62.449 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.207 * * * [progress]: [2/2] Setting up program. 0.213 * [progress]: [Phase 2 of 3] Improving. 0.213 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.213 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.214 * * [simplify]: iteration 1: (13 enodes) 0.219 * * [simplify]: iteration 2: (29 enodes) 0.229 * * [simplify]: iteration 3: (60 enodes) 0.263 * * [simplify]: iteration 4: (123 enodes) 0.715 * * [simplify]: iteration 5: (322 enodes) 0.940 * * [simplify]: iteration 6: (821 enodes) 1.953 * * [simplify]: Extracting #0: cost 1 inf + 0 1.953 * * [simplify]: Extracting #1: cost 58 inf + 0 1.955 * * [simplify]: Extracting #2: cost 184 inf + 1 1.957 * * [simplify]: Extracting #3: cost 251 inf + 46 1.961 * * [simplify]: Extracting #4: cost 228 inf + 1879 1.971 * * [simplify]: Extracting #5: cost 157 inf + 21169 2.005 * * [simplify]: Extracting #6: cost 45 inf + 113683 2.036 * * [simplify]: Extracting #7: cost 0 inf + 157567 2.082 * * [simplify]: Extracting #8: cost 0 inf + 157407 2.140 * [simplify]: Simplified to: (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 2.148 * * [progress]: iteration 1 / 4 2.148 * * * [progress]: picking best candidate 2.161 * * * * [pick]: Picked # 2.161 * * * [progress]: localizing error 2.183 * * * [progress]: generating rewritten candidates 2.183 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 2.208 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 2.234 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 2.295 * * * [progress]: generating series expansions 2.295 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 2.295 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 2.295 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 2.295 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.295 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.295 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.295 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.295 * [taylor]: Taking taylor expansion of 1/2 in k 2.295 * [backup-simplify]: Simplify 1/2 into 1/2 2.295 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.295 * [taylor]: Taking taylor expansion of 1/2 in k 2.295 * [backup-simplify]: Simplify 1/2 into 1/2 2.295 * [taylor]: Taking taylor expansion of k in k 2.295 * [backup-simplify]: Simplify 0 into 0 2.295 * [backup-simplify]: Simplify 1 into 1 2.295 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.295 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.295 * [taylor]: Taking taylor expansion of 2 in k 2.295 * [backup-simplify]: Simplify 2 into 2 2.295 * [taylor]: Taking taylor expansion of (* n PI) in k 2.296 * [taylor]: Taking taylor expansion of n in k 2.296 * [backup-simplify]: Simplify n into n 2.296 * [taylor]: Taking taylor expansion of PI in k 2.296 * [backup-simplify]: Simplify PI into PI 2.296 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.296 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.296 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.297 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.297 * [backup-simplify]: Simplify (- 0) into 0 2.298 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.298 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.298 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.298 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.298 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.298 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.298 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.298 * [taylor]: Taking taylor expansion of 1/2 in n 2.298 * [backup-simplify]: Simplify 1/2 into 1/2 2.298 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.298 * [taylor]: Taking taylor expansion of 1/2 in n 2.298 * [backup-simplify]: Simplify 1/2 into 1/2 2.298 * [taylor]: Taking taylor expansion of k in n 2.298 * [backup-simplify]: Simplify k into k 2.298 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.298 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.298 * [taylor]: Taking taylor expansion of 2 in n 2.298 * [backup-simplify]: Simplify 2 into 2 2.298 * [taylor]: Taking taylor expansion of (* n PI) in n 2.298 * [taylor]: Taking taylor expansion of n in n 2.298 * [backup-simplify]: Simplify 0 into 0 2.298 * [backup-simplify]: Simplify 1 into 1 2.298 * [taylor]: Taking taylor expansion of PI in n 2.298 * [backup-simplify]: Simplify PI into PI 2.299 * [backup-simplify]: Simplify (* 0 PI) into 0 2.299 * [backup-simplify]: Simplify (* 2 0) into 0 2.300 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.302 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.302 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.302 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.303 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.303 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.304 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.304 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.305 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.305 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.305 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.305 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.305 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.305 * [taylor]: Taking taylor expansion of 1/2 in n 2.305 * [backup-simplify]: Simplify 1/2 into 1/2 2.305 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.305 * [taylor]: Taking taylor expansion of 1/2 in n 2.305 * [backup-simplify]: Simplify 1/2 into 1/2 2.305 * [taylor]: Taking taylor expansion of k in n 2.305 * [backup-simplify]: Simplify k into k 2.305 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.305 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.305 * [taylor]: Taking taylor expansion of 2 in n 2.305 * [backup-simplify]: Simplify 2 into 2 2.305 * [taylor]: Taking taylor expansion of (* n PI) in n 2.305 * [taylor]: Taking taylor expansion of n in n 2.305 * [backup-simplify]: Simplify 0 into 0 2.305 * [backup-simplify]: Simplify 1 into 1 2.305 * [taylor]: Taking taylor expansion of PI in n 2.305 * [backup-simplify]: Simplify PI into PI 2.306 * [backup-simplify]: Simplify (* 0 PI) into 0 2.306 * [backup-simplify]: Simplify (* 2 0) into 0 2.307 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.308 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.308 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.309 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.309 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.309 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.310 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.310 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.311 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.311 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.311 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.311 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.311 * [taylor]: Taking taylor expansion of 1/2 in k 2.311 * [backup-simplify]: Simplify 1/2 into 1/2 2.311 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.311 * [taylor]: Taking taylor expansion of 1/2 in k 2.311 * [backup-simplify]: Simplify 1/2 into 1/2 2.311 * [taylor]: Taking taylor expansion of k in k 2.311 * [backup-simplify]: Simplify 0 into 0 2.311 * [backup-simplify]: Simplify 1 into 1 2.311 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.311 * [taylor]: Taking taylor expansion of (log n) in k 2.311 * [taylor]: Taking taylor expansion of n in k 2.311 * [backup-simplify]: Simplify n into n 2.311 * [backup-simplify]: Simplify (log n) into (log n) 2.311 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.311 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.311 * [taylor]: Taking taylor expansion of 2 in k 2.311 * [backup-simplify]: Simplify 2 into 2 2.311 * [taylor]: Taking taylor expansion of PI in k 2.311 * [backup-simplify]: Simplify PI into PI 2.312 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.312 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.313 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.313 * [backup-simplify]: Simplify (- 0) into 0 2.313 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.314 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.314 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.315 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.316 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.317 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.317 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.318 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.319 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.319 * [backup-simplify]: Simplify (- 0) into 0 2.319 * [backup-simplify]: Simplify (+ 0 0) into 0 2.320 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.321 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.322 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.322 * [taylor]: Taking taylor expansion of 0 in k 2.322 * [backup-simplify]: Simplify 0 into 0 2.322 * [backup-simplify]: Simplify 0 into 0 2.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.324 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.325 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.325 * [backup-simplify]: Simplify (+ 0 0) into 0 2.325 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.326 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.326 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.327 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.329 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.331 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.332 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.332 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.334 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.335 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.335 * [backup-simplify]: Simplify (- 0) into 0 2.335 * [backup-simplify]: Simplify (+ 0 0) into 0 2.336 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.337 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.339 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.339 * [taylor]: Taking taylor expansion of 0 in k 2.339 * [backup-simplify]: Simplify 0 into 0 2.339 * [backup-simplify]: Simplify 0 into 0 2.339 * [backup-simplify]: Simplify 0 into 0 2.341 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.342 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.346 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.346 * [backup-simplify]: Simplify (+ 0 0) into 0 2.347 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.348 * [backup-simplify]: Simplify (- 0) into 0 2.348 * [backup-simplify]: Simplify (+ 0 0) into 0 2.350 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.354 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.367 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.378 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) 2.379 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.379 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 2.379 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.379 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.379 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.379 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.379 * [taylor]: Taking taylor expansion of 1/2 in k 2.379 * [backup-simplify]: Simplify 1/2 into 1/2 2.379 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.379 * [taylor]: Taking taylor expansion of 1/2 in k 2.379 * [backup-simplify]: Simplify 1/2 into 1/2 2.379 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.379 * [taylor]: Taking taylor expansion of k in k 2.379 * [backup-simplify]: Simplify 0 into 0 2.379 * [backup-simplify]: Simplify 1 into 1 2.379 * [backup-simplify]: Simplify (/ 1 1) into 1 2.379 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.379 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.379 * [taylor]: Taking taylor expansion of 2 in k 2.379 * [backup-simplify]: Simplify 2 into 2 2.379 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.379 * [taylor]: Taking taylor expansion of PI in k 2.380 * [backup-simplify]: Simplify PI into PI 2.380 * [taylor]: Taking taylor expansion of n in k 2.380 * [backup-simplify]: Simplify n into n 2.380 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.380 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.380 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.380 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.380 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.380 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.381 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.381 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.381 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.381 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.381 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.381 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.381 * [taylor]: Taking taylor expansion of 1/2 in n 2.381 * [backup-simplify]: Simplify 1/2 into 1/2 2.381 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.381 * [taylor]: Taking taylor expansion of 1/2 in n 2.381 * [backup-simplify]: Simplify 1/2 into 1/2 2.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.381 * [taylor]: Taking taylor expansion of k in n 2.381 * [backup-simplify]: Simplify k into k 2.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.381 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.381 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.381 * [taylor]: Taking taylor expansion of 2 in n 2.381 * [backup-simplify]: Simplify 2 into 2 2.381 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.381 * [taylor]: Taking taylor expansion of PI in n 2.381 * [backup-simplify]: Simplify PI into PI 2.381 * [taylor]: Taking taylor expansion of n in n 2.381 * [backup-simplify]: Simplify 0 into 0 2.381 * [backup-simplify]: Simplify 1 into 1 2.381 * [backup-simplify]: Simplify (/ PI 1) into PI 2.382 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.382 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.383 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.383 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.383 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.384 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.385 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.385 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.385 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.385 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.385 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.385 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.385 * [taylor]: Taking taylor expansion of 1/2 in n 2.385 * [backup-simplify]: Simplify 1/2 into 1/2 2.385 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.385 * [taylor]: Taking taylor expansion of 1/2 in n 2.385 * [backup-simplify]: Simplify 1/2 into 1/2 2.386 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.386 * [taylor]: Taking taylor expansion of k in n 2.386 * [backup-simplify]: Simplify k into k 2.386 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.386 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.386 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.386 * [taylor]: Taking taylor expansion of 2 in n 2.386 * [backup-simplify]: Simplify 2 into 2 2.386 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.386 * [taylor]: Taking taylor expansion of PI in n 2.386 * [backup-simplify]: Simplify PI into PI 2.386 * [taylor]: Taking taylor expansion of n in n 2.386 * [backup-simplify]: Simplify 0 into 0 2.386 * [backup-simplify]: Simplify 1 into 1 2.386 * [backup-simplify]: Simplify (/ PI 1) into PI 2.386 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.387 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.387 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.387 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.387 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.388 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.389 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.389 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.390 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.390 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.390 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.390 * [taylor]: Taking taylor expansion of 1/2 in k 2.390 * [backup-simplify]: Simplify 1/2 into 1/2 2.390 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.390 * [taylor]: Taking taylor expansion of 1/2 in k 2.390 * [backup-simplify]: Simplify 1/2 into 1/2 2.390 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.390 * [taylor]: Taking taylor expansion of k in k 2.390 * [backup-simplify]: Simplify 0 into 0 2.390 * [backup-simplify]: Simplify 1 into 1 2.390 * [backup-simplify]: Simplify (/ 1 1) into 1 2.390 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.390 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.390 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.390 * [taylor]: Taking taylor expansion of 2 in k 2.390 * [backup-simplify]: Simplify 2 into 2 2.390 * [taylor]: Taking taylor expansion of PI in k 2.390 * [backup-simplify]: Simplify PI into PI 2.390 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.391 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.391 * [taylor]: Taking taylor expansion of (log n) in k 2.391 * [taylor]: Taking taylor expansion of n in k 2.391 * [backup-simplify]: Simplify n into n 2.391 * [backup-simplify]: Simplify (log n) into (log n) 2.391 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.392 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.392 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.392 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.393 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.393 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.394 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.395 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.395 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.396 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.397 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.397 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.398 * [backup-simplify]: Simplify (- 0) into 0 2.398 * [backup-simplify]: Simplify (+ 0 0) into 0 2.399 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.399 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.401 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.401 * [taylor]: Taking taylor expansion of 0 in k 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify 0 into 0 2.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.402 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.404 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.404 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.405 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.405 * [backup-simplify]: Simplify (- 0) into 0 2.405 * [backup-simplify]: Simplify (+ 0 0) into 0 2.406 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.407 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.409 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.409 * [taylor]: Taking taylor expansion of 0 in k 2.409 * [backup-simplify]: Simplify 0 into 0 2.410 * [backup-simplify]: Simplify 0 into 0 2.410 * [backup-simplify]: Simplify 0 into 0 2.410 * [backup-simplify]: Simplify 0 into 0 2.