 * [backup-simplify]: Simplify (/ PI 1) into PI 3.852 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.854 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.854 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.854 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.857 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.858 * [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)))) 3.860 * [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))))) 3.861 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.863 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.864 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.864 * [backup-simplify]: Simplify 0 into 0 3.867 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.868 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.870 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.870 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.870 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.870 * [taylor]: Taking taylor expansion of +nan.0 in n 3.870 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.870 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.870 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.870 * [taylor]: Taking taylor expansion of 0.5 in n 3.870 * [backup-simplify]: Simplify 0.5 into 0.5 3.870 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.870 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.870 * [taylor]: Taking taylor expansion of 1.0 in n 3.870 * [backup-simplify]: Simplify 1.0 into 1.0 3.870 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.870 * [taylor]: Taking taylor expansion of k in n 3.870 * [backup-simplify]: Simplify k into k 3.870 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.870 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.870 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.870 * [taylor]: Taking taylor expansion of 2.0 in n 3.870 * [backup-simplify]: Simplify 2.0 into 2.0 3.870 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.870 * [taylor]: Taking taylor expansion of PI in n 3.870 * [backup-simplify]: Simplify PI into PI 3.870 * [taylor]: Taking taylor expansion of n in n 3.870 * [backup-simplify]: Simplify 0 into 0 3.870 * [backup-simplify]: Simplify 1 into 1 3.871 * [backup-simplify]: Simplify (/ PI 1) into PI 3.872 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.873 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.873 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.873 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.876 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.877 * [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)))) 3.878 * [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))))) 3.883 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.884 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.885 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.885 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.886 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.887 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.887 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.887 * [backup-simplify]: Simplify (- 0) into 0 3.888 * [backup-simplify]: Simplify (+ 0 0) into 0 3.889 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.889 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 3.890 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0 3.891 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.892 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0 3.893 * [backup-simplify]: Simplify (- 0) into 0 3.893 * [backup-simplify]: Simplify 0 into 0 3.893 * [backup-simplify]: Simplify 0 into 0 3.895 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.896 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.897 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) 3.897 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n 3.897 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n 3.897 * [taylor]: Taking taylor expansion of +nan.0 in n 3.897 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.897 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n 3.897 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n 3.897 * [taylor]: Taking taylor expansion of 0.5 in n 3.897 * [backup-simplify]: Simplify 0.5 into 0.5 3.897 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n 3.897 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.897 * [taylor]: Taking taylor expansion of 1.0 in n 3.897 * [backup-simplify]: Simplify 1.0 into 1.0 3.897 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.897 * [taylor]: Taking taylor expansion of k in n 3.897 * [backup-simplify]: Simplify k into k 3.897 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.897 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.897 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.897 * [taylor]: Taking taylor expansion of 2.0 in n 3.897 * [backup-simplify]: Simplify 2.0 into 2.0 3.897 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.897 * [taylor]: Taking taylor expansion of PI in n 3.897 * [backup-simplify]: Simplify PI into PI 3.897 * [taylor]: Taking taylor expansion of n in n 3.897 * [backup-simplify]: Simplify 0 into 0 3.897 * [backup-simplify]: Simplify 1 into 1 3.897 * [backup-simplify]: Simplify (/ PI 1) into PI 3.898 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.898 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.898 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.899 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.900 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) 3.901 * [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)))) 3.902 * [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))))) 3.903 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 3.903 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.904 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) 3.907 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3)))))))) 3.908 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 3.908 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 3.908 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 3.908 * [taylor]: Taking taylor expansion of 1.0 in n 3.908 * [backup-simplify]: Simplify 1.0 into 1.0 3.908 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 3.908 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.908 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.908 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.908 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.908 * [taylor]: Taking taylor expansion of 0.5 in n 3.908 * [backup-simplify]: Simplify 0.5 into 0.5 3.908 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.908 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.908 * [taylor]: Taking taylor expansion of k in n 3.908 * [backup-simplify]: Simplify k into k 3.908 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.908 * [taylor]: Taking taylor expansion of 1.0 in n 3.908 * [backup-simplify]: Simplify 1.0 into 1.0 3.908 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.908 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.908 * [taylor]: Taking taylor expansion of -2.0 in n 3.908 * [backup-simplify]: Simplify -2.0 into -2.0 3.908 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.908 * [taylor]: Taking taylor expansion of PI in n 3.908 * [backup-simplify]: Simplify PI into PI 3.908 * [taylor]: Taking taylor expansion of n in n 3.908 * [backup-simplify]: Simplify 0 into 0 3.908 * [backup-simplify]: Simplify 1 into 1 3.909 * [backup-simplify]: Simplify (/ PI 1) into PI 3.909 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.910 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.910 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.910 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.911 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.912 * [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))) 3.913 * [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)))) 3.913 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.913 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.913 * [taylor]: Taking taylor expansion of -1 in n 3.913 * [backup-simplify]: Simplify -1 into -1 3.913 * [taylor]: Taking taylor expansion of k in n 3.913 * [backup-simplify]: Simplify k into k 3.914 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.914 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.914 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.914 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.915 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) 3.915 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.915 * [taylor]: Taking taylor expansion of 1.0 in k 3.915 * [backup-simplify]: Simplify 1.0 into 1.0 3.915 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.916 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.916 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.916 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.916 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.916 * [taylor]: Taking taylor expansion of 0.5 in k 3.916 * [backup-simplify]: Simplify 0.5 into 0.5 3.916 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.916 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.916 * [taylor]: Taking taylor expansion of k in k 3.916 * [backup-simplify]: Simplify 0 into 0 3.916 * [backup-simplify]: Simplify 1 into 1 3.916 * [backup-simplify]: Simplify (/ 1 1) into 1 3.916 * [taylor]: Taking taylor expansion of 1.0 in k 3.916 * [backup-simplify]: Simplify 1.0 into 1.0 3.916 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.916 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.916 * [taylor]: Taking taylor expansion of -2.0 in k 3.916 * [backup-simplify]: Simplify -2.0 into -2.0 3.917 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.917 * [taylor]: Taking taylor expansion of PI in k 3.917 * [backup-simplify]: Simplify PI into PI 3.917 * [taylor]: Taking taylor expansion of n in k 3.917 * [backup-simplify]: Simplify n into n 3.917 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.917 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.917 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.917 * [backup-simplify]: Simplify (+ 1 0) into 1 3.918 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.918 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.919 * [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)))) 3.919 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.919 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.919 * [taylor]: Taking taylor expansion of -1 in k 3.919 * [backup-simplify]: Simplify -1 into -1 3.919 * [taylor]: Taking taylor expansion of k in k 3.919 * [backup-simplify]: Simplify 0 into 0 3.919 * [backup-simplify]: Simplify 1 into 1 3.919 * [backup-simplify]: Simplify (/ -1 1) into -1 3.920 * [backup-simplify]: Simplify (sqrt 0) into 0 3.921 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.921 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.921 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.921 * [taylor]: Taking taylor expansion of 1.0 in k 3.921 * [backup-simplify]: Simplify 1.0 into 1.0 3.922 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.922 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.922 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.922 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.922 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.922 * [taylor]: Taking taylor expansion of 0.5 in k 3.922 * [backup-simplify]: Simplify 0.5 into 0.5 3.922 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.922 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.922 * [taylor]: Taking taylor expansion of k in k 3.922 * [backup-simplify]: Simplify 0 into 0 3.922 * [backup-simplify]: Simplify 1 into 1 3.922 * [backup-simplify]: Simplify (/ 1 1) into 1 3.922 * [taylor]: Taking taylor expansion of 1.0 in k 3.922 * [backup-simplify]: Simplify 1.0 into 1.0 3.922 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.922 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.922 * [taylor]: Taking taylor expansion of -2.0 in k 3.922 * [backup-simplify]: Simplify -2.0 into -2.0 3.922 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.922 * [taylor]: Taking taylor expansion of PI in k 3.923 * [backup-simplify]: Simplify PI into PI 3.923 * [taylor]: Taking taylor expansion of n in k 3.923 * [backup-simplify]: Simplify n into n 3.923 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.923 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.923 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.923 * [backup-simplify]: Simplify (+ 1 0) into 1 3.924 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.924 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.924 * [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)))) 3.924 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.924 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.924 * [taylor]: Taking taylor expansion of -1 in k 3.924 * [backup-simplify]: Simplify -1 into -1 3.924 * [taylor]: Taking taylor expansion of k in k 3.924 * [backup-simplify]: Simplify 0 into 0 3.924 * [backup-simplify]: Simplify 1 into 1 3.925 * [backup-simplify]: Simplify (/ -1 1) into -1 3.925 * [backup-simplify]: Simplify (sqrt 0) into 0 3.927 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.927 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.927 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) 3.927 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.927 * [taylor]: Taking taylor expansion of +nan.0 in n 3.927 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.928 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.928 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.928 * [taylor]: Taking taylor expansion of 0.5 in n 3.928 * [backup-simplify]: Simplify 0.5 into 0.5 3.928 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.928 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.928 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.928 * [taylor]: Taking taylor expansion of -2.0 in n 3.928 * [backup-simplify]: Simplify -2.0 into -2.0 3.928 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.928 * [taylor]: Taking taylor expansion of PI in n 3.928 * [backup-simplify]: Simplify PI into PI 3.928 * [taylor]: Taking taylor expansion of n in n 3.928 * [backup-simplify]: Simplify 0 into 0 3.928 * [backup-simplify]: Simplify 1 into 1 3.929 * [backup-simplify]: Simplify (/ PI 1) into PI 3.929 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.930 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.930 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.930 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.930 * [taylor]: Taking taylor expansion of k in n 3.931 * [backup-simplify]: Simplify k into k 3.931 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.931 * [taylor]: Taking taylor expansion of 1.0 in n 3.931 * [backup-simplify]: Simplify 1.0 into 1.0 3.932 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.933 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.934 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.935 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.936 * [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)))) 3.938 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.939 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.943 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.944 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.944 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.944 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.945 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.945 * [taylor]: Taking taylor expansion of +nan.0 in n 3.945 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.945 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.945 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.945 * [taylor]: Taking taylor expansion of 0.5 in n 3.945 * [backup-simplify]: Simplify 0.5 into 0.5 3.945 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.945 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.945 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.945 * [taylor]: Taking taylor expansion of -2.0 in n 3.945 * [backup-simplify]: Simplify -2.0 into -2.0 3.945 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.945 * [taylor]: Taking taylor expansion of PI in n 3.945 * [backup-simplify]: Simplify PI into PI 3.945 * [taylor]: Taking taylor expansion of n in n 3.945 * [backup-simplify]: Simplify 0 into 0 3.945 * [backup-simplify]: Simplify 1 into 1 3.945 * [backup-simplify]: Simplify (/ PI 1) into PI 3.946 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.947 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.947 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.947 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.947 * [taylor]: Taking taylor expansion of k in n 3.947 * [backup-simplify]: Simplify k into k 3.947 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.947 * [taylor]: Taking taylor expansion of 1.0 in n 3.947 * [backup-simplify]: Simplify 1.0 into 1.0 3.948 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.948 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.950 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.951 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.953 * [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)))) 3.954 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.956 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.957 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.960 * [backup-simplify]: Simplify (+ 0 0) into 0 3.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.961 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.965 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 3.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 3.968 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.970 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0 3.970 * [backup-simplify]: Simplify 0 into 0 3.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.976 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.977 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.978 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) 3.979 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n 3.979 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n 3.979 * [taylor]: Taking taylor expansion of +nan.0 in n 3.979 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.979 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 3.979 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n 3.979 * [taylor]: Taking taylor expansion of 0.5 in n 3.979 * [backup-simplify]: Simplify 0.5 into 0.5 3.979 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n 3.979 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.979 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.979 * [taylor]: Taking taylor expansion of -2.0 in n 3.979 * [backup-simplify]: Simplify -2.0 into -2.0 3.979 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.979 * [taylor]: Taking taylor expansion of PI in n 3.979 * [backup-simplify]: Simplify PI into PI 3.979 * [taylor]: Taking taylor expansion of n in n 3.979 * [backup-simplify]: Simplify 0 into 0 3.979 * [backup-simplify]: Simplify 1 into 1 3.980 * [backup-simplify]: Simplify (/ PI 1) into PI 3.980 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.981 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.981 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.982 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.982 * [taylor]: Taking taylor expansion of k in n 3.982 * [backup-simplify]: Simplify k into k 3.982 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.982 * [taylor]: Taking taylor expansion of 1.0 in n 3.982 * [backup-simplify]: Simplify 1.0 into 1.0 3.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.983 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.984 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) 3.985 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) 3.986 * [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)))) 3.986 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) 3.987 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.988 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) 3.991 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)))))))) 3.991 * * * [progress]: simplifying candidates 3.993 * [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)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.25 (* (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)))))))) 3.997 * * [simplify]: iteration 0: 361 enodes 4.115 * * [simplify]: iteration 1: 1004 enodes 4.692 * * [simplify]: iteration 2: 3445 enodes 6.180 * * [simplify]: iteration complete: 5004 enodes 6.180 * * [simplify]: Extracting #0: cost 125 inf + 0 6.183 * * [simplify]: Extracting #1: cost 635 inf + 2 6.187 * * [simplify]: Extracting #2: cost 1123 inf + 2802 6.196 * * [simplify]: Extracting #3: cost 1125 inf + 37571 6.238 * * [simplify]: Extracting #4: cost 740 inf + 164402 6.349 * * [simplify]: Extracting #5: cost 432 inf + 325779 6.459 * * [simplify]: Extracting #6: cost 266 inf + 428235 6.618 * * [simplify]: Extracting #7: cost 69 inf + 606033 6.778 * * [simplify]: Extracting #8: cost 12 inf + 681945 6.984 * * [simplify]: Extracting #9: cost 1 inf + 696348 7.232 * * [simplify]: Extracting #10: cost 0 inf + 694281 7.455 * * [simplify]: Extracting #11: cost 0 inf + 693991 7.674 * * [simplify]: Extracting #12: cost 0 inf + 693801 7.903 * [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))) (* (* 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)) (/ (* (log (* (* PI 2.0) n)) (- 1.0 k)) 2.0) (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) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* PI 2.0) n) (/ (/ (- 1.0 k) 2.0) 2)) (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 2.0) PI) (* (* n 2.0) PI)) (* n 2.0)) PI) (* (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* n 2.0)) PI) (* (cbrt (* (* PI 2.0) n)) (cbrt (* (* PI 2.0) n))) (cbrt (* (* PI 2.0) n)) (* (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* n 2.0)) PI) (sqrt (* (* PI 2.0) n)) (sqrt (* (* PI 2.0) n)) (* (* (cbrt n) (* PI 2.0)) (cbrt n)) (* (* 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 (sqrt k))) (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (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)))) 7.926 * * * [progress]: adding candidates to table 8.993 * * [progress]: iteration 2 / 4 8.993 * * * [progress]: picking best candidate 9.061 * * * * [pick]: Picked # 9.061 * * * [progress]: localizing error 9.089 * * * [progress]: generating rewritten candidates 9.089 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 9.113 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 9.131 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 9.136 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 9.175 * * * [progress]: generating series expansions 9.175 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 9.176 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 9.176 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 9.176 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 9.176 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.176 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.176 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 9.176 * [taylor]: Taking taylor expansion of 0.5 in k 9.176 * [backup-simplify]: Simplify 0.5 into 0.5 9.176 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.176 * [taylor]: Taking taylor expansion of 1.0 in k 9.176 * [backup-simplify]: Simplify 1.0 into 1.0 9.176 * [taylor]: Taking taylor expansion of k in k 9.176 * [backup-simplify]: Simplify 0 into 0 9.176 * [backup-simplify]: Simplify 1 into 1 9.176 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.176 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.176 * [taylor]: Taking taylor expansion of 2.0 in k 9.176 * [backup-simplify]: Simplify 2.0 into 2.0 9.176 * [taylor]: Taking taylor expansion of (* n PI) in k 9.176 * [taylor]: Taking taylor expansion of n in k 9.176 * [backup-simplify]: Simplify n into n 9.176 * [taylor]: Taking taylor expansion of PI in k 9.176 * [backup-simplify]: Simplify PI into PI 9.176 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.176 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.176 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.176 * [backup-simplify]: Simplify (- 0) into 0 9.177 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.177 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 9.177 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 9.177 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 9.177 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 9.177 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.177 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.177 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 9.177 * [taylor]: Taking taylor expansion of 0.5 in n 9.177 * [backup-simplify]: Simplify 0.5 into 0.5 9.177 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.177 * [taylor]: Taking taylor expansion of 1.0 in n 9.177 * [backup-simplify]: Simplify 1.0 into 1.0 9.177 * [taylor]: Taking taylor expansion of k in n 9.177 * [backup-simplify]: Simplify k into k 9.177 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.177 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.177 * [taylor]: Taking taylor expansion of 2.0 in n 9.177 * [backup-simplify]: Simplify 2.0 into 2.0 9.177 * [taylor]: Taking taylor expansion of (* n PI) in n 9.177 * [taylor]: Taking taylor expansion of n in n 9.178 * [backup-simplify]: Simplify 0 into 0 9.178 * [backup-simplify]: Simplify 1 into 1 9.178 * [taylor]: Taking taylor expansion of PI in n 9.178 * [backup-simplify]: Simplify PI into PI 9.178 * [backup-simplify]: Simplify (* 0 PI) into 0 9.178 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.179 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.180 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.181 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.181 * [backup-simplify]: Simplify (- k) into (- k) 9.181 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.181 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 9.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.183 * [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)))) 9.183 * [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))))) 9.183 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 9.183 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.183 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.183 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 9.184 * [taylor]: Taking taylor expansion of 0.5 in n 9.184 * [backup-simplify]: Simplify 0.5 into 0.5 9.184 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.184 * [taylor]: Taking taylor expansion of 1.0 in n 9.184 * [backup-simplify]: Simplify 1.0 into 1.0 9.184 * [taylor]: Taking taylor expansion of k in n 9.184 * [backup-simplify]: Simplify k into k 9.184 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.184 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.184 * [taylor]: Taking taylor expansion of 2.0 in n 9.184 * [backup-simplify]: Simplify 2.0 into 2.0 9.184 * [taylor]: Taking taylor expansion of (* n PI) in n 9.184 * [taylor]: Taking taylor expansion of n in n 9.184 * [backup-simplify]: Simplify 0 into 0 9.184 * [backup-simplify]: Simplify 1 into 1 9.184 * [taylor]: Taking taylor expansion of PI in n 9.184 * [backup-simplify]: Simplify PI into PI 9.184 * [backup-simplify]: Simplify (* 0 PI) into 0 9.185 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.186 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.188 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.189 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.189 * [backup-simplify]: Simplify (- k) into (- k) 9.189 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.189 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 9.191 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.192 * [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)))) 9.193 * [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))))) 9.193 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.193 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.193 * [taylor]: Taking taylor expansion of 0.5 in k 9.193 * [backup-simplify]: Simplify 0.5 into 0.5 9.193 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.193 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.193 * [taylor]: Taking taylor expansion of 1.0 in k 9.194 * [backup-simplify]: Simplify 1.0 into 1.0 9.194 * [taylor]: Taking taylor expansion of k in k 9.194 * [backup-simplify]: Simplify 0 into 0 9.194 * [backup-simplify]: Simplify 1 into 1 9.194 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.194 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.194 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.194 * [taylor]: Taking taylor expansion of 2.0 in k 9.194 * [backup-simplify]: Simplify 2.0 into 2.0 9.194 * [taylor]: Taking taylor expansion of PI in k 9.194 * [backup-simplify]: Simplify PI into PI 9.194 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.195 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.195 * [taylor]: Taking taylor expansion of (log n) in k 9.195 * [taylor]: Taking taylor expansion of n in k 9.195 * [backup-simplify]: Simplify n into n 9.196 * [backup-simplify]: Simplify (log n) into (log n) 9.196 * [backup-simplify]: Simplify (- 0) into 0 9.196 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.197 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.199 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.200 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 9.200 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 9.201 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 9.202 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.203 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.204 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.204 * [backup-simplify]: Simplify (- 0) into 0 9.204 * [backup-simplify]: Simplify (+ 0 0) into 0 9.205 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 9.206 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.206 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.211 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.211 * [taylor]: Taking taylor expansion of 0 in k 9.211 * [backup-simplify]: Simplify 0 into 0 9.211 * [backup-simplify]: Simplify 0 into 0 9.211 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.212 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.213 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.213 * [backup-simplify]: Simplify (+ 0 0) into 0 9.213 * [backup-simplify]: Simplify (- 1) into -1 9.214 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.214 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.216 * [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)))) 9.218 * [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)))))) 9.220 * [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)))))) 9.221 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.221 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.223 * [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 9.223 * [backup-simplify]: Simplify (- 0) into 0 9.224 * [backup-simplify]: Simplify (+ 0 0) into 0 9.224 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.225 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.226 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.228 * [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 9.228 * [taylor]: Taking taylor expansion of 0 in k 9.228 * [backup-simplify]: Simplify 0 into 0 9.228 * [backup-simplify]: Simplify 0 into 0 9.228 * [backup-simplify]: Simplify 0 into 0 9.229 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.233 * [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 9.235 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.235 * [backup-simplify]: Simplify (+ 0 0) into 0 9.235 * [backup-simplify]: Simplify (- 0) into 0 9.236 * [backup-simplify]: Simplify (+ 0 0) into 0 9.238 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.241 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.245 * [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)))))) 9.251 * [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)))))) 9.262 * [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))))) 9.263 * [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)))) 9.263 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 9.263 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 9.263 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.263 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.263 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 9.263 * [taylor]: Taking taylor expansion of 0.5 in k 9.263 * [backup-simplify]: Simplify 0.5 into 0.5 9.263 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.263 * [taylor]: Taking taylor expansion of 1.0 in k 9.263 * [backup-simplify]: Simplify 1.0 into 1.0 9.263 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.263 * [taylor]: Taking taylor expansion of k in k 9.263 * [backup-simplify]: Simplify 0 into 0 9.263 * [backup-simplify]: Simplify 1 into 1 9.264 * [backup-simplify]: Simplify (/ 1 1) into 1 9.264 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.264 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.264 * [taylor]: Taking taylor expansion of 2.0 in k 9.264 * [backup-simplify]: Simplify 2.0 into 2.0 9.264 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.264 * [taylor]: Taking taylor expansion of PI in k 9.264 * [backup-simplify]: Simplify PI into PI 9.264 * [taylor]: Taking taylor expansion of n in k 9.264 * [backup-simplify]: Simplify n into n 9.264 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.264 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.264 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.265 * [backup-simplify]: Simplify (- 1) into -1 9.265 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.266 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 9.266 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 9.266 * [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)))))) 9.266 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 9.266 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.266 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.266 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 9.266 * [taylor]: Taking taylor expansion of 0.5 in n 9.266 * [backup-simplify]: Simplify 0.5 into 0.5 9.266 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.266 * [taylor]: Taking taylor expansion of 1.0 in n 9.266 * [backup-simplify]: Simplify 1.0 into 1.0 9.266 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.266 * [taylor]: Taking taylor expansion of k in n 9.266 * [backup-simplify]: Simplify k into k 9.266 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.266 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.267 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.267 * [taylor]: Taking taylor expansion of 2.0 in n 9.267 * [backup-simplify]: Simplify 2.0 into 2.0 9.267 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.267 * [taylor]: Taking taylor expansion of PI in n 9.267 * [backup-simplify]: Simplify PI into PI 9.267 * [taylor]: Taking taylor expansion of n in n 9.267 * [backup-simplify]: Simplify 0 into 0 9.267 * [backup-simplify]: Simplify 1 into 1 9.268 * [backup-simplify]: Simplify (/ PI 1) into PI 9.268 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.269 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.269 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.269 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.269 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 9.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.272 * [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)))) 9.273 * [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))))) 9.273 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 9.273 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.273 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.274 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 9.274 * [taylor]: Taking taylor expansion of 0.5 in n 9.274 * [backup-simplify]: Simplify 0.5 into 0.5 9.274 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.274 * [taylor]: Taking taylor expansion of 1.0 in n 9.274 * [backup-simplify]: Simplify 1.0 into 1.0 9.274 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.274 * [taylor]: Taking taylor expansion of k in n 9.274 * [backup-simplify]: Simplify k into k 9.274 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.274 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.274 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.274 * [taylor]: Taking taylor expansion of 2.0 in n 9.274 * [backup-simplify]: Simplify 2.0 into 2.0 9.274 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.274 * [taylor]: Taking taylor expansion of PI in n 9.274 * [backup-simplify]: Simplify PI into PI 9.274 * [taylor]: Taking taylor expansion of n in n 9.274 * [backup-simplify]: Simplify 0 into 0 9.274 * [backup-simplify]: Simplify 1 into 1 9.275 * [backup-simplify]: Simplify (/ PI 1) into PI 9.275 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.276 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.276 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.277 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.277 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 9.278 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.280 * [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)))) 9.282 * [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))))) 9.282 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 9.282 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 9.282 * [taylor]: Taking taylor expansion of 0.5 in k 9.282 * [backup-simplify]: Simplify 0.5 into 0.5 9.282 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 9.282 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.282 * [taylor]: Taking taylor expansion of 1.0 in k 9.282 * [backup-simplify]: Simplify 1.0 into 1.0 9.282 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.282 * [taylor]: Taking taylor expansion of k in k 9.282 * [backup-simplify]: Simplify 0 into 0 9.282 * [backup-simplify]: Simplify 1 into 1 9.282 * [backup-simplify]: Simplify (/ 1 1) into 1 9.283 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.283 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.283 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.283 * [taylor]: Taking taylor expansion of 2.0 in k 9.283 * [backup-simplify]: Simplify 2.0 into 2.0 9.283 * [taylor]: Taking taylor expansion of PI in k 9.283 * [backup-simplify]: Simplify PI into PI 9.283 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.284 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.284 * [taylor]: Taking taylor expansion of (log n) in k 9.284 * [taylor]: Taking taylor expansion of n in k 9.284 * [backup-simplify]: Simplify n into n 9.285 * [backup-simplify]: Simplify (log n) into (log n) 9.285 * [backup-simplify]: Simplify (- 1) into -1 9.285 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.285 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.287 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.288 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.289 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 9.290 * [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))))) 9.292 * [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))))) 9.