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.412 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.418 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.418 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.420 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.420 * [backup-simplify]: Simplify (- 0) into 0 2.420 * [backup-simplify]: Simplify (+ 0 0) into 0 2.422 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.424 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.427 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.427 * [taylor]: Taking taylor expansion of 0 in k 2.427 * [backup-simplify]: Simplify 0 into 0 2.427 * [backup-simplify]: Simplify 0 into 0 2.428 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) 2.428 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.428 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.428 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.428 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.429 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.429 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.429 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.429 * [taylor]: Taking taylor expansion of 1/2 in k 2.429 * [backup-simplify]: Simplify 1/2 into 1/2 2.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.429 * [taylor]: Taking taylor expansion of k in k 2.429 * [backup-simplify]: Simplify 0 into 0 2.429 * [backup-simplify]: Simplify 1 into 1 2.429 * [backup-simplify]: Simplify (/ 1 1) into 1 2.429 * [taylor]: Taking taylor expansion of 1/2 in k 2.429 * [backup-simplify]: Simplify 1/2 into 1/2 2.429 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.429 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.429 * [taylor]: Taking taylor expansion of -2 in k 2.429 * [backup-simplify]: Simplify -2 into -2 2.429 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.429 * [taylor]: Taking taylor expansion of PI in k 2.429 * [backup-simplify]: Simplify PI into PI 2.429 * [taylor]: Taking taylor expansion of n in k 2.429 * [backup-simplify]: Simplify n into n 2.430 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.430 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.430 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.430 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.431 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.431 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.431 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 2.431 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.431 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.431 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.431 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.431 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.431 * [taylor]: Taking taylor expansion of 1/2 in n 2.431 * [backup-simplify]: Simplify 1/2 into 1/2 2.431 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.431 * [taylor]: Taking taylor expansion of k in n 2.431 * [backup-simplify]: Simplify k into k 2.431 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.431 * [taylor]: Taking taylor expansion of 1/2 in n 2.431 * [backup-simplify]: Simplify 1/2 into 1/2 2.431 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.432 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.432 * [taylor]: Taking taylor expansion of -2 in n 2.432 * [backup-simplify]: Simplify -2 into -2 2.432 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.432 * [taylor]: Taking taylor expansion of PI in n 2.432 * [backup-simplify]: Simplify PI into PI 2.432 * [taylor]: Taking taylor expansion of n in n 2.432 * [backup-simplify]: Simplify 0 into 0 2.432 * [backup-simplify]: Simplify 1 into 1 2.432 * [backup-simplify]: Simplify (/ PI 1) into PI 2.433 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.434 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.435 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.435 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.438 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.439 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.439 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.439 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.439 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.439 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.439 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.439 * [taylor]: Taking taylor expansion of 1/2 in n 2.439 * [backup-simplify]: Simplify 1/2 into 1/2 2.440 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.440 * [taylor]: Taking taylor expansion of k in n 2.440 * [backup-simplify]: Simplify k into k 2.440 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.440 * [taylor]: Taking taylor expansion of 1/2 in n 2.440 * [backup-simplify]: Simplify 1/2 into 1/2 2.440 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.440 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.440 * [taylor]: Taking taylor expansion of -2 in n 2.440 * [backup-simplify]: Simplify -2 into -2 2.440 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.440 * [taylor]: Taking taylor expansion of PI in n 2.440 * [backup-simplify]: Simplify PI into PI 2.440 * [taylor]: Taking taylor expansion of n in n 2.440 * [backup-simplify]: Simplify 0 into 0 2.440 * [backup-simplify]: Simplify 1 into 1 2.440 * [backup-simplify]: Simplify (/ PI 1) into PI 2.441 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.442 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.442 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.442 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.445 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.446 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.446 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.446 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.446 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.446 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.447 * [taylor]: Taking taylor expansion of 1/2 in k 2.447 * [backup-simplify]: Simplify 1/2 into 1/2 2.447 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.447 * [taylor]: Taking taylor expansion of k in k 2.447 * [backup-simplify]: Simplify 0 into 0 2.447 * [backup-simplify]: Simplify 1 into 1 2.447 * [backup-simplify]: Simplify (/ 1 1) into 1 2.447 * [taylor]: Taking taylor expansion of 1/2 in k 2.447 * [backup-simplify]: Simplify 1/2 into 1/2 2.447 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.447 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.447 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.447 * [taylor]: Taking taylor expansion of -2 in k 2.447 * [backup-simplify]: Simplify -2 into -2 2.447 * [taylor]: Taking taylor expansion of PI in k 2.447 * [backup-simplify]: Simplify PI into PI 2.448 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.449 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.449 * [taylor]: Taking taylor expansion of (log n) in k 2.449 * [taylor]: Taking taylor expansion of n in k 2.449 * [backup-simplify]: Simplify n into n 2.449 * [backup-simplify]: Simplify (log n) into (log n) 2.450 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.450 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.450 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.451 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.453 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.454 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.455 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.456 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.457 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.459 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.459 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.460 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.460 * [backup-simplify]: Simplify (+ 0 0) into 0 2.462 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.463 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.465 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.465 * [taylor]: Taking taylor expansion of 0 in k 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify 0 into 0 2.466 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.467 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.471 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 2.471 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.472 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.472 * [backup-simplify]: Simplify (+ 0 0) into 0 2.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.475 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.478 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.478 * [taylor]: Taking taylor expansion of 0 in k 2.478 * [backup-simplify]: Simplify 0 into 0 2.478 * [backup-simplify]: Simplify 0 into 0 2.478 * [backup-simplify]: Simplify 0 into 0 2.478 * [backup-simplify]: Simplify 0 into 0 2.479 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.481 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.485 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0 2.485 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.486 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.486 * [backup-simplify]: Simplify (+ 0 0) into 0 2.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.488 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.490 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.490 * [taylor]: Taking taylor expansion of 0 in k 2.490 * [backup-simplify]: Simplify 0 into 0 2.490 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 2.493 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.493 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 2.493 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.493 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.493 * [taylor]: Taking taylor expansion of 2 in n 2.493 * [backup-simplify]: Simplify 2 into 2 2.493 * [taylor]: Taking taylor expansion of (* n PI) in n 2.493 * [taylor]: Taking taylor expansion of n in n 2.493 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify 1 into 1 2.493 * [taylor]: Taking taylor expansion of PI in n 2.493 * [backup-simplify]: Simplify PI into PI 2.493 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.493 * [taylor]: Taking taylor expansion of 2 in n 2.493 * [backup-simplify]: Simplify 2 into 2 2.493 * [taylor]: Taking taylor expansion of (* n PI) in n 2.493 * [taylor]: Taking taylor expansion of n in n 2.493 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify 1 into 1 2.493 * [taylor]: Taking taylor expansion of PI in n 2.493 * [backup-simplify]: Simplify PI into PI 2.494 * [backup-simplify]: Simplify (* 0 PI) into 0 2.494 * [backup-simplify]: Simplify (* 2 0) into 0 2.494 * [backup-simplify]: Simplify 0 into 0 2.495 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.496 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.496 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.497 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.497 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.497 * [backup-simplify]: Simplify 0 into 0 2.498 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.499 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.499 * [backup-simplify]: Simplify 0 into 0 2.500 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.500 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.500 * [backup-simplify]: Simplify 0 into 0 2.501 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.502 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.502 * [backup-simplify]: Simplify 0 into 0 2.503 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.504 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.505 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.507 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.507 * [backup-simplify]: Simplify 0 into 0 2.507 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.507 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 2.507 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.507 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.507 * [taylor]: Taking taylor expansion of 2 in n 2.507 * [backup-simplify]: Simplify 2 into 2 2.508 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.508 * [taylor]: Taking taylor expansion of PI in n 2.508 * [backup-simplify]: Simplify PI into PI 2.508 * [taylor]: Taking taylor expansion of n in n 2.508 * [backup-simplify]: Simplify 0 into 0 2.508 * [backup-simplify]: Simplify 1 into 1 2.508 * [backup-simplify]: Simplify (/ PI 1) into PI 2.508 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.508 * [taylor]: Taking taylor expansion of 2 in n 2.508 * [backup-simplify]: Simplify 2 into 2 2.508 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.508 * [taylor]: Taking taylor expansion of PI in n 2.508 * [backup-simplify]: Simplify PI into PI 2.508 * [taylor]: Taking taylor expansion of n in n 2.508 * [backup-simplify]: Simplify 0 into 0 2.508 * [backup-simplify]: Simplify 1 into 1 2.508 * [backup-simplify]: Simplify (/ PI 1) into PI 2.509 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.509 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.510 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.510 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.510 * [backup-simplify]: Simplify 0 into 0 2.511 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.511 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.511 * [backup-simplify]: Simplify 0 into 0 2.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.513 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.513 * [backup-simplify]: Simplify 0 into 0 2.513 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.514 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.514 * [backup-simplify]: Simplify 0 into 0 2.515 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.516 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.516 * [backup-simplify]: Simplify 0 into 0 2.516 * [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 2.517 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.517 * [backup-simplify]: Simplify 0 into 0 2.518 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.518 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 2.518 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.518 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.518 * [taylor]: Taking taylor expansion of -2 in n 2.518 * [backup-simplify]: Simplify -2 into -2 2.518 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.518 * [taylor]: Taking taylor expansion of PI in n 2.518 * [backup-simplify]: Simplify PI into PI 2.518 * [taylor]: Taking taylor expansion of n in n 2.518 * [backup-simplify]: Simplify 0 into 0 2.518 * [backup-simplify]: Simplify 1 into 1 2.518 * [backup-simplify]: Simplify (/ PI 1) into PI 2.518 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.518 * [taylor]: Taking taylor expansion of -2 in n 2.518 * [backup-simplify]: Simplify -2 into -2 2.518 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.518 * [taylor]: Taking taylor expansion of PI in n 2.518 * [backup-simplify]: Simplify PI into PI 2.518 * [taylor]: Taking taylor expansion of n in n 2.518 * [backup-simplify]: Simplify 0 into 0 2.518 * [backup-simplify]: Simplify 1 into 1 2.519 * [backup-simplify]: Simplify (/ PI 1) into PI 2.519 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.519 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.520 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.520 * [backup-simplify]: Simplify 0 into 0 2.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.522 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.522 * [backup-simplify]: Simplify 0 into 0 2.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.523 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.523 * [backup-simplify]: Simplify 0 into 0 2.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.524 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.524 * [backup-simplify]: Simplify 0 into 0 2.525 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.526 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.526 * [backup-simplify]: Simplify 0 into 0 2.527 * [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 2.528 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.528 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.528 * [backup-simplify]: Simplify (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 2.528 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.528 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.528 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.528 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.528 * [taylor]: Taking taylor expansion of k in k 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify 1 into 1 2.529 * [backup-simplify]: Simplify (/ 1 1) into 1 2.529 * [backup-simplify]: Simplify (sqrt 0) into 0 2.530 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.530 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.530 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.530 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.530 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.530 * [taylor]: Taking taylor expansion of 1/2 in k 2.530 * [backup-simplify]: Simplify 1/2 into 1/2 2.530 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.530 * [taylor]: Taking taylor expansion of 1/2 in k 2.530 * [backup-simplify]: Simplify 1/2 into 1/2 2.530 * [taylor]: Taking taylor expansion of k in k 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify 1 into 1 2.530 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.530 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.530 * [taylor]: Taking taylor expansion of 2 in k 2.530 * [backup-simplify]: Simplify 2 into 2 2.530 * [taylor]: Taking taylor expansion of (* n PI) in k 2.530 * [taylor]: Taking taylor expansion of n in k 2.530 * [backup-simplify]: Simplify n into n 2.530 * [taylor]: Taking taylor expansion of PI in k 2.530 * [backup-simplify]: Simplify PI into PI 2.530 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.530 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.530 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.531 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.531 * [backup-simplify]: Simplify (- 0) into 0 2.531 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.531 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.531 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.531 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.531 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.531 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.531 * [taylor]: Taking taylor expansion of k in n 2.532 * [backup-simplify]: Simplify k into k 2.532 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.532 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.532 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.532 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.532 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.532 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.532 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.532 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.532 * [taylor]: Taking taylor expansion of 1/2 in n 2.532 * [backup-simplify]: Simplify 1/2 into 1/2 2.532 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.532 * [taylor]: Taking taylor expansion of 1/2 in n 2.532 * [backup-simplify]: Simplify 1/2 into 1/2 2.532 * [taylor]: Taking taylor expansion of k in n 2.532 * [backup-simplify]: Simplify k into k 2.532 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.532 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.532 * [taylor]: Taking taylor expansion of 2 in n 2.532 * [backup-simplify]: Simplify 2 into 2 2.532 * [taylor]: Taking taylor expansion of (* n PI) in n 2.532 * [taylor]: Taking taylor expansion of n in n 2.532 * [backup-simplify]: Simplify 0 into 0 2.532 * [backup-simplify]: Simplify 1 into 1 2.532 * [taylor]: Taking taylor expansion of PI in n 2.532 * [backup-simplify]: Simplify PI into PI 2.532 * [backup-simplify]: Simplify (* 0 PI) into 0 2.533 * [backup-simplify]: Simplify (* 2 0) into 0 2.534 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.535 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.535 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.536 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.536 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.536 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.537 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.537 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.538 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.538 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.538 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.538 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.538 * [taylor]: Taking taylor expansion of k in n 2.538 * [backup-simplify]: Simplify k into k 2.538 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.538 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.538 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.538 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.538 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.538 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.538 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.538 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.538 * [taylor]: Taking taylor expansion of 1/2 in n 2.538 * [backup-simplify]: Simplify 1/2 into 1/2 2.538 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.538 * [taylor]: Taking taylor expansion of 1/2 in n 2.538 * [backup-simplify]: Simplify 1/2 into 1/2 2.538 * [taylor]: Taking taylor expansion of k in n 2.538 * [backup-simplify]: Simplify k into k 2.538 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.538 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.538 * [taylor]: Taking taylor expansion of 2 in n 2.538 * [backup-simplify]: Simplify 2 into 2 2.538 * [taylor]: Taking taylor expansion of (* n PI) in n 2.538 * [taylor]: Taking taylor expansion of n in n 2.539 * [backup-simplify]: Simplify 0 into 0 2.539 * [backup-simplify]: Simplify 1 into 1 2.539 * [taylor]: Taking taylor expansion of PI in n 2.539 * [backup-simplify]: Simplify PI into PI 2.539 * [backup-simplify]: Simplify (* 0 PI) into 0 2.539 * [backup-simplify]: Simplify (* 2 0) into 0 2.540 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.541 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.542 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.542 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.542 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.542 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.543 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.543 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.544 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) 2.545 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) 2.545 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.545 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.545 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.545 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.545 * [taylor]: Taking taylor expansion of 1/2 in k 2.545 * [backup-simplify]: Simplify 1/2 into 1/2 2.545 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.545 * [taylor]: Taking taylor expansion of 1/2 in k 2.545 * [backup-simplify]: Simplify 1/2 into 1/2 2.545 * [taylor]: Taking taylor expansion of k in k 2.545 * [backup-simplify]: Simplify 0 into 0 2.545 * [backup-simplify]: Simplify 1 into 1 2.545 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.545 * [taylor]: Taking taylor expansion of (log n) in k 2.545 * [taylor]: Taking taylor expansion of n in k 2.545 * [backup-simplify]: Simplify n into n 2.545 * [backup-simplify]: Simplify (log n) into (log n) 2.545 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.545 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.545 * [taylor]: Taking taylor expansion of 2 in k 2.545 * [backup-simplify]: Simplify 2 into 2 2.545 * [taylor]: Taking taylor expansion of PI in k 2.545 * [backup-simplify]: Simplify PI into PI 2.546 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.546 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.547 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.547 * [backup-simplify]: Simplify (- 0) into 0 2.547 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.548 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.548 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.549 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.549 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.549 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.549 * [taylor]: Taking taylor expansion of k in k 2.549 * [backup-simplify]: Simplify 0 into 0 2.549 * [backup-simplify]: Simplify 1 into 1 2.549 * [backup-simplify]: Simplify (/ 1 1) into 1 2.550 * [backup-simplify]: Simplify (sqrt 0) into 0 2.551 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.551 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.551 * [backup-simplify]: Simplify 0 into 0 2.552 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.552 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.553 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.554 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.554 * [backup-simplify]: Simplify (- 0) into 0 2.554 * [backup-simplify]: Simplify (+ 0 0) into 0 2.555 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.556 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.557 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.558 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.558 * [taylor]: Taking taylor expansion of 0 in k 2.558 * [backup-simplify]: Simplify 0 into 0 2.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.559 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.560 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.560 * [backup-simplify]: Simplify (+ 0 0) into 0 2.561 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.561 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.561 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.562 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.564 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.567 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.568 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.568 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.569 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.571 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.572 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.572 * [backup-simplify]: Simplify (- 0) into 0 2.572 * [backup-simplify]: Simplify (+ 0 0) into 0 2.574 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.575 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.578 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.579 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.581 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.581 * [taylor]: Taking taylor expansion of 0 in k 2.581 * [backup-simplify]: Simplify 0 into 0 2.581 * [backup-simplify]: Simplify 0 into 0 2.581 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.588 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.590 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.591 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.595 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.595 * [backup-simplify]: Simplify (+ 0 0) into 0 2.596 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.596 * [backup-simplify]: Simplify (- 0) into 0 2.597 * [backup-simplify]: Simplify (+ 0 0) into 0 2.599 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.603 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 2.612 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.617 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) 2.618 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.620 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.626 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.627 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.627 * [backup-simplify]: Simplify (- 0) into 0 2.628 * [backup-simplify]: Simplify (+ 0 0) into 0 2.629 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.631 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.634 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.634 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.635 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.637 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 2.637 * [taylor]: Taking taylor expansion of 0 in k 2.637 * [backup-simplify]: Simplify 0 into 0 2.637 * [backup-simplify]: Simplify 0 into 0 2.637 * [backup-simplify]: Simplify 0 into 0 2.638 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.642 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.645 * [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 2.647 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.652 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.653 * [backup-simplify]: Simplify (+ 0 0) into 0 2.654 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.654 * [backup-simplify]: Simplify (- 0) into 0 2.655 * [backup-simplify]: Simplify (+ 0 0) into 0 2.657 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.663 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.678 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.685 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) 2.697 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) 2.697 * [backup-simplify]: Simplify (/ (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 2.697 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.697 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.697 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.697 * [taylor]: Taking taylor expansion of k in k 2.697 * [backup-simplify]: Simplify 0 into 0 2.697 * [backup-simplify]: Simplify 1 into 1 2.697 * [backup-simplify]: Simplify (sqrt 0) into 0 2.698 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.698 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.698 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.698 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.698 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.698 * [taylor]: Taking taylor expansion of 1/2 in k 2.698 * [backup-simplify]: Simplify 1/2 into 1/2 2.698 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.698 * [taylor]: Taking taylor expansion of 1/2 in k 2.698 * [backup-simplify]: Simplify 1/2 into 1/2 2.698 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.698 * [taylor]: Taking taylor expansion of k in k 2.698 * [backup-simplify]: Simplify 0 into 0 2.698 * [backup-simplify]: Simplify 1 into 1 2.699 * [backup-simplify]: Simplify (/ 1 1) into 1 2.699 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.699 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.699 * [taylor]: Taking taylor expansion of 2 in k 2.699 * [backup-simplify]: Simplify 2 into 2 2.699 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.699 * [taylor]: Taking taylor expansion of PI in k 2.699 * [backup-simplify]: Simplify PI into PI 2.699 * [taylor]: Taking taylor expansion of n in k 2.699 * [backup-simplify]: Simplify n into n 2.699 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.699 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.699 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.699 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.699 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.700 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.700 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.700 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.700 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.700 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.700 * [taylor]: Taking taylor expansion of k in n 2.700 * [backup-simplify]: Simplify k into k 2.700 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.700 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.700 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.700 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.700 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.700 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.700 * [taylor]: Taking taylor expansion of 1/2 in n 2.700 * [backup-simplify]: Simplify 1/2 into 1/2 2.700 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.700 * [taylor]: Taking taylor expansion of 1/2 in n 2.700 * [backup-simplify]: Simplify 1/2 into 1/2 2.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.700 * [taylor]: Taking taylor expansion of k in n 2.700 * [backup-simplify]: Simplify k into k 2.700 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.700 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.700 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.700 * [taylor]: Taking taylor expansion of 2 in n 2.700 * [backup-simplify]: Simplify 2 into 2 2.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.700 * [taylor]: Taking taylor expansion of PI in n 2.700 * [backup-simplify]: Simplify PI into PI 2.700 * [taylor]: Taking taylor expansion of n in n 2.700 * [backup-simplify]: Simplify 0 into 0 2.700 * [backup-simplify]: Simplify 1 into 1 2.701 * [backup-simplify]: Simplify (/ PI 1) into PI 2.701 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.704 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.704 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.704 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.704 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.705 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.706 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.707 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.707 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.707 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.707 * [taylor]: Taking taylor expansion of k in n 2.707 * [backup-simplify]: Simplify k into k 2.707 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.707 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.707 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.707 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.707 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.707 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.707 * [taylor]: Taking taylor expansion of 1/2 in n 2.707 * [backup-simplify]: Simplify 1/2 into 1/2 2.707 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.707 * [taylor]: Taking taylor expansion of 1/2 in n 2.707 * [backup-simplify]: Simplify 1/2 into 1/2 2.707 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.707 * [taylor]: Taking taylor expansion of k in n 2.707 * [backup-simplify]: Simplify k into k 2.707 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.707 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.707 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.707 * [taylor]: Taking taylor expansion of 2 in n 2.707 * [backup-simplify]: Simplify 2 into 2 2.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.707 * [taylor]: Taking taylor expansion of PI in n 2.707 * [backup-simplify]: Simplify PI into PI 2.707 * [taylor]: Taking taylor expansion of n in n 2.707 * [backup-simplify]: Simplify 0 into 0 2.707 * [backup-simplify]: Simplify 1 into 1 2.708 * [backup-simplify]: Simplify (/ PI 1) into PI 2.708 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.708 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.709 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.709 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.709 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.710 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) 2.711 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.712 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) 2.712 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.712 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.713 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.713 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.713 * [taylor]: Taking taylor expansion of 1/2 in k 2.713 * [backup-simplify]: Simplify 1/2 into 1/2 2.713 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.713 * [taylor]: Taking taylor expansion of 1/2 in k 2.713 * [backup-simplify]: Simplify 1/2 into 1/2 2.713 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.713 * [taylor]: Taking taylor expansion of k in k 2.713 * [backup-simplify]: Simplify 0 into 0 2.713 * [backup-simplify]: Simplify 1 into 1 2.713 * [backup-simplify]: Simplify (/ 1 1) into 1 2.713 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.713 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.713 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.713 * [taylor]: Taking taylor expansion of 2 in k 2.713 * [backup-simplify]: Simplify 2 into 2 2.713 * [taylor]: Taking taylor expansion of PI in k 2.713 * [backup-simplify]: Simplify PI into PI 2.714 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.715 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.715 * [taylor]: Taking taylor expansion of (log n) in k 2.715 * [taylor]: Taking taylor expansion of n in k 2.715 * [backup-simplify]: Simplify n into n 2.715 * [backup-simplify]: Simplify (log n) into (log n) 2.715 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.716 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.716 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.716 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.717 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.719 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.720 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 2.720 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.720 * [taylor]: Taking taylor expansion of k in k 2.720 * [backup-simplify]: Simplify 0 into 0 2.720 * [backup-simplify]: Simplify 1 into 1 2.720 * [backup-simplify]: Simplify (sqrt 0) into 0 2.722 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.723 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.723 * [backup-simplify]: Simplify 0 into 0 2.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.725 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.727 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.727 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.727 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.728 * [backup-simplify]: Simplify (- 0) into 0 2.728 * [backup-simplify]: Simplify (+ 0 0) into 0 2.730 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.731 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.733 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.734 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.734 * [taylor]: Taking taylor expansion of 0 in k 2.734 * [backup-simplify]: Simplify 0 into 0 2.734 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.737 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.740 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.743 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0 2.743 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.744 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.744 * [backup-simplify]: Simplify (- 0) into 0 2.744 * [backup-simplify]: Simplify (+ 0 0) into 0 2.