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.293 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.295 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.295 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.296 * [backup-simplify]: Simplify (- 0) into 0 9.296 * [backup-simplify]: Simplify (+ 0 0) into 0 9.297 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.300 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.302 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.302 * [taylor]: Taking taylor expansion of 0 in k 9.302 * [backup-simplify]: Simplify 0 into 0 9.302 * [backup-simplify]: Simplify 0 into 0 9.302 * [backup-simplify]: Simplify 0 into 0 9.303 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.304 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.308 * [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 9.308 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.308 * [backup-simplify]: Simplify (- 0) into 0 9.309 * [backup-simplify]: Simplify (+ 0 0) into 0 9.309 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.313 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.315 * [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 9.315 * [taylor]: Taking taylor expansion of 0 in k 9.315 * [backup-simplify]: Simplify 0 into 0 9.315 * [backup-simplify]: Simplify 0 into 0 9.315 * [backup-simplify]: Simplify 0 into 0 9.315 * [backup-simplify]: Simplify 0 into 0 9.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.318 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.324 * [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 9.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.325 * [backup-simplify]: Simplify (- 0) into 0 9.326 * [backup-simplify]: Simplify (+ 0 0) into 0 9.327 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.330 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.333 * [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 9.333 * [taylor]: Taking taylor expansion of 0 in k 9.333 * [backup-simplify]: Simplify 0 into 0 9.333 * [backup-simplify]: Simplify 0 into 0 9.335 * [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)))))) 9.335 * [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))) 9.335 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 9.335 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 9.335 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 9.336 * [taylor]: Taking taylor expansion of 0.5 in k 9.336 * [backup-simplify]: Simplify 0.5 into 0.5 9.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.336 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.336 * [taylor]: Taking taylor expansion of k in k 9.336 * [backup-simplify]: Simplify 0 into 0 9.336 * [backup-simplify]: Simplify 1 into 1 9.336 * [backup-simplify]: Simplify (/ 1 1) into 1 9.336 * [taylor]: Taking taylor expansion of 1.0 in k 9.336 * [backup-simplify]: Simplify 1.0 into 1.0 9.336 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.336 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.336 * [taylor]: Taking taylor expansion of -2.0 in k 9.336 * [backup-simplify]: Simplify -2.0 into -2.0 9.336 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.336 * [taylor]: Taking taylor expansion of PI in k 9.336 * [backup-simplify]: Simplify PI into PI 9.336 * [taylor]: Taking taylor expansion of n in k 9.336 * [backup-simplify]: Simplify n into n 9.337 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.337 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.337 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.337 * [backup-simplify]: Simplify (+ 1 0) into 1 9.338 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 9.338 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 9.338 * [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)))) 9.338 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 9.338 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.338 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.338 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 9.338 * [taylor]: Taking taylor expansion of 0.5 in n 9.338 * [backup-simplify]: Simplify 0.5 into 0.5 9.338 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.338 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.338 * [taylor]: Taking taylor expansion of k in n 9.338 * [backup-simplify]: Simplify k into k 9.338 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.338 * [taylor]: Taking taylor expansion of 1.0 in n 9.339 * [backup-simplify]: Simplify 1.0 into 1.0 9.339 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.339 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.339 * [taylor]: Taking taylor expansion of -2.0 in n 9.339 * [backup-simplify]: Simplify -2.0 into -2.0 9.339 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.339 * [taylor]: Taking taylor expansion of PI in n 9.339 * [backup-simplify]: Simplify PI into PI 9.339 * [taylor]: Taking taylor expansion of n in n 9.339 * [backup-simplify]: Simplify 0 into 0 9.339 * [backup-simplify]: Simplify 1 into 1 9.339 * [backup-simplify]: Simplify (/ PI 1) into PI 9.340 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.341 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.341 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.341 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 9.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.344 * [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))) 9.345 * [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)))) 9.345 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 9.345 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.345 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.345 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 9.345 * [taylor]: Taking taylor expansion of 0.5 in n 9.345 * [backup-simplify]: Simplify 0.5 into 0.5 9.345 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.345 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.345 * [taylor]: Taking taylor expansion of k in n 9.345 * [backup-simplify]: Simplify k into k 9.345 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.345 * [taylor]: Taking taylor expansion of 1.0 in n 9.345 * [backup-simplify]: Simplify 1.0 into 1.0 9.345 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.345 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.345 * [taylor]: Taking taylor expansion of -2.0 in n 9.346 * [backup-simplify]: Simplify -2.0 into -2.0 9.346 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.346 * [taylor]: Taking taylor expansion of PI in n 9.346 * [backup-simplify]: Simplify PI into PI 9.346 * [taylor]: Taking taylor expansion of n in n 9.346 * [backup-simplify]: Simplify 0 into 0 9.346 * [backup-simplify]: Simplify 1 into 1 9.346 * [backup-simplify]: Simplify (/ PI 1) into PI 9.347 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.350 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.350 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.350 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 9.351 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.352 * [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))) 9.352 * [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)))) 9.352 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 9.352 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 9.352 * [taylor]: Taking taylor expansion of 0.5 in k 9.353 * [backup-simplify]: Simplify 0.5 into 0.5 9.353 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 9.353 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.353 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.353 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.353 * [taylor]: Taking taylor expansion of -2.0 in k 9.353 * [backup-simplify]: Simplify -2.0 into -2.0 9.353 * [taylor]: Taking taylor expansion of PI in k 9.353 * [backup-simplify]: Simplify PI into PI 9.353 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.354 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.354 * [taylor]: Taking taylor expansion of (log n) in k 9.354 * [taylor]: Taking taylor expansion of n in k 9.354 * [backup-simplify]: Simplify n into n 9.354 * [backup-simplify]: Simplify (log n) into (log n) 9.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.354 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.354 * [taylor]: Taking taylor expansion of k in k 9.354 * [backup-simplify]: Simplify 0 into 0 9.354 * [backup-simplify]: Simplify 1 into 1 9.354 * [backup-simplify]: Simplify (/ 1 1) into 1 9.354 * [taylor]: Taking taylor expansion of 1.0 in k 9.354 * [backup-simplify]: Simplify 1.0 into 1.0 9.354 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.355 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.355 * [backup-simplify]: Simplify (+ 1 0) into 1 9.356 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 9.356 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 9.357 * [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)))) 9.358 * [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)))) 9.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.359 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.360 * [backup-simplify]: Simplify (+ 0 0) into 0 9.361 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.362 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.363 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.364 * [taylor]: Taking taylor expansion of 0 in k 9.364 * [backup-simplify]: Simplify 0 into 0 9.364 * [backup-simplify]: Simplify 0 into 0 9.364 * [backup-simplify]: Simplify 0 into 0 9.364 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.365 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.367 * [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 9.367 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.367 * [backup-simplify]: Simplify (+ 0 0) into 0 9.368 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.370 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.371 * [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 9.371 * [taylor]: Taking taylor expansion of 0 in k 9.371 * [backup-simplify]: Simplify 0 into 0 9.371 * [backup-simplify]: Simplify 0 into 0 9.372 * [backup-simplify]: Simplify 0 into 0 9.372 * [backup-simplify]: Simplify 0 into 0 9.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.373 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.377 * [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 9.377 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.378 * [backup-simplify]: Simplify (+ 0 0) into 0 9.379 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.381 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.383 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.385 * [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 9.386 * [taylor]: Taking taylor expansion of 0 in k 9.386 * [backup-simplify]: Simplify 0 into 0 9.386 * [backup-simplify]: Simplify 0 into 0 9.387 * [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)))))) 9.387 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 9.388 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.388 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.388 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.388 * [taylor]: Taking taylor expansion of 2.0 in n 9.388 * [backup-simplify]: Simplify 2.0 into 2.0 9.388 * [taylor]: Taking taylor expansion of (* n PI) in n 9.388 * [taylor]: Taking taylor expansion of n in n 9.388 * [backup-simplify]: Simplify 0 into 0 9.388 * [backup-simplify]: Simplify 1 into 1 9.388 * [taylor]: Taking taylor expansion of PI in n 9.388 * [backup-simplify]: Simplify PI into PI 9.388 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.388 * [taylor]: Taking taylor expansion of 2.0 in n 9.388 * [backup-simplify]: Simplify 2.0 into 2.0 9.388 * [taylor]: Taking taylor expansion of (* n PI) in n 9.388 * [taylor]: Taking taylor expansion of n in n 9.388 * [backup-simplify]: Simplify 0 into 0 9.388 * [backup-simplify]: Simplify 1 into 1 9.388 * [taylor]: Taking taylor expansion of PI in n 9.388 * [backup-simplify]: Simplify PI into PI 9.389 * [backup-simplify]: Simplify (* 0 PI) into 0 9.389 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.389 * [backup-simplify]: Simplify 0 into 0 9.391 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.392 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.392 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.393 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.394 * [backup-simplify]: Simplify 0 into 0 9.394 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.395 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.395 * [backup-simplify]: Simplify 0 into 0 9.396 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.396 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.396 * [backup-simplify]: Simplify 0 into 0 9.397 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.398 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.398 * [backup-simplify]: Simplify 0 into 0 9.399 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.400 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.400 * [backup-simplify]: Simplify 0 into 0 9.401 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.403 * [backup-simplify]: Simplify 0 into 0 9.403 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.403 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.403 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.403 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.403 * [taylor]: Taking taylor expansion of 2.0 in n 9.403 * [backup-simplify]: Simplify 2.0 into 2.0 9.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.403 * [taylor]: Taking taylor expansion of PI in n 9.403 * [backup-simplify]: Simplify PI into PI 9.403 * [taylor]: Taking taylor expansion of n in n 9.403 * [backup-simplify]: Simplify 0 into 0 9.403 * [backup-simplify]: Simplify 1 into 1 9.404 * [backup-simplify]: Simplify (/ PI 1) into PI 9.404 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.404 * [taylor]: Taking taylor expansion of 2.0 in n 9.404 * [backup-simplify]: Simplify 2.0 into 2.0 9.404 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.404 * [taylor]: Taking taylor expansion of PI in n 9.404 * [backup-simplify]: Simplify PI into PI 9.404 * [taylor]: Taking taylor expansion of n in n 9.404 * [backup-simplify]: Simplify 0 into 0 9.404 * [backup-simplify]: Simplify 1 into 1 9.404 * [backup-simplify]: Simplify (/ PI 1) into PI 9.405 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.405 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.406 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.406 * [backup-simplify]: Simplify 0 into 0 9.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.407 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.407 * [backup-simplify]: Simplify 0 into 0 9.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.409 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.409 * [backup-simplify]: Simplify 0 into 0 9.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.410 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.410 * [backup-simplify]: Simplify 0 into 0 9.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.412 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.412 * [backup-simplify]: Simplify 0 into 0 9.413 * [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 9.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.415 * [backup-simplify]: Simplify 0 into 0 9.416 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.416 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.416 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.416 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.416 * [taylor]: Taking taylor expansion of -2.0 in n 9.417 * [backup-simplify]: Simplify -2.0 into -2.0 9.417 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.417 * [taylor]: Taking taylor expansion of PI in n 9.417 * [backup-simplify]: Simplify PI into PI 9.417 * [taylor]: Taking taylor expansion of n in n 9.417 * [backup-simplify]: Simplify 0 into 0 9.417 * [backup-simplify]: Simplify 1 into 1 9.417 * [backup-simplify]: Simplify (/ PI 1) into PI 9.417 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.417 * [taylor]: Taking taylor expansion of -2.0 in n 9.417 * [backup-simplify]: Simplify -2.0 into -2.0 9.417 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.417 * [taylor]: Taking taylor expansion of PI in n 9.418 * [backup-simplify]: Simplify PI into PI 9.418 * [taylor]: Taking taylor expansion of n in n 9.418 * [backup-simplify]: Simplify 0 into 0 9.418 * [backup-simplify]: Simplify 1 into 1 9.418 * [backup-simplify]: Simplify (/ PI 1) into PI 9.419 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.419 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.421 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.421 * [backup-simplify]: Simplify 0 into 0 9.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.423 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.423 * [backup-simplify]: Simplify 0 into 0 9.425 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.426 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.426 * [backup-simplify]: Simplify 0 into 0 9.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.428 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.428 * [backup-simplify]: Simplify 0 into 0 9.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.431 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.431 * [backup-simplify]: Simplify 0 into 0 9.433 * [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 9.434 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.434 * [backup-simplify]: Simplify 0 into 0 9.435 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.435 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 9.435 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 9.435 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 9.435 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.435 * [taylor]: Taking taylor expansion of 1.0 in k 9.435 * [backup-simplify]: Simplify 1.0 into 1.0 9.435 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.435 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.435 * [taylor]: Taking taylor expansion of k in k 9.435 * [backup-simplify]: Simplify 0 into 0 9.435 * [backup-simplify]: Simplify 1 into 1 9.436 * [backup-simplify]: Simplify (/ 1 1) into 1 9.436 * [backup-simplify]: Simplify (sqrt 0) into 0 9.437 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.437 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.437 * [taylor]: Taking taylor expansion of 1.0 in k 9.437 * [backup-simplify]: Simplify 1.0 into 1.0 9.437 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.437 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.437 * [taylor]: Taking taylor expansion of k in k 9.437 * [backup-simplify]: Simplify 0 into 0 9.437 * [backup-simplify]: Simplify 1 into 1 9.437 * [backup-simplify]: Simplify (/ 1 1) into 1 9.438 * [backup-simplify]: Simplify (sqrt 0) into 0 9.438 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.439 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.439 * [backup-simplify]: Simplify 0 into 0 9.440 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.440 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.440 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.442 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.443 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.443 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.444 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.447 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.448 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.448 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.449 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 9.449 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.449 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.449 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.449 * [taylor]: Taking taylor expansion of 1.0 in k 9.449 * [backup-simplify]: Simplify 1.0 into 1.0 9.449 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.449 * [taylor]: Taking taylor expansion of k in k 9.449 * [backup-simplify]: Simplify 0 into 0 9.449 * [backup-simplify]: Simplify 1 into 1 9.449 * [backup-simplify]: Simplify (sqrt 0) into 0 9.450 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.450 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.450 * [taylor]: Taking taylor expansion of 1.0 in k 9.450 * [backup-simplify]: Simplify 1.0 into 1.0 9.450 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.450 * [taylor]: Taking taylor expansion of k in k 9.450 * [backup-simplify]: Simplify 0 into 0 9.450 * [backup-simplify]: Simplify 1 into 1 9.451 * [backup-simplify]: Simplify (sqrt 0) into 0 9.451 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.452 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.452 * [backup-simplify]: Simplify 0 into 0 9.453 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.453 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.457 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.458 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.459 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.461 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.462 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.463 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.464 * [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)))))))) 9.464 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.464 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.464 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.464 * [taylor]: Taking taylor expansion of 1.0 in k 9.464 * [backup-simplify]: Simplify 1.0 into 1.0 9.464 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.464 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.464 * [taylor]: Taking taylor expansion of -1 in k 9.464 * [backup-simplify]: Simplify -1 into -1 9.464 * [taylor]: Taking taylor expansion of k in k 9.464 * [backup-simplify]: Simplify 0 into 0 9.464 * [backup-simplify]: Simplify 1 into 1 9.465 * [backup-simplify]: Simplify (/ -1 1) into -1 9.466 * [backup-simplify]: Simplify (sqrt 0) into 0 9.467 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.468 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.468 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.468 * [taylor]: Taking taylor expansion of 1.0 in k 9.468 * [backup-simplify]: Simplify 1.0 into 1.0 9.468 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.468 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.468 * [taylor]: Taking taylor expansion of -1 in k 9.468 * [backup-simplify]: Simplify -1 into -1 9.468 * [taylor]: Taking taylor expansion of k in k 9.468 * [backup-simplify]: Simplify 0 into 0 9.468 * [backup-simplify]: Simplify 1 into 1 9.469 * [backup-simplify]: Simplify (/ -1 1) into -1 9.469 * [backup-simplify]: Simplify (sqrt 0) into 0 9.471 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.471 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.471 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.472 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.475 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.478 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.478 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.483 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.487 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.488 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.489 * [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))))) 9.489 * * * * [progress]: [ 4 / 4 ] generating series at (2) 9.490 * [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)))) 9.490 * [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 9.490 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 9.490 * [taylor]: Taking taylor expansion of 1.0 in k 9.490 * [backup-simplify]: Simplify 1.0 into 1.0 9.490 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 9.490 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 9.490 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.490 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.490 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 9.490 * [taylor]: Taking taylor expansion of 0.5 in k 9.490 * [backup-simplify]: Simplify 0.5 into 0.5 9.490 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.490 * [taylor]: Taking taylor expansion of 1.0 in k 9.490 * [backup-simplify]: Simplify 1.0 into 1.0 9.490 * [taylor]: Taking taylor expansion of k in k 9.490 * [backup-simplify]: Simplify 0 into 0 9.490 * [backup-simplify]: Simplify 1 into 1 9.490 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.490 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.490 * [taylor]: Taking taylor expansion of 2.0 in k 9.490 * [backup-simplify]: Simplify 2.0 into 2.0 9.490 * [taylor]: Taking taylor expansion of (* n PI) in k 9.490 * [taylor]: Taking taylor expansion of n in k 9.490 * [backup-simplify]: Simplify n into n 9.490 * [taylor]: Taking taylor expansion of PI in k 9.490 * [backup-simplify]: Simplify PI into PI 9.491 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.491 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.491 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.491 * [backup-simplify]: Simplify (- 0) into 0 9.492 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.492 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 9.492 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 9.492 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 9.492 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.492 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.492 * [taylor]: Taking taylor expansion of k in k 9.492 * [backup-simplify]: Simplify 0 into 0 9.492 * [backup-simplify]: Simplify 1 into 1 9.493 * [backup-simplify]: Simplify (/ 1 1) into 1 9.493 * [backup-simplify]: Simplify (sqrt 0) into 0 9.494 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.494 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 9.494 * [taylor]: Taking taylor expansion of 1.0 in n 9.494 * [backup-simplify]: Simplify 1.0 into 1.0 9.494 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 9.494 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 9.495 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.495 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.495 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 9.495 * [taylor]: Taking taylor expansion of 0.5 in n 9.495 * [backup-simplify]: Simplify 0.5 into 0.5 9.495 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.495 * [taylor]: Taking taylor expansion of 1.0 in n 9.495 * [backup-simplify]: Simplify 1.0 into 1.0 9.495 * [taylor]: Taking taylor expansion of k in n 9.495 * [backup-simplify]: Simplify k into k 9.495 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.495 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.495 * [taylor]: Taking taylor expansion of 2.0 in n 9.495 * [backup-simplify]: Simplify 2.0 into 2.0 9.495 * [taylor]: Taking taylor expansion of (* n PI) in n 9.495 * [taylor]: Taking taylor expansion of n in n 9.495 * [backup-simplify]: Simplify 0 into 0 9.495 * [backup-simplify]: Simplify 1 into 1 9.495 * [taylor]: Taking taylor expansion of PI in n 9.495 * [backup-simplify]: Simplify PI into PI 9.496 * [backup-simplify]: Simplify (* 0 PI) into 0 9.496 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.497 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.499 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.500 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.500 * [backup-simplify]: Simplify (- k) into (- k) 9.500 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.500 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 9.502 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.503 * [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)))) 9.504 * [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))))) 9.504 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 9.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.504 * [taylor]: Taking taylor expansion of k in n 9.504 * [backup-simplify]: Simplify k into k 9.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.504 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 9.504 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.504 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 9.504 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 9.504 * [taylor]: Taking taylor expansion of 1.0 in n 9.504 * [backup-simplify]: Simplify 1.0 into 1.0 9.504 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 9.504 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 9.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.504 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.504 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 9.504 * [taylor]: Taking taylor expansion of 0.5 in n 9.504 * [backup-simplify]: Simplify 0.5 into 0.5 9.505 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.505 * [taylor]: Taking taylor expansion of 1.0 in n 9.505 * [backup-simplify]: Simplify 1.0 into 1.0 9.505 * [taylor]: Taking taylor expansion of k in n 9.505 * [backup-simplify]: Simplify k into k 9.505 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.505 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.505 * [taylor]: Taking taylor expansion of 2.0 in n 9.505 * [backup-simplify]: Simplify 2.0 into 2.0 9.505 * [taylor]: Taking taylor expansion of (* n PI) in n 9.505 * [taylor]: Taking taylor expansion of n in n 9.505 * [backup-simplify]: Simplify 0 into 0 9.505 * [backup-simplify]: Simplify 1 into 1 9.505 * [taylor]: Taking taylor expansion of PI in n 9.505 * [backup-simplify]: Simplify PI into PI 9.505 * [backup-simplify]: Simplify (* 0 PI) into 0 9.506 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.507 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.509 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.509 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.510 * [backup-simplify]: Simplify (- k) into (- k) 9.510 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.510 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 9.511 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.512 * [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)))) 9.513 * [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))))) 9.513 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 9.513 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.513 * [taylor]: Taking taylor expansion of k in n 9.513 * [backup-simplify]: Simplify k into k 9.513 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.513 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 9.514 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.514 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 9.515 * [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))) 9.516 * [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)))) 9.516 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k 9.516 * [taylor]: Taking taylor expansion of 1.0 in k 9.516 * [backup-simplify]: Simplify 1.0 into 1.0 9.516 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k 9.516 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.516 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.516 * [taylor]: Taking taylor expansion of 0.5 in k 9.516 * [backup-simplify]: Simplify 0.5 into 0.5 9.516 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.516 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.516 * [taylor]: Taking taylor expansion of 1.0 in k 9.516 * [backup-simplify]: Simplify 1.0 into 1.0 9.516 * [taylor]: Taking taylor expansion of k in k 9.517 * [backup-simplify]: Simplify 0 into 0 9.517 * [backup-simplify]: Simplify 1 into 1 9.517 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.517 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.517 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.517 * [taylor]: Taking taylor expansion of 2.0 in k 9.517 * [backup-simplify]: Simplify 2.0 into 2.0 9.517 * [taylor]: Taking taylor expansion of PI in k 9.517 * [backup-simplify]: Simplify PI into PI 9.517 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.518 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.518 * [taylor]: Taking taylor expansion of (log n) in k 9.518 * [taylor]: Taking taylor expansion of n in k 9.518 * [backup-simplify]: Simplify n into n 9.518 * [backup-simplify]: Simplify (log n) into (log n) 9.519 * [backup-simplify]: Simplify (- 0) into 0 9.519 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.520 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.521 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.522 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 9.523 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 9.523 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.523 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.523 * [taylor]: Taking taylor expansion of k in k 9.524 * [backup-simplify]: Simplify 0 into 0 9.524 * [backup-simplify]: Simplify 1 into 1 9.524 * [backup-simplify]: Simplify (/ 1 1) into 1 9.524 * [backup-simplify]: Simplify (sqrt 0) into 0 9.526 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.528 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0 9.528 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.528 * [backup-simplify]: Simplify 0 into 0 9.529 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.530 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.532 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.533 * [backup-simplify]: Simplify (- 0) into 0 9.533 * [backup-simplify]: Simplify (+ 0 0) into 0 9.534 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 9.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.536 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.538 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.540 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 9.542 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0 9.542 * [taylor]: Taking taylor expansion of 0 in k 9.542 * [backup-simplify]: Simplify 0 into 0 9.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.544 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.545 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.545 * [backup-simplify]: Simplify (+ 0 0) into 0 9.546 * [backup-simplify]: Simplify (- 1) into -1 9.546 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.548 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.550 * [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)))) 9.553 * [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)))))) 9.558 * [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)))))) 9.560 * [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)))))) 9.561 * [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)))))) 9.561 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.562 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 9.563 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.564 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.568 * [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 9.568 * [backup-simplify]: Simplify (- 0) into 0 9.568 * [backup-simplify]: Simplify (+ 0 0) into 0 9.569 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.570 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.571 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.572 * [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 9.573 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 9.575 * [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 9.575 * [taylor]: Taking taylor expansion of 0 in k 9.575 * [backup-simplify]: Simplify 0 into 0 9.575 * [backup-simplify]: Simplify 0 into 0 9.575 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.577 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.578 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.580 * [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 9.581 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.581 * [backup-simplify]: Simplify (+ 0 0) into 0 9.581 * [backup-simplify]: Simplify (- 0) into 0 9.581 * [backup-simplify]: Simplify (+ 0 0) into 0 9.583 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.584 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.589 * [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)))))) 9.595 * [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))))))))))) 9.602 * [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))))))))))) 9.608 * [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))))))))))) 9.608 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.609 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 9.610 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.612 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.618 * [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 9.618 * [backup-simplify]: Simplify (- 0) into 0 9.619 * [backup-simplify]: Simplify (+ 0 0) into 0 9.621 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 9.622 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.624 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.627 * [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 9.628 * [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 9.630 * [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 9.630 * [taylor]: Taking taylor expansion of 0 in k 9.630 * [backup-simplify]: Simplify 0 into 0 9.630 * [backup-simplify]: Simplify 0 into 0 9.630 * [backup-simplify]: Simplify 0 into 0 9.630 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.633 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.634 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.637 * [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 9.639 * [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 9.639 * [backup-simplify]: Simplify (+ 0 0) into 0 9.639 * [backup-simplify]: Simplify (- 0) into 0 9.639 * [backup-simplify]: Simplify (+ 0 0) into 0 9.641 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.643 * [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 9.647 * [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)))))) 9.660 * [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))))))))))))))))) 9.682 * [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))))))))))))))))) 9.696 * [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))))))))))))))))) 9.721 * [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))))))))))))))))))))) 9.722 * [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))) 9.722 * [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 9.722 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 9.722 * [taylor]: Taking taylor expansion of 1.0 in k 9.722 * [backup-simplify]: Simplify 1.0 into 1.0 9.722 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 9.722 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 9.722 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.722 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.722 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 9.722 * [taylor]: Taking taylor expansion of 0.5 in k 9.722 * [backup-simplify]: Simplify 0.5 into 0.5 9.722 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.722 * [taylor]: Taking taylor expansion of 1.0 in k 9.722 * [backup-simplify]: Simplify 1.0 into 1.0 9.722 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.722 * [taylor]: Taking taylor expansion of k in k 9.722 * [backup-simplify]: Simplify 0 into 0 9.722 * [backup-simplify]: Simplify 1 into 1 9.722 * [backup-simplify]: Simplify (/ 1 1) into 1 9.722 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.722 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.722 * [taylor]: Taking taylor expansion of 2.0 in k 9.722 * [backup-simplify]: Simplify 2.0 into 2.0 9.722 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.722 * [taylor]: Taking taylor expansion of PI in k 9.722 * [backup-simplify]: Simplify PI into PI 9.722 * [taylor]: Taking taylor expansion of n in k 9.722 * [backup-simplify]: Simplify n into n 9.722 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.722 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.723 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.723 * [backup-simplify]: Simplify (- 1) into -1 9.723 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.723 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 9.723 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 9.724 * [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)))))) 9.724 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.724 * [taylor]: Taking taylor expansion of k in k 9.724 * [backup-simplify]: Simplify 0 into 0 9.724 * [backup-simplify]: Simplify 1 into 1 9.724 * [backup-simplify]: Simplify (sqrt 0) into 0 9.725 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.725 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 9.725 * [taylor]: Taking taylor expansion of 1.0 in n 9.725 * [backup-simplify]: Simplify 1.0 into 1.0 9.725 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 9.725 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 9.725 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.725 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.725 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 9.725 * [taylor]: Taking taylor expansion of 0.5 in n 9.725 * [backup-simplify]: Simplify 0.5 into 0.5 9.725 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.725 * [taylor]: Taking taylor expansion of 1.0 in n 9.725 * [backup-simplify]: Simplify 1.0 into 1.0 9.725 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.725 * [taylor]: Taking taylor expansion of k in n 9.725 * [backup-simplify]: Simplify k into k 9.725 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.725 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.725 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.725 * [taylor]: Taking taylor expansion of 2.0 in n 9.725 * [backup-simplify]: Simplify 2.0 into 2.0 9.725 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.725 * [taylor]: Taking taylor expansion of PI in n 9.725 * [backup-simplify]: Simplify PI into PI 9.725 * [taylor]: Taking taylor expansion of n in n 9.725 * [backup-simplify]: Simplify 0 into 0 9.725 * [backup-simplify]: Simplify 1 into 1 9.726 * [backup-simplify]: Simplify (/ PI 1) into PI 9.726 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.727 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.727 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.727 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.727 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 9.728 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.728 * [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)))) 9.729 * [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))))) 9.729 * [taylor]: Taking taylor expansion of (sqrt k) in n 9.729 * [taylor]: Taking taylor expansion of k in n 9.729 * [backup-simplify]: Simplify k into k 9.729 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 9.729 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 9.729 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 9.729 * [taylor]: Taking taylor expansion of 1.0 in n 9.729 * [backup-simplify]: Simplify 1.0 into 1.0 9.729 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 9.729 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 9.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.730 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.730 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 9.730 * [taylor]: Taking taylor expansion of 0.5 in n 9.730 * [backup-simplify]: Simplify 0.5 into 0.5 9.730 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.730 * [taylor]: Taking taylor expansion of 1.0 in n 9.730 * [backup-simplify]: Simplify 1.0 into 1.0 9.730 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.730 * [taylor]: Taking taylor expansion of k in n 9.730 * [backup-simplify]: Simplify k into k 9.730 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.730 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.730 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.730 * [taylor]: Taking taylor expansion of 2.0 in n 9.730 * [backup-simplify]: Simplify 2.0 into 2.0 9.730 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.730 * [taylor]: Taking taylor expansion of PI in n 9.730 * [backup-simplify]: Simplify PI into PI 9.730 * [taylor]: Taking taylor expansion of n in n 9.730 * [backup-simplify]: Simplify 0 into 0 9.730 * [backup-simplify]: Simplify 1 into 1 9.730 * [backup-simplify]: Simplify (/ PI 1) into PI 9.730 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.731 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.731 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.731 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.731 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 9.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.733 * [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)))) 9.734 * [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))))) 9.734 * [taylor]: Taking taylor expansion of (sqrt k) in n 9.734 * [taylor]: Taking taylor expansion of k in n 9.734 * [backup-simplify]: Simplify k into k 9.734 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 9.734 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 9.735 * [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)) 9.735 * [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))) 9.736 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k 9.736 * [taylor]: Taking taylor expansion of 1.0 in k 9.736 * [backup-simplify]: Simplify 1.0 into 1.0 9.736 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k 9.736 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 9.736 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 9.736 * [taylor]: Taking taylor expansion of 0.5 in k 9.736 * [backup-simplify]: Simplify 0.5 into 0.5 9.736 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 9.736 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.736 * [taylor]: Taking taylor expansion of 1.0 in k 9.736 * [backup-simplify]: Simplify 1.0 into 1.0 9.736 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.736 * [taylor]: Taking taylor expansion of k in k 9.736 * [backup-simplify]: Simplify 0 into 0 9.736 * [backup-simplify]: Simplify 1 into 1 9.736 * [backup-simplify]: Simplify (/ 1 1) into 1 9.736 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.736 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.736 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.736 * [taylor]: Taking taylor expansion of 2.0 in k 9.736 * [backup-simplify]: Simplify 2.0 into 2.0 9.736 * [taylor]: Taking taylor expansion of PI in k 9.736 * [backup-simplify]: Simplify PI into PI 9.736 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.737 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.737 * [taylor]: Taking taylor expansion of (log n) in k 9.737 * [taylor]: Taking taylor expansion of n in k 9.737 * [backup-simplify]: Simplify n into n 9.737 * [backup-simplify]: Simplify (log n) into (log n) 9.737 * [backup-simplify]: Simplify (- 1) into -1 9.738 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.738 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.738 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.739 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.740 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 9.741 * [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))))) 9.741 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.741 * [taylor]: Taking taylor expansion of k in k 9.741 * [backup-simplify]: Simplify 0 into 0 9.741 * [backup-simplify]: Simplify 1 into 1 9.741 * [backup-simplify]: Simplify (sqrt 0) into 0 9.742 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.743 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0 9.743 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.743 * [backup-simplify]: Simplify 0 into 0 9.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.745 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.745 * [backup-simplify]: Simplify (- 0) into 0 9.746 * [backup-simplify]: Simplify (+ 0 0) into 0 9.746 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.747 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.748 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.750 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.752 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0 9.754 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0 9.754 * [taylor]: Taking taylor expansion of 0 in k 9.754 * [backup-simplify]: Simplify 0 into 0 9.754 * [backup-simplify]: Simplify 0 into 0 9.756 * [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))))))) 9.757 * [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))))))) 9.759 * [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))))))) 9.760 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 9.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.762 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.765 * [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 9.766 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.766 * [backup-simplify]: Simplify (- 0) into 0 9.767 * [backup-simplify]: Simplify (+ 0 0) into 0 9.767 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.771 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.773 * [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 9.775 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 9.777 * [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 9.777 * [taylor]: Taking taylor expansion of 0 in k 9.777 * [backup-simplify]: Simplify 0 into 0 9.777 * [backup-simplify]: Simplify 0 into 0 9.777 * [backup-simplify]: Simplify 0 into 0 9.780 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.782 * [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))))))) 9.785 * [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))))))) 9.786 * [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))))))) 9.787 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 9.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.788 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.792 * [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 9.792 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.792 * [backup-simplify]: Simplify (- 0) into 0 9.793 * [backup-simplify]: Simplify (+ 0 0) into 0 9.794 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.795 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.796 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.798 * [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 9.799 * [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 9.801 * [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 9.801 * [taylor]: Taking taylor expansion of 0 in k 9.801 * [backup-simplify]: Simplify 0 into 0 9.801 * [backup-simplify]: Simplify 0 into 0 9.801 * [backup-simplify]: Simplify 0 into 0 9.801 * [backup-simplify]: Simplify 0 into 0 9.803 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.805 * [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))))))) 9.808 * [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))))))) 9.809 * [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))))))) 9.812 * [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)))))))) 9.813 * [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)))) 9.813 * [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 9.813 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 9.813 * [taylor]: Taking taylor expansion of 1.0 in k 9.813 * [backup-simplify]: Simplify 1.0 into 1.0 9.813 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 9.813 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 9.813 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.813 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.813 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 9.813 * [taylor]: Taking taylor expansion of 0.5 in k 9.813 * [backup-simplify]: Simplify 0.5 into 0.5 9.813 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.813 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.813 * [taylor]: Taking taylor expansion of k in k 9.813 * [backup-simplify]: Simplify 0 into 0 9.813 * [backup-simplify]: Simplify 1 into 1 9.813 * [backup-simplify]: Simplify (/ 1 1) into 1 9.813 * [taylor]: Taking taylor expansion of 1.0 in k 9.813 * [backup-simplify]: Simplify 1.0 into 1.0 9.813 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.813 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.813 * [taylor]: Taking taylor expansion of -2.0 in k 9.813 * [backup-simplify]: Simplify -2.0 into -2.0 9.813 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.814 * [taylor]: Taking taylor expansion of PI in k 9.814 * [backup-simplify]: Simplify PI into PI 9.814 * [taylor]: Taking taylor expansion of n in k 9.814 * [backup-simplify]: Simplify n into n 9.814 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.814 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.814 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.814 * [backup-simplify]: Simplify (+ 1 0) into 1 9.814 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 9.814 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 9.815 * [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)))) 9.815 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.815 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.815 * [taylor]: Taking taylor expansion of -1 in k 9.815 * [backup-simplify]: Simplify -1 into -1 9.815 * [taylor]: Taking taylor expansion of k in k 9.815 * [backup-simplify]: Simplify 0 into 0 9.815 * [backup-simplify]: Simplify 1 into 1 9.815 * [backup-simplify]: Simplify (/ -1 1) into -1 9.815 * [backup-simplify]: Simplify (sqrt 0) into 0 9.816 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.816 * [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))))) 9.816 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 9.816 * [taylor]: Taking taylor expansion of 1.0 in n 9.816 * [backup-simplify]: Simplify 1.0 into 1.0 9.816 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 9.817 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 9.817 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.817 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.817 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 9.817 * [taylor]: Taking taylor expansion of 0.5 in n 9.817 * [backup-simplify]: Simplify 0.5 into 0.5 9.817 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.817 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.817 * [taylor]: Taking taylor expansion of k in n 9.817 * [backup-simplify]: Simplify k into k 9.817 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.817 * [taylor]: Taking taylor expansion of 1.0 in n 9.817 * [backup-simplify]: Simplify 1.0 into 1.0 9.817 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.817 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.817 * [taylor]: Taking taylor expansion of -2.0 in n 9.817 * [backup-simplify]: Simplify -2.0 into -2.0 9.817 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.817 * [taylor]: Taking taylor expansion of PI in n 9.817 * [backup-simplify]: Simplify PI into PI 9.817 * [taylor]: Taking taylor expansion of n in n 9.817 * [backup-simplify]: Simplify 0 into 0 9.817 * [backup-simplify]: Simplify 1 into 1 9.817 * [backup-simplify]: Simplify (/ PI 1) into PI 9.818 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.818 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.818 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.818 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 9.819 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.820 * [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))) 9.823 * [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)))) 9.823 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 9.823 * [taylor]: Taking taylor expansion of (/ -1 k) in n 9.823 * [taylor]: Taking taylor expansion of -1 in n 9.823 * [backup-simplify]: Simplify -1 into -1 9.823 * [taylor]: Taking taylor expansion of k in n 9.823 * [backup-simplify]: Simplify k into k 9.823 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 9.824 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 9.824 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 9.824 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 9.824 * [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))) 9.825 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 9.825 * [taylor]: Taking taylor expansion of 1.0 in n 9.825 * [backup-simplify]: Simplify 1.0 into 1.0 9.825 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 9.825 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 9.825 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.825 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.825 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 9.825 * [taylor]: Taking taylor expansion of 0.5 in n 9.825 * [backup-simplify]: Simplify 0.5 into 0.5 9.825 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.825 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.825 * [taylor]: Taking taylor expansion of k in n 9.825 * [backup-simplify]: Simplify k into k 9.825 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.825 * [taylor]: Taking taylor expansion of 1.0 in n 9.825 * [backup-simplify]: Simplify 1.0 into 1.0 9.825 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.825 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.825 * [taylor]: Taking taylor expansion of -2.0 in n 9.825 * [backup-simplify]: Simplify -2.0 into -2.0 9.825 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.825 * [taylor]: Taking taylor expansion of PI in n 9.825 * [backup-simplify]: Simplify PI into PI 9.825 * [taylor]: Taking taylor expansion of n in n 9.825 * [backup-simplify]: Simplify 0 into 0 9.825 * [backup-simplify]: Simplify 1 into 1 9.825 * [backup-simplify]: Simplify (/ PI 1) into PI 9.826 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.826 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.826 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.826 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 9.827 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.828 * [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))) 9.829 * [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)))) 9.829 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 9.829 * [taylor]: Taking taylor expansion of (/ -1 k) in n 9.829 * [taylor]: Taking taylor expansion of -1 in n 9.829 * [backup-simplify]: Simplify -1 into -1 9.829 * [taylor]: Taking taylor expansion of k in n 9.829 * [backup-simplify]: Simplify k into k 9.829 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 9.829 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 9.829 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 9.829 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 9.830 * [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))) 9.831 * [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)))) 9.831 * [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 9.831 * [taylor]: Taking taylor expansion of 1.0 in k 9.831 * [backup-simplify]: Simplify 1.0 into 1.0 9.831 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k 9.831 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 9.831 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 9.831 * [taylor]: Taking taylor expansion of 0.5 in k 9.831 * [backup-simplify]: Simplify 0.5 into 0.5 9.831 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 9.831 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.831 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.831 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.831 * [taylor]: Taking taylor expansion of -2.0 in k 9.831 * [backup-simplify]: Simplify -2.0 into -2.0 9.831 * [taylor]: Taking taylor expansion of PI in k 9.831 * [backup-simplify]: Simplify PI into PI 9.832 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.832 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.832 * [taylor]: Taking taylor expansion of (log n) in k 9.832 * [taylor]: Taking taylor expansion of n in k 9.832 * [backup-simplify]: Simplify n into n 9.832 * [backup-simplify]: Simplify (log n) into (log n) 9.832 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.832 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.832 * [taylor]: Taking taylor expansion of k in k 9.832 * [backup-simplify]: Simplify 0 into 0 9.832 * [backup-simplify]: Simplify 1 into 1 9.833 * [backup-simplify]: Simplify (/ 1 1) into 1 9.833 * [taylor]: Taking taylor expansion of 1.0 in k 9.833 * [backup-simplify]: Simplify 1.0 into 1.0 9.833 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.833 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.834 * [backup-simplify]: Simplify (+ 1 0) into 1 9.834 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 9.835 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 9.836 * [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)))) 9.836 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.836 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.836 * [taylor]: Taking taylor expansion of -1 in k 9.836 * [backup-simplify]: Simplify -1 into -1 9.836 * [taylor]: Taking taylor expansion of k in k 9.836 * [backup-simplify]: Simplify 0 into 0 9.836 * [backup-simplify]: Simplify 1 into 1 9.836 * [backup-simplify]: Simplify (/ -1 1) into -1 9.836 * [backup-simplify]: Simplify (sqrt 0) into 0 9.837 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.838 * [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))))) 9.839 * [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))))) 9.840 * [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))))) 9.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.841 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.842 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.842 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.842 * [backup-simplify]: Simplify (+ 0 0) into 0 9.843 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.844 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.844 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.845 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.846 * [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 9.848 * [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 9.848 * [taylor]: Taking taylor expansion of 0 in k 9.848 * [backup-simplify]: Simplify 0 into 0 9.848 * [backup-simplify]: Simplify 0 into 0 9.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.852 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.854 * [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)))))) 9.857 * [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)))))) 9.858 * [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)))))) 9.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.860 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.863 * [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 9.864 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.864 * [backup-simplify]: Simplify (+ 0 0) into 0 9.865 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.868 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.871 * [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 9.871 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.872 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 9.873 * [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 9.875 * [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 9.875 * [taylor]: Taking taylor expansion of 0 in k 9.875 * [backup-simplify]: Simplify 0 into 0 9.875 * [backup-simplify]: Simplify 0 into 0 9.875 * [backup-simplify]: Simplify 0 into 0 9.876 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.880 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.883 * [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)))))) 9.887 * [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)))))) 9.889 * [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)))))) 9.893 * [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)))))))) 9.893 * * * [progress]: simplifying candidates 9.898 * [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 (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (log1p (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (+ (* (+ (+ (log 2.0) (log PI)) (log 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 (sqrt k)))) (+ (* (+ (log (* 2.0 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 (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 (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 (sqrt k)))) (+ (log (pow (* (* 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 (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (exp (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (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)))) (* (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) 1.0) (* (pow (* (* 2.0 PI) n) (/ k 2.0)) (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)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt 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)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (* (cbrt k) (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 1))) (* (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) 1)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt 1))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (sqrt k)))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (/ 1 1)) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (* (pow n (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (* (sqrt (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) 2)) (/ 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)) (/ 1.0 (sqrt k))) (- (+ (* 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 (* (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)))))))) 9.904 * * [simplify]: iteration 0: 343 enodes 10.027 * * [simplify]: iteration 1: 952 enodes 10.524 * * [simplify]: iteration 2: 3248 enodes 12.026 * * [simplify]: iteration complete: 5006 enodes 12.026 * * [simplify]: Extracting #0: cost 127 inf + 0 12.027 * * [simplify]: Extracting #1: cost 649 inf + 43 12.031 * * [simplify]: Extracting #2: cost 1087 inf + 2170 12.051 * * [simplify]: Extracting #3: cost 1035 inf + 42202 12.111 * * [simplify]: Extracting #4: cost 602 inf + 189427 12.187 * * [simplify]: Extracting #5: cost 235 inf + 374211 12.345 * * [simplify]: Extracting #6: cost 64 inf + 464767 12.548 * * [simplify]: Extracting #7: cost 4 inf + 494921 12.702 * * [simplify]: Extracting #8: cost 0 inf + 498450 12.877 * * [simplify]: Extracting #9: cost 0 inf + 496270 13.060 * * [simplify]: Extracting #10: cost 0 inf + 495310 13.245 * * [simplify]: Extracting #11: cost 0 inf + 495080 13.403 * [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))))) 13.422 * * * [progress]: adding candidates to table 14.257 * * [progress]: iteration 3 / 4 14.257 * * * [progress]: picking best candidate 14.315 * * * * [pick]: Picked # 14.315 * * * [progress]: localizing error 14.358 * * * [progress]: generating rewritten candidates 14.358 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 14.387 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 14.398 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 14.408 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 14.446 * * * [progress]: generating series expansions 14.446 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 14.447 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 14.447 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 14.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.447 * [taylor]: Taking taylor expansion of 0.5 in k 14.447 * [backup-simplify]: Simplify 0.5 into 0.5 14.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.447 * [taylor]: Taking taylor expansion of 1.0 in k 14.447 * [backup-simplify]: Simplify 1.0 into 1.0 14.447 * [taylor]: Taking taylor expansion of k in k 14.447 * [backup-simplify]: Simplify 0 into 0 14.447 * [backup-simplify]: Simplify 1 into 1 14.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.447 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.447 * [taylor]: Taking taylor expansion of 2.0 in k 14.447 * [backup-simplify]: Simplify 2.0 into 2.0 14.447 * [taylor]: Taking taylor expansion of (* n PI) in k 14.447 * [taylor]: Taking taylor expansion of n in k 14.447 * [backup-simplify]: Simplify n into n 14.447 * [taylor]: Taking taylor expansion of PI in k 14.447 * [backup-simplify]: Simplify PI into PI 14.447 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.447 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.448 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.448 * [backup-simplify]: Simplify (- 0) into 0 14.449 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.449 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.449 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.450 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.450 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.450 * [taylor]: Taking taylor expansion of 0.5 in n 14.450 * [backup-simplify]: Simplify 0.5 into 0.5 14.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.450 * [taylor]: Taking taylor expansion of 1.0 in n 14.450 * [backup-simplify]: Simplify 1.0 into 1.0 14.450 * [taylor]: Taking taylor expansion of k in n 14.450 * [backup-simplify]: Simplify k into k 14.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.450 * [taylor]: Taking taylor expansion of 2.0 in n 14.450 * [backup-simplify]: Simplify 2.0 into 2.0 14.450 * [taylor]: Taking taylor expansion of (* n PI) in n 14.450 * [taylor]: Taking taylor expansion of n in n 14.450 * [backup-simplify]: Simplify 0 into 0 14.450 * [backup-simplify]: Simplify 1 into 1 14.450 * [taylor]: Taking taylor expansion of PI in n 14.450 * [backup-simplify]: Simplify PI into PI 14.451 * [backup-simplify]: Simplify (* 0 PI) into 0 14.451 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.453 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.454 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.455 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.455 * [backup-simplify]: Simplify (- k) into (- k) 14.455 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.455 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.457 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.458 * [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)))) 14.459 * [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))))) 14.460 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.460 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.460 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.460 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.460 * [taylor]: Taking taylor expansion of 0.5 in n 14.460 * [backup-simplify]: Simplify 0.5 into 0.5 14.460 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.460 * [taylor]: Taking taylor expansion of 1.0 in n 14.460 * [backup-simplify]: Simplify 1.0 into 1.0 14.460 * [taylor]: Taking taylor expansion of k in n 14.460 * [backup-simplify]: Simplify k into k 14.460 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.460 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.460 * [taylor]: Taking taylor expansion of 2.0 in n 14.460 * [backup-simplify]: Simplify 2.0 into 2.0 14.460 * [taylor]: Taking taylor expansion of (* n PI) in n 14.460 * [taylor]: Taking taylor expansion of n in n 14.460 * [backup-simplify]: Simplify 0 into 0 14.460 * [backup-simplify]: Simplify 1 into 1 14.460 * [taylor]: Taking taylor expansion of PI in n 14.460 * [backup-simplify]: Simplify PI into PI 14.461 * [backup-simplify]: Simplify (* 0 PI) into 0 14.461 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.462 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.464 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.465 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.465 * [backup-simplify]: Simplify (- k) into (- k) 14.465 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.465 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.467 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.468 * [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)))) 14.469 * [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))))) 14.469 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 14.469 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 14.469 * [taylor]: Taking taylor expansion of 0.5 in k 14.469 * [backup-simplify]: Simplify 0.5 into 0.5 14.469 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 14.469 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.469 * [taylor]: Taking taylor expansion of 1.0 in k 14.469 * [backup-simplify]: Simplify 1.0 into 1.0 14.469 * [taylor]: Taking taylor expansion of k in k 14.470 * [backup-simplify]: Simplify 0 into 0 14.470 * [backup-simplify]: Simplify 1 into 1 14.470 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 14.470 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.470 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.470 * [taylor]: Taking taylor expansion of 2.0 in k 14.470 * [backup-simplify]: Simplify 2.0 into 2.0 14.470 * [taylor]: Taking taylor expansion of PI in k 14.470 * [backup-simplify]: Simplify PI into PI 14.470 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.471 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.471 * [taylor]: Taking taylor expansion of (log n) in k 14.471 * [taylor]: Taking taylor expansion of n in k 14.471 * [backup-simplify]: Simplify n into n 14.471 * [backup-simplify]: Simplify (log n) into (log n) 14.472 * [backup-simplify]: Simplify (- 0) into 0 14.472 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.473 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 14.474 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 14.476 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 14.477 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.478 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.479 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.482 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.483 * [backup-simplify]: Simplify (- 0) into 0 14.483 * [backup-simplify]: Simplify (+ 0 0) into 0 14.