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.746 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.748 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.748 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.750 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.750 * [taylor]: Taking taylor expansion of 0 in k 2.750 * [backup-simplify]: Simplify 0 into 0 2.750 * [backup-simplify]: Simplify 0 into 0 2.750 * [backup-simplify]: Simplify 0 into 0 2.752 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.753 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.754 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.756 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.759 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0 2.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.760 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.760 * [backup-simplify]: Simplify (- 0) into 0 2.760 * [backup-simplify]: Simplify (+ 0 0) into 0 2.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.762 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.764 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.764 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.766 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 2.766 * [taylor]: Taking taylor expansion of 0 in k 2.766 * [backup-simplify]: Simplify 0 into 0 2.766 * [backup-simplify]: Simplify 0 into 0 2.766 * [backup-simplify]: Simplify 0 into 0 2.766 * [backup-simplify]: Simplify 0 into 0 2.768 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.769 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.770 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) 2.773 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) 2.773 * [backup-simplify]: Simplify (/ (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 2.773 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.773 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.773 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.773 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.773 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.773 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.773 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.773 * [taylor]: Taking taylor expansion of 1/2 in k 2.773 * [backup-simplify]: Simplify 1/2 into 1/2 2.773 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.773 * [taylor]: Taking taylor expansion of k in k 2.773 * [backup-simplify]: Simplify 0 into 0 2.773 * [backup-simplify]: Simplify 1 into 1 2.773 * [backup-simplify]: Simplify (/ 1 1) into 1 2.773 * [taylor]: Taking taylor expansion of 1/2 in k 2.773 * [backup-simplify]: Simplify 1/2 into 1/2 2.773 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.773 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.773 * [taylor]: Taking taylor expansion of -2 in k 2.773 * [backup-simplify]: Simplify -2 into -2 2.773 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.774 * [taylor]: Taking taylor expansion of PI in k 2.774 * [backup-simplify]: Simplify PI into PI 2.774 * [taylor]: Taking taylor expansion of n in k 2.774 * [backup-simplify]: Simplify n into n 2.774 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.774 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.774 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.774 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.774 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.774 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.774 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) 2.774 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.774 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.774 * [taylor]: Taking taylor expansion of -1 in k 2.774 * [backup-simplify]: Simplify -1 into -1 2.775 * [taylor]: Taking taylor expansion of k in k 2.775 * [backup-simplify]: Simplify 0 into 0 2.775 * [backup-simplify]: Simplify 1 into 1 2.775 * [backup-simplify]: Simplify (/ -1 1) into -1 2.775 * [backup-simplify]: Simplify (sqrt 0) into 0 2.777 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.777 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 2.777 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.777 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.777 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.777 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.777 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.777 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.777 * [taylor]: Taking taylor expansion of 1/2 in n 2.777 * [backup-simplify]: Simplify 1/2 into 1/2 2.777 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.777 * [taylor]: Taking taylor expansion of k in n 2.777 * [backup-simplify]: Simplify k into k 2.777 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.777 * [taylor]: Taking taylor expansion of 1/2 in n 2.777 * [backup-simplify]: Simplify 1/2 into 1/2 2.777 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.777 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.777 * [taylor]: Taking taylor expansion of -2 in n 2.777 * [backup-simplify]: Simplify -2 into -2 2.777 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.777 * [taylor]: Taking taylor expansion of PI in n 2.777 * [backup-simplify]: Simplify PI into PI 2.777 * [taylor]: Taking taylor expansion of n in n 2.777 * [backup-simplify]: Simplify 0 into 0 2.777 * [backup-simplify]: Simplify 1 into 1 2.778 * [backup-simplify]: Simplify (/ PI 1) into PI 2.779 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.780 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.780 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.780 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.783 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.784 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.784 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.784 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.784 * [taylor]: Taking taylor expansion of -1 in n 2.784 * [backup-simplify]: Simplify -1 into -1 2.784 * [taylor]: Taking taylor expansion of k in n 2.784 * [backup-simplify]: Simplify k into k 2.784 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.784 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.784 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.785 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.786 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.786 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.786 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.786 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.786 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.786 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.786 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.786 * [taylor]: Taking taylor expansion of 1/2 in n 2.786 * [backup-simplify]: Simplify 1/2 into 1/2 2.786 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.786 * [taylor]: Taking taylor expansion of k in n 2.786 * [backup-simplify]: Simplify k into k 2.786 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.786 * [taylor]: Taking taylor expansion of 1/2 in n 2.786 * [backup-simplify]: Simplify 1/2 into 1/2 2.786 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.786 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.786 * [taylor]: Taking taylor expansion of -2 in n 2.786 * [backup-simplify]: Simplify -2 into -2 2.786 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.786 * [taylor]: Taking taylor expansion of PI in n 2.786 * [backup-simplify]: Simplify PI into PI 2.787 * [taylor]: Taking taylor expansion of n in n 2.787 * [backup-simplify]: Simplify 0 into 0 2.787 * [backup-simplify]: Simplify 1 into 1 2.787 * [backup-simplify]: Simplify (/ PI 1) into PI 2.788 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.789 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.789 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.789 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.790 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.792 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 2.793 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.793 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.793 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.793 * [taylor]: Taking taylor expansion of -1 in n 2.793 * [backup-simplify]: Simplify -1 into -1 2.793 * [taylor]: Taking taylor expansion of k in n 2.793 * [backup-simplify]: Simplify k into k 2.793 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.793 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.793 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.793 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.795 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) 2.795 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.795 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.795 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.795 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.795 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.795 * [taylor]: Taking taylor expansion of 1/2 in k 2.795 * [backup-simplify]: Simplify 1/2 into 1/2 2.795 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.795 * [taylor]: Taking taylor expansion of k in k 2.795 * [backup-simplify]: Simplify 0 into 0 2.795 * [backup-simplify]: Simplify 1 into 1 2.796 * [backup-simplify]: Simplify (/ 1 1) into 1 2.796 * [taylor]: Taking taylor expansion of 1/2 in k 2.796 * [backup-simplify]: Simplify 1/2 into 1/2 2.796 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.796 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.796 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.796 * [taylor]: Taking taylor expansion of -2 in k 2.796 * [backup-simplify]: Simplify -2 into -2 2.796 * [taylor]: Taking taylor expansion of PI in k 2.796 * [backup-simplify]: Simplify PI into PI 2.796 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.798 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.798 * [taylor]: Taking taylor expansion of (log n) in k 2.798 * [taylor]: Taking taylor expansion of n in k 2.798 * [backup-simplify]: Simplify n into n 2.798 * [backup-simplify]: Simplify (log n) into (log n) 2.798 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.799 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.799 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.800 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.801 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.802 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) 2.802 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.802 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.802 * [taylor]: Taking taylor expansion of -1 in k 2.802 * [backup-simplify]: Simplify -1 into -1 2.802 * [taylor]: Taking taylor expansion of k in k 2.802 * [backup-simplify]: Simplify 0 into 0 2.802 * [backup-simplify]: Simplify 1 into 1 2.803 * [backup-simplify]: Simplify (/ -1 1) into -1 2.803 * [backup-simplify]: Simplify (sqrt 0) into 0 2.805 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.806 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.807 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 2.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.809 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.811 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.812 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.812 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.813 * [backup-simplify]: Simplify (+ 0 0) into 0 2.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.815 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.817 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.819 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 2.819 * [taylor]: Taking taylor expansion of 0 in k 2.819 * [backup-simplify]: Simplify 0 into 0 2.819 * [backup-simplify]: Simplify 0 into 0 2.820 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.823 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.829 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.830 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.831 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.832 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.836 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0 2.837 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.838 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.838 * [backup-simplify]: Simplify (+ 0 0) into 0 2.840 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.841 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.844 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.844 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.845 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.846 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 2.846 * [taylor]: Taking taylor expansion of 0 in k 2.846 * [backup-simplify]: Simplify 0 into 0 2.847 * [backup-simplify]: Simplify 0 into 0 2.847 * [backup-simplify]: Simplify 0 into 0 2.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.851 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.855 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.857 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) 2.862 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.862 * * * [progress]: simplifying candidates 2.862 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.862 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.863 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.863 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 2.863 * * * * [progress]: [ 11 / 445 ] simplifiying candidate # 2.863 * * * * [progress]: [ 12 / 445 ] simplifiying candidate # 2.863 * * * * [progress]: [ 13 / 445 ] simplifiying candidate # 2.863 * * * * [progress]: [ 14 / 445 ] simplifiying candidate # 2.863 * * * * 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46 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 47 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 48 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 49 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 50 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 51 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 52 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 53 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 54 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 55 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 56 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 57 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 58 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 59 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 60 / 445 ] simplifiying candidate # 2.866 * * * * [progress]: [ 61 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 62 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 63 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 64 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 65 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 66 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 67 / 445 ] simplifiying candidate #real (real->posit16 (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) (sqrt k)))> 2.867 * * * * [progress]: [ 68 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 69 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 70 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 71 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 72 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 73 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 74 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 75 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 76 / 445 ] simplifiying candidate # 2.867 * * * * [progress]: [ 77 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 78 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 79 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 80 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 81 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 82 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 83 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 84 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 85 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 86 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 87 / 445 ] simplifiying candidate #real (real->posit16 (* PI (* n 2)))) (- 1/2 (/ k 2))) (sqrt k)))> 2.868 * * * * [progress]: [ 88 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 89 / 445 ] simplifiying candidate # 2.868 * * * * [progress]: [ 90 / 445 ] simplifiying candidate # 2.868 * 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candidate # 2.898 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 2.898 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 2.898 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 2.912 * [simplify]: Simplifying: (expm1 (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (log1p (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) (* (+ (log PI) (+ (log n) (log 2))) (- 1/2 (/ k 2))) (* (+ (log PI) (log (* n 2))) (- 1/2 (/ k 2))) (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (* (log (* PI (* n 2))) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* PI (* n 2)) 1/2) (pow (* PI (* n 2)) (/ k 2)) (pow (* PI (* n 2)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* PI (* n 2)) (sqrt (- 1/2 (/ k 2)))) (pow (* PI (* n 2)) 1) (pow (* PI (* n 2)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* PI (* n 2)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* PI (* n 2)) 1) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* PI (* n 2)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (pow (* PI (* n 2)) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (cbrt 2))) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* PI (* n 2)) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* PI (* n 2)) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* PI (* n 2)) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* PI (* n 2)) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* PI (* n 2)) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* PI (* n 2)) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* PI (* n 2)) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* PI (* n 2)) (fma (- (/ 1 2)) k (* (/ 1 2) k))) (pow (* PI (* n 2)) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* PI (* n 2)) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) 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(* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 2.928 * * [simplify]: iteration 1: (698 enodes) 3.245 * * [simplify]: iteration 2: (1515 enodes) 4.656 * * [simplify]: Extracting #0: cost 212 inf + 0 4.660 * * [simplify]: Extracting #1: cost 835 inf + 1 4.669 * * [simplify]: Extracting #2: cost 1371 inf + 2843 4.691 * * [simplify]: Extracting #3: cost 1490 inf + 50740 4.743 * * [simplify]: Extracting #4: cost 1165 inf + 173880 4.803 * * [simplify]: Extracting #5: cost 717 inf + 363097 4.921 * * [simplify]: Extracting #6: cost 398 inf + 548093 5.050 * * [simplify]: Extracting #7: cost 79 inf + 764685 5.271 * * [simplify]: Extracting #8: cost 2 inf + 822930 5.477 * * [simplify]: Extracting #9: cost 0 inf + 824546 5.644 * * [simplify]: Extracting #10: cost 0 inf + 824451 5.855 * * [simplify]: Extracting #11: cost 0 inf + 824426 6.031 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (log1p (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (* (- 1/2 (* 1/2 k)) 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(fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (cbrt 2)) (/ -1 (* (cbrt 2) (cbrt 2))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (* (/ (sqrt k) (sqrt 2)) (+ (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (cbrt 2)) (/ -1 (* (cbrt 2) (cbrt 2))) (/ (/ k (cbrt 2)) (* (cbrt 2) (cbrt 2)))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2))))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (fma -1/2 k (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (* -1/2 k))) (/ (sqrt k) (pow (* (* 2 n) PI) (* -1/2 k))) (/ (sqrt k) (pow (* 2 n) (- 1/2 (* 1/2 k)))) (/ (sqrt k) (cbrt (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))))) (/ (sqrt k) (sqrt (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/4 (/ k 4)))) (* (pow (* (* 2 n) PI) (* 1/2 k)) (sqrt k)) (real->posit16 (/ (pow (* (* 2 n) PI) (- 1/2 (* 1/2 k))) (sqrt k))) (fma (* 1/4 (log (* PI 2))) (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k)) (- (fma (* 1/8 (exp (* (log (* (* 2 n) PI)) 1/2))) (* (* (log n) k) (* (log n) k)) (fma 1/8 (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) (* (log (* PI 2)) (log (* PI 2))))) (exp (* (log (* (* 2 n) PI)) 1/2)))) (* (* k (+ (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* (log (* PI 2)) (exp (* (log (* (* 2 n) PI)) 1/2))))) 1/2))) (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (fma +nan.0 (* (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k)) (log (* PI 2))) (- (- (* (log (* PI 2)) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) +nan.0))) (fma (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* (log n) k) (* (log n) k)) (- (- (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) k) (+ (- (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0) (* (* (log (* PI 2)) (log (* PI 2))) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) +nan.0)))) (+ (- (* +nan.0 (* (* (exp (* (log (* (* 2 n) PI)) 1/2)) (log n)) (* k k))) (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* (* k k) +nan.0))) (- (* +nan.0 (* (exp (* (log (* (* 2 n) PI)) 1/2)) (* k (log (* PI 2))))) (* (* (log n) k) (* (exp (* (log (* (* 2 n) PI)) 1/2)) +nan.0)))))))))))) (- (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) (* k (* k k)))) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) k) (/ (exp (* (- 1/2 (* 1/2 k)) (log (* (* 2 n) PI)))) (* k k)))))) (+ (* (- +nan.0) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k)) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))))) 6.158 * * * [progress]: adding candidates to table 9.095 * * [progress]: iteration 2 / 4 9.095 * * * [progress]: picking best candidate 9.143 * * * * [pick]: Picked # 9.144 * * * [progress]: localizing error 9.204 * * * [progress]: generating rewritten candidates 9.204 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 9.223 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 9.237 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 9.271 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 9.337 * * * [progress]: generating series expansions 9.337 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 9.337 * [backup-simplify]: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 9.337 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 9.337 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 9.337 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 9.337 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 9.337 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.337 * [taylor]: Taking taylor expansion of 1/2 in k 9.337 * [backup-simplify]: Simplify 1/2 into 1/2 9.337 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.337 * [taylor]: Taking taylor expansion of 1/2 in k 9.337 * [backup-simplify]: Simplify 1/2 into 1/2 9.337 * [taylor]: Taking taylor expansion of k in k 9.337 * [backup-simplify]: Simplify 0 into 0 9.337 * [backup-simplify]: Simplify 1 into 1 9.337 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 9.337 * [taylor]: Taking taylor expansion of (* 2 n) in k 9.337 * [taylor]: Taking taylor expansion of 2 in k 9.337 * [backup-simplify]: Simplify 2 into 2 9.337 * [taylor]: Taking taylor expansion of n in k 9.337 * [backup-simplify]: Simplify n into n 9.337 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 9.337 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 9.338 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.338 * [backup-simplify]: Simplify (- 0) into 0 9.339 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.339 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 9.339 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 9.339 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 9.339 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 9.339 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 9.339 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 9.339 * [taylor]: Taking taylor expansion of 1/2 in n 9.339 * [backup-simplify]: Simplify 1/2 into 1/2 9.339 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 9.339 * [taylor]: Taking taylor expansion of 1/2 in n 9.339 * [backup-simplify]: Simplify 1/2 into 1/2 9.339 * [taylor]: Taking taylor expansion of k in n 9.339 * [backup-simplify]: Simplify k into k 9.339 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 9.339 * [taylor]: Taking taylor expansion of (* 2 n) in n 9.339 * [taylor]: Taking taylor expansion of 2 in n 9.339 * [backup-simplify]: Simplify 2 into 2 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 (* 2 0) into 0 9.340 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 9.340 * [backup-simplify]: Simplify (log 2) into (log 2) 9.340 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 9.340 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 9.340 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 9.341 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.341 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 9.341 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 9.341 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 9.341 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 9.341 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 9.341 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 9.342 * [taylor]: Taking taylor expansion of 1/2 in n 9.342 * [backup-simplify]: Simplify 1/2 into 1/2 9.342 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 9.342 * [taylor]: Taking taylor expansion of 1/2 in n 9.342 * [backup-simplify]: Simplify 1/2 into 1/2 9.342 * [taylor]: Taking taylor expansion of k in n 9.342 * [backup-simplify]: Simplify k into k 9.342 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 9.342 * [taylor]: Taking taylor expansion of (* 2 n) in n 9.342 * [taylor]: Taking taylor expansion of 2 in n 9.342 * [backup-simplify]: Simplify 2 into 2 9.342 * [taylor]: Taking taylor expansion of n in n 9.342 * [backup-simplify]: Simplify 0 into 0 9.342 * [backup-simplify]: Simplify 1 into 1 9.342 * [backup-simplify]: Simplify (* 2 0) into 0 9.342 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 9.343 * [backup-simplify]: Simplify (log 2) into (log 2) 9.343 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 9.343 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 9.343 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 9.343 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.344 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 9.344 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 9.344 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 9.344 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 9.344 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 9.344 * [taylor]: Taking taylor expansion of (log 2) in k 9.344 * [taylor]: Taking taylor expansion of 2 in k 9.344 * [backup-simplify]: Simplify 2 into 2 9.344 * [backup-simplify]: Simplify (log 2) into (log 2) 9.344 * [taylor]: Taking taylor expansion of (log n) in k 9.344 * [taylor]: Taking taylor expansion of n in k 9.344 * [backup-simplify]: Simplify n into n 9.345 * [backup-simplify]: Simplify (log n) into (log n) 9.345 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.345 * [taylor]: Taking taylor expansion of 1/2 in k 9.345 * [backup-simplify]: Simplify 1/2 into 1/2 9.345 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.345 * [taylor]: Taking taylor expansion of 1/2 in k 9.345 * [backup-simplify]: Simplify 1/2 into 1/2 9.345 * [taylor]: Taking taylor expansion of k in k 9.345 * [backup-simplify]: Simplify 0 into 0 9.345 * [backup-simplify]: Simplify 1 into 1 9.345 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 9.345 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.345 * [backup-simplify]: Simplify (- 0) into 0 9.346 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.346 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 9.346 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 9.347 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 9.347 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 9.348 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 9.348 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 9.349 * [backup-simplify]: Simplify (- 0) into 0 9.349 * [backup-simplify]: Simplify (+ 0 0) into 0 9.349 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.350 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 9.350 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.350 * [taylor]: Taking taylor expansion of 0 in k 9.350 * [backup-simplify]: Simplify 0 into 0 9.350 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 9.351 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.352 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.353 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 9.354 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.355 * [backup-simplify]: Simplify (+ 0 0) into 0 9.356 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 9.357 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 9.359 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 9.360 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 9.363 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 9.364 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 9.364 * [backup-simplify]: Simplify (- 0) into 0 9.364 * [backup-simplify]: Simplify (+ 0 0) into 0 9.365 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.366 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 9.368 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.368 * [taylor]: Taking taylor expansion of 0 in k 9.368 * [backup-simplify]: Simplify 0 into 0 9.368 * [backup-simplify]: Simplify 0 into 0 9.368 * [backup-simplify]: Simplify 0 into 0 9.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 9.370 * [backup-simplify]: Simplify (- 0) into 0 9.370 * [backup-simplify]: Simplify (+ 0 0) into 0 9.373 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 9.375 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.375 * [backup-simplify]: Simplify (+ 0 0) into 0 9.376 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 9.379 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 9.381 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 9.386 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 9.387 * [backup-simplify]: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 9.387 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 9.387 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 9.387 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 9.387 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 9.387 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.387 * [taylor]: Taking taylor expansion of 1/2 in k 9.387 * [backup-simplify]: Simplify 1/2 into 1/2 9.387 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.387 * [taylor]: Taking taylor expansion of 1/2 in k 9.387 * [backup-simplify]: Simplify 1/2 into 1/2 9.387 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.387 * [taylor]: Taking taylor expansion of k in k 9.387 * [backup-simplify]: Simplify 0 into 0 9.387 * [backup-simplify]: Simplify 1 into 1 9.388 * [backup-simplify]: Simplify (/ 1 1) into 1 9.388 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 9.388 * [taylor]: Taking taylor expansion of (/ 2 n) in k 9.388 * [taylor]: Taking taylor expansion of 2 in k 9.388 * [backup-simplify]: Simplify 2 into 2 9.388 * [taylor]: Taking taylor expansion of n in k 9.388 * [backup-simplify]: Simplify n into n 9.388 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 9.388 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 9.388 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.389 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.389 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.389 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 9.389 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 9.389 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 9.389 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 9.389 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 9.389 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 9.389 * [taylor]: Taking taylor expansion of 1/2 in n 9.389 * [backup-simplify]: Simplify 1/2 into 1/2 9.389 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.390 * [taylor]: Taking taylor expansion of 1/2 in n 9.390 * [backup-simplify]: Simplify 1/2 into 1/2 9.390 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.390 * [taylor]: Taking taylor expansion of k in n 9.390 * [backup-simplify]: Simplify k into k 9.390 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.390 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 9.390 * [taylor]: Taking taylor expansion of (/ 2 n) in n 9.390 * [taylor]: Taking taylor expansion of 2 in n 9.390 * [backup-simplify]: Simplify 2 into 2 9.390 * [taylor]: Taking taylor expansion of n in n 9.390 * [backup-simplify]: Simplify 0 into 0 9.390 * [backup-simplify]: Simplify 1 into 1 9.390 * [backup-simplify]: Simplify (/ 2 1) into 2 9.391 * [backup-simplify]: Simplify (log 2) into (log 2) 9.391 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.391 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 9.391 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 9.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.392 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 9.393 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.393 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 9.393 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 9.393 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 9.393 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 9.393 * [taylor]: Taking taylor expansion of 1/2 in n 9.393 * [backup-simplify]: Simplify 1/2 into 1/2 9.393 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.393 * [taylor]: Taking taylor expansion of 1/2 in n 9.393 * [backup-simplify]: Simplify 1/2 into 1/2 9.393 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.393 * [taylor]: Taking taylor expansion of k in n 9.393 * [backup-simplify]: Simplify k into k 9.393 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.393 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 9.393 * [taylor]: Taking taylor expansion of (/ 2 n) in n 9.393 * [taylor]: Taking taylor expansion of 2 in n 9.393 * [backup-simplify]: Simplify 2 into 2 9.393 * [taylor]: Taking taylor expansion of n in n 9.393 * [backup-simplify]: Simplify 0 into 0 9.393 * [backup-simplify]: Simplify 1 into 1 9.394 * [backup-simplify]: Simplify (/ 2 1) into 2 9.394 * [backup-simplify]: Simplify (log 2) into (log 2) 9.394 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.394 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 9.395 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 9.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.396 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 9.396 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.397 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 9.397 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 9.397 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.397 * [taylor]: Taking taylor expansion of 1/2 in k 9.397 * [backup-simplify]: Simplify 1/2 into 1/2 9.397 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.397 * [taylor]: Taking taylor expansion of 1/2 in k 9.397 * [backup-simplify]: Simplify 1/2 into 1/2 9.397 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.397 * [taylor]: Taking taylor expansion of k in k 9.397 * [backup-simplify]: Simplify 0 into 0 9.397 * [backup-simplify]: Simplify 1 into 1 9.397 * [backup-simplify]: Simplify (/ 1 1) into 1 9.397 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 9.398 * [taylor]: Taking taylor expansion of (log 2) in k 9.398 * [taylor]: Taking taylor expansion of 2 in k 9.398 * [backup-simplify]: Simplify 2 into 2 9.398 * [backup-simplify]: Simplify (log 2) into (log 2) 9.398 * [taylor]: Taking taylor expansion of (log n) in k 9.398 * [taylor]: Taking taylor expansion of n in k 9.398 * [backup-simplify]: Simplify n into n 9.398 * [backup-simplify]: Simplify (log n) into (log n) 9.399 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.399 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.399 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.399 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.400 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 9.400 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 9.400 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.401 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 9.402 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 9.402 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.403 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 9.403 * [backup-simplify]: Simplify (- 0) into 0 9.403 * [backup-simplify]: Simplify (+ 0 0) into 0 9.404 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.404 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 9.405 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.405 * [taylor]: Taking taylor expansion of 0 in k 9.405 * [backup-simplify]: Simplify 0 into 0 9.405 * [backup-simplify]: Simplify 0 into 0 9.405 * [backup-simplify]: Simplify 0 into 0 9.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.407 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 9.407 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.408 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 9.408 * [backup-simplify]: Simplify (- 0) into 0 9.408 * [backup-simplify]: Simplify (+ 0 0) into 0 9.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.409 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 9.410 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.411 * [taylor]: Taking taylor expansion of 0 in k 9.411 * [backup-simplify]: Simplify 0 into 0 9.411 * [backup-simplify]: Simplify 0 into 0 9.411 * [backup-simplify]: Simplify 0 into 0 9.411 * [backup-simplify]: Simplify 0 into 0 9.