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 14.485 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.486 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 14.488 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.488 * [taylor]: Taking taylor expansion of 0 in k 14.488 * [backup-simplify]: Simplify 0 into 0 14.488 * [backup-simplify]: Simplify 0 into 0 14.489 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.491 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.492 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 14.492 * [backup-simplify]: Simplify (+ 0 0) into 0 14.492 * [backup-simplify]: Simplify (- 1) into -1 14.492 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.493 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 14.495 * [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)))) 14.497 * [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)))))) 14.499 * [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)))))) 14.500 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.503 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.505 * [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 14.506 * [backup-simplify]: Simplify (- 0) into 0 14.506 * [backup-simplify]: Simplify (+ 0 0) into 0 14.506 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 14.507 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.508 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.510 * [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 14.510 * [taylor]: Taking taylor expansion of 0 in k 14.510 * [backup-simplify]: Simplify 0 into 0 14.510 * [backup-simplify]: Simplify 0 into 0 14.510 * [backup-simplify]: Simplify 0 into 0 14.510 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.512 * [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 14.514 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 14.514 * [backup-simplify]: Simplify (+ 0 0) into 0 14.514 * [backup-simplify]: Simplify (- 0) into 0 14.514 * [backup-simplify]: Simplify (+ 0 0) into 0 14.516 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.517 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.520 * [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)))))) 14.526 * [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)))))) 14.536 * [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))))) 14.536 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 14.536 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 14.537 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.537 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.537 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.537 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.537 * [taylor]: Taking taylor expansion of 0.5 in k 14.537 * [backup-simplify]: Simplify 0.5 into 0.5 14.537 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.537 * [taylor]: Taking taylor expansion of 1.0 in k 14.537 * [backup-simplify]: Simplify 1.0 into 1.0 14.537 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.537 * [taylor]: Taking taylor expansion of k in k 14.537 * [backup-simplify]: Simplify 0 into 0 14.537 * [backup-simplify]: Simplify 1 into 1 14.537 * [backup-simplify]: Simplify (/ 1 1) into 1 14.537 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.537 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.537 * [taylor]: Taking taylor expansion of 2.0 in k 14.537 * [backup-simplify]: Simplify 2.0 into 2.0 14.537 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.537 * [taylor]: Taking taylor expansion of PI in k 14.537 * [backup-simplify]: Simplify PI into PI 14.537 * [taylor]: Taking taylor expansion of n in k 14.537 * [backup-simplify]: Simplify n into n 14.538 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.538 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.538 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.538 * [backup-simplify]: Simplify (- 1) into -1 14.538 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.539 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.539 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.539 * [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)))))) 14.539 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.539 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.539 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.539 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.539 * [taylor]: Taking taylor expansion of 0.5 in n 14.539 * [backup-simplify]: Simplify 0.5 into 0.5 14.539 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.540 * [taylor]: Taking taylor expansion of 1.0 in n 14.540 * [backup-simplify]: Simplify 1.0 into 1.0 14.540 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.540 * [taylor]: Taking taylor expansion of k in n 14.540 * [backup-simplify]: Simplify k into k 14.540 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.540 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.540 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) 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 (/ PI n) in n 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 n in n 14.540 * [backup-simplify]: Simplify 0 into 0 14.540 * [backup-simplify]: Simplify 1 into 1 14.540 * [backup-simplify]: Simplify (/ PI 1) into PI 14.541 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.542 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.542 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.542 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.542 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.544 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.545 * [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)))) 14.546 * [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))))) 14.546 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.546 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.546 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.546 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.546 * [taylor]: Taking taylor expansion of 0.5 in n 14.546 * [backup-simplify]: Simplify 0.5 into 0.5 14.546 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.546 * [taylor]: Taking taylor expansion of 1.0 in n 14.546 * [backup-simplify]: Simplify 1.0 into 1.0 14.546 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.546 * [taylor]: Taking taylor expansion of k in n 14.546 * [backup-simplify]: Simplify k into k 14.547 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.547 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.547 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.547 * [taylor]: Taking taylor expansion of 2.0 in n 14.547 * [backup-simplify]: Simplify 2.0 into 2.0 14.547 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.547 * [taylor]: Taking taylor expansion of PI in n 14.547 * [backup-simplify]: Simplify PI into PI 14.547 * [taylor]: Taking taylor expansion of n in n 14.547 * [backup-simplify]: Simplify 0 into 0 14.547 * [backup-simplify]: Simplify 1 into 1 14.547 * [backup-simplify]: Simplify (/ PI 1) into PI 14.548 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.549 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.549 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.549 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.549 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.552 * [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)))) 14.553 * [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))))) 14.553 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 14.553 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 14.553 * [taylor]: Taking taylor expansion of 0.5 in k 14.553 * [backup-simplify]: Simplify 0.5 into 0.5 14.553 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 14.553 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.553 * [taylor]: Taking taylor expansion of 1.0 in k 14.553 * [backup-simplify]: Simplify 1.0 into 1.0 14.553 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.553 * [taylor]: Taking taylor expansion of k in k 14.553 * [backup-simplify]: Simplify 0 into 0 14.553 * [backup-simplify]: Simplify 1 into 1 14.554 * [backup-simplify]: Simplify (/ 1 1) into 1 14.554 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 14.554 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.554 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.554 * [taylor]: Taking taylor expansion of 2.0 in k 14.554 * [backup-simplify]: Simplify 2.0 into 2.0 14.554 * [taylor]: Taking taylor expansion of PI in k 14.554 * [backup-simplify]: Simplify PI into PI 14.555 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.556 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.556 * [taylor]: Taking taylor expansion of (log n) in k 14.556 * [taylor]: Taking taylor expansion of n in k 14.556 * [backup-simplify]: Simplify n into n 14.556 * [backup-simplify]: Simplify (log n) into (log n) 14.556 * [backup-simplify]: Simplify (- 1) into -1 14.557 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.557 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.558 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 14.559 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 14.560 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 14.561 * [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))))) 14.563 * [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))))) 14.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.565 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.567 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.567 * [backup-simplify]: Simplify (- 0) into 0 14.568 * [backup-simplify]: Simplify (+ 0 0) into 0 14.568 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 14.570 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.571 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 14.573 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.573 * [taylor]: Taking taylor expansion of 0 in k 14.573 * [backup-simplify]: Simplify 0 into 0 14.573 * [backup-simplify]: Simplify 0 into 0 14.573 * [backup-simplify]: Simplify 0 into 0 14.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.576 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.580 * [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 14.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.580 * [backup-simplify]: Simplify (- 0) into 0 14.581 * [backup-simplify]: Simplify (+ 0 0) into 0 14.582 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 14.583 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.585 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 14.588 * [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 14.588 * [taylor]: Taking taylor expansion of 0 in k 14.588 * [backup-simplify]: Simplify 0 into 0 14.588 * [backup-simplify]: Simplify 0 into 0 14.588 * [backup-simplify]: Simplify 0 into 0 14.588 * [backup-simplify]: Simplify 0 into 0 14.589 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.590 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.597 * [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 14.597 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.598 * [backup-simplify]: Simplify (- 0) into 0 14.598 * [backup-simplify]: Simplify (+ 0 0) into 0 14.599 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 14.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.603 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 14.605 * [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 14.605 * [taylor]: Taking taylor expansion of 0 in k 14.605 * [backup-simplify]: Simplify 0 into 0 14.605 * [backup-simplify]: Simplify 0 into 0 14.606 * [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)))))) 14.606 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 14.606 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 14.606 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 14.606 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 14.606 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 14.606 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 14.606 * [taylor]: Taking taylor expansion of 0.5 in k 14.606 * [backup-simplify]: Simplify 0.5 into 0.5 14.606 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) 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 * [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 (log (* -2.0 (/ PI n))) in k 14.606 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 14.606 * [taylor]: Taking taylor expansion of -2.0 in k 14.606 * [backup-simplify]: Simplify -2.0 into -2.0 14.606 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.606 * [taylor]: Taking taylor expansion of PI in k 14.606 * [backup-simplify]: Simplify PI into PI 14.606 * [taylor]: Taking taylor expansion of n in k 14.606 * [backup-simplify]: Simplify n into n 14.607 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.607 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 14.607 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 14.607 * [backup-simplify]: Simplify (+ 1 0) into 1 14.607 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 14.607 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 14.607 * [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)))) 14.607 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.608 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.608 * [taylor]: Taking taylor expansion of 0.5 in n 14.608 * [backup-simplify]: Simplify 0.5 into 0.5 14.608 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.608 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.608 * [taylor]: Taking taylor expansion of k in n 14.608 * [backup-simplify]: Simplify k into k 14.608 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.608 * [taylor]: Taking taylor expansion of 1.0 in n 14.608 * [backup-simplify]: Simplify 1.0 into 1.0 14.608 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.608 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.608 * [taylor]: Taking taylor expansion of -2.0 in n 14.608 * [backup-simplify]: Simplify -2.0 into -2.0 14.608 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.608 * [taylor]: Taking taylor expansion of PI in n 14.608 * [backup-simplify]: Simplify PI into PI 14.608 * [taylor]: Taking taylor expansion of n in n 14.608 * [backup-simplify]: Simplify 0 into 0 14.608 * [backup-simplify]: Simplify 1 into 1 14.608 * [backup-simplify]: Simplify (/ PI 1) into PI 14.609 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.609 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.609 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.609 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.611 * [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))) 14.612 * [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)))) 14.612 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 14.612 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 14.612 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 14.612 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 14.612 * [taylor]: Taking taylor expansion of 0.5 in n 14.612 * [backup-simplify]: Simplify 0.5 into 0.5 14.612 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 14.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.612 * [taylor]: Taking taylor expansion of k in n 14.612 * [backup-simplify]: Simplify k into k 14.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.612 * [taylor]: Taking taylor expansion of 1.0 in n 14.612 * [backup-simplify]: Simplify 1.0 into 1.0 14.612 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 14.612 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 14.612 * [taylor]: Taking taylor expansion of -2.0 in n 14.612 * [backup-simplify]: Simplify -2.0 into -2.0 14.612 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.612 * [taylor]: Taking taylor expansion of PI in n 14.612 * [backup-simplify]: Simplify PI into PI 14.612 * [taylor]: Taking taylor expansion of n in n 14.612 * [backup-simplify]: Simplify 0 into 0 14.612 * [backup-simplify]: Simplify 1 into 1 14.613 * [backup-simplify]: Simplify (/ PI 1) into PI 14.613 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.614 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.614 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 14.614 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 14.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.615 * [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))) 14.616 * [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)))) 14.616 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 14.616 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 14.616 * [taylor]: Taking taylor expansion of 0.5 in k 14.616 * [backup-simplify]: Simplify 0.5 into 0.5 14.616 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 14.616 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 14.616 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 14.616 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 14.616 * [taylor]: Taking taylor expansion of -2.0 in k 14.616 * [backup-simplify]: Simplify -2.0 into -2.0 14.616 * [taylor]: Taking taylor expansion of PI in k 14.616 * [backup-simplify]: Simplify PI into PI 14.617 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 14.617 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 14.617 * [taylor]: Taking taylor expansion of (log n) in k 14.617 * [taylor]: Taking taylor expansion of n in k 14.618 * [backup-simplify]: Simplify n into n 14.618 * [backup-simplify]: Simplify (log n) into (log n) 14.618 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 14.618 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.618 * [taylor]: Taking taylor expansion of k in k 14.618 * [backup-simplify]: Simplify 0 into 0 14.618 * [backup-simplify]: Simplify 1 into 1 14.618 * [backup-simplify]: Simplify (/ 1 1) into 1 14.618 * [taylor]: Taking taylor expansion of 1.0 in k 14.618 * [backup-simplify]: Simplify 1.0 into 1.0 14.618 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.619 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 14.619 * [backup-simplify]: Simplify (+ 1 0) into 1 14.620 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 14.620 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 14.621 * [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)))) 14.622 * [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)))) 14.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.623 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 14.624 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 14.624 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.624 * [backup-simplify]: Simplify (+ 0 0) into 0 14.625 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 14.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.628 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 14.630 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 14.630 * [taylor]: Taking taylor expansion of 0 in k 14.630 * [backup-simplify]: Simplify 0 into 0 14.630 * [backup-simplify]: Simplify 0 into 0 14.630 * [backup-simplify]: Simplify 0 into 0 14.630 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.631 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.633 * [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 14.633 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.633 * [backup-simplify]: Simplify (+ 0 0) into 0 14.634 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 14.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.636 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 14.638 * [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 14.638 * [taylor]: Taking taylor expansion of 0 in k 14.639 * [backup-simplify]: Simplify 0 into 0 14.639 * [backup-simplify]: Simplify 0 into 0 14.639 * [backup-simplify]: Simplify 0 into 0 14.639 * [backup-simplify]: Simplify 0 into 0 14.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.642 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.648 * [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 14.648 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.649 * [backup-simplify]: Simplify (+ 0 0) into 0 14.650 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 14.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 14.653 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 14.656 * [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 14.656 * [taylor]: Taking taylor expansion of 0 in k 14.656 * [backup-simplify]: Simplify 0 into 0 14.657 * [backup-simplify]: Simplify 0 into 0 14.658 * [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)))))) 14.658 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 14.658 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.658 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 14.658 * [taylor]: Taking taylor expansion of (* n PI) in n 14.658 * [taylor]: Taking taylor expansion of n in n 14.658 * [backup-simplify]: Simplify 0 into 0 14.658 * [backup-simplify]: Simplify 1 into 1 14.658 * [taylor]: Taking taylor expansion of PI in n 14.658 * [backup-simplify]: Simplify PI into PI 14.658 * [taylor]: Taking taylor expansion of (* n PI) in n 14.658 * [taylor]: Taking taylor expansion of n in n 14.658 * [backup-simplify]: Simplify 0 into 0 14.658 * [backup-simplify]: Simplify 1 into 1 14.658 * [taylor]: Taking taylor expansion of PI in n 14.658 * [backup-simplify]: Simplify PI into PI 14.659 * [backup-simplify]: Simplify (* 0 PI) into 0 14.659 * [backup-simplify]: Simplify 0 into 0 14.661 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.661 * [backup-simplify]: Simplify PI into PI 14.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.662 * [backup-simplify]: Simplify 0 into 0 14.663 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.663 * [backup-simplify]: Simplify 0 into 0 14.665 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.665 * [backup-simplify]: Simplify 0 into 0 14.666 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.666 * [backup-simplify]: Simplify 0 into 0 14.668 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.668 * [backup-simplify]: Simplify 0 into 0 14.669 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 14.669 * [backup-simplify]: Simplify 0 into 0 14.669 * [backup-simplify]: Simplify (* PI n) into (* n PI) 14.669 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 14.669 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 14.669 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.669 * [taylor]: Taking taylor expansion of PI in n 14.669 * [backup-simplify]: Simplify PI into PI 14.669 * [taylor]: Taking taylor expansion of n in n 14.669 * [backup-simplify]: Simplify 0 into 0 14.669 * [backup-simplify]: Simplify 1 into 1 14.670 * [backup-simplify]: Simplify (/ PI 1) into PI 14.670 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.670 * [taylor]: Taking taylor expansion of PI in n 14.670 * [backup-simplify]: Simplify PI into PI 14.670 * [taylor]: Taking taylor expansion of n in n 14.670 * [backup-simplify]: Simplify 0 into 0 14.670 * [backup-simplify]: Simplify 1 into 1 14.670 * [backup-simplify]: Simplify (/ PI 1) into PI 14.670 * [backup-simplify]: Simplify PI into PI 14.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.671 * [backup-simplify]: Simplify 0 into 0 14.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.671 * [backup-simplify]: Simplify 0 into 0 14.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.672 * [backup-simplify]: Simplify 0 into 0 14.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.673 * [backup-simplify]: Simplify 0 into 0 14.673 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.673 * [backup-simplify]: Simplify 0 into 0 14.674 * [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 14.674 * [backup-simplify]: Simplify 0 into 0 14.674 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 14.674 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 14.674 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 14.674 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 14.674 * [taylor]: Taking taylor expansion of -1 in n 14.674 * [backup-simplify]: Simplify -1 into -1 14.674 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.674 * [taylor]: Taking taylor expansion of PI in n 14.674 * [backup-simplify]: Simplify PI into PI 14.674 * [taylor]: Taking taylor expansion of n in n 14.674 * [backup-simplify]: Simplify 0 into 0 14.674 * [backup-simplify]: Simplify 1 into 1 14.675 * [backup-simplify]: Simplify (/ PI 1) into PI 14.675 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 14.675 * [taylor]: Taking taylor expansion of -1 in n 14.675 * [backup-simplify]: Simplify -1 into -1 14.675 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.675 * [taylor]: Taking taylor expansion of PI in n 14.675 * [backup-simplify]: Simplify PI into PI 14.675 * [taylor]: Taking taylor expansion of n in n 14.675 * [backup-simplify]: Simplify 0 into 0 14.675 * [backup-simplify]: Simplify 1 into 1 14.675 * [backup-simplify]: Simplify (/ PI 1) into PI 14.675 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 14.676 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 14.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.677 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 14.677 * [backup-simplify]: Simplify 0 into 0 14.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.678 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 14.678 * [backup-simplify]: Simplify 0 into 0 14.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.679 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.679 * [backup-simplify]: Simplify 0 into 0 14.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.681 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.681 * [backup-simplify]: Simplify 0 into 0 14.681 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.682 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 14.682 * [backup-simplify]: Simplify 0 into 0 14.683 * [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 14.684 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 14.684 * [backup-simplify]: Simplify 0 into 0 14.684 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 14.684 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 14.684 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 14.684 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 14.684 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.684 * [taylor]: Taking taylor expansion of 1.0 in k 14.684 * [backup-simplify]: Simplify 1.0 into 1.0 14.684 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.685 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.685 * [taylor]: Taking taylor expansion of k in k 14.685 * [backup-simplify]: Simplify 0 into 0 14.685 * [backup-simplify]: Simplify 1 into 1 14.685 * [backup-simplify]: Simplify (/ 1 1) into 1 14.685 * [backup-simplify]: Simplify (sqrt 0) into 0 14.686 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.686 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 14.686 * [taylor]: Taking taylor expansion of 1.0 in k 14.686 * [backup-simplify]: Simplify 1.0 into 1.0 14.686 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.686 * [taylor]: Taking taylor expansion of k in k 14.686 * [backup-simplify]: Simplify 0 into 0 14.686 * [backup-simplify]: Simplify 1 into 1 14.686 * [backup-simplify]: Simplify (/ 1 1) into 1 14.687 * [backup-simplify]: Simplify (sqrt 0) into 0 14.687 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.688 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.688 * [backup-simplify]: Simplify 0 into 0 14.689 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.689 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.689 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.691 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.692 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.693 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.693 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.696 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.698 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.698 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.700 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 14.700 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 14.700 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 14.700 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.700 * [taylor]: Taking taylor expansion of 1.0 in k 14.700 * [backup-simplify]: Simplify 1.0 into 1.0 14.700 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.700 * [taylor]: Taking taylor expansion of k in k 14.700 * [backup-simplify]: Simplify 0 into 0 14.700 * [backup-simplify]: Simplify 1 into 1 14.701 * [backup-simplify]: Simplify (sqrt 0) into 0 14.702 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.702 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 14.702 * [taylor]: Taking taylor expansion of 1.0 in k 14.702 * [backup-simplify]: Simplify 1.0 into 1.0 14.702 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.702 * [taylor]: Taking taylor expansion of k in k 14.702 * [backup-simplify]: Simplify 0 into 0 14.702 * [backup-simplify]: Simplify 1 into 1 14.703 * [backup-simplify]: Simplify (sqrt 0) into 0 14.704 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.705 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.705 * [backup-simplify]: Simplify 0 into 0 14.706 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 14.707 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.710 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.712 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 14.712 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.717 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.719 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 14.719 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.721 * [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)))))))) 14.721 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 14.721 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 14.721 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.721 * [taylor]: Taking taylor expansion of 1.0 in k 14.721 * [backup-simplify]: Simplify 1.0 into 1.0 14.721 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.721 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.721 * [taylor]: Taking taylor expansion of -1 in k 14.721 * [backup-simplify]: Simplify -1 into -1 14.722 * [taylor]: Taking taylor expansion of k in k 14.722 * [backup-simplify]: Simplify 0 into 0 14.722 * [backup-simplify]: Simplify 1 into 1 14.722 * [backup-simplify]: Simplify (/ -1 1) into -1 14.722 * [backup-simplify]: Simplify (sqrt 0) into 0 14.724 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.724 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.724 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 14.724 * [taylor]: Taking taylor expansion of 1.0 in k 14.724 * [backup-simplify]: Simplify 1.0 into 1.0 14.724 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.724 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.724 * [taylor]: Taking taylor expansion of -1 in k 14.724 * [backup-simplify]: Simplify -1 into -1 14.724 * [taylor]: Taking taylor expansion of k in k 14.725 * [backup-simplify]: Simplify 0 into 0 14.725 * [backup-simplify]: Simplify 1 into 1 14.725 * [backup-simplify]: Simplify (/ -1 1) into -1 14.725 * [backup-simplify]: Simplify (sqrt 0) into 0 14.727 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.727 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 14.727 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.731 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.734 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 14.735 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.740 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.742 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 14.743 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 14.743 * [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))))) 14.743 * * * * [progress]: [ 4 / 4 ] generating series at (2) 14.744 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) (/ (- 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)))) 14.744 * [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 14.744 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 14.744 * [taylor]: Taking taylor expansion of 1.0 in k 14.744 * [backup-simplify]: Simplify 1.0 into 1.0 14.744 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 14.744 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 14.744 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 14.744 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 14.744 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 14.744 * [taylor]: Taking taylor expansion of 0.5 in k 14.744 * [backup-simplify]: Simplify 0.5 into 0.5 14.744 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.744 * [taylor]: Taking taylor expansion of 1.0 in k 14.744 * [backup-simplify]: Simplify 1.0 into 1.0 14.744 * [taylor]: Taking taylor expansion of k in k 14.744 * [backup-simplify]: Simplify 0 into 0 14.744 * [backup-simplify]: Simplify 1 into 1 14.744 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 14.744 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 14.744 * [taylor]: Taking taylor expansion of 2.0 in k 14.744 * [backup-simplify]: Simplify 2.0 into 2.0 14.744 * [taylor]: Taking taylor expansion of (* n PI) in k 14.744 * [taylor]: Taking taylor expansion of n in k 14.744 * [backup-simplify]: Simplify n into n 14.744 * [taylor]: Taking taylor expansion of PI in k 14.744 * [backup-simplify]: Simplify PI into PI 14.744 * [backup-simplify]: Simplify (* n PI) into (* n PI) 14.744 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 14.744 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 14.745 * [backup-simplify]: Simplify (- 0) into 0 14.745 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.745 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 14.745 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 14.745 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 14.745 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.746 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.746 * [taylor]: Taking taylor expansion of k in k 14.746 * [backup-simplify]: Simplify 0 into 0 14.746 * [backup-simplify]: Simplify 1 into 1 14.746 * [backup-simplify]: Simplify (/ 1 1) into 1 14.746 * [backup-simplify]: Simplify (sqrt 0) into 0 14.750 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.750 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 14.750 * [taylor]: Taking taylor expansion of 1.0 in n 14.750 * [backup-simplify]: Simplify 1.0 into 1.0 14.750 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 14.750 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.750 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.750 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.750 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.750 * [taylor]: Taking taylor expansion of 0.5 in n 14.750 * [backup-simplify]: Simplify 0.5 into 0.5 14.750 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.750 * [taylor]: Taking taylor expansion of 1.0 in n 14.750 * [backup-simplify]: Simplify 1.0 into 1.0 14.750 * [taylor]: Taking taylor expansion of k in n 14.750 * [backup-simplify]: Simplify k into k 14.750 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.750 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.750 * [taylor]: Taking taylor expansion of 2.0 in n 14.750 * [backup-simplify]: Simplify 2.0 into 2.0 14.750 * [taylor]: Taking taylor expansion of (* n PI) in n 14.750 * [taylor]: Taking taylor expansion of n in n 14.750 * [backup-simplify]: Simplify 0 into 0 14.750 * [backup-simplify]: Simplify 1 into 1 14.750 * [taylor]: Taking taylor expansion of PI in n 14.750 * [backup-simplify]: Simplify PI into PI 14.751 * [backup-simplify]: Simplify (* 0 PI) into 0 14.751 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.752 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.753 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.754 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.754 * [backup-simplify]: Simplify (- k) into (- k) 14.754 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.754 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.755 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.755 * [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)))) 14.756 * [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))))) 14.756 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 14.756 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.756 * [taylor]: Taking taylor expansion of k in n 14.756 * [backup-simplify]: Simplify k into k 14.756 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.756 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 14.756 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.757 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 14.757 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 14.757 * [taylor]: Taking taylor expansion of 1.0 in n 14.757 * [backup-simplify]: Simplify 1.0 into 1.0 14.757 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 14.757 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 14.757 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 14.757 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 14.757 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 14.757 * [taylor]: Taking taylor expansion of 0.5 in n 14.757 * [backup-simplify]: Simplify 0.5 into 0.5 14.757 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 14.757 * [taylor]: Taking taylor expansion of 1.0 in n 14.757 * [backup-simplify]: Simplify 1.0 into 1.0 14.757 * [taylor]: Taking taylor expansion of k in n 14.757 * [backup-simplify]: Simplify k into k 14.757 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 14.757 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 14.757 * [taylor]: Taking taylor expansion of 2.0 in n 14.757 * [backup-simplify]: Simplify 2.0 into 2.0 14.757 * [taylor]: Taking taylor expansion of (* n PI) in n 14.757 * [taylor]: Taking taylor expansion of n in n 14.757 * [backup-simplify]: Simplify 0 into 0 14.757 * [backup-simplify]: Simplify 1 into 1 14.757 * [taylor]: Taking taylor expansion of PI in n 14.757 * [backup-simplify]: Simplify PI into PI 14.757 * [backup-simplify]: Simplify (* 0 PI) into 0 14.758 * [backup-simplify]: Simplify (* 2.0 0) into 0 14.758 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 14.759 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 14.760 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.760 * [backup-simplify]: Simplify (- k) into (- k) 14.760 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 14.760 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 14.761 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.762 * [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)))) 14.762 * [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))))) 14.763 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 14.763 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.763 * [taylor]: Taking taylor expansion of k in n 14.763 * [backup-simplify]: Simplify k into k 14.763 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.763 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 14.763 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.763 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 14.764 * [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))) 14.764 * [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)))) 14.764 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k 14.765 * [taylor]: Taking taylor expansion of 1.0 in k 14.765 * [backup-simplify]: Simplify 1.0 into 1.0 14.765 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k 14.765 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 14.765 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 14.765 * [taylor]: Taking taylor expansion of 0.5 in k 14.765 * [backup-simplify]: Simplify 0.5 into 0.5 14.765 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 14.765 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 14.765 * [taylor]: Taking taylor expansion of 1.0 in k 14.765 * [backup-simplify]: Simplify 1.0 into 1.0 14.765 * [taylor]: Taking taylor expansion of k in k 14.765 * [backup-simplify]: Simplify 0 into 0 14.765 * [backup-simplify]: Simplify 1 into 1 14.765 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 14.765 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.765 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.765 * [taylor]: Taking taylor expansion of 2.0 in k 14.765 * [backup-simplify]: Simplify 2.0 into 2.0 14.765 * [taylor]: Taking taylor expansion of PI in k 14.765 * [backup-simplify]: Simplify PI into PI 14.765 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.766 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.766 * [taylor]: Taking taylor expansion of (log n) in k 14.766 * [taylor]: Taking taylor expansion of n in k 14.766 * [backup-simplify]: Simplify n into n 14.766 * [backup-simplify]: Simplify (log n) into (log n) 14.766 * [backup-simplify]: Simplify (- 0) into 0 14.766 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 14.767 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 14.768 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 14.769 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 14.771 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 14.771 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 14.771 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.771 * [taylor]: Taking taylor expansion of k in k 14.771 * [backup-simplify]: Simplify 0 into 0 14.771 * [backup-simplify]: Simplify 1 into 1 14.771 * [backup-simplify]: Simplify (/ 1 1) into 1 14.772 * [backup-simplify]: Simplify (sqrt 0) into 0 14.773 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.774 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0 14.775 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.775 * [backup-simplify]: Simplify 0 into 0 14.776 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.777 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 14.779 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.779 * [backup-simplify]: Simplify (- 0) into 0 14.780 * [backup-simplify]: Simplify (+ 0 0) into 0 14.780 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 14.782 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.783 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 14.785 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 14.787 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 14.789 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0 14.789 * [taylor]: Taking taylor expansion of 0 in k 14.789 * [backup-simplify]: Simplify 0 into 0 14.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.792 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.793 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 14.793 * [backup-simplify]: Simplify (+ 0 0) into 0 14.794 * [backup-simplify]: Simplify (- 1) into -1 14.794 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.796 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 14.798 * [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)))) 14.802 * [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)))))) 14.806 * [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)))))) 14.808 * [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)))))) 14.809 * [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)))))) 14.810 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.810 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 14.812 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 14.813 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 14.817 * [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 14.817 * [backup-simplify]: Simplify (- 0) into 0 14.818 * [backup-simplify]: Simplify (+ 0 0) into 0 14.819 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 14.820 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.822 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.825 * [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 14.827 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 14.829 * [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 14.829 * [taylor]: Taking taylor expansion of 0 in k 14.829 * [backup-simplify]: Simplify 0 into 0 14.829 * [backup-simplify]: Simplify 0 into 0 14.830 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.833 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.834 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 14.837 * [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 14.839 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 14.840 * [backup-simplify]: Simplify (+ 0 0) into 0 14.840 * [backup-simplify]: Simplify (- 0) into 0 14.840 * [backup-simplify]: Simplify (+ 0 0) into 0 14.842 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 14.845 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.849 * [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)))))) 14.859 * [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))))))))))) 14.866 * [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))))))))))) 14.871 * [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))))))))))) 14.871 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 14.872 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 14.873 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 14.875 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 14.881 * [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 14.881 * [backup-simplify]: Simplify (- 0) into 0 14.882 * [backup-simplify]: Simplify (+ 0 0) into 0 14.883 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 14.885 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 14.890 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.893 * [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 14.895 * [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 14.898 * [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 14.898 * [taylor]: Taking taylor expansion of 0 in k 14.898 * [backup-simplify]: Simplify 0 into 0 14.898 * [backup-simplify]: Simplify 0 into 0 14.898 * [backup-simplify]: Simplify 0 into 0 14.899 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.901 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.902 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 14.906 * [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 14.907 * [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 14.908 * [backup-simplify]: Simplify (+ 0 0) into 0 14.908 * [backup-simplify]: Simplify (- 0) into 0 14.908 * [backup-simplify]: Simplify (+ 0 0) into 0 14.909 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 14.912 * [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 14.916 * [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)))))) 14.926 * [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))))))))))))))))) 14.938 * [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))))))))))))))))) 14.946 * [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))))))))))))))))) 14.965 * [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))))))))))))))))))))) 14.966 * [backup-simplify]: Simplify (* (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 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))) 14.966 * [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 14.966 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k 14.966 * [taylor]: Taking taylor expansion of 1.0 in k 14.966 * [backup-simplify]: Simplify 1.0 into 1.0 14.966 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k 14.966 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 14.966 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 14.966 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 14.966 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 14.966 * [taylor]: Taking taylor expansion of 0.5 in k 14.966 * [backup-simplify]: Simplify 0.5 into 0.5 14.966 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.966 * [taylor]: Taking taylor expansion of 1.0 in k 14.966 * [backup-simplify]: Simplify 1.0 into 1.0 14.966 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.966 * [taylor]: Taking taylor expansion of k in k 14.966 * [backup-simplify]: Simplify 0 into 0 14.966 * [backup-simplify]: Simplify 1 into 1 14.966 * [backup-simplify]: Simplify (/ 1 1) into 1 14.966 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 14.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 14.967 * [taylor]: Taking taylor expansion of 2.0 in k 14.967 * [backup-simplify]: Simplify 2.0 into 2.0 14.967 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.967 * [taylor]: Taking taylor expansion of PI in k 14.967 * [backup-simplify]: Simplify PI into PI 14.967 * [taylor]: Taking taylor expansion of n in k 14.967 * [backup-simplify]: Simplify n into n 14.967 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.967 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 14.967 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 14.967 * [backup-simplify]: Simplify (- 1) into -1 14.967 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.968 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 14.968 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 14.968 * [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)))))) 14.968 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.968 * [taylor]: Taking taylor expansion of k in k 14.968 * [backup-simplify]: Simplify 0 into 0 14.968 * [backup-simplify]: Simplify 1 into 1 14.968 * [backup-simplify]: Simplify (sqrt 0) into 0 14.969 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.969 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 14.969 * [taylor]: Taking taylor expansion of 1.0 in n 14.969 * [backup-simplify]: Simplify 1.0 into 1.0 14.969 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 14.969 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.969 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.969 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.969 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.969 * [taylor]: Taking taylor expansion of 0.5 in n 14.969 * [backup-simplify]: Simplify 0.5 into 0.5 14.969 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.969 * [taylor]: Taking taylor expansion of 1.0 in n 14.969 * [backup-simplify]: Simplify 1.0 into 1.0 14.969 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.969 * [taylor]: Taking taylor expansion of k in n 14.969 * [backup-simplify]: Simplify k into k 14.969 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.969 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.969 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.969 * [taylor]: Taking taylor expansion of 2.0 in n 14.969 * [backup-simplify]: Simplify 2.0 into 2.0 14.969 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.969 * [taylor]: Taking taylor expansion of PI in n 14.969 * [backup-simplify]: Simplify PI into PI 14.969 * [taylor]: Taking taylor expansion of n in n 14.969 * [backup-simplify]: Simplify 0 into 0 14.969 * [backup-simplify]: Simplify 1 into 1 14.970 * [backup-simplify]: Simplify (/ PI 1) into PI 14.970 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.971 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.971 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.971 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.971 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.972 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.972 * [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)))) 14.973 * [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))))) 14.973 * [taylor]: Taking taylor expansion of (sqrt k) in n 14.973 * [taylor]: Taking taylor expansion of k in n 14.973 * [backup-simplify]: Simplify k into k 14.973 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 14.973 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 14.973 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n 14.973 * [taylor]: Taking taylor expansion of 1.0 in n 14.973 * [backup-simplify]: Simplify 1.0 into 1.0 14.973 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n 14.973 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 14.973 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 14.973 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 14.974 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 14.974 * [taylor]: Taking taylor expansion of 0.5 in n 14.974 * [backup-simplify]: Simplify 0.5 into 0.5 14.974 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 14.974 * [taylor]: Taking taylor expansion of 1.0 in n 14.974 * [backup-simplify]: Simplify 1.0 into 1.0 14.974 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.974 * [taylor]: Taking taylor expansion of k in n 14.974 * [backup-simplify]: Simplify k into k 14.974 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.974 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 14.974 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 14.974 * [taylor]: Taking taylor expansion of 2.0 in n 14.974 * [backup-simplify]: Simplify 2.0 into 2.0 14.974 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.974 * [taylor]: Taking taylor expansion of PI in n 14.974 * [backup-simplify]: Simplify PI into PI 14.974 * [taylor]: Taking taylor expansion of n in n 14.974 * [backup-simplify]: Simplify 0 into 0 14.974 * [backup-simplify]: Simplify 1 into 1 14.974 * [backup-simplify]: Simplify (/ PI 1) into PI 14.974 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 14.975 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 14.975 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 14.975 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 14.975 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 14.976 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.977 * [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)))) 14.978 * [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))))) 14.978 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt k) into (sqrt k) 14.978 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 14.979 * [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)) 14.980 * [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))) 14.980 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k 14.980 * [taylor]: Taking taylor expansion of 1.0 in k 14.980 * [backup-simplify]: Simplify 1.0 into 1.0 14.980 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k 14.980 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k 14.980 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k 14.980 * [taylor]: Taking taylor expansion of 0.5 in k 14.980 * [backup-simplify]: Simplify 0.5 into 0.5 14.980 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k 14.980 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 14.980 * [taylor]: Taking taylor expansion of 1.0 in k 14.980 * [backup-simplify]: Simplify 1.0 into 1.0 14.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.980 * [taylor]: Taking taylor expansion of k in k 14.980 * [backup-simplify]: Simplify 0 into 0 14.980 * [backup-simplify]: Simplify 1 into 1 14.980 * [backup-simplify]: Simplify (/ 1 1) into 1 14.980 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 14.980 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 14.980 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 14.980 * [taylor]: Taking taylor expansion of 2.0 in k 14.980 * [backup-simplify]: Simplify 2.0 into 2.0 14.980 * [taylor]: Taking taylor expansion of PI in k 14.980 * [backup-simplify]: Simplify PI into PI 14.981 * [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 * [taylor]: Taking taylor expansion of (log n) in k 14.981 * [taylor]: Taking taylor expansion of n in k 14.981 * [backup-simplify]: Simplify n into n 14.981 * [backup-simplify]: Simplify (log n) into (log n) 14.982 * [backup-simplify]: Simplify (- 1) into -1 14.982 * [backup-simplify]: Simplify (+ 0 -1) into -1 14.982 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 14.983 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 14.986 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n))) 14.987 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 14.987 * [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))))) 14.987 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.987 * [taylor]: Taking taylor expansion of k in k 14.987 * [backup-simplify]: Simplify 0 into 0 14.987 * [backup-simplify]: Simplify 1 into 1 14.988 * [backup-simplify]: Simplify (sqrt 0) into 0 14.988 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.989 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0 14.989 * [backup-simplify]: Simplify (* 1.0 0) into 0 14.989 * [backup-simplify]: Simplify 0 into 0 14.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.991 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 14.992 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 14.993 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.993 * [backup-simplify]: Simplify (- 0) into 0 14.993 * [backup-simplify]: Simplify (+ 0 0) into 0 14.994 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 14.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 14.997 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 14.999 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 15.000 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0 15.002 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0 15.002 * [taylor]: Taking taylor expansion of 0 in k 15.002 * [backup-simplify]: Simplify 0 into 0 15.002 * [backup-simplify]: Simplify 0 into 0 15.004 * [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))))))) 15.006 * [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))))))) 15.007 * [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))))))) 15.008 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 15.009 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.010 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.014 * [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 15.014 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.015 * [backup-simplify]: Simplify (- 0) into 0 15.015 * [backup-simplify]: Simplify (+ 0 0) into 0 15.016 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 15.018 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.019 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 15.022 * [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 15.024 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 15.026 * [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 15.026 * [taylor]: Taking taylor expansion of 0 in k 15.026 * [backup-simplify]: Simplify 0 into 0 15.026 * [backup-simplify]: Simplify 0 into 0 15.026 * [backup-simplify]: Simplify 0 into 0 15.029 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.031 * [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))))))) 15.034 * [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))))))) 15.036 * [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))))))) 15.037 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 15.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.039 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 15.045 * [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 15.046 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.046 * [backup-simplify]: Simplify (- 0) into 0 15.047 * [backup-simplify]: Simplify (+ 0 0) into 0 15.048 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 15.049 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 15.052 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 15.055 * [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 15.057 * [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 15.060 * [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 15.060 * [taylor]: Taking taylor expansion of 0 in k 15.060 * [backup-simplify]: Simplify 0 into 0 15.060 * [backup-simplify]: Simplify 0 into 0 15.060 * [backup-simplify]: Simplify 0 into 0 15.060 * [backup-simplify]: Simplify 0 into 0 15.064 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.066 * [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))))))) 15.071 * [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))))))) 15.073 * [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))))))) 15.078 * [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)))))))) 15.079 * [backup-simplify]: Simplify (* (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 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)))) 15.079 * [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 15.079 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 15.079 * [taylor]: Taking taylor expansion of 1.0 in k 15.079 * [backup-simplify]: Simplify 1.0 into 1.0 15.079 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 15.079 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 15.079 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 15.079 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 15.079 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 15.079 * [taylor]: Taking taylor expansion of 0.5 in k 15.079 * [backup-simplify]: Simplify 0.5 into 0.5 15.079 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.079 * [taylor]: Taking taylor expansion of k in k 15.079 * [backup-simplify]: Simplify 0 into 0 15.079 * [backup-simplify]: Simplify 1 into 1 15.079 * [backup-simplify]: Simplify (/ 1 1) into 1 15.080 * [taylor]: Taking taylor expansion of 1.0 in k 15.080 * [backup-simplify]: Simplify 1.0 into 1.0 15.080 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 15.080 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 15.080 * [taylor]: Taking taylor expansion of -2.0 in k 15.080 * [backup-simplify]: Simplify -2.0 into -2.0 15.080 * [taylor]: Taking taylor expansion of (/ PI n) in k 15.080 * [taylor]: Taking taylor expansion of PI in k 15.080 * [backup-simplify]: Simplify PI into PI 15.080 * [taylor]: Taking taylor expansion of n in k 15.080 * [backup-simplify]: Simplify n into n 15.080 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 15.080 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 15.080 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 15.081 * [backup-simplify]: Simplify (+ 1 0) into 1 15.081 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 15.081 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 15.081 * [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)))) 15.081 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.081 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.081 * [taylor]: Taking taylor expansion of -1 in k 15.081 * [backup-simplify]: Simplify -1 into -1 15.082 * [taylor]: Taking taylor expansion of k in k 15.082 * [backup-simplify]: Simplify 0 into 0 15.082 * [backup-simplify]: Simplify 1 into 1 15.082 * [backup-simplify]: Simplify (/ -1 1) into -1 15.082 * [backup-simplify]: Simplify (sqrt 0) into 0 15.084 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.084 * [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))))) 15.084 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 15.084 * [taylor]: Taking taylor expansion of 1.0 in n 15.084 * [backup-simplify]: Simplify 1.0 into 1.0 15.084 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 15.084 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.084 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 15.084 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 15.084 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 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 (+ (/ 1 k) 1.0) in n 15.085 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.085 * [taylor]: Taking taylor expansion of k in n 15.085 * [backup-simplify]: Simplify k into k 15.085 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.085 * [taylor]: Taking taylor expansion of 1.0 in n 15.085 * [backup-simplify]: Simplify 1.0 into 1.0 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 15.086 * [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 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.087 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.090 * [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))) 15.091 * [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)))) 15.092 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 15.092 * [taylor]: Taking taylor expansion of (/ -1 k) in n 15.092 * [taylor]: Taking taylor expansion of -1 in n 15.092 * [backup-simplify]: Simplify -1 into -1 15.092 * [taylor]: Taking taylor expansion of k in n 15.092 * [backup-simplify]: Simplify k into k 15.092 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 15.092 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 15.092 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 15.092 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 15.093 * [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))) 15.094 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 15.094 * [taylor]: Taking taylor expansion of 1.0 in n 15.094 * [backup-simplify]: Simplify 1.0 into 1.0 15.094 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 15.094 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 15.094 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 15.094 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 15.094 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 15.094 * [taylor]: Taking taylor expansion of 0.5 in n 15.094 * [backup-simplify]: Simplify 0.5 into 0.5 15.094 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 15.094 * [taylor]: Taking taylor expansion of (/ 1 k) in n 15.094 * [taylor]: Taking taylor expansion of k in n 15.094 * [backup-simplify]: Simplify k into k 15.094 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 15.094 * [taylor]: Taking taylor expansion of 1.0 in n 15.094 * [backup-simplify]: Simplify 1.0 into 1.0 15.094 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 15.094 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 15.094 * [taylor]: Taking taylor expansion of -2.0 in n 15.094 * [backup-simplify]: Simplify -2.0 into -2.0 15.094 * [taylor]: Taking taylor expansion of (/ PI n) in n 15.094 * [taylor]: Taking taylor expansion of PI in n 15.094 * [backup-simplify]: Simplify PI into PI 15.094 * [taylor]: Taking taylor expansion of n in n 15.094 * [backup-simplify]: Simplify 0 into 0 15.094 * [backup-simplify]: Simplify 1 into 1 15.095 * [backup-simplify]: Simplify (/ PI 1) into PI 15.095 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.097 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.097 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 15.097 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 15.098 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.100 * [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))) 15.101 * [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)))) 15.101 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 15.101 * [taylor]: Taking taylor expansion of (/ -1 k) in n 15.101 * [taylor]: Taking taylor expansion of -1 in n 15.101 * [backup-simplify]: Simplify -1 into -1 15.101 * [taylor]: Taking taylor expansion of k in n 15.101 * [backup-simplify]: Simplify k into k 15.101 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 15.101 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 15.101 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 15.101 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 15.103 * [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))) 15.104 * [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)))) 15.104 * [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 15.104 * [taylor]: Taking taylor expansion of 1.0 in k 15.104 * [backup-simplify]: Simplify 1.0 into 1.0 15.104 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k 15.104 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 15.105 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 15.105 * [taylor]: Taking taylor expansion of 0.5 in k 15.105 * [backup-simplify]: Simplify 0.5 into 0.5 15.105 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 15.105 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 15.105 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 15.105 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 15.105 * [taylor]: Taking taylor expansion of -2.0 in k 15.105 * [backup-simplify]: Simplify -2.0 into -2.0 15.105 * [taylor]: Taking taylor expansion of PI in k 15.105 * [backup-simplify]: Simplify PI into PI 15.105 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 15.106 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 15.106 * [taylor]: Taking taylor expansion of (log n) in k 15.106 * [taylor]: Taking taylor expansion of n in k 15.106 * [backup-simplify]: Simplify n into n 15.107 * [backup-simplify]: Simplify (log n) into (log n) 15.107 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 15.107 * [taylor]: Taking taylor expansion of (/ 1 k) in k 15.107 * [taylor]: Taking taylor expansion of k in k 15.107 * [backup-simplify]: Simplify 0 into 0 15.107 * [backup-simplify]: Simplify 1 into 1 15.107 * [backup-simplify]: Simplify (/ 1 1) into 1 15.107 * [taylor]: Taking taylor expansion of 1.0 in k 15.107 * [backup-simplify]: Simplify 1.0 into 1.0 15.107 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 15.108 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 15.109 * [backup-simplify]: Simplify (+ 1 0) into 1 15.110 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n)) 15.111 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 15.112 * [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)))) 15.112 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 15.113 * [taylor]: Taking taylor expansion of (/ -1 k) in k 15.113 * [taylor]: Taking taylor expansion of -1 in k 15.113 * [backup-simplify]: Simplify -1 into -1 15.113 * [taylor]: Taking taylor expansion of k in k 15.113 * [backup-simplify]: Simplify 0 into 0 15.113 * [backup-simplify]: Simplify 1 into 1 15.113 * [backup-simplify]: Simplify (/ -1 1) into -1 15.113 * [backup-simplify]: Simplify (sqrt 0) into 0 15.115 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 15.116 * [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))))) 15.117 * [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))))) 15.117 * [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))))) 15.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 15.118 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 15.119 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 15.120 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 15.120 * [backup-simplify]: Simplify (+ 0 0) into 0 15.120 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 15.121 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.122 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 15.123 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 15.124 * [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 15.125 * [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 15.125 * [taylor]: Taking taylor expansion of 0 in k 15.125 * [backup-simplify]: Simplify 0 into 0 15.125 * [backup-simplify]: Simplify 0 into 0 15.128 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 15.130 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 15.131 * [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)))))) 15.133 * [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)))))) 15.133 * [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 (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.135 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 15.137 * [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 15.137 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.137 * [backup-simplify]: Simplify (+ 0 0) into 0 15.138 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 15.139 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 15.139 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 15.141 * [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 15.141 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 15.141 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 15.142 * [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 15.144 * [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 15.144 * [taylor]: Taking taylor expansion of 0 in k 15.144 * [backup-simplify]: Simplify 0 into 0 15.144 * [backup-simplify]: Simplify 0 into 0 15.144 * [backup-simplify]: Simplify 0 into 0 15.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 15.147 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 15.150 * [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)))))) 15.154 * [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)))))) 15.156 * [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)))))) 15.160 * [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)))))))) 15.161 * * * [progress]: simplifying candidates 15.166 * [simplify]: Simplifying: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (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 (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (log1p (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (+ (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (- (log 1.0) (log (sqrt k)))) (+ (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (log (/ 1.0 (sqrt k)))) (+ (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (- (log 1.0) (log (sqrt k)))) (+ (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log (/ 1.0 (sqrt k)))) (log (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (exp (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (* (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))) (* (cbrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))) (cbrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (sqrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) 1.0) (* (pow (* 2.0 (* n PI)) (/ k 2.0)) (sqrt k)) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt 1))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) 1)) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt 1))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1 (sqrt (sqrt k)))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1 1)) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (* (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) (/ 1.0 (sqrt k))) (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0) (* (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (- (+ (* 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)))))) (* n PI) (* n PI) (* 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)))))))) 15.172 * * [simplify]: iteration 0: 342 enodes 15.289 * * [simplify]: iteration 1: 925 enodes 15.738 * * [simplify]: iteration 2: 2960 enodes 16.919 * * [simplify]: iteration complete: 5000 enodes 16.919 * * [simplify]: Extracting #0: cost 129 inf + 0 16.922 * * [simplify]: Extracting #1: cost 618 inf + 3 16.930 * * [simplify]: Extracting #2: cost 1018 inf + 9865 16.951 * * [simplify]: Extracting #3: cost 1020 inf + 59741 17.029 * * [simplify]: Extracting #4: cost 566 inf + 248207 17.147 * * [simplify]: Extracting #5: cost 255 inf + 378507 17.271 * * [simplify]: Extracting #6: cost 118 inf + 444603 17.437 * * [simplify]: Extracting #7: cost 16 inf + 495911 17.606 * * [simplify]: Extracting #8: cost 0 inf + 509685 17.809 * * [simplify]: Extracting #9: cost 0 inf + 508490 17.993 * * [simplify]: Extracting #10: cost 0 inf + 508275 18.160 * * [simplify]: Extracting #11: cost 0 inf + 508250 18.385 * [simplify]: Simplified to: (expm1 (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (* (- 1.0 k) (log (* (* PI n) 2.0))) 2.0) (/ (* (- 1.0 k) (log (* (* PI n) 2.0))) 2.0) (/ (* (- 1.0 k) (log (* (* PI n) 2.0))) 2.0) (/ (* (- 1.0 k) (log (* (* PI n) 2.0))) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* PI n) 2.0) (/ 1.0 2.0)) (pow (* (* PI n) 2.0) (/ k 2.0)) (pow (* (* PI n) 2.0) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* PI n) 2.0) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* PI n) 2.0) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k)))) (pow (* (* PI n) 2.0) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* PI n) 2.0) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* PI n) 2.0) (sqrt (- 1.0 k))) (pow (* (* PI n) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ 1 (sqrt 2.0))) (* (* PI n) 2.0) (pow (* (* PI n) 2.0) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0))) (pow (* (* PI n) 2.0) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* (* PI n) 2.0) (+ (sqrt k) (sqrt 1.0))) (pow (* (* PI n) 2.0) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* PI n) 2.0) (/ 1 (sqrt 2.0))) (* (* PI n) 2.0) (* (* PI n) 2.0) (pow (* (* PI n) 2.0) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* PI n) (/ (- 1.0 k) 2.0)) (/ (* (- 1.0 k) (log (* (* PI n) 2.0))) 2.0) (exp (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* PI n)) (log1p (* PI n)) (* PI n) (log (* PI n)) (log (* PI n)) (exp (* PI n)) (* PI (* n (* (* n PI) (* n PI)))) (* (cbrt (* PI n)) (cbrt (* PI n))) (cbrt (* PI n)) (* (* PI n) (* (* PI n) (* PI n))) (sqrt (* PI n)) (sqrt (* PI n)) (* (sqrt PI) (sqrt n)) (* (sqrt PI) (sqrt n)) (* (* n (cbrt PI)) (cbrt PI)) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* PI n) (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 1.0) (sqrt k)) (/ 1.0 k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (/ (* 1.0 1.0) (sqrt k)) (/ 1.0 k)) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (log1p (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (fma (/ (- 1.0 k) 2.0) (log (* (* PI n) 2.0)) (log (/ 1.0 (sqrt k)))) (exp (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (* (* (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (/ 1.0 (sqrt k))) (* (* (* (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (/ 1.0 (sqrt k))) (* (cbrt (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (cbrt (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (* (* (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (/ 1.0 (sqrt k))) (sqrt (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (* (pow (* (* PI n) 2.0) (/ 1.0 2.0)) 1.0) (* (sqrt k) (pow (* (* PI n) 2.0) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (/ (* (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt 1.0)) (sqrt (sqrt k))) (/ (* (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt 1.0)) (sqrt (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k)))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))) (/ (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (/ (fabs (cbrt k)) (cbrt 1.0))) (* (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k)))) (/ (* (sqrt 1.0) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (fabs (cbrt k))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k)))) (* (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (fabs (cbrt k))) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (* 1.0 (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ (pow (* PI n) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (* (cbrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (* (sqrt (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k))) (/ (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (* 1.0 (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt k)) (* 1.0 (pow (* (* PI n) 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* (* PI n) 2.0) (/ 1.0 2.0)) (/ 1.0 (sqrt k))) (- (fma (* (log n) (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0)))))) (* (log (* 2.0 PI)) 0.25) (fma 0.125 (* (* (* (log n) k) (* (log n) k)) (exp (* 0.5 (log (* (* PI n) 2.0))))) (fma (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) 0.125) (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0))))) (exp (* 0.5 (log (* (* PI n) 2.0))))))) (* 0.5 (* k (fma (log n) (exp (* 0.5 (log (* (* PI n) 2.0)))) (* (exp (* 0.5 (log (* (* PI n) 2.0)))) (log (* 2.0 PI))))))) (exp (* (* (- 1.0 k) (log (* (* PI n) 2.0))) 0.5)) (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n))))) (* PI n) (* PI n) (* PI n) (- (* (* k k) (- +nan.0)) (fma +nan.0 k (- +nan.0))) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k))))) (- (- (fma (/ +nan.0 k) (/ 1 k) +nan.0) (/ +nan.0 k))) (- (fma (* (log n) (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0)))))) (* (log (* 2.0 PI)) +nan.0) (fma (exp (* 0.5 (log (* (* PI n) 2.0)))) (- +nan.0) (fma (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0))))) (* +nan.0 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (fma (- +nan.0) (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0))))) (fma (* +nan.0 (* (* (log n) k) (* (log n) k))) (exp (* 0.5 (log (* (* PI n) 2.0)))) (fma (- +nan.0) (* (log n) (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0)))))) (fma (* (log (* 2.0 PI)) +nan.0) (* (* k k) (exp (* 0.5 (log (* (* PI n) 2.0))))) (fma (* k (exp (* 0.5 (log (* (* PI n) 2.0))))) (fma +nan.0 (log (* 2.0 PI)) (- +nan.0)) (* (- +nan.0) (* (exp (* 0.5 (log (* (* PI n) 2.0)))) (* (log n) k)))))))))))) (fma (- +nan.0) (/ (exp (* (* (- 1.0 k) (log (* (* PI n) 2.0))) 0.5)) (* k k)) (fma +nan.0 (/ (exp (* (* (- 1.0 k) (log (* (* PI n) 2.0))) 0.5)) k) (* (/ (- +nan.0) (* k k)) (/ (exp (* (* (- 1.0 k) (log (* (* PI n) 2.0))) 0.5)) k)))) (fma (- (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n)))))) +nan.0 (- (* +nan.0 (/ (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n))))) k)) (* (/ (exp (* (* 0.5 (- 1.0 k)) (- (log (* PI -2.0)) (log (/ -1 n))))) k) (/ +nan.0 k)))) 18.397 * * * [progress]: adding candidates to table 19.417 * * [progress]: iteration 4 / 4 19.417 * * * [progress]: picking best candidate 19.482 * * * * [pick]: Picked # 19.482 * * * [progress]: localizing error 19.522 * * * [progress]: generating rewritten candidates 19.522 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2) 19.531 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 19.540 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 19.547 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1) 19.593 * * * [progress]: generating series expansions 19.593 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2) 19.593 * [backup-simplify]: Simplify (pow (* n PI) (/ (- 1.0 k) 2.0)) into (pow (* n PI) (* 0.5 (- 1.0 k))) 19.593 * [approximate]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in (n k) around 0 19.593 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 19.593 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 19.593 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 19.593 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 19.593 * [taylor]: Taking taylor expansion of 0.5 in k 19.593 * [backup-simplify]: Simplify 0.5 into 0.5 19.593 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 19.593 * [taylor]: Taking taylor expansion of 1.0 in k 19.593 * [backup-simplify]: Simplify 1.0 into 1.0 19.593 * [taylor]: Taking taylor expansion of k in k 19.594 * [backup-simplify]: Simplify 0 into 0 19.594 * [backup-simplify]: Simplify 1 into 1 19.594 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 19.594 * [taylor]: Taking taylor expansion of (* n PI) in k 19.594 * [taylor]: Taking taylor expansion of n in k 19.594 * [backup-simplify]: Simplify n into n 19.594 * [taylor]: Taking taylor expansion of PI in k 19.594 * [backup-simplify]: Simplify PI into PI 19.594 * [backup-simplify]: Simplify (* n PI) into (* n PI) 19.594 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 19.594 * [backup-simplify]: Simplify (- 0) into 0 19.595 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 19.595 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 19.596 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 19.596 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 19.596 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 19.596 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 19.596 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 19.596 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 19.596 * [taylor]: Taking taylor expansion of 0.5 in n 19.596 * [backup-simplify]: Simplify 0.5 into 0.5 19.596 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 19.596 * [taylor]: Taking taylor expansion of 1.0 in n 19.596 * [backup-simplify]: Simplify 1.0 into 1.0 19.596 * [taylor]: Taking taylor expansion of k in n 19.596 * [backup-simplify]: Simplify k into k 19.596 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 19.596 * [taylor]: Taking taylor expansion of (* n PI) in n 19.596 * [taylor]: Taking taylor expansion of n in n 19.596 * [backup-simplify]: Simplify 0 into 0 19.596 * [backup-simplify]: Simplify 1 into 1 19.596 * [taylor]: Taking taylor expansion of PI in n 19.596 * [backup-simplify]: Simplify PI into PI 19.597 * [backup-simplify]: Simplify (* 0 PI) into 0 19.598 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 19.599 * [backup-simplify]: Simplify (log PI) into (log PI) 19.599 * [backup-simplify]: Simplify (- k) into (- k) 19.599 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 19.599 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 19.600 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.600 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log PI) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) 19.601 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) 19.601 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 19.601 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 19.601 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 19.601 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 19.601 * [taylor]: Taking taylor expansion of 0.5 in n 19.601 * [backup-simplify]: Simplify 0.5 into 0.5 19.601 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 19.601 * [taylor]: Taking taylor expansion of 1.0 in n 19.601 * [backup-simplify]: Simplify 1.0 into 1.0 19.601 * [taylor]: Taking taylor expansion of k in n 19.601 * [backup-simplify]: Simplify k into k 19.601 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 19.601 * [taylor]: Taking taylor expansion of (* n PI) in n 19.601 * [taylor]: Taking taylor expansion of n in n 19.601 * [backup-simplify]: Simplify 0 into 0 19.601 * [backup-simplify]: Simplify 1 into 1 19.601 * [taylor]: Taking taylor expansion of PI in n 19.601 * [backup-simplify]: Simplify PI into PI 19.602 * [backup-simplify]: Simplify (* 0 PI) into 0 19.603 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 19.604 * [backup-simplify]: Simplify (log PI) into (log PI) 19.604 * [backup-simplify]: Simplify (- k) into (- k) 19.604 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 19.604 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 19.