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.414 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 9.414 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.424 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 9.424 * [backup-simplify]: Simplify (- 0) into 0 9.424 * [backup-simplify]: Simplify (+ 0 0) into 0 9.425 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.426 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 9.427 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.427 * [taylor]: Taking taylor expansion of 0 in k 9.427 * [backup-simplify]: Simplify 0 into 0 9.427 * [backup-simplify]: Simplify 0 into 0 9.428 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 9.428 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 9.428 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 9.428 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 9.428 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 9.428 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 9.428 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.428 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.428 * [taylor]: Taking taylor expansion of 1/2 in k 9.428 * [backup-simplify]: Simplify 1/2 into 1/2 9.428 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.428 * [taylor]: Taking taylor expansion of k in k 9.428 * [backup-simplify]: Simplify 0 into 0 9.428 * [backup-simplify]: Simplify 1 into 1 9.428 * [backup-simplify]: Simplify (/ 1 1) into 1 9.428 * [taylor]: Taking taylor expansion of 1/2 in k 9.428 * [backup-simplify]: Simplify 1/2 into 1/2 9.428 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 9.428 * [taylor]: Taking taylor expansion of (/ -2 n) in k 9.428 * [taylor]: Taking taylor expansion of -2 in k 9.428 * [backup-simplify]: Simplify -2 into -2 9.428 * [taylor]: Taking taylor expansion of n in k 9.428 * [backup-simplify]: Simplify n into n 9.428 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 9.428 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 9.429 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.429 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.429 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 9.429 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 9.429 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 9.429 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 9.429 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 9.429 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 9.429 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.429 * [taylor]: Taking taylor expansion of 1/2 in n 9.429 * [backup-simplify]: Simplify 1/2 into 1/2 9.429 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.429 * [taylor]: Taking taylor expansion of k in n 9.429 * [backup-simplify]: Simplify k into k 9.429 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.429 * [taylor]: Taking taylor expansion of 1/2 in n 9.429 * [backup-simplify]: Simplify 1/2 into 1/2 9.429 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 9.429 * [taylor]: Taking taylor expansion of (/ -2 n) in n 9.429 * [taylor]: Taking taylor expansion of -2 in n 9.429 * [backup-simplify]: Simplify -2 into -2 9.429 * [taylor]: Taking taylor expansion of n in n 9.429 * [backup-simplify]: Simplify 0 into 0 9.429 * [backup-simplify]: Simplify 1 into 1 9.430 * [backup-simplify]: Simplify (/ -2 1) into -2 9.430 * [backup-simplify]: Simplify (log -2) into (log -2) 9.430 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.430 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 9.431 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.431 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 9.432 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.432 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 9.432 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 9.432 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 9.432 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 9.432 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.432 * [taylor]: Taking taylor expansion of 1/2 in n 9.432 * [backup-simplify]: Simplify 1/2 into 1/2 9.432 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.432 * [taylor]: Taking taylor expansion of k in n 9.432 * [backup-simplify]: Simplify k into k 9.432 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.432 * [taylor]: Taking taylor expansion of 1/2 in n 9.432 * [backup-simplify]: Simplify 1/2 into 1/2 9.432 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 9.432 * [taylor]: Taking taylor expansion of (/ -2 n) in n 9.432 * [taylor]: Taking taylor expansion of -2 in n 9.432 * [backup-simplify]: Simplify -2 into -2 9.432 * [taylor]: Taking taylor expansion of n in n 9.432 * [backup-simplify]: Simplify 0 into 0 9.432 * [backup-simplify]: Simplify 1 into 1 9.433 * [backup-simplify]: Simplify (/ -2 1) into -2 9.433 * [backup-simplify]: Simplify (log -2) into (log -2) 9.433 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.433 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 9.434 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.435 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 9.435 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.436 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 9.436 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 9.436 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.436 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.436 * [taylor]: Taking taylor expansion of 1/2 in k 9.436 * [backup-simplify]: Simplify 1/2 into 1/2 9.436 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.436 * [taylor]: Taking taylor expansion of k in k 9.436 * [backup-simplify]: Simplify 0 into 0 9.436 * [backup-simplify]: Simplify 1 into 1 9.436 * [backup-simplify]: Simplify (/ 1 1) into 1 9.436 * [taylor]: Taking taylor expansion of 1/2 in k 9.436 * [backup-simplify]: Simplify 1/2 into 1/2 9.436 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 9.436 * [taylor]: Taking taylor expansion of (log -2) in k 9.436 * [taylor]: Taking taylor expansion of -2 in k 9.436 * [backup-simplify]: Simplify -2 into -2 9.437 * [backup-simplify]: Simplify (log -2) into (log -2) 9.437 * [taylor]: Taking taylor expansion of (log n) in k 9.437 * [taylor]: Taking taylor expansion of n in k 9.437 * [backup-simplify]: Simplify n into n 9.437 * [backup-simplify]: Simplify (log n) into (log n) 9.437 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.438 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.438 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.438 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 9.439 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 9.439 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.440 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.441 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 9.442 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 9.442 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.443 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 9.443 * [backup-simplify]: Simplify (+ 0 0) into 0 9.444 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.445 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 9.446 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.446 * [taylor]: Taking taylor expansion of 0 in k 9.446 * [backup-simplify]: Simplify 0 into 0 9.446 * [backup-simplify]: Simplify 0 into 0 9.446 * [backup-simplify]: Simplify 0 into 0 9.448 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.451 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 9.451 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.452 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 9.452 * [backup-simplify]: Simplify (+ 0 0) into 0 9.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.454 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 9.456 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.456 * [taylor]: Taking taylor expansion of 0 in k 9.456 * [backup-simplify]: Simplify 0 into 0 9.456 * [backup-simplify]: Simplify 0 into 0 9.456 * [backup-simplify]: Simplify 0 into 0 9.456 * [backup-simplify]: Simplify 0 into 0 9.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.463 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 9.463 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.465 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 9.465 * [backup-simplify]: Simplify (+ 0 0) into 0 9.466 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.467 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 9.470 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.470 * [taylor]: Taking taylor expansion of 0 in k 9.470 * [backup-simplify]: Simplify 0 into 0 9.470 * [backup-simplify]: Simplify 0 into 0 9.471 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 9.471 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 9.471 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 9.471 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 9.471 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 9.471 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 9.471 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 9.471 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.471 * [taylor]: Taking taylor expansion of 1/2 in k 9.471 * [backup-simplify]: Simplify 1/2 into 1/2 9.471 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.471 * [taylor]: Taking taylor expansion of 1/2 in k 9.471 * [backup-simplify]: Simplify 1/2 into 1/2 9.472 * [taylor]: Taking taylor expansion of k in k 9.472 * [backup-simplify]: Simplify 0 into 0 9.472 * [backup-simplify]: Simplify 1 into 1 9.472 * [taylor]: Taking taylor expansion of (log PI) in k 9.472 * [taylor]: Taking taylor expansion of PI in k 9.472 * [backup-simplify]: Simplify PI into PI 9.472 * [backup-simplify]: Simplify (log PI) into (log PI) 9.473 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.473 * [backup-simplify]: Simplify (- 0) into 0 9.474 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.475 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.476 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 9.476 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 9.476 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 9.476 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 9.476 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.476 * [taylor]: Taking taylor expansion of 1/2 in k 9.476 * [backup-simplify]: Simplify 1/2 into 1/2 9.476 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.476 * [taylor]: Taking taylor expansion of 1/2 in k 9.476 * [backup-simplify]: Simplify 1/2 into 1/2 9.476 * [taylor]: Taking taylor expansion of k in k 9.476 * [backup-simplify]: Simplify 0 into 0 9.476 * [backup-simplify]: Simplify 1 into 1 9.476 * [taylor]: Taking taylor expansion of (log PI) in k 9.476 * [taylor]: Taking taylor expansion of PI in k 9.476 * [backup-simplify]: Simplify PI into PI 9.476 * [backup-simplify]: Simplify (log PI) into (log PI) 9.476 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.477 * [backup-simplify]: Simplify (- 0) into 0 9.477 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.478 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.479 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 9.479 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 9.480 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 9.480 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 9.481 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.481 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.482 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 9.488 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 9.489 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 9.491 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 9.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 9.492 * [backup-simplify]: Simplify (- 0) into 0 9.492 * [backup-simplify]: Simplify (+ 0 0) into 0 9.493 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 9.504 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 9.507 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 9.514 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 9.514 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 9.514 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 9.514 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 9.514 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 9.514 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 9.514 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.514 * [taylor]: Taking taylor expansion of 1/2 in k 9.514 * [backup-simplify]: Simplify 1/2 into 1/2 9.514 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.514 * [taylor]: Taking taylor expansion of 1/2 in k 9.514 * [backup-simplify]: Simplify 1/2 into 1/2 9.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.514 * [taylor]: Taking taylor expansion of k in k 9.514 * [backup-simplify]: Simplify 0 into 0 9.514 * [backup-simplify]: Simplify 1 into 1 9.515 * [backup-simplify]: Simplify (/ 1 1) into 1 9.515 * [taylor]: Taking taylor expansion of (log PI) in k 9.515 * [taylor]: Taking taylor expansion of PI in k 9.515 * [backup-simplify]: Simplify PI into PI 9.515 * [backup-simplify]: Simplify (log PI) into (log PI) 9.516 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.516 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.517 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.518 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 9.518 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 9.518 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 9.518 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 9.518 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 9.518 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.518 * [taylor]: Taking taylor expansion of 1/2 in k 9.518 * [backup-simplify]: Simplify 1/2 into 1/2 9.518 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.518 * [taylor]: Taking taylor expansion of 1/2 in k 9.518 * [backup-simplify]: Simplify 1/2 into 1/2 9.518 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.518 * [taylor]: Taking taylor expansion of k in k 9.518 * [backup-simplify]: Simplify 0 into 0 9.519 * [backup-simplify]: Simplify 1 into 1 9.519 * [backup-simplify]: Simplify (/ 1 1) into 1 9.519 * [taylor]: Taking taylor expansion of (log PI) in k 9.519 * [taylor]: Taking taylor expansion of PI in k 9.519 * [backup-simplify]: Simplify PI into PI 9.519 * [backup-simplify]: Simplify (log PI) into (log PI) 9.520 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.520 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.521 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.522 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 9.522 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 9.522 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 9.523 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 9.523 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 9.523 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 9.523 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 9.523 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 9.523 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.523 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.523 * [taylor]: Taking taylor expansion of 1/2 in k 9.523 * [backup-simplify]: Simplify 1/2 into 1/2 9.523 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.523 * [taylor]: Taking taylor expansion of k in k 9.523 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify 1 into 1 9.524 * [backup-simplify]: Simplify (/ 1 1) into 1 9.524 * [taylor]: Taking taylor expansion of 1/2 in k 9.524 * [backup-simplify]: Simplify 1/2 into 1/2 9.524 * [taylor]: Taking taylor expansion of (log PI) in k 9.524 * [taylor]: Taking taylor expansion of PI in k 9.524 * [backup-simplify]: Simplify PI into PI 9.524 * [backup-simplify]: Simplify (log PI) into (log PI) 9.525 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.525 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.526 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.527 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 9.527 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 9.527 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 9.527 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 9.527 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.527 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.527 * [taylor]: Taking taylor expansion of 1/2 in k 9.527 * [backup-simplify]: Simplify 1/2 into 1/2 9.527 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.527 * [taylor]: Taking taylor expansion of k in k 9.527 * [backup-simplify]: Simplify 0 into 0 9.527 * [backup-simplify]: Simplify 1 into 1 9.528 * [backup-simplify]: Simplify (/ 1 1) into 1 9.528 * [taylor]: Taking taylor expansion of 1/2 in k 9.528 * [backup-simplify]: Simplify 1/2 into 1/2 9.528 * [taylor]: Taking taylor expansion of (log PI) in k 9.528 * [taylor]: Taking taylor expansion of PI in k 9.528 * [backup-simplify]: Simplify PI into PI 9.528 * [backup-simplify]: Simplify (log PI) into (log PI) 9.529 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.529 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.530 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.531 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 9.531 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify 0 into 0 9.531 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 9.531 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 9.532 * [backup-simplify]: Simplify (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) 9.532 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) in (k) around 0 9.532 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) in k 9.532 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 9.532 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 9.532 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 9.532 * [taylor]: Taking taylor expansion of 1/4 in k 9.532 * [backup-simplify]: Simplify 1/4 into 1/4 9.532 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 9.532 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.532 * [taylor]: Taking taylor expansion of k in k 9.532 * [backup-simplify]: Simplify 0 into 0 9.532 * [backup-simplify]: Simplify 1 into 1 9.532 * [backup-simplify]: Simplify (/ 1 1) into 1 9.533 * [backup-simplify]: Simplify (log 1) into 0 9.533 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.533 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 9.533 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 9.533 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 9.533 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 9.533 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 9.533 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.533 * [taylor]: Taking taylor expansion of 1/2 in k 9.533 * [backup-simplify]: Simplify 1/2 into 1/2 9.534 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.534 * [taylor]: Taking taylor expansion of 1/2 in k 9.534 * [backup-simplify]: Simplify 1/2 into 1/2 9.534 * [taylor]: Taking taylor expansion of k in k 9.534 * [backup-simplify]: Simplify 0 into 0 9.534 * [backup-simplify]: Simplify 1 into 1 9.534 * [taylor]: Taking taylor expansion of (log PI) in k 9.534 * [taylor]: Taking taylor expansion of PI in k 9.534 * [backup-simplify]: Simplify PI into PI 9.534 * [backup-simplify]: Simplify (log PI) into (log PI) 9.535 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.535 * [backup-simplify]: Simplify (- 0) into 0 9.535 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.536 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.538 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 9.538 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) in k 9.538 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 9.538 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 9.538 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 9.538 * [taylor]: Taking taylor expansion of 1/4 in k 9.538 * [backup-simplify]: Simplify 1/4 into 1/4 9.538 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 9.538 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.538 * [taylor]: Taking taylor expansion of k in k 9.538 * [backup-simplify]: Simplify 0 into 0 9.538 * [backup-simplify]: Simplify 1 into 1 9.539 * [backup-simplify]: Simplify (/ 1 1) into 1 9.539 * [backup-simplify]: Simplify (log 1) into 0 9.540 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.540 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 