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.605 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log PI) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) 19.606 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) 19.606 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) in k 19.606 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) in k 19.606 * [taylor]: Taking taylor expansion of 0.5 in k 19.606 * [backup-simplify]: Simplify 0.5 into 0.5 19.606 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log PI) (log n))) in k 19.606 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 19.606 * [taylor]: Taking taylor expansion of 1.0 in k 19.606 * [backup-simplify]: Simplify 1.0 into 1.0 19.606 * [taylor]: Taking taylor expansion of k in k 19.606 * [backup-simplify]: Simplify 0 into 0 19.606 * [backup-simplify]: Simplify 1 into 1 19.606 * [taylor]: Taking taylor expansion of (+ (log PI) (log n)) in k 19.606 * [taylor]: Taking taylor expansion of (log PI) in k 19.606 * [taylor]: Taking taylor expansion of PI in k 19.606 * [backup-simplify]: Simplify PI into PI 19.607 * [backup-simplify]: Simplify (log PI) into (log PI) 19.607 * [taylor]: Taking taylor expansion of (log n) in k 19.607 * [taylor]: Taking taylor expansion of n in k 19.607 * [backup-simplify]: Simplify n into n 19.607 * [backup-simplify]: Simplify (log n) into (log n) 19.607 * [backup-simplify]: Simplify (- 0) into 0 19.608 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 19.608 * [backup-simplify]: Simplify (+ (log PI) (log n)) into (+ (log PI) (log n)) 19.609 * [backup-simplify]: Simplify (* 1.0 (+ (log PI) (log n))) into (* 1.0 (+ (log PI) (log n))) 19.609 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log PI) (log n)))) into (* 0.5 (+ (log PI) (log n))) 19.610 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log PI) (log n)))) into (exp (* 0.5 (+ (log PI) (log n)))) 19.610 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log PI) (log n)))) into (exp (* 0.5 (+ (log PI) (log n)))) 19.612 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 19.613 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.614 * [backup-simplify]: Simplify (- 0) into 0 19.614 * [backup-simplify]: Simplify (+ 0 0) into 0 19.615 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 19.616 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.616 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log PI) (log n)))) into 0 19.618 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 19.618 * [taylor]: Taking taylor expansion of 0 in k 19.618 * [backup-simplify]: Simplify 0 into 0 19.618 * [backup-simplify]: Simplify 0 into 0 19.619 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.620 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 19.621 * [backup-simplify]: Simplify (+ 0 0) into 0 19.621 * [backup-simplify]: Simplify (- 1) into -1 19.621 * [backup-simplify]: Simplify (+ 0 -1) into -1 19.622 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log PI) (log n)))) into (- (+ (log PI) (log n))) 19.623 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log PI) (log n))))) into (- (+ (* 0.5 (log PI)) (* 0.5 (log n)))) 19.625 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log PI)) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) 19.626 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) into (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) 19.626 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 19.628 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.628 * [backup-simplify]: Simplify (- 0) into 0 19.629 * [backup-simplify]: Simplify (+ 0 0) into 0 19.629 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 19.630 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.630 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log PI) (log n))))) into 0 19.631 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.632 * [taylor]: Taking taylor expansion of 0 in k 19.632 * [backup-simplify]: Simplify 0 into 0 19.632 * [backup-simplify]: Simplify 0 into 0 19.632 * [backup-simplify]: Simplify 0 into 0 19.633 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.634 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 19.635 * [backup-simplify]: Simplify (+ 0 0) into 0 19.635 * [backup-simplify]: Simplify (- 0) into 0 19.635 * [backup-simplify]: Simplify (+ 0 0) into 0 19.636 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log PI) (log n))))) into 0 19.637 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log PI) (log n)))))) into 0 19.638 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log PI) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log PI)) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) 19.640 * [backup-simplify]: Simplify (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) 19.644 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log PI) (log n))))) (exp (* 0.5 (+ (log PI) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log PI)) (* 0.5 (log n))) (exp (* 0.5 (+ (log PI) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log PI) (log n)))))) into (- (+ (exp (* 0.5 (+ (log PI) (log n)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (* 0.25 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2)))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log n) k))) (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) k))))) 19.644 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) 19.644 * [approximate]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 19.644 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 19.644 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 19.644 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 19.644 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 19.644 * [taylor]: Taking taylor expansion of 0.5 in k 19.644 * [backup-simplify]: Simplify 0.5 into 0.5 19.644 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 19.644 * [taylor]: Taking taylor expansion of 1.0 in k 19.644 * [backup-simplify]: Simplify 1.0 into 1.0 19.644 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.644 * [taylor]: Taking taylor expansion of k in k 19.644 * [backup-simplify]: Simplify 0 into 0 19.644 * [backup-simplify]: Simplify 1 into 1 19.645 * [backup-simplify]: Simplify (/ 1 1) into 1 19.645 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 19.645 * [taylor]: Taking taylor expansion of (/ PI n) in k 19.645 * [taylor]: Taking taylor expansion of PI in k 19.645 * [backup-simplify]: Simplify PI into PI 19.645 * [taylor]: Taking taylor expansion of n in k 19.645 * [backup-simplify]: Simplify n into n 19.645 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 19.645 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 19.645 * [backup-simplify]: Simplify (- 1) into -1 19.645 * [backup-simplify]: Simplify (+ 0 -1) into -1 19.646 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 19.646 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 19.646 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 19.646 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 19.646 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 19.646 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 19.646 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 19.646 * [taylor]: Taking taylor expansion of 0.5 in n 19.646 * [backup-simplify]: Simplify 0.5 into 0.5 19.646 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 19.646 * [taylor]: Taking taylor expansion of 1.0 in n 19.646 * [backup-simplify]: Simplify 1.0 into 1.0 19.646 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.646 * [taylor]: Taking taylor expansion of k in n 19.646 * [backup-simplify]: Simplify k into k 19.646 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.646 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 19.646 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.646 * [taylor]: Taking taylor expansion of PI in n 19.646 * [backup-simplify]: Simplify PI into PI 19.646 * [taylor]: Taking taylor expansion of n in n 19.646 * [backup-simplify]: Simplify 0 into 0 19.646 * [backup-simplify]: Simplify 1 into 1 19.646 * [backup-simplify]: Simplify (/ PI 1) into PI 19.647 * [backup-simplify]: Simplify (log PI) into (log PI) 19.647 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 19.647 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 19.647 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 19.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 19.648 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 19.648 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 19.648 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 19.648 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 19.648 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 19.648 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 19.648 * [taylor]: Taking taylor expansion of 0.5 in n 19.648 * [backup-simplify]: Simplify 0.5 into 0.5 19.648 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 19.648 * [taylor]: Taking taylor expansion of 1.0 in n 19.648 * [backup-simplify]: Simplify 1.0 into 1.0 19.648 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.648 * [taylor]: Taking taylor expansion of k in n 19.648 * [backup-simplify]: Simplify k into k 19.648 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.648 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 19.648 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.648 * [taylor]: Taking taylor expansion of PI in n 19.648 * [backup-simplify]: Simplify PI into PI 19.649 * [taylor]: Taking taylor expansion of n in n 19.649 * [backup-simplify]: Simplify 0 into 0 19.649 * [backup-simplify]: Simplify 1 into 1 19.649 * [backup-simplify]: Simplify (/ PI 1) into PI 19.649 * [backup-simplify]: Simplify (log PI) into (log PI) 19.649 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 19.649 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 19.649 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 19.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 19.650 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 19.654 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 19.654 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) in k 19.654 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) in k 19.654 * [taylor]: Taking taylor expansion of 0.5 in k 19.655 * [backup-simplify]: Simplify 0.5 into 0.5 19.655 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log PI) (log n))) in k 19.655 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 19.655 * [taylor]: Taking taylor expansion of 1.0 in k 19.655 * [backup-simplify]: Simplify 1.0 into 1.0 19.655 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.655 * [taylor]: Taking taylor expansion of k in k 19.655 * [backup-simplify]: Simplify 0 into 0 19.655 * [backup-simplify]: Simplify 1 into 1 19.655 * [backup-simplify]: Simplify (/ 1 1) into 1 19.655 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k 19.655 * [taylor]: Taking taylor expansion of (log PI) in k 19.655 * [taylor]: Taking taylor expansion of PI in k 19.655 * [backup-simplify]: Simplify PI into PI 19.656 * [backup-simplify]: Simplify (log PI) into (log PI) 19.656 * [taylor]: Taking taylor expansion of (log n) in k 19.656 * [taylor]: Taking taylor expansion of n in k 19.656 * [backup-simplify]: Simplify n into n 19.656 * [backup-simplify]: Simplify (log n) into (log n) 19.656 * [backup-simplify]: Simplify (- 1) into -1 19.656 * [backup-simplify]: Simplify (+ 0 -1) into -1 19.657 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 19.657 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 19.658 * [backup-simplify]: Simplify (* -1 (- (log PI) (log n))) into (* -1 (- (log PI) (log n))) 19.658 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log PI) (log n)))) into (* -0.5 (- (log PI) (log n))) 19.659 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 19.659 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 19.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 19.661 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.661 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.661 * [backup-simplify]: Simplify (- 0) into 0 19.662 * [backup-simplify]: Simplify (+ 0 0) into 0 19.662 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 19.662 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 19.663 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 19.664 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 19.664 * [taylor]: Taking taylor expansion of 0 in k 19.664 * [backup-simplify]: Simplify 0 into 0 19.664 * [backup-simplify]: Simplify 0 into 0 19.664 * [backup-simplify]: Simplify 0 into 0 19.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.666 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 19.666 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.666 * [backup-simplify]: Simplify (- 0) into 0 19.667 * [backup-simplify]: Simplify (+ 0 0) into 0 19.667 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 19.668 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 19.668 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 19.669 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.669 * [taylor]: Taking taylor expansion of 0 in k 19.669 * [backup-simplify]: Simplify 0 into 0 19.669 * [backup-simplify]: Simplify 0 into 0 19.669 * [backup-simplify]: Simplify 0 into 0 19.669 * [backup-simplify]: Simplify 0 into 0 19.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.673 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 19.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.673 * [backup-simplify]: Simplify (- 0) into 0 19.674 * [backup-simplify]: Simplify (+ 0 0) into 0 19.674 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 19.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 19.676 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 19.677 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 19.677 * [taylor]: Taking taylor expansion of 0 in k 19.677 * [backup-simplify]: Simplify 0 into 0 19.677 * [backup-simplify]: Simplify 0 into 0 19.677 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) 19.678 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 19.678 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 19.678 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 19.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 19.678 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 19.678 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 19.678 * [taylor]: Taking taylor expansion of 0.5 in k 19.678 * [backup-simplify]: Simplify 0.5 into 0.5 19.678 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 19.678 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.678 * [taylor]: Taking taylor expansion of k in k 19.678 * [backup-simplify]: Simplify 0 into 0 19.678 * [backup-simplify]: Simplify 1 into 1 19.678 * [backup-simplify]: Simplify (/ 1 1) into 1 19.678 * [taylor]: Taking taylor expansion of 1.0 in k 19.678 * [backup-simplify]: Simplify 1.0 into 1.0 19.678 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 19.678 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 19.678 * [taylor]: Taking taylor expansion of -1 in k 19.678 * [backup-simplify]: Simplify -1 into -1 19.678 * [taylor]: Taking taylor expansion of (/ PI n) in k 19.678 * [taylor]: Taking taylor expansion of PI in k 19.678 * [backup-simplify]: Simplify PI into PI 19.678 * [taylor]: Taking taylor expansion of n in k 19.678 * [backup-simplify]: Simplify n into n 19.678 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 19.678 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 19.678 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 19.679 * [backup-simplify]: Simplify (+ 1 0) into 1 19.679 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 19.679 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 19.679 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 19.679 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 19.679 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 19.679 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 19.679 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 19.679 * [taylor]: Taking taylor expansion of 0.5 in n 19.679 * [backup-simplify]: Simplify 0.5 into 0.5 19.679 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 19.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.679 * [taylor]: Taking taylor expansion of k in n 19.679 * [backup-simplify]: Simplify k into k 19.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.679 * [taylor]: Taking taylor expansion of 1.0 in n 19.680 * [backup-simplify]: Simplify 1.0 into 1.0 19.680 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 19.680 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 19.680 * [taylor]: Taking taylor expansion of -1 in n 19.680 * [backup-simplify]: Simplify -1 into -1 19.680 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.680 * [taylor]: Taking taylor expansion of PI in n 19.680 * [backup-simplify]: Simplify PI into PI 19.680 * [taylor]: Taking taylor expansion of n in n 19.680 * [backup-simplify]: Simplify 0 into 0 19.680 * [backup-simplify]: Simplify 1 into 1 19.680 * [backup-simplify]: Simplify (/ PI 1) into PI 19.680 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 19.681 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 19.681 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 19.681 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 19.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 19.683 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 19.683 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 19.683 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 19.683 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 19.684 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 19.684 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 19.684 * [taylor]: Taking taylor expansion of 0.5 in n 19.684 * [backup-simplify]: Simplify 0.5 into 0.5 19.684 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 19.684 * [taylor]: Taking taylor expansion of (/ 1 k) in n 19.684 * [taylor]: Taking taylor expansion of k in n 19.684 * [backup-simplify]: Simplify k into k 19.684 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 19.684 * [taylor]: Taking taylor expansion of 1.0 in n 19.684 * [backup-simplify]: Simplify 1.0 into 1.0 19.684 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 19.684 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 19.684 * [taylor]: Taking taylor expansion of -1 in n 19.684 * [backup-simplify]: Simplify -1 into -1 19.684 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.684 * [taylor]: Taking taylor expansion of PI in n 19.684 * [backup-simplify]: Simplify PI into PI 19.684 * [taylor]: Taking taylor expansion of n in n 19.684 * [backup-simplify]: Simplify 0 into 0 19.684 * [backup-simplify]: Simplify 1 into 1 19.684 * [backup-simplify]: Simplify (/ PI 1) into PI 19.684 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 19.685 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 19.685 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 19.685 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 19.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 19.687 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 19.688 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 19.688 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 19.688 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 19.688 * [taylor]: Taking taylor expansion of 0.5 in k 19.688 * [backup-simplify]: Simplify 0.5 into 0.5 19.688 * [taylor]: Taking taylor expansion of (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 19.688 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 19.688 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k 19.688 * [taylor]: Taking taylor expansion of (* -1 PI) in k 19.688 * [taylor]: Taking taylor expansion of -1 in k 19.688 * [backup-simplify]: Simplify -1 into -1 19.688 * [taylor]: Taking taylor expansion of PI in k 19.688 * [backup-simplify]: Simplify PI into PI 19.688 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 19.689 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 19.689 * [taylor]: Taking taylor expansion of (log n) in k 19.689 * [taylor]: Taking taylor expansion of n in k 19.689 * [backup-simplify]: Simplify n into n 19.689 * [backup-simplify]: Simplify (log n) into (log n) 19.689 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 19.689 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.689 * [taylor]: Taking taylor expansion of k in k 19.689 * [backup-simplify]: Simplify 0 into 0 19.689 * [backup-simplify]: Simplify 1 into 1 19.689 * [backup-simplify]: Simplify (/ 1 1) into 1 19.689 * [taylor]: Taking taylor expansion of 1.0 in k 19.689 * [backup-simplify]: Simplify 1.0 into 1.0 19.690 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 19.690 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 19.690 * [backup-simplify]: Simplify (+ 1 0) into 1 19.691 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) 1) into (- (log (* -1 PI)) (log n)) 19.692 * [backup-simplify]: Simplify (* 0.5 (- (log (* -1 PI)) (log n))) into (* 0.5 (- (log (* -1 PI)) (log n))) 19.693 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 19.694 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 19.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 19.695 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 19.696 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 19.696 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 19.696 * [backup-simplify]: Simplify (+ 0 0) into 0 19.696 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 19.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 19.698 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 19.699 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 19.699 * [taylor]: Taking taylor expansion of 0 in k 19.699 * [backup-simplify]: Simplify 0 into 0 19.699 * [backup-simplify]: Simplify 0 into 0 19.699 * [backup-simplify]: Simplify 0 into 0 19.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.701 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 19.702 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 19.703 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.703 * [backup-simplify]: Simplify (+ 0 0) into 0 19.703 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 19.705 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 19.707 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 19.710 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 19.710 * [taylor]: Taking taylor expansion of 0 in k 19.710 * [backup-simplify]: Simplify 0 into 0 19.710 * [backup-simplify]: Simplify 0 into 0 19.710 * [backup-simplify]: Simplify 0 into 0 19.710 * [backup-simplify]: Simplify 0 into 0 19.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.713 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 19.719 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 19.720 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 19.720 * [backup-simplify]: Simplify (+ 0 0) into 0 19.722 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 19.723 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 19.725 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 19.728 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 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 19.728 * [taylor]: Taking taylor expansion of 0 in k 19.728 * [backup-simplify]: Simplify 0 into 0 19.728 * [backup-simplify]: Simplify 0 into 0 19.730 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k)))) 19.730 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 19.730 * [backup-simplify]: Simplify (* n PI) into (* n PI) 19.730 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 19.730 * [taylor]: Taking taylor expansion of (* n PI) in n 19.730 * [taylor]: Taking taylor expansion of n in n 19.730 * [backup-simplify]: Simplify 0 into 0 19.730 * [backup-simplify]: Simplify 1 into 1 19.730 * [taylor]: Taking taylor expansion of PI in n 19.730 * [backup-simplify]: Simplify PI into PI 19.730 * [taylor]: Taking taylor expansion of (* n PI) in n 19.730 * [taylor]: Taking taylor expansion of n in n 19.730 * [backup-simplify]: Simplify 0 into 0 19.730 * [backup-simplify]: Simplify 1 into 1 19.730 * [taylor]: Taking taylor expansion of PI in n 19.730 * [backup-simplify]: Simplify PI into PI 19.731 * [backup-simplify]: Simplify (* 0 PI) into 0 19.731 * [backup-simplify]: Simplify 0 into 0 19.732 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 19.732 * [backup-simplify]: Simplify PI into PI 19.733 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 19.733 * [backup-simplify]: Simplify 0 into 0 19.733 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 19.733 * [backup-simplify]: Simplify 0 into 0 19.734 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 19.734 * [backup-simplify]: Simplify 0 into 0 19.735 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 19.735 * [backup-simplify]: Simplify 0 into 0 19.736 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 19.736 * [backup-simplify]: Simplify 0 into 0 19.737 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 19.738 * [backup-simplify]: Simplify 0 into 0 19.738 * [backup-simplify]: Simplify (* PI n) into (* n PI) 19.738 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 19.738 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 19.738 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.738 * [taylor]: Taking taylor expansion of PI in n 19.738 * [backup-simplify]: Simplify PI into PI 19.738 * [taylor]: Taking taylor expansion of n in n 19.738 * [backup-simplify]: Simplify 0 into 0 19.738 * [backup-simplify]: Simplify 1 into 1 19.738 * [backup-simplify]: Simplify (/ PI 1) into PI 19.738 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.738 * [taylor]: Taking taylor expansion of PI in n 19.738 * [backup-simplify]: Simplify PI into PI 19.738 * [taylor]: Taking taylor expansion of n in n 19.738 * [backup-simplify]: Simplify 0 into 0 19.738 * [backup-simplify]: Simplify 1 into 1 19.739 * [backup-simplify]: Simplify (/ PI 1) into PI 19.739 * [backup-simplify]: Simplify PI into PI 19.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 19.739 * [backup-simplify]: Simplify 0 into 0 19.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.740 * [backup-simplify]: Simplify 0 into 0 19.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.741 * [backup-simplify]: Simplify 0 into 0 19.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.741 * [backup-simplify]: Simplify 0 into 0 19.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.742 * [backup-simplify]: Simplify 0 into 0 19.743 * [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 19.743 * [backup-simplify]: Simplify 0 into 0 19.743 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 19.743 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 19.743 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 19.743 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 19.743 * [taylor]: Taking taylor expansion of -1 in n 19.743 * [backup-simplify]: Simplify -1 into -1 19.743 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.743 * [taylor]: Taking taylor expansion of PI in n 19.743 * [backup-simplify]: Simplify PI into PI 19.743 * [taylor]: Taking taylor expansion of n in n 19.743 * [backup-simplify]: Simplify 0 into 0 19.743 * [backup-simplify]: Simplify 1 into 1 19.743 * [backup-simplify]: Simplify (/ PI 1) into PI 19.743 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 19.743 * [taylor]: Taking taylor expansion of -1 in n 19.743 * [backup-simplify]: Simplify -1 into -1 19.743 * [taylor]: Taking taylor expansion of (/ PI n) in n 19.743 * [taylor]: Taking taylor expansion of PI in n 19.744 * [backup-simplify]: Simplify PI into PI 19.744 * [taylor]: Taking taylor expansion of n in n 19.744 * [backup-simplify]: Simplify 0 into 0 19.744 * [backup-simplify]: Simplify 1 into 1 19.744 * [backup-simplify]: Simplify (/ PI 1) into PI 19.744 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 19.744 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 19.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 19.745 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 19.745 * [backup-simplify]: Simplify 0 into 0 19.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.747 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 19.747 * [backup-simplify]: Simplify 0 into 0 19.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.748 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 19.748 * [backup-simplify]: Simplify 0 into 0 19.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.749 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 19.750 * [backup-simplify]: Simplify 0 into 0 19.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.751 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 19.751 * [backup-simplify]: Simplify 0 into 0 19.752 * [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 19.753 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 19.753 * [backup-simplify]: Simplify 0 into 0 19.753 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 19.753 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 19.753 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 19.753 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 19.753 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 19.753 * [taylor]: Taking taylor expansion of 1.0 in k 19.753 * [backup-simplify]: Simplify 1.0 into 1.0 19.753 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 19.753 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.753 * [taylor]: Taking taylor expansion of k in k 19.753 * [backup-simplify]: Simplify 0 into 0 19.753 * [backup-simplify]: Simplify 1 into 1 19.754 * [backup-simplify]: Simplify (/ 1 1) into 1 19.754 * [backup-simplify]: Simplify (sqrt 0) into 0 19.755 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.755 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 19.755 * [taylor]: Taking taylor expansion of 1.0 in k 19.755 * [backup-simplify]: Simplify 1.0 into 1.0 19.755 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 19.755 * [taylor]: Taking taylor expansion of (/ 1 k) in k 19.755 * [taylor]: Taking taylor expansion of k in k 19.755 * [backup-simplify]: Simplify 0 into 0 19.755 * [backup-simplify]: Simplify 1 into 1 19.755 * [backup-simplify]: Simplify (/ 1 1) into 1 19.755 * [backup-simplify]: Simplify (sqrt 0) into 0 19.757 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.757 * [backup-simplify]: Simplify (* 1.0 0) into 0 19.757 * [backup-simplify]: Simplify 0 into 0 19.759 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 19.759 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.760 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 19.769 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 19.771 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 19.772 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.773 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.777 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 19.779 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 19.779 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.781 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 19.781 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 19.781 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 19.781 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 19.781 * [taylor]: Taking taylor expansion of 1.0 in k 19.781 * [backup-simplify]: Simplify 1.0 into 1.0 19.781 * [taylor]: Taking taylor expansion of (sqrt k) in k 19.781 * [taylor]: Taking taylor expansion of k in k 19.781 * [backup-simplify]: Simplify 0 into 0 19.781 * [backup-simplify]: Simplify 1 into 1 19.781 * [backup-simplify]: Simplify (sqrt 0) into 0 19.783 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.783 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 19.783 * [taylor]: Taking taylor expansion of 1.0 in k 19.783 * [backup-simplify]: Simplify 1.0 into 1.0 19.783 * [taylor]: Taking taylor expansion of (sqrt k) in k 19.783 * [taylor]: Taking taylor expansion of k in k 19.783 * [backup-simplify]: Simplify 0 into 0 19.783 * [backup-simplify]: Simplify 1 into 1 19.783 * [backup-simplify]: Simplify (sqrt 0) into 0 19.785 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 19.785 * [backup-simplify]: Simplify (* 1.0 0) into 0 19.786 * [backup-simplify]: Simplify 0 into 0 19.787 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 19.788 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.791 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 19.793 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 19.793 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.797 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 19.800 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 19.800 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.801 * [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)))))))) 19.801 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 19.801 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 19.801 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 19.801 * [taylor]: Taking taylor expansion of 1.0 in k 19.801 * [backup-simplify]: Simplify 1.0 into 1.0 19.801 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 19.801 * [taylor]: Taking taylor expansion of (/ -1 k) in k 19.801 * [taylor]: Taking taylor expansion of -1 in k 19.801 * [backup-simplify]: Simplify -1 into -1 19.801 * [taylor]: Taking taylor expansion of k in k 19.801 * [backup-simplify]: Simplify 0 into 0 19.801 * [backup-simplify]: Simplify 1 into 1 19.802 * [backup-simplify]: Simplify (/ -1 1) into -1 19.802 * [backup-simplify]: Simplify (sqrt 0) into 0 19.803 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 19.803 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 19.803 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 19.803 * [taylor]: Taking taylor expansion of 1.0 in k 19.803 * [backup-simplify]: Simplify 1.0 into 1.0 19.803 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 19.803 * [taylor]: Taking taylor expansion of (/ -1 k) in k 19.803 * [taylor]: Taking taylor expansion of -1 in k 19.803 * [backup-simplify]: Simplify -1 into -1 19.803 * [taylor]: Taking taylor expansion of k in k 19.803 * [backup-simplify]: Simplify 0 into 0 19.803 * [backup-simplify]: Simplify 1 into 1 19.803 * [backup-simplify]: Simplify (/ -1 1) into -1 19.804 * [backup-simplify]: Simplify (sqrt 0) into 0 19.804 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 19.805 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 19.805 * [backup-simplify]: Simplify +nan.0 into +nan.0 19.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 19.807 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 19.809 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 19.809 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 19.812 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 19.814 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 19.815 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 19.815 * [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))))) 19.816 * * * * [progress]: [ 4 / 4 ] generating series at (2 1) 19.816 * [backup-simplify]: Simplify (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) into (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) 19.816 * [approximate]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in (k n) around 0 19.816 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in n 19.816 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in n 19.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in n 19.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in n 19.816 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 19.816 * [taylor]: Taking taylor expansion of 0.5 in n 19.816 * [backup-simplify]: Simplify 0.5 into 0.5 19.816 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 19.816 * [taylor]: Taking taylor expansion of 1.0 in n 19.816 * [backup-simplify]: Simplify 1.0 into 1.0 19.816 * [taylor]: Taking taylor expansion of k in n 19.816 * [backup-simplify]: Simplify k into k 19.816 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.816 * [taylor]: Taking taylor expansion of 2.0 in n 19.816 * [backup-simplify]: Simplify 2.0 into 2.0 19.816 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.816 * [backup-simplify]: Simplify (- k) into (- k) 19.816 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 19.816 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 19.817 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (log 2.0)) into (* 0.5 (* (- 1.0 k) (log 2.0))) 19.817 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) into (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) 19.817 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 19.817 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 19.817 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 19.817 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 19.817 * [taylor]: Taking taylor expansion of 0.5 in n 19.817 * [backup-simplify]: Simplify 0.5 into 0.5 19.817 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 19.817 * [taylor]: Taking taylor expansion of 1.0 in n 19.817 * [backup-simplify]: Simplify 1.0 into 1.0 19.817 * [taylor]: Taking taylor expansion of k in n 19.817 * [backup-simplify]: Simplify k into k 19.817 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 19.817 * [taylor]: Taking taylor expansion of (* n PI) in n 19.817 * [taylor]: Taking taylor expansion of n in n 19.817 * [backup-simplify]: Simplify 0 into 0 19.817 * [backup-simplify]: Simplify 1 into 1 19.817 * [taylor]: Taking taylor expansion of PI in n 19.817 * [backup-simplify]: Simplify PI into PI 19.818 * [backup-simplify]: Simplify (* 0 PI) into 0 19.819 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 19.819 * [backup-simplify]: Simplify (log PI) into (log PI) 19.819 * [backup-simplify]: Simplify (- k) into (- k) 19.819 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 19.819 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 19.820 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.820 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log PI) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log PI) (log n)))) 19.821 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log PI) (log n))))) 19.821 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in k 19.821 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in k 19.821 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in k 19.821 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in k 19.821 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 19.821 * [taylor]: Taking taylor expansion of 0.5 in k 19.821 * [backup-simplify]: Simplify 0.5 into 0.5 19.821 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 19.821 * [taylor]: Taking taylor expansion of 1.0 in k 19.821 * [backup-simplify]: Simplify 1.0 into 1.0 19.821 * [taylor]: Taking taylor expansion of k in k 19.821 * [backup-simplify]: Simplify 0 into 0 19.821 * [backup-simplify]: Simplify 1 into 1 19.821 * [taylor]: Taking taylor expansion of (log 2.0) in k 19.821 * [taylor]: Taking taylor expansion of 2.0 in k 19.821 * [backup-simplify]: Simplify 2.0 into 2.0 19.821 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.821 * [backup-simplify]: Simplify (- 0) into 0 19.822 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 19.822 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 19.823 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 19.823 * [backup-simplify]: Simplify (exp (* 0.5 (log 2.0))) into (pow 2.0 0.5) 19.823 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 19.823 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 19.823 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 19.824 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 19.824 * [taylor]: Taking taylor expansion of 0.5 in k 19.824 * [backup-simplify]: Simplify 0.5 into 0.5 19.824 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 19.824 * [taylor]: Taking taylor expansion of 1.0 in k 19.824 * [backup-simplify]: Simplify 1.0 into 1.0 19.824 * [taylor]: Taking taylor expansion of k in k 19.824 * [backup-simplify]: Simplify 0 into 0 19.824 * [backup-simplify]: Simplify 1 into 1 19.824 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 19.824 * [taylor]: Taking taylor expansion of (* n PI) in k 19.824 * [taylor]: Taking taylor expansion of n in k 19.824 * [backup-simplify]: Simplify n into n 19.824 * [taylor]: Taking taylor expansion of PI in k 19.824 * [backup-simplify]: Simplify PI into PI 19.824 * [backup-simplify]: Simplify (* n PI) into (* n PI) 19.824 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 19.824 * [backup-simplify]: Simplify (- 0) into 0 19.824 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 19.825 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 19.825 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 19.825 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 19.825 * [taylor]: Taking taylor expansion of (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow (* n PI) (* 0.5 (- 1.0 k)))) in k 19.825 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 k))) in k 19.825 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log 2.0))) in k 19.825 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log 2.0)) in k 19.825 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 19.825 * [taylor]: Taking taylor expansion of 0.5 in k 19.825 * [backup-simplify]: Simplify 0.5 into 0.5 19.825 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 19.825 * [taylor]: Taking taylor expansion of 1.0 in k 19.825 * [backup-simplify]: Simplify 1.0 into 1.0 19.825 * [taylor]: Taking taylor expansion of k in k 19.825 * [backup-simplify]: Simplify 0 into 0 19.825 * [backup-simplify]: Simplify 1 into 1 19.825 * [taylor]: Taking taylor expansion of (log 2.0) in k 19.825 * [taylor]: Taking taylor expansion of 2.0 in k 19.825 * [backup-simplify]: Simplify 2.0 into 2.0 19.825 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.826 * [backup-simplify]: Simplify (- 0) into 0 19.826 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 19.826 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 19.827 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 19.828 * [backup-simplify]: Simplify (exp (* 0.5 (log 2.0))) into (pow 2.0 0.5) 19.828 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 19.828 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 19.828 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 19.828 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 19.828 * [taylor]: Taking taylor expansion of 0.5 in k 19.828 * [backup-simplify]: Simplify 0.5 into 0.5 19.828 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 19.828 * [taylor]: Taking taylor expansion of 1.0 in k 19.828 * [backup-simplify]: Simplify 1.0 into 1.0 19.828 * [taylor]: Taking taylor expansion of k in k 19.828 * [backup-simplify]: Simplify 0 into 0 19.828 * [backup-simplify]: Simplify 1 into 1 19.828 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 19.828 * [taylor]: Taking taylor expansion of (* n PI) in k 19.828 * [taylor]: Taking taylor expansion of n in k 19.828 * [backup-simplify]: Simplify n into n 19.828 * [taylor]: Taking taylor expansion of PI in k 19.828 * [backup-simplify]: Simplify PI into PI 19.828 * [backup-simplify]: Simplify (* n PI) into (* n PI) 19.828 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 19.828 * [backup-simplify]: Simplify (- 0) into 0 19.828 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 19.829 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 19.829 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 19.829 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 19.829 * [backup-simplify]: Simplify (* (pow 2.0 0.5) (pow (* n PI) 0.5)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) 19.829 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 19.829 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 19.829 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 19.829 * [taylor]: Taking taylor expansion of 0.5 in n 19.829 * [backup-simplify]: Simplify 0.5 into 0.5 19.829 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 19.829 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 19.829 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 19.830 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 19.830 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 19.830 * [taylor]: Taking taylor expansion of 1.0 in n 19.830 * [backup-simplify]: Simplify 1.0 into 1.0 19.830 * [taylor]: Taking taylor expansion of (log PI) in n 19.830 * [taylor]: Taking taylor expansion of PI in n 19.830 * [backup-simplify]: Simplify PI into PI 19.830 * [backup-simplify]: Simplify (log PI) into (log PI) 19.831 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 19.832 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 19.832 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 19.832 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 19.832 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 19.832 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 19.832 * [taylor]: Taking taylor expansion of 1.0 in n 19.832 * [backup-simplify]: Simplify 1.0 into 1.0 19.832 * [taylor]: Taking taylor expansion of (log n) in n 19.832 * [taylor]: Taking taylor expansion of n in n 19.832 * [backup-simplify]: Simplify 0 into 0 19.832 * [backup-simplify]: Simplify 1 into 1 19.832 * [backup-simplify]: Simplify (log 1) into 0 19.832 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 19.832 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 19.832 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 19.832 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 19.832 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 19.832 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 19.832 * [taylor]: Taking taylor expansion of 1.0 in n 19.832 * [backup-simplify]: Simplify 1.0 into 1.0 19.832 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.832 * [taylor]: Taking taylor expansion of 2.0 in n 19.833 * [backup-simplify]: Simplify 2.0 into 2.0 19.833 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.833 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 19.834 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 19.835 * [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) 19.836 * [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) 19.837 * [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)) 19.839 * [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))) 19.840 * [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) 19.842 * [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) into (pow (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) 1.0) 0.5) 19.843 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 19.843 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* n PI) 1)))) 1) into 0 19.844 * [backup-simplify]: Simplify (- 1) into -1 19.844 * [backup-simplify]: Simplify (+ 0 -1) into -1 19.846 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 19.848 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* n PI)))) into (- (* 0.5 (log (* n PI)))) 19.848 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* n PI)))) (+ (* (/ (pow (- (* 0.5 (log (* n PI)))) 1) 1)))) into (* -0.5 (* (log (* n PI)) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5))) 19.850 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 19.850 * [backup-simplify]: Simplify (- 1) into -1 19.850 * [backup-simplify]: Simplify (+ 0 -1) into -1 19.852 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 19.855 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log 2.0))) into (- (* 0.5 (log 2.0))) 19.864 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 1) 1)))) into (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) 19.869 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) (* -0.5 (* (log (* n PI)) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5)))) (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) (pow (* n PI) 0.5))) into (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))))) 19.869 * [taylor]: Taking taylor expansion of (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))))) in n 19.869 * [taylor]: Taking taylor expansion of (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0)))) in n 19.869 * [taylor]: Taking taylor expansion of (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI)))) in n 19.869 * [taylor]: Taking taylor expansion of 0.5 in n 19.869 * [backup-simplify]: Simplify 0.5 into 0.5 19.869 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* n PI))) in n 19.869 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 19.869 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 19.869 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 19.870 * [taylor]: Taking taylor expansion of 0.5 in n 19.870 * [backup-simplify]: Simplify 0.5 into 0.5 19.870 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 19.870 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 19.870 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 19.870 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 19.870 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 19.870 * [taylor]: Taking taylor expansion of 1.0 in n 19.870 * [backup-simplify]: Simplify 1.0 into 1.0 19.870 * [taylor]: Taking taylor expansion of (log PI) in n 19.870 * [taylor]: Taking taylor expansion of PI in n 19.870 * [backup-simplify]: Simplify PI into PI 19.870 * [backup-simplify]: Simplify (log PI) into (log PI) 19.871 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 19.873 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 19.873 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 19.873 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 19.873 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 19.873 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 19.873 * [taylor]: Taking taylor expansion of 1.0 in n 19.873 * [backup-simplify]: Simplify 1.0 into 1.0 19.873 * [taylor]: Taking taylor expansion of (log n) in n 19.873 * [taylor]: Taking taylor expansion of n in n 19.873 * [backup-simplify]: Simplify 0 into 0 19.873 * [backup-simplify]: Simplify 1 into 1 19.874 * [backup-simplify]: Simplify (log 1) into 0 19.874 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 19.874 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 19.875 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 19.875 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 19.875 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 19.875 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 19.875 * [taylor]: Taking taylor expansion of 1.0 in n 19.875 * [backup-simplify]: Simplify 1.0 into 1.0 19.875 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.875 * [taylor]: Taking taylor expansion of 2.0 in n 19.875 * [backup-simplify]: Simplify 2.0 into 2.0 19.875 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.876 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 19.878 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 19.879 * [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) 19.880 * [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) 19.881 * [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)) 19.883 * [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))) 19.884 * [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) 19.884 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 19.884 * [taylor]: Taking taylor expansion of (* n PI) in n 19.884 * [taylor]: Taking taylor expansion of n in n 19.884 * [backup-simplify]: Simplify 0 into 0 19.884 * [backup-simplify]: Simplify 1 into 1 19.884 * [taylor]: Taking taylor expansion of PI in n 19.884 * [backup-simplify]: Simplify PI into PI 19.885 * [backup-simplify]: Simplify (* 0 PI) into 0 19.887 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 19.887 * [backup-simplify]: Simplify (log PI) into (log PI) 19.887 * [taylor]: Taking taylor expansion of (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) in n 19.887 * [taylor]: Taking taylor expansion of 0.5 in n 19.887 * [backup-simplify]: Simplify 0.5 into 0.5 19.887 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0)) in n 19.887 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 19.887 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 19.887 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 19.887 * [taylor]: Taking taylor expansion of 0.5 in n 19.887 * [backup-simplify]: Simplify 0.5 into 0.5 19.887 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 19.887 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 19.887 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 19.887 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 19.887 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 19.887 * [taylor]: Taking taylor expansion of 1.0 in n 19.887 * [backup-simplify]: Simplify 1.0 into 1.0 19.887 * [taylor]: Taking taylor expansion of (log PI) in n 19.887 * [taylor]: Taking taylor expansion of PI in n 19.888 * [backup-simplify]: Simplify PI into PI 19.888 * [backup-simplify]: Simplify (log PI) into (log PI) 19.889 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 19.891 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 19.891 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 19.891 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 19.891 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 19.891 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 19.891 * [taylor]: Taking taylor expansion of 1.0 in n 19.891 * [backup-simplify]: Simplify 1.0 into 1.0 19.891 * [taylor]: Taking taylor expansion of (log n) in n 19.891 * [taylor]: Taking taylor expansion of n in n 19.891 * [backup-simplify]: Simplify 0 into 0 19.891 * [backup-simplify]: Simplify 1 into 1 19.891 * [backup-simplify]: Simplify (log 1) into 0 19.892 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 19.892 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 19.892 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 19.892 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 19.892 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 19.892 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 19.892 * [taylor]: Taking taylor expansion of 1.0 in n 19.892 * [backup-simplify]: Simplify 1.0 into 1.0 19.892 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.892 * [taylor]: Taking taylor expansion of 2.0 in n 19.892 * [backup-simplify]: Simplify 2.0 into 2.0 19.893 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.894 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 19.895 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 19.896 * [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) 19.904 * [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) 19.905 * [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)) 19.907 * [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))) 19.908 * [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) 19.908 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.908 * [taylor]: Taking taylor expansion of 2.0 in n 19.908 * [backup-simplify]: Simplify 2.0 into 2.0 19.909 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.910 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.912 * [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 PI) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log PI) (log n))) 19.914 * [backup-simplify]: Simplify (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log PI) (log n)))) into (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log PI) (log n)))) 19.916 * [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)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0)) 19.917 * [backup-simplify]: Simplify (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) into (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0))) 19.921 * [backup-simplify]: Simplify (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log PI) (log n)))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0)))) into (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI))))) 19.927 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI)))))) into (- (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log PI))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0)))))) 19.933 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log PI))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log 2.0)))))) into (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI)))))) 19.934 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 19.935 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 19.937 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 19.938 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 19.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 19.939 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 19.940 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 19.941 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 19.943 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 19.944 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 19.946 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 19.947 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 19.949 * [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 19.951 * [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 19.953 * [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 19.953 * [backup-simplify]: Simplify 0 into 0 19.954 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 19.956 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* n PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* n PI) 1)))) 2) into 0 19.956 * [backup-simplify]: Simplify (- 0) into 0 19.956 * [backup-simplify]: Simplify (+ 0 0) into 0 19.957 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 19.957 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* n PI))))) into 0 19.958 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* n PI)))) (+ (* (/ (pow (- (* 0.5 (log (* n PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* n PI)) 2) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5))) 19.960 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 19.960 * [backup-simplify]: Simplify (- 0) into 0 19.960 * [backup-simplify]: Simplify (+ 0 0) into 0 19.961 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 19.962 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log 2.0)))) into 0 19.968 * [backup-simplify]: Simplify (* (exp (* 0.5 (log 2.0))) (+ (* (/ (pow (- (* 0.5 (log 2.0))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) 19.975 * [backup-simplify]: Simplify (+ (* (pow 2.0 0.5) (* 0.125 (* (pow (log (* n PI)) 2) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5)))) (+ (* (* -0.5 (* (pow (pow 2.0 1.0) 0.5) (log 2.0))) (* -0.5 (* (log (* n PI)) (pow (* (pow n 1.0) (pow PI 1.0)) 0.5)))) (* (* 0.125 (* (pow (pow 2.0 1.0) 0.5) (pow (log 2.0) 2))) (pow (* n PI) 0.5)))) into (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))))) 19.975 * [taylor]: Taking taylor expansion of (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))))) in n 19.975 * [taylor]: Taking taylor expansion of (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2))) in n 19.975 * [taylor]: Taking taylor expansion of 0.125 in n 19.975 * [backup-simplify]: Simplify 0.125 into 0.125 19.975 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* n PI)) 2)) in n 19.975 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 19.975 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 19.975 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 19.975 * [taylor]: Taking taylor expansion of 0.5 in n 19.975 * [backup-simplify]: Simplify 0.5 into 0.5 19.975 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 19.975 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 19.975 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 19.975 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 19.975 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 19.975 * [taylor]: Taking taylor expansion of 1.0 in n 19.975 * [backup-simplify]: Simplify 1.0 into 1.0 19.975 * [taylor]: Taking taylor expansion of (log PI) in n 19.975 * [taylor]: Taking taylor expansion of PI in n 19.975 * [backup-simplify]: Simplify PI into PI 19.976 * [backup-simplify]: Simplify (log PI) into (log PI) 19.976 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 19.977 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 19.977 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 19.977 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 19.977 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 19.977 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 19.977 * [taylor]: Taking taylor expansion of 1.0 in n 19.977 * [backup-simplify]: Simplify 1.0 into 1.0 19.977 * [taylor]: Taking taylor expansion of (log n) in n 19.977 * [taylor]: Taking taylor expansion of n in n 19.977 * [backup-simplify]: Simplify 0 into 0 19.977 * [backup-simplify]: Simplify 1 into 1 19.978 * [backup-simplify]: Simplify (log 1) into 0 19.978 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 19.978 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 19.978 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 19.978 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 19.978 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 19.978 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 19.978 * [taylor]: Taking taylor expansion of 1.0 in n 19.978 * [backup-simplify]: Simplify 1.0 into 1.0 19.978 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.978 * [taylor]: Taking taylor expansion of 2.0 in n 19.978 * [backup-simplify]: Simplify 2.0 into 2.0 19.978 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.979 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 19.980 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 19.980 * [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) 19.981 * [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) 19.982 * [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)) 19.983 * [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))) 19.984 * [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) 19.985 * [taylor]: Taking taylor expansion of (pow (log (* n PI)) 2) in n 19.985 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 19.985 * [taylor]: Taking taylor expansion of (* n PI) in n 19.985 * [taylor]: Taking taylor expansion of n in n 19.985 * [backup-simplify]: Simplify 0 into 0 19.985 * [backup-simplify]: Simplify 1 into 1 19.985 * [taylor]: Taking taylor expansion of PI in n 19.985 * [backup-simplify]: Simplify PI into PI 19.985 * [backup-simplify]: Simplify (* 0 PI) into 0 19.987 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 19.987 * [backup-simplify]: Simplify (log PI) into (log PI) 19.988 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 19.988 * [taylor]: Taking taylor expansion of (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))) in n 19.988 * [taylor]: Taking taylor expansion of (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0)))) in n 19.988 * [taylor]: Taking taylor expansion of 0.25 in n 19.988 * [backup-simplify]: Simplify 0.25 into 0.25 19.988 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* n PI)) (log 2.0))) in n 19.988 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 19.988 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 19.988 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 19.988 * [taylor]: Taking taylor expansion of 0.5 in n 19.989 * [backup-simplify]: Simplify 0.5 into 0.5 19.989 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 19.989 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 19.989 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 19.989 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 19.989 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 19.989 * [taylor]: Taking taylor expansion of 1.0 in n 19.989 * [backup-simplify]: Simplify 1.0 into 1.0 19.989 * [taylor]: Taking taylor expansion of (log PI) in n 19.989 * [taylor]: Taking taylor expansion of PI in n 19.989 * [backup-simplify]: Simplify PI into PI 19.989 * [backup-simplify]: Simplify (log PI) into (log PI) 19.990 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 19.992 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 19.992 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 19.992 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 19.992 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 19.992 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 19.992 * [taylor]: Taking taylor expansion of 1.0 in n 19.992 * [backup-simplify]: Simplify 1.0 into 1.0 19.992 * [taylor]: Taking taylor expansion of (log n) in n 19.992 * [taylor]: Taking taylor expansion of n in n 19.992 * [backup-simplify]: Simplify 0 into 0 19.992 * [backup-simplify]: Simplify 1 into 1 19.993 * [backup-simplify]: Simplify (log 1) into 0 19.993 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 19.993 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 19.993 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 19.993 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 19.993 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 19.993 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 19.994 * [taylor]: Taking taylor expansion of 1.0 in n 19.994 * [backup-simplify]: Simplify 1.0 into 1.0 19.994 * [taylor]: Taking taylor expansion of (log 2.0) in n 19.994 * [taylor]: Taking taylor expansion of 2.0 in n 19.994 * [backup-simplify]: Simplify 2.0 into 2.0 19.994 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 19.995 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 19.996 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 19.997 * [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) 19.999 * [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) 20.000 * [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)) 20.001 * [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))) 20.003 * [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) 20.003 * [taylor]: Taking taylor expansion of (* (log (* n PI)) (log 2.0)) in n 20.003 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 20.003 * [taylor]: Taking taylor expansion of (* n PI) in n 20.003 * [taylor]: Taking taylor expansion of n in n 20.003 * [backup-simplify]: Simplify 0 into 0 20.003 * [backup-simplify]: Simplify 1 into 1 20.003 * [taylor]: Taking taylor expansion of PI in n 20.003 * [backup-simplify]: Simplify PI into PI 20.004 * [backup-simplify]: Simplify (* 0 PI) into 0 20.005 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 20.006 * [backup-simplify]: Simplify (log PI) into (log PI) 20.006 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.006 * [taylor]: Taking taylor expansion of 2.0 in n 20.006 * [backup-simplify]: Simplify 2.0 into 2.0 20.006 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.006 * [taylor]: Taking taylor expansion of (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))) in n 20.006 * [taylor]: Taking taylor expansion of 0.125 in n 20.006 * [backup-simplify]: Simplify 0.125 into 0.125 20.006 * [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) 2)) in n 20.006 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 20.006 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 20.006 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 20.006 * [taylor]: Taking taylor expansion of 0.5 in n 20.006 * [backup-simplify]: Simplify 0.5 into 0.5 20.006 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 20.007 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 20.007 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 20.007 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 20.007 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 20.007 * [taylor]: Taking taylor expansion of 1.0 in n 20.007 * [backup-simplify]: Simplify 1.0 into 1.0 20.007 * [taylor]: Taking taylor expansion of (log PI) in n 20.007 * [taylor]: Taking taylor expansion of PI in n 20.007 * [backup-simplify]: Simplify PI into PI 20.007 * [backup-simplify]: Simplify (log PI) into (log PI) 20.008 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 20.010 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 20.010 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 20.010 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 20.010 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 20.010 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 20.010 * [taylor]: Taking taylor expansion of 1.0 in n 20.010 * [backup-simplify]: Simplify 1.0 into 1.0 20.010 * [taylor]: Taking taylor expansion of (log n) in n 20.010 * [taylor]: Taking taylor expansion of n in n 20.010 * [backup-simplify]: Simplify 0 into 0 20.010 * [backup-simplify]: Simplify 1 into 1 20.011 * [backup-simplify]: Simplify (log 1) into 0 20.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 20.011 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 20.011 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 20.011 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 20.011 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 20.011 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 20.011 * [taylor]: Taking taylor expansion of 1.0 in n 20.011 * [backup-simplify]: Simplify 1.0 into 1.0 20.011 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.011 * [taylor]: Taking taylor expansion of 2.0 in n 20.011 * [backup-simplify]: Simplify 2.0 into 2.0 20.012 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.013 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 20.014 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 20.015 * [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) 20.016 * [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) 20.018 * [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)) 20.019 * [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))) 20.020 * [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) 20.020 * [taylor]: Taking taylor expansion of (pow (log 2.0) 2) in n 20.020 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.020 * [taylor]: Taking taylor expansion of 2.0 in n 20.020 * [backup-simplify]: Simplify 2.0 into 2.0 20.020 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.021 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 20.021 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 20.022 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (+ (log PI) (log n))) into (pow (+ (log PI) (log n)) 2) 20.023 * [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 PI) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log PI) (log n)) 2)) 20.024 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log PI) (log n)) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log PI) (log n)) 2))) 20.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log PI) (log n)) 20.025 * [backup-simplify]: Simplify (* (+ (log PI) (log n)) (log 2.0)) into (* (+ (log PI) (log n)) (log 2.0)) 20.027 * [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 PI) (log n)) (log 2.0))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0))) 20.028 * [backup-simplify]: Simplify (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0)))) into (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0)))) 20.034 * [backup-simplify]: Simplify (* (log 2.0) (log 2.0)) into (pow (log 2.0) 2) 20.036 * [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) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)) 20.037 * [backup-simplify]: Simplify (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))) into (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2))) 20.040 * [backup-simplify]: Simplify (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (+ (log PI) (log n)) (log 2.0)))) (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2)))) into (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2))))) 20.046 * [backup-simplify]: Simplify (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log PI) (log n)) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))))) into (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log PI) 2)))))))) 20.055 * [backup-simplify]: Simplify (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log 2.0) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (log 2.0)))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log PI) 2)))))))) into (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log PI) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))))))) 20.070 * [backup-simplify]: Simplify (+ (* (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) (log n)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log PI) (log 2.0)))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log PI) 2))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log n) (log 2.0)))) (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log 2.0) 2)))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (+ (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log 2.0))) (* 0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log PI)))))) (* 1 k)) (pow (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) 1.0) 0.5))) into (- (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow k 2) (* (log PI) (log n))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log PI) (log 2.0))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (pow (log 2.0) 2)))) (+ (pow (pow (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) 1.0) 1.0) 0.5) (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log n) (log 2.0))))))))))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* k (log 2.0)))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) k))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k)))))) 20.071 * [backup-simplify]: Simplify (* (pow 2.0 (/ (- 1.0 (/ 1 k)) 2.0)) (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0))) into (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) 20.071 * [approximate]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in (k n) around 0 20.071 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in n 20.071 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 20.