9.540 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 9.540 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 9.540 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 9.540 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 9.540 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.540 * [taylor]: Taking taylor expansion of 1/2 in k 9.540 * [backup-simplify]: Simplify 1/2 into 1/2 9.540 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.540 * [taylor]: Taking taylor expansion of 1/2 in k 9.540 * [backup-simplify]: Simplify 1/2 into 1/2 9.540 * [taylor]: Taking taylor expansion of k in k 9.540 * [backup-simplify]: Simplify 0 into 0 9.540 * [backup-simplify]: Simplify 1 into 1 9.540 * [taylor]: Taking taylor expansion of (log PI) in k 9.540 * [taylor]: Taking taylor expansion of PI in k 9.540 * [backup-simplify]: Simplify PI into PI 9.541 * [backup-simplify]: Simplify (log PI) into (log PI) 9.541 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.542 * [backup-simplify]: Simplify (- 0) into 0 9.542 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.543 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.545 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 9.546 * [backup-simplify]: Simplify (* (pow k -1/4) (pow PI 1/2)) into (* (sqrt PI) (pow (/ 1 k) 1/4)) 9.547 * [backup-simplify]: Simplify (* (sqrt PI) (pow (/ 1 k) 1/4)) into (* (sqrt PI) (pow (/ 1 k) 1/4)) 9.548 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 9.549 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 9.549 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.550 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.552 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 9.568 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 9.569 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.571 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 9.571 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.572 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 9.573 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 9.576 * [backup-simplify]: Simplify (+ (* (pow k -1/4) (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2))) into (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) 9.577 * [backup-simplify]: Simplify (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) into (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) 9.580 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 9.581 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 9.582 * [backup-simplify]: Simplify (- 0) into 0 9.582 * [backup-simplify]: Simplify (+ 0 0) into 0 9.583 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 9.594 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 9.594 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.596 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 9.596 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.597 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 9.597 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.600 * [backup-simplify]: Simplify (+ (* (pow k -1/4) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* 0 (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2)))) into (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) 9.601 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) into (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) 9.604 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) (pow k 2)) (+ (* (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) k) (* (sqrt PI) (pow (/ 1 k) 1/4)))) into (- (+ (* (sqrt PI) (pow (/ 1 k) 1/4)) (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (pow k 7) 1/4))))) (* 1/2 (* (log PI) (* (sqrt PI) (pow (pow k 3) 1/4))))) 9.604 * [backup-simplify]: Simplify (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 9.604 * [approximate]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in (k) around 0 9.604 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 9.604 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 9.604 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 9.604 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 9.604 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.604 * [taylor]: Taking taylor expansion of 1/2 in k 9.604 * [backup-simplify]: Simplify 1/2 into 1/2 9.604 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.604 * [taylor]: Taking taylor expansion of 1/2 in k 9.604 * [backup-simplify]: Simplify 1/2 into 1/2 9.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.604 * [taylor]: Taking taylor expansion of k in k 9.604 * [backup-simplify]: Simplify 0 into 0 9.604 * [backup-simplify]: Simplify 1 into 1 9.604 * [backup-simplify]: Simplify (/ 1 1) into 1 9.604 * [taylor]: Taking taylor expansion of (log PI) in k 9.604 * [taylor]: Taking taylor expansion of PI in k 9.604 * [backup-simplify]: Simplify PI into PI 9.605 * [backup-simplify]: Simplify (log PI) into (log PI) 9.605 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.605 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.605 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.606 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 9.607 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 9.607 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 9.607 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 9.607 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 9.607 * [taylor]: Taking taylor expansion of 1/4 in k 9.607 * [backup-simplify]: Simplify 1/4 into 1/4 9.607 * [taylor]: Taking taylor expansion of (log k) in k 9.607 * [taylor]: Taking taylor expansion of k in k 9.607 * [backup-simplify]: Simplify 0 into 0 9.607 * [backup-simplify]: Simplify 1 into 1 9.607 * [backup-simplify]: Simplify (log 1) into 0 9.608 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.608 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 9.608 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 9.608 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 9.608 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 9.608 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 9.608 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 9.608 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.608 * [taylor]: Taking taylor expansion of 1/2 in k 9.608 * [backup-simplify]: Simplify 1/2 into 1/2 9.608 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.608 * [taylor]: Taking taylor expansion of 1/2 in k 9.608 * [backup-simplify]: Simplify 1/2 into 1/2 9.608 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.608 * [taylor]: Taking taylor expansion of k in k 9.608 * [backup-simplify]: Simplify 0 into 0 9.608 * [backup-simplify]: Simplify 1 into 1 9.608 * [backup-simplify]: Simplify (/ 1 1) into 1 9.608 * [taylor]: Taking taylor expansion of (log PI) in k 9.608 * [taylor]: Taking taylor expansion of PI in k 9.608 * [backup-simplify]: Simplify PI into PI 9.608 * [backup-simplify]: Simplify (log PI) into (log PI) 9.609 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.609 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.609 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.610 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 9.610 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 9.610 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 9.610 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 9.610 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 9.610 * [taylor]: Taking taylor expansion of 1/4 in k 9.610 * [backup-simplify]: Simplify 1/4 into 1/4 9.610 * [taylor]: Taking taylor expansion of (log k) in k 9.610 * [taylor]: Taking taylor expansion of k in k 9.610 * [backup-simplify]: Simplify 0 into 0 9.610 * [backup-simplify]: Simplify 1 into 1 9.611 * [backup-simplify]: Simplify (log 1) into 0 9.611 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.611 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 9.611 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 9.611 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 9.611 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 9.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 9.612 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.613 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 9.613 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 9.613 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow k 1/4))) into 0 9.613 * [backup-simplify]: Simplify 0 into 0 9.615 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 9.615 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.616 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 9.616 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.617 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 9.617 * [backup-simplify]: Simplify 0 into 0 9.620 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 9.621 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.622 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 9.624 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.625 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 9.625 * [backup-simplify]: Simplify 0 into 0 9.636 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 9.637 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.639 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 9.641 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.643 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 9.643 * [backup-simplify]: Simplify 0 into 0 9.661 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 9.662 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.664 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 9.668 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.670 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 9.670 * [backup-simplify]: Simplify 0 into 0 9.709 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 9.710 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.712 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 9.718 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.721 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 9.721 * [backup-simplify]: Simplify 0 into 0 9.721 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (pow (/ 1 k) 1/4)) into (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) 9.722 * [backup-simplify]: Simplify (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 9.722 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in (k) around 0 9.722 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 9.722 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 9.722 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 9.722 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.722 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.722 * [taylor]: Taking taylor expansion of -1 in k 9.722 * [backup-simplify]: Simplify -1 into -1 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 9.723 * [backup-simplify]: Simplify (sqrt 0) into 0 9.724 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.725 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 9.725 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 9.726 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.729 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.732 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.734 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 9.734 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 9.734 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 9.734 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 9.734 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.734 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.734 * [taylor]: Taking taylor expansion of 1/2 in k 9.734 * [backup-simplify]: Simplify 1/2 into 1/2 9.734 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.734 * [taylor]: Taking taylor expansion of k in k 9.734 * [backup-simplify]: Simplify 0 into 0 9.734 * [backup-simplify]: Simplify 1 into 1 9.734 * [backup-simplify]: Simplify (/ 1 1) into 1 9.734 * [taylor]: Taking taylor expansion of 1/2 in k 9.734 * [backup-simplify]: Simplify 1/2 into 1/2 9.734 * [taylor]: Taking taylor expansion of (log PI) in k 9.734 * [taylor]: Taking taylor expansion of PI in k 9.734 * [backup-simplify]: Simplify PI into PI 9.735 * [backup-simplify]: Simplify (log PI) into (log PI) 9.735 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.736 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.737 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.737 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 9.737 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 9.737 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 9.738 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 9.738 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.738 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.738 * [taylor]: Taking taylor expansion of -1 in k 9.738 * [backup-simplify]: Simplify -1 into -1 9.738 * [taylor]: Taking taylor expansion of k in k 9.738 * [backup-simplify]: Simplify 0 into 0 9.738 * [backup-simplify]: Simplify 1 into 1 9.738 * [backup-simplify]: Simplify (/ -1 1) into -1 9.739 * [backup-simplify]: Simplify (sqrt 0) into 0 9.740 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.740 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 9.741 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 9.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.744 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.746 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.748 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 9.749 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 9.749 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 9.749 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 9.749 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.749 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.749 * [taylor]: Taking taylor expansion of 1/2 in k 9.749 * [backup-simplify]: Simplify 1/2 into 1/2 9.749 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.749 * [taylor]: Taking taylor expansion of k in k 9.749 * [backup-simplify]: Simplify 0 into 0 9.749 * [backup-simplify]: Simplify 1 into 1 9.749 * [backup-simplify]: Simplify (/ 1 1) into 1 9.749 * [taylor]: Taking taylor expansion of 1/2 in k 9.749 * [backup-simplify]: Simplify 1/2 into 1/2 9.749 * [taylor]: Taking taylor expansion of (log PI) in k 9.749 * [taylor]: Taking taylor expansion of PI in k 9.749 * [backup-simplify]: Simplify PI into PI 9.750 * [backup-simplify]: Simplify (log PI) into (log PI) 9.750 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.751 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.752 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 9.752 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 9.753 * [backup-simplify]: Simplify (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 9.753 * [backup-simplify]: Simplify (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 9.755 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +nan.0)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) 9.755 * [backup-simplify]: Simplify (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) into (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) 9.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.760 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.764 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.770 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 9.779 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) 9.780 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) 9.784 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (sqrt +nan.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (sqrt +nan.0)))) (/ 1 (- k))) (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (* (sqrt +nan.0) (pow PI (- 1/2 (* 1/2 k)))) (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* k (sqrt +nan.0)))) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* (pow k 2) (pow (sqrt +nan.0) 3)))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* (pow k 2) (sqrt +nan.0))))))))) 9.784 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 9.784 * [backup-simplify]: Simplify (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) 9.784 * [approximate]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in (n k) around 0 9.784 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in k 9.785 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 9.785 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 9.785 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 9.785 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.785 * [taylor]: Taking taylor expansion of 1/2 in k 9.785 * [backup-simplify]: Simplify 1/2 into 1/2 9.785 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.785 * [taylor]: Taking taylor expansion of 1/2 in k 9.785 * [backup-simplify]: Simplify 1/2 into 1/2 9.785 * [taylor]: Taking taylor expansion of k in k 9.785 * [backup-simplify]: Simplify 0 into 0 9.785 * [backup-simplify]: Simplify 1 into 1 9.785 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 9.785 * [taylor]: Taking taylor expansion of (* 2 n) in k 9.785 * [taylor]: Taking taylor expansion of 2 in k 9.785 * [backup-simplify]: Simplify 2 into 2 9.785 * [taylor]: Taking taylor expansion of n in k 9.785 * [backup-simplify]: Simplify n into n 9.785 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 9.785 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 9.786 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.786 * [backup-simplify]: Simplify (- 0) into 0 9.786 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.787 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 9.787 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 9.787 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 9.787 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 9.787 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 9.787 * [taylor]: Taking taylor expansion of 1/4 in k 9.787 * [backup-simplify]: Simplify 1/4 into 1/4 9.787 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 9.787 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.787 * [taylor]: Taking taylor expansion of k in k 9.787 * [backup-simplify]: Simplify 0 into 0 9.787 * [backup-simplify]: Simplify 1 into 1 9.787 * [backup-simplify]: Simplify (/ 1 1) into 1 9.788 * [backup-simplify]: Simplify (log 1) into 0 9.788 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.788 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 9.788 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 9.788 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in n 9.788 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 9.789 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 9.789 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 9.789 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 9.789 * [taylor]: Taking taylor expansion of 1/2 in n 9.789 * [backup-simplify]: Simplify 1/2 into 1/2 9.789 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 9.789 * [taylor]: Taking taylor expansion of 1/2 in n 9.789 * [backup-simplify]: Simplify 1/2 into 1/2 9.789 * [taylor]: Taking taylor expansion of k in n 9.789 * [backup-simplify]: Simplify k into k 9.789 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 9.789 * [taylor]: Taking taylor expansion of (* 2 n) in n 9.789 * [taylor]: Taking taylor expansion of 2 in n 9.789 * [backup-simplify]: Simplify 2 into 2 9.789 * [taylor]: Taking taylor expansion of n in n 9.789 * [backup-simplify]: Simplify 0 into 0 9.789 * [backup-simplify]: Simplify 1 into 1 9.790 * [backup-simplify]: Simplify (* 2 0) into 0 9.790 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 9.791 * [backup-simplify]: Simplify (log 2) into (log 2) 9.791 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 9.791 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 9.791 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 9.792 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.792 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 9.793 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 9.793 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 9.793 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 9.793 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 9.793 * [taylor]: Taking taylor expansion of 1/4 in n 9.793 * [backup-simplify]: Simplify 1/4 into 1/4 9.793 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 9.793 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.793 * [taylor]: Taking taylor expansion of k in n 9.793 * [backup-simplify]: Simplify k into k 9.793 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.793 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 9.793 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 9.793 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 9.794 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in n 9.794 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 9.794 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 9.794 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 9.794 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 9.794 * [taylor]: Taking taylor expansion of 1/2 in n 9.794 * [backup-simplify]: Simplify 1/2 into 1/2 9.794 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 9.794 * [taylor]: Taking taylor expansion of 1/2 in n 9.794 * [backup-simplify]: Simplify 1/2 into 1/2 9.794 * [taylor]: Taking taylor expansion of k in n 9.794 * [backup-simplify]: Simplify k into k 9.794 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 9.794 * [taylor]: Taking taylor expansion of (* 2 n) in n 9.794 * [taylor]: Taking taylor expansion of 2 in n 9.794 * [backup-simplify]: Simplify 2 into 2 9.794 * [taylor]: Taking taylor expansion of n in n 9.794 * [backup-simplify]: Simplify 0 into 0 9.794 * [backup-simplify]: Simplify 1 into 1 9.794 * [backup-simplify]: Simplify (* 2 0) into 0 9.795 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 9.796 * [backup-simplify]: Simplify (log 2) into (log 2) 9.796 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 9.796 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 9.796 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 9.797 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.797 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 9.798 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 9.798 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 9.798 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 9.798 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 9.798 * [taylor]: Taking taylor expansion of 1/4 in n 9.798 * [backup-simplify]: Simplify 1/4 into 1/4 9.798 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 9.798 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.798 * [taylor]: Taking taylor expansion of k in n 9.798 * [backup-simplify]: Simplify k into k 9.798 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.798 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 9.798 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 9.798 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 9.799 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow (/ 1 k) 1/4)) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow (/ 1 k) 1/4)) 9.799 * [taylor]: Taking taylor expansion of (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (pow (/ 1 k) 1/4)) in k 9.799 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 9.799 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 9.799 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 9.799 * [taylor]: Taking taylor expansion of (log 2) in k 9.799 * [taylor]: Taking taylor expansion of 2 in k 9.799 * [backup-simplify]: Simplify 2 into 2 9.799 * [backup-simplify]: Simplify (log 2) into (log 2) 9.799 * [taylor]: Taking taylor expansion of (log n) in k 9.799 * [taylor]: Taking taylor expansion of n in k 9.799 * [backup-simplify]: Simplify n into n 9.799 * [backup-simplify]: Simplify (log n) into (log n) 9.799 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 9.799 * [taylor]: Taking taylor expansion of 1/2 in k 9.799 * [backup-simplify]: Simplify 1/2 into 1/2 9.799 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 9.799 * [taylor]: Taking taylor expansion of 1/2 in k 9.799 * [backup-simplify]: Simplify 1/2 into 1/2 9.799 * [taylor]: Taking taylor expansion of k in k 9.799 * [backup-simplify]: Simplify 0 into 0 9.799 * [backup-simplify]: Simplify 1 into 1 9.800 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 9.800 * [backup-simplify]: Simplify (* 1/2 0) into 0 9.800 * [backup-simplify]: Simplify (- 0) into 0 9.801 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.801 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 9.801 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 9.801 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 9.801 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 9.801 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 9.801 * [taylor]: Taking taylor expansion of 1/4 in k 9.801 * [backup-simplify]: Simplify 1/4 into 1/4 9.801 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 9.801 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.801 * [taylor]: Taking taylor expansion of k in k 9.801 * [backup-simplify]: Simplify 0 into 0 9.801 * [backup-simplify]: Simplify 1 into 1 9.802 * [backup-simplify]: Simplify (/ 1 1) into 1 9.802 * [backup-simplify]: Simplify (log 1) into 0 9.802 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.802 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 9.802 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 9.803 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k -1/4)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) 9.803 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) into (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) 9.803 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 9.804 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 9.804 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.805 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 9.806 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 9.806 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 9.806 * [backup-simplify]: Simplify (- 0) into 0 9.807 * [backup-simplify]: Simplify (+ 0 0) into 0 9.807 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.807 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 9.808 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.809 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (* 0 (pow (/ 1 k) 1/4))) into 0 9.809 * [taylor]: Taking taylor expansion of 0 in k 9.809 * [backup-simplify]: Simplify 0 into 0 9.809 * [backup-simplify]: Simplify 0 into 0 9.809 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.810 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 9.810 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.810 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 9.811 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 9.811 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 9.812 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.812 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.813 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 9.813 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.814 * [backup-simplify]: Simplify (+ 0 0) into 0 9.814 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 9.815 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 9.817 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) 0) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (pow k -1/4))) into (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) 9.818 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) into (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) 9.818 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.819 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 k) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 k) 1)))) 2) into 0 9.819 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 9.820 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.821 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 9.823 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 9.823 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 9.823 * [backup-simplify]: Simplify (- 0) into 0 9.824 * [backup-simplify]: Simplify (+ 0 0) into 0 9.824 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 9.825 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 9.831 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.832 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 1 k) 1/4)))) into 0 9.832 * [taylor]: Taking taylor expansion of 0 in k 9.832 * [backup-simplify]: Simplify 0 into 0 9.832 * [backup-simplify]: Simplify 0 into 0 9.832 * [backup-simplify]: Simplify 0 into 0 9.832 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.834 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 9.834 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 9.835 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 9.836 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.836 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 9.837 * [backup-simplify]: Simplify (- 0) into 0 9.837 * [backup-simplify]: Simplify (+ 0 0) into 0 9.838 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 9.840 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.840 * [backup-simplify]: Simplify (+ 0 0) into 0 9.842 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 9.844 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 9.849 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) 0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 0) (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow k -1/4)))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) 9.853 * [backup-simplify]: Simplify (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) into (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) 9.860 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (/ 1 k) 1/4))) (+ (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (/ 1 k) 1/4))) (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (/ 1 k) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (/ 1 k) 1/4))))) (* k 1)) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)))) into (- (+ (* 1/8 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2)) (pow (pow k 7) 1/4))) (+ (* 1/8 (* (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 7) 1/4))) (+ (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (/ 1 k) 1/4)) (* 1/4 (* (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (pow (pow k 7) 1/4)))))) (+ (* 1/2 (* (* (log 2) (exp (* 1/2 (+ (log 2) (log n))))) (pow (pow k 3) 1/4))) (* 1/2 (* (* (exp (* 1/2 (+ (log 2) (log n)))) (log n)) (pow (pow k 3) 1/4))))) 9.861 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 9.861 * [approximate]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in (n k) around 0 9.861 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 9.861 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 9.861 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 9.861 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 9.861 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.861 * [taylor]: Taking taylor expansion of 1/2 in k 9.861 * [backup-simplify]: Simplify 1/2 into 1/2 9.861 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.861 * [taylor]: Taking taylor expansion of 1/2 in k 9.861 * [backup-simplify]: Simplify 1/2 into 1/2 9.861 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.861 * [taylor]: Taking taylor expansion of k in k 9.861 * [backup-simplify]: Simplify 0 into 0 9.861 * [backup-simplify]: Simplify 1 into 1 9.862 * [backup-simplify]: Simplify (/ 1 1) into 1 9.862 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 9.862 * [taylor]: Taking taylor expansion of (/ 2 n) in k 9.862 * [taylor]: Taking taylor expansion of 2 in k 9.862 * [backup-simplify]: Simplify 2 into 2 9.862 * [taylor]: Taking taylor expansion of n in k 9.862 * [backup-simplify]: Simplify n into n 9.862 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 9.862 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 9.863 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.863 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.863 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.864 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 9.864 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 9.864 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 9.864 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 9.864 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 9.864 * [taylor]: Taking taylor expansion of 1/4 in k 9.864 * [backup-simplify]: Simplify 1/4 into 1/4 9.864 * [taylor]: Taking taylor expansion of (log k) in k 9.864 * [taylor]: Taking taylor expansion of k in k 9.864 * [backup-simplify]: Simplify 0 into 0 9.864 * [backup-simplify]: Simplify 1 into 1 9.864 * [backup-simplify]: Simplify (log 1) into 0 9.865 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.865 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 9.865 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 9.865 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in n 9.865 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 9.865 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 9.865 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 9.865 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 9.865 * [taylor]: Taking taylor expansion of 1/2 in n 9.865 * [backup-simplify]: Simplify 1/2 into 1/2 9.865 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.865 * [taylor]: Taking taylor expansion of 1/2 in n 9.865 * [backup-simplify]: Simplify 1/2 into 1/2 9.865 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.865 * [taylor]: Taking taylor expansion of k in n 9.865 * [backup-simplify]: Simplify k into k 9.865 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.866 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 9.866 * [taylor]: Taking taylor expansion of (/ 2 n) in n 9.866 * [taylor]: Taking taylor expansion of 2 in n 9.866 * [backup-simplify]: Simplify 2 into 2 9.866 * [taylor]: Taking taylor expansion of n in n 9.866 * [backup-simplify]: Simplify 0 into 0 9.866 * [backup-simplify]: Simplify 1 into 1 9.866 * [backup-simplify]: Simplify (/ 2 1) into 2 9.867 * [backup-simplify]: Simplify (log 2) into (log 2) 9.867 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.867 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 9.867 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 9.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.868 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 9.869 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.869 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 9.869 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 9.869 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 9.869 * [taylor]: Taking taylor expansion of 1/4 in n 9.869 * [backup-simplify]: Simplify 1/4 into 1/4 9.869 * [taylor]: Taking taylor expansion of (log k) in n 9.869 * [taylor]: Taking taylor expansion of k in n 9.869 * [backup-simplify]: Simplify k into k 9.869 * [backup-simplify]: Simplify (log k) into (log k) 9.869 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 9.869 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 9.869 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in n 9.869 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 9.869 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 9.869 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 9.869 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 9.869 * [taylor]: Taking taylor expansion of 1/2 in n 9.869 * [backup-simplify]: Simplify 1/2 into 1/2 9.869 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.869 * [taylor]: Taking taylor expansion of 1/2 in n 9.869 * [backup-simplify]: Simplify 1/2 into 1/2 9.869 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.869 * [taylor]: Taking taylor expansion of k in n 9.869 * [backup-simplify]: Simplify k into k 9.869 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.869 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 9.869 * [taylor]: Taking taylor expansion of (/ 2 n) in n 9.870 * [taylor]: Taking taylor expansion of 2 in n 9.870 * [backup-simplify]: Simplify 2 into 2 9.870 * [taylor]: Taking taylor expansion of n in n 9.870 * [backup-simplify]: Simplify 0 into 0 9.870 * [backup-simplify]: Simplify 1 into 1 9.870 * [backup-simplify]: Simplify (/ 2 1) into 2 9.870 * [backup-simplify]: Simplify (log 2) into (log 2) 9.871 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.871 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 9.871 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 9.871 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.872 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 9.873 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.873 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 9.873 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 9.873 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 9.873 * [taylor]: Taking taylor expansion of 1/4 in n 9.873 * [backup-simplify]: Simplify 1/4 into 1/4 9.873 * [taylor]: Taking taylor expansion of (log k) in n 9.873 * [taylor]: Taking taylor expansion of k in n 9.873 * [backup-simplify]: Simplify k into k 9.873 * [backup-simplify]: Simplify (log k) into (log k) 9.873 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 9.873 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 9.874 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (pow k 1/4)) into (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 9.874 * [taylor]: Taking taylor expansion of (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k 9.874 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 9.874 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 9.874 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 9.874 * [taylor]: Taking taylor expansion of 1/4 in k 9.874 * [backup-simplify]: Simplify 1/4 into 1/4 9.874 * [taylor]: Taking taylor expansion of (log k) in k 9.874 * [taylor]: Taking taylor expansion of k in k 9.874 * [backup-simplify]: Simplify 0 into 0 9.874 * [backup-simplify]: Simplify 1 into 1 9.874 * [backup-simplify]: Simplify (log 1) into 0 9.875 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.875 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 9.875 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 9.875 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 9.875 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 9.875 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 9.875 * [taylor]: Taking taylor expansion of 1/2 in k 9.875 * [backup-simplify]: Simplify 1/2 into 1/2 9.875 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.875 * [taylor]: Taking taylor expansion of 1/2 in k 9.875 * [backup-simplify]: Simplify 1/2 into 1/2 9.875 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.875 * [taylor]: Taking taylor expansion of k in k 9.875 * [backup-simplify]: Simplify 0 into 0 9.875 * [backup-simplify]: Simplify 1 into 1 9.876 * [backup-simplify]: Simplify (/ 1 1) into 