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 20.071 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 20.071 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 20.071 * [taylor]: Taking taylor expansion of 0.5 in n 20.072 * [backup-simplify]: Simplify 0.5 into 0.5 20.072 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.072 * [taylor]: Taking taylor expansion of 1.0 in n 20.072 * [backup-simplify]: Simplify 1.0 into 1.0 20.072 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.072 * [taylor]: Taking taylor expansion of k in n 20.072 * [backup-simplify]: Simplify k into k 20.072 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.072 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 20.072 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.072 * [taylor]: Taking taylor expansion of PI in n 20.072 * [backup-simplify]: Simplify PI into PI 20.072 * [taylor]: Taking taylor expansion of n in n 20.072 * [backup-simplify]: Simplify 0 into 0 20.072 * [backup-simplify]: Simplify 1 into 1 20.073 * [backup-simplify]: Simplify (/ PI 1) into PI 20.073 * [backup-simplify]: Simplify (log PI) into (log PI) 20.073 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.073 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.073 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 20.074 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 20.075 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 20.075 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 20.076 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in n 20.076 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in n 20.076 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in n 20.076 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 20.076 * [taylor]: Taking taylor expansion of 0.5 in n 20.076 * [backup-simplify]: Simplify 0.5 into 0.5 20.076 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.076 * [taylor]: Taking taylor expansion of 1.0 in n 20.076 * [backup-simplify]: Simplify 1.0 into 1.0 20.076 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.076 * [taylor]: Taking taylor expansion of k in n 20.076 * [backup-simplify]: Simplify k into k 20.076 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.076 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.076 * [taylor]: Taking taylor expansion of 2.0 in n 20.076 * [backup-simplify]: Simplify 2.0 into 2.0 20.076 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.077 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.077 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.077 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 20.077 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) into (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) 20.078 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 20.078 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in k 20.078 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 20.078 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 20.078 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 20.078 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 20.078 * [taylor]: Taking taylor expansion of 0.5 in k 20.078 * [backup-simplify]: Simplify 0.5 into 0.5 20.078 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.078 * [taylor]: Taking taylor expansion of 1.0 in k 20.078 * [backup-simplify]: Simplify 1.0 into 1.0 20.078 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.078 * [taylor]: Taking taylor expansion of k in k 20.078 * [backup-simplify]: Simplify 0 into 0 20.078 * [backup-simplify]: Simplify 1 into 1 20.079 * [backup-simplify]: Simplify (/ 1 1) into 1 20.079 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 20.079 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.079 * [taylor]: Taking taylor expansion of PI in k 20.079 * [backup-simplify]: Simplify PI into PI 20.079 * [taylor]: Taking taylor expansion of n in k 20.079 * [backup-simplify]: Simplify n into n 20.079 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.079 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 20.079 * [backup-simplify]: Simplify (- 1) into -1 20.080 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.080 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 20.080 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 20.080 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 20.081 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in k 20.081 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in k 20.081 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in k 20.081 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 20.081 * [taylor]: Taking taylor expansion of 0.5 in k 20.081 * [backup-simplify]: Simplify 0.5 into 0.5 20.081 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.081 * [taylor]: Taking taylor expansion of 1.0 in k 20.081 * [backup-simplify]: Simplify 1.0 into 1.0 20.081 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.081 * [taylor]: Taking taylor expansion of k in k 20.081 * [backup-simplify]: Simplify 0 into 0 20.081 * [backup-simplify]: Simplify 1 into 1 20.081 * [backup-simplify]: Simplify (/ 1 1) into 1 20.081 * [taylor]: Taking taylor expansion of (log 2.0) in k 20.081 * [taylor]: Taking taylor expansion of 2.0 in k 20.081 * [backup-simplify]: Simplify 2.0 into 2.0 20.082 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.082 * [backup-simplify]: Simplify (- 1) into -1 20.082 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.083 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 20.084 * [backup-simplify]: Simplify (* -0.5 (log 2.0)) into (* -0.5 (log 2.0)) 20.084 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 20.084 * [taylor]: Taking taylor expansion of (* (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) (pow 2.0 (* 0.5 (- 1.0 (/ 1 k))))) in k 20.084 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 20.084 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 20.084 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 20.084 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 20.085 * [taylor]: Taking taylor expansion of 0.5 in k 20.085 * [backup-simplify]: Simplify 0.5 into 0.5 20.085 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.085 * [taylor]: Taking taylor expansion of 1.0 in k 20.085 * [backup-simplify]: Simplify 1.0 into 1.0 20.085 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.085 * [taylor]: Taking taylor expansion of k in k 20.085 * [backup-simplify]: Simplify 0 into 0 20.085 * [backup-simplify]: Simplify 1 into 1 20.085 * [backup-simplify]: Simplify (/ 1 1) into 1 20.085 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 20.085 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.085 * [taylor]: Taking taylor expansion of PI in k 20.085 * [backup-simplify]: Simplify PI into PI 20.085 * [taylor]: Taking taylor expansion of n in k 20.085 * [backup-simplify]: Simplify n into n 20.085 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.085 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 20.086 * [backup-simplify]: Simplify (- 1) into -1 20.086 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.087 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 20.087 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 20.087 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 20.087 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (- 1.0 (/ 1 k)))) in k 20.087 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) in k 20.087 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0)) in k 20.087 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 20.087 * [taylor]: Taking taylor expansion of 0.5 in k 20.087 * [backup-simplify]: Simplify 0.5 into 0.5 20.087 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 20.087 * [taylor]: Taking taylor expansion of 1.0 in k 20.087 * [backup-simplify]: Simplify 1.0 into 1.0 20.087 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.087 * [taylor]: Taking taylor expansion of k in k 20.087 * [backup-simplify]: Simplify 0 into 0 20.087 * [backup-simplify]: Simplify 1 into 1 20.088 * [backup-simplify]: Simplify (/ 1 1) into 1 20.088 * [taylor]: Taking taylor expansion of (log 2.0) in k 20.088 * [taylor]: Taking taylor expansion of 2.0 in k 20.088 * [backup-simplify]: Simplify 2.0 into 2.0 20.088 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.089 * [backup-simplify]: Simplify (- 1) into -1 20.089 * [backup-simplify]: Simplify (+ 0 -1) into -1 20.090 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 20.090 * [backup-simplify]: Simplify (* -0.5 (log 2.0)) into (* -0.5 (log 2.0)) 20.091 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log 2.0))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 20.092 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) 20.092 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) in n 20.092 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) in n 20.092 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n)))) in n 20.092 * [taylor]: Taking taylor expansion of 0.5 in n 20.092 * [backup-simplify]: Simplify 0.5 into 0.5 20.092 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (/ PI n))) in n 20.092 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.092 * [taylor]: Taking taylor expansion of 1.0 in n 20.092 * [backup-simplify]: Simplify 1.0 into 1.0 20.092 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.092 * [taylor]: Taking taylor expansion of k in n 20.092 * [backup-simplify]: Simplify k into k 20.092 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.092 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 20.092 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.092 * [taylor]: Taking taylor expansion of PI in n 20.092 * [backup-simplify]: Simplify PI into PI 20.092 * [taylor]: Taking taylor expansion of n in n 20.093 * [backup-simplify]: Simplify 0 into 0 20.093 * [backup-simplify]: Simplify 1 into 1 20.093 * [backup-simplify]: Simplify (/ PI 1) into PI 20.094 * [backup-simplify]: Simplify (log PI) into (log PI) 20.094 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.094 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.095 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 20.095 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log PI) (log n))) into (* (- 1.0 (/ 1 k)) (- (log PI) (log n))) 20.096 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))) 20.096 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 20.097 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) in n 20.097 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) in n 20.097 * [taylor]: Taking taylor expansion of 0.5 in n 20.097 * [backup-simplify]: Simplify 0.5 into 0.5 20.097 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log 2.0)) in n 20.097 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 20.097 * [taylor]: Taking taylor expansion of 1.0 in n 20.097 * [backup-simplify]: Simplify 1.0 into 1.0 20.097 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.097 * [taylor]: Taking taylor expansion of k in n 20.097 * [backup-simplify]: Simplify k into k 20.097 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.097 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.097 * [taylor]: Taking taylor expansion of 2.0 in n 20.097 * [backup-simplify]: Simplify 2.0 into 2.0 20.097 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.098 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 20.098 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 20.098 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (log 2.0)) into (* (- 1.0 (/ 1 k)) (log 2.0)) 20.099 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) into (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))) 20.099 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) 20.100 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) 20.101 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) 20.102 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into 0 20.102 * [taylor]: Taking taylor expansion of 0 in n 20.102 * [backup-simplify]: Simplify 0 into 0 20.102 * [backup-simplify]: Simplify 0 into 0 20.104 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 20.104 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.104 * [backup-simplify]: Simplify (- 0) into 0 20.105 * [backup-simplify]: Simplify (+ 0 0) into 0 20.105 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (log 2.0))) into 0 20.106 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (log 2.0)))) into 0 20.108 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.109 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.110 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 20.110 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.111 * [backup-simplify]: Simplify (- 0) into 0 20.111 * [backup-simplify]: Simplify (+ 0 0) into 0 20.112 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 20.112 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log PI) (log n)))) into 0 20.113 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) into 0 20.115 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 20.116 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))) into 0 20.116 * [backup-simplify]: Simplify 0 into 0 20.117 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) into 0 20.118 * [taylor]: Taking taylor expansion of 0 in n 20.118 * [backup-simplify]: Simplify 0 into 0 20.118 * [backup-simplify]: Simplify 0 into 0 20.118 * [backup-simplify]: Simplify 0 into 0 20.121 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 20.121 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.121 * [backup-simplify]: Simplify (- 0) into 0 20.122 * [backup-simplify]: Simplify (+ 0 0) into 0 20.123 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (+ (* 0 0) (* 0 (log 2.0)))) into 0 20.124 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (- 1.0 (/ 1 k)) (log 2.0))))) into 0 20.126 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.130 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 20.130 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.131 * [backup-simplify]: Simplify (- 0) into 0 20.131 * [backup-simplify]: Simplify (+ 0 0) into 0 20.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 20.133 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 20.135 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log PI) (log n)))))) into 0 20.137 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.139 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log PI) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0))))))) into 0 20.139 * [backup-simplify]: Simplify 0 into 0 20.140 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (/ PI n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log 2.0)))))))) into 0 20.140 * [taylor]: Taking taylor expansion of 0 in n 20.140 * [backup-simplify]: Simplify 0 into 0 20.140 * [backup-simplify]: Simplify 0 into 0 20.141 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (log 2.0)))) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log PI) (log (/ 1 n))))))) into (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n))))))) 20.142 * [backup-simplify]: Simplify (* (pow 2.0 (/ (- 1.0 (/ 1 (- k))) 2.0)) (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) 20.142 * [approximate]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in (k n) around 0 20.142 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in n 20.142 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 20.142 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 20.142 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 20.142 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 20.142 * [taylor]: Taking taylor expansion of 0.5 in n 20.142 * [backup-simplify]: Simplify 0.5 into 0.5 20.142 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.142 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.142 * [taylor]: Taking taylor expansion of k in n 20.142 * [backup-simplify]: Simplify k into k 20.142 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.142 * [taylor]: Taking taylor expansion of 1.0 in n 20.142 * [backup-simplify]: Simplify 1.0 into 1.0 20.142 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 20.142 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 20.143 * [taylor]: Taking taylor expansion of -1 in n 20.143 * [backup-simplify]: Simplify -1 into -1 20.143 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.143 * [taylor]: Taking taylor expansion of PI in n 20.143 * [backup-simplify]: Simplify PI into PI 20.143 * [taylor]: Taking taylor expansion of n in n 20.143 * [backup-simplify]: Simplify 0 into 0 20.143 * [backup-simplify]: Simplify 1 into 1 20.143 * [backup-simplify]: Simplify (/ PI 1) into PI 20.144 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 20.145 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 20.145 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.145 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 20.147 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 20.148 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 20.149 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 20.149 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in n 20.149 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in n 20.149 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in n 20.149 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 20.149 * [taylor]: Taking taylor expansion of 0.5 in n 20.149 * [backup-simplify]: Simplify 0.5 into 0.5 20.149 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.149 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.150 * [taylor]: Taking taylor expansion of k in n 20.150 * [backup-simplify]: Simplify k into k 20.150 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.150 * [taylor]: Taking taylor expansion of 1.0 in n 20.150 * [backup-simplify]: Simplify 1.0 into 1.0 20.150 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.150 * [taylor]: Taking taylor expansion of 2.0 in n 20.150 * [backup-simplify]: Simplify 2.0 into 2.0 20.150 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.150 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.150 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 20.151 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) into (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))) 20.151 * [backup-simplify]: Simplify (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 20.151 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in k 20.152 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 20.152 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 20.152 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 20.152 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 20.152 * [taylor]: Taking taylor expansion of 0.5 in k 20.152 * [backup-simplify]: Simplify 0.5 into 0.5 20.152 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.152 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.152 * [taylor]: Taking taylor expansion of k in k 20.152 * [backup-simplify]: Simplify 0 into 0 20.152 * [backup-simplify]: Simplify 1 into 1 20.152 * [backup-simplify]: Simplify (/ 1 1) into 1 20.152 * [taylor]: Taking taylor expansion of 1.0 in k 20.152 * [backup-simplify]: Simplify 1.0 into 1.0 20.152 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 20.152 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 20.152 * [taylor]: Taking taylor expansion of -1 in k 20.152 * [backup-simplify]: Simplify -1 into -1 20.152 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.152 * [taylor]: Taking taylor expansion of PI in k 20.152 * [backup-simplify]: Simplify PI into PI 20.152 * [taylor]: Taking taylor expansion of n in k 20.152 * [backup-simplify]: Simplify n into n 20.153 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.153 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 20.153 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 20.153 * [backup-simplify]: Simplify (+ 1 0) into 1 20.153 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 20.154 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 20.154 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 20.154 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in k 20.154 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in k 20.154 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in k 20.154 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 20.154 * [taylor]: Taking taylor expansion of 0.5 in k 20.154 * [backup-simplify]: Simplify 0.5 into 0.5 20.154 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.154 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.154 * [taylor]: Taking taylor expansion of k in k 20.154 * [backup-simplify]: Simplify 0 into 0 20.154 * [backup-simplify]: Simplify 1 into 1 20.155 * [backup-simplify]: Simplify (/ 1 1) into 1 20.155 * [taylor]: Taking taylor expansion of 1.0 in k 20.155 * [backup-simplify]: Simplify 1.0 into 1.0 20.155 * [taylor]: Taking taylor expansion of (log 2.0) in k 20.155 * [taylor]: Taking taylor expansion of 2.0 in k 20.155 * [backup-simplify]: Simplify 2.0 into 2.0 20.155 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.156 * [backup-simplify]: Simplify (+ 1 0) into 1 20.156 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 20.157 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 20.157 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 20.157 * [taylor]: Taking taylor expansion of (* (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0)))) in k 20.158 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 20.158 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 20.158 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 20.158 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 20.158 * [taylor]: Taking taylor expansion of 0.5 in k 20.158 * [backup-simplify]: Simplify 0.5 into 0.5 20.158 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.158 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.158 * [taylor]: Taking taylor expansion of k in k 20.158 * [backup-simplify]: Simplify 0 into 0 20.158 * [backup-simplify]: Simplify 1 into 1 20.158 * [backup-simplify]: Simplify (/ 1 1) into 1 20.158 * [taylor]: Taking taylor expansion of 1.0 in k 20.158 * [backup-simplify]: Simplify 1.0 into 1.0 20.158 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 20.158 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 20.158 * [taylor]: Taking taylor expansion of -1 in k 20.158 * [backup-simplify]: Simplify -1 into -1 20.158 * [taylor]: Taking taylor expansion of (/ PI n) in k 20.158 * [taylor]: Taking taylor expansion of PI in k 20.159 * [backup-simplify]: Simplify PI into PI 20.159 * [taylor]: Taking taylor expansion of n in k 20.159 * [backup-simplify]: Simplify n into n 20.159 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 20.159 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 20.159 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 20.159 * [backup-simplify]: Simplify (+ 1 0) into 1 20.160 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 20.160 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 20.160 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 20.160 * [taylor]: Taking taylor expansion of (pow 2.0 (* 0.5 (+ (/ 1 k) 1.0))) in k 20.160 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) in k 20.160 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0)) in k 20.160 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 20.160 * [taylor]: Taking taylor expansion of 0.5 in k 20.160 * [backup-simplify]: Simplify 0.5 into 0.5 20.160 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 20.160 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.160 * [taylor]: Taking taylor expansion of k in k 20.160 * [backup-simplify]: Simplify 0 into 0 20.160 * [backup-simplify]: Simplify 1 into 1 20.166 * [backup-simplify]: Simplify (/ 1 1) into 1 20.166 * [taylor]: Taking taylor expansion of 1.0 in k 20.166 * [backup-simplify]: Simplify 1.0 into 1.0 20.166 * [taylor]: Taking taylor expansion of (log 2.0) in k 20.166 * [taylor]: Taking taylor expansion of 2.0 in k 20.166 * [backup-simplify]: Simplify 2.0 into 2.0 20.167 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.167 * [backup-simplify]: Simplify (+ 1 0) into 1 20.168 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 20.168 * [backup-simplify]: Simplify (* 0.5 (log 2.0)) into (* 0.5 (log 2.0)) 20.169 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log 2.0))) into (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) 20.170 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) into (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) 20.170 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))) in n 20.170 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) in n 20.170 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0))) in n 20.170 * [taylor]: Taking taylor expansion of 0.5 in n 20.170 * [backup-simplify]: Simplify 0.5 into 0.5 20.170 * [taylor]: Taking taylor expansion of (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)) in n 20.170 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 20.170 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 20.170 * [taylor]: Taking taylor expansion of -1 in n 20.170 * [backup-simplify]: Simplify -1 into -1 20.170 * [taylor]: Taking taylor expansion of (/ PI n) in n 20.170 * [taylor]: Taking taylor expansion of PI in n 20.170 * [backup-simplify]: Simplify PI into PI 20.170 * [taylor]: Taking taylor expansion of n in n 20.170 * [backup-simplify]: Simplify 0 into 0 20.170 * [backup-simplify]: Simplify 1 into 1 20.171 * [backup-simplify]: Simplify (/ PI 1) into PI 20.172 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 20.173 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 20.173 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.173 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.173 * [taylor]: Taking taylor expansion of k in n 20.173 * [backup-simplify]: Simplify k into k 20.173 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.173 * [taylor]: Taking taylor expansion of 1.0 in n 20.173 * [backup-simplify]: Simplify 1.0 into 1.0 20.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 20.174 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.176 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) 20.177 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 20.178 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 20.178 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))) in n 20.178 * [taylor]: Taking taylor expansion of (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))) in n 20.178 * [taylor]: Taking taylor expansion of 0.5 in n 20.178 * [backup-simplify]: Simplify 0.5 into 0.5 20.178 * [taylor]: Taking taylor expansion of (* (log 2.0) (+ (/ 1 k) 1.0)) in n 20.178 * [taylor]: Taking taylor expansion of (log 2.0) in n 20.178 * [taylor]: Taking taylor expansion of 2.0 in n 20.178 * [backup-simplify]: Simplify 2.0 into 2.0 20.179 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 20.179 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 20.179 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.179 * [taylor]: Taking taylor expansion of k in n 20.179 * [backup-simplify]: Simplify k into k 20.179 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.179 * [taylor]: Taking taylor expansion of 1.0 in n 20.179 * [backup-simplify]: Simplify 1.0 into 1.0 20.179 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 20.180 * [backup-simplify]: Simplify (* (log 2.0) (+ (/ 1 k) 1.0)) into (* (+ (/ 1 k) 1.0) (log 2.0)) 20.180 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))) into (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))) 20.181 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) 20.183 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))))) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) 20.184 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) 20.185 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 0) (* 0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))) into 0 20.185 * [taylor]: Taking taylor expansion of 0 in n 20.186 * [backup-simplify]: Simplify 0 into 0 20.186 * [backup-simplify]: Simplify 0 into 0 20.186 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.186 * [backup-simplify]: Simplify (+ 0 0) into 0 20.188 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 20.188 * [backup-simplify]: Simplify (+ (* (log 2.0) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 20.189 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (log 2.0)))) into 0 20.191 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.192 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 20.192 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.193 * [backup-simplify]: Simplify (+ 0 0) into 0 20.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 20.194 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 20.197 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 20.198 * [backup-simplify]: Simplify (+ (* (- (log (* -1 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0 20.200 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0 20.202 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.204 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))))) into 0 20.204 * [backup-simplify]: Simplify 0 into 0 20.205 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0))))))) into 0 20.205 * [taylor]: Taking taylor expansion of 0 in n 20.205 * [backup-simplify]: Simplify 0 into 0 20.205 * [backup-simplify]: Simplify 0 into 0 20.205 * [backup-simplify]: Simplify 0 into 0 20.206 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.206 * [backup-simplify]: Simplify (+ 0 0) into 0 20.209 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2.0 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2.0 1)))) 2) into 0 20.210 * [backup-simplify]: Simplify (+ (* (log 2.0) 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 20.211 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (+ (/ 1 k) 1.0) (log 2.0))))) into 0 20.213 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.215 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 20.215 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.215 * [backup-simplify]: Simplify (+ 0 0) into 0 20.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.217 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 20.221 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 20.223 * [backup-simplify]: Simplify (+ (* (- (log (* -1 PI)) (log n)) 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 20.225 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))))) into 0 20.227 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.229 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log 2.0))))))) into 0 20.229 * [backup-simplify]: Simplify 0 into 0 20.231 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (log (* -1 (/ PI n))) (+ (/ 1 k) 1.0)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (log 2.0) (+ (/ 1 k) 1.0)))))))) into 0 20.231 * [taylor]: Taking taylor expansion of 0 in n 20.231 * [backup-simplify]: Simplify 0 into 0 20.231 * [backup-simplify]: Simplify 0 into 0 20.233 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))) into (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k))))) 20.233 * * * [progress]: simplifying candidates 20.237 * [simplify]: Simplifying: (expm1 (pow (* n PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) 1) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (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 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (log1p (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* 2.0 (* n PI)) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0)))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (* (log 2.0) (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0)))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (* (log (* n PI)) (/ (- 1.0 k) 2.0))) (+ (log (pow 2.0 (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0)))) (log (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (exp (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))))) (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ 1.0 2.0))) (* (pow 2.0 (/ k 2.0)) (pow (* n PI) (/ k 2.0))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) 1) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2))) (* (pow (cbrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (- (+ (exp (* 0.5 (+ (log PI) (log n)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (pow (log n) 2) (pow k 2)))) (* 0.25 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) (* (log n) (pow k 2)))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log n) k))) (* 0.5 (* (exp (* 0.5 (+ (log PI) (log n)))) (* (log PI) k))))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k)))) (* n PI) (* n PI) (* 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))))) (- (+ (* 0.25 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow k 2) (* (log PI) (log n))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))) (+ (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log PI) (log 2.0))))) (+ (* 0.125 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (pow (log PI) 2) (pow k 2)))) (+ (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (pow (log 2.0) 2)))) (+ (pow (pow (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) 1.0) 1.0) 0.5) (* 0.25 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow k 2) (* (log n) (log 2.0))))))))))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* k (log 2.0)))) (+ (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log PI) k))) (* 0.5 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k)))))) (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n))))))) (* (exp (* 0.5 (* (- 1.0 k) (log 2.0)))) (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ -1 n))) (- 1.0 k))))) 20.243 * * [simplify]: iteration 0: 340 enodes 20.336 * * [simplify]: iteration 1: 912 enodes 20.711 * * [simplify]: iteration 2: 2913 enodes 21.542 * * [simplify]: iteration complete: 5001 enodes 21.543 * * [simplify]: Extracting #0: cost 123 inf + 0 21.544 * * [simplify]: Extracting #1: cost 595 inf + 44 21.552 * * [simplify]: Extracting #2: cost 1119 inf + 5101 21.573 * * [simplify]: Extracting #3: cost 1118 inf + 43486 21.601 * * [simplify]: Extracting #4: cost 801 inf + 155045 21.679 * * [simplify]: Extracting #5: cost 357 inf + 443142 21.794 * * [simplify]: Extracting #6: cost 162 inf + 608855 21.976 * * [simplify]: Extracting #7: cost 109 inf + 637230 22.091 * * [simplify]: Extracting #8: cost 94 inf + 647314 22.245 * * [simplify]: Extracting #9: cost 101 inf + 649385 22.383 * * [simplify]: Extracting #10: cost 104 inf + 656383 22.514 * * [simplify]: Extracting #11: cost 69 inf + 727712 22.670 * * [simplify]: Extracting #12: cost 30 inf + 825059 22.912 * * [simplify]: Extracting #13: cost 5 inf + 886338 23.133 * * [simplify]: Extracting #14: cost 0 inf + 889577 23.370 * * [simplify]: Extracting #15: cost 0 inf + 889552 23.615 * [simplify]: Simplified to: (expm1 (pow (* n PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0)))) (pow (* n PI) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k))))) (pow (* n PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (sqrt (- 1.0 k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* n PI) (pow (* n PI) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0))) (pow (* n PI) (+ (sqrt k) (sqrt 1.0))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* n PI) (* n PI) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (* (/ (- 1.0 k) 2.0) (log (* n PI))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (* (* n PI) (* (* n PI) (* n PI))) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* n PI) (* (* n PI) (* n PI))) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* (cbrt PI) (* (cbrt PI) n)) (* (sqrt PI) n) n (* PI (cbrt n)) (* (sqrt n) PI) (* 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 1.0) (sqrt k)) (/ 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) (fabs (cbrt k))) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (log1p (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* 2.0 PI) n) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (* (/ (- 1.0 k) 2.0) (+ (log 2.0) (log (* n PI)))) (exp (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))))) (* (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))))) (cbrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))))) (sqrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (sqrt (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ 1.0 2.0))) (* (pow (* n PI) (/ k 2.0)) (pow 2.0 (/ k 2.0))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (pow (sqrt 2.0) (/ (- 1.0 k) 2.0))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow 2.0 (* 1/2 (/ (- 1.0 k) 2.0)))) (* (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow 2.0 (* 1/2 (/ (- 1.0 k) 2.0)))) (* (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (pow 2.0 (* 1/2 (/ (- 1.0 k) 2.0)))) (* (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (pow 2.0 (* 1/2 (/ (- 1.0 k) 2.0)))) (* (pow n (/ (- 1.0 k) 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (pow 2.0 (/ (- 1.0 k) 2.0)) (* (pow (* n PI) (* 1/2 (/ (- 1.0 k) 2.0))) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (pow (cbrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (sqrt 2.0) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (sqrt (pow 2.0 (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow 2.0 (* 1/2 (/ (- 1.0 k) 2.0)))) (* (pow (* n PI) (/ 1.0 2.0)) (pow 2.0 (/ (- 1.0 k) 2.0))) (* (pow 2.0 (/ 1.0 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (- (fma (* 0.125 (exp (* 0.5 (log (* n PI))))) (fma (* k k) (* (log PI) (log PI)) (* (* (log n) (log n)) (* k k))) (fma (* (* (log PI) (exp (* 0.5 (log (* n PI))))) (* (* k k) (log n))) 0.25 (exp (* 0.5 (log (* n PI)))))) (* 0.5 (* (exp (* 0.5 (log (* n PI)))) (fma (log n) k (* k (log PI)))))) (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) (exp (* (- (log (- PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (* n PI) (* n PI) (* n PI) (fma (* k k) (- +nan.0) (fma (- +nan.0) k +nan.0)) (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k))))) (- (- (fma (/ +nan.0 k) (/ 1 k) +nan.0) (/ +nan.0 k))) (fma (* (* (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) 0.25) (* (* k k) (log n))) (log PI) (fma (* (* k (log n)) (* k (log n))) (* (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) 0.125) (- (fma (* 0.25 (* (* (* k k) (log PI)) (log 2.0))) (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) (fma 0.125 (fma (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) (* (* k (log PI)) (* k (log PI))) (* (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) (* (* k (log 2.0)) (* k (log 2.0))))) (fma (* (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) (* (* (* k k) (log n)) (log 2.0))) 0.25 (pow (pow (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) 1.0) 1.0) 0.5)))) (fma (* (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) 0.5) (* k (log n)) (* (* (pow (* (* (pow PI 1.0) (pow n 1.0)) (pow 2.0 1.0)) 0.5) 0.5) (fma (log 2.0) k (* k (log PI)))))))) (exp (* (* 0.5 (- 1.0 k)) (+ (log 2.0) (log (* n PI))))) (exp (fma (* 0.5 (- 1.0 k)) (log 2.0) (* (- (log (- PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))) 23.626 * * * [progress]: adding candidates to table 24.741 * [progress]: [Phase 3 of 3] Extracting. 24.741 * * [regime]: Finding splitpoints for: (# # # # # # #) 24.743 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 24.743 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 24.848 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # #) 24.893 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 24.971 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 25.084 * * * [regime]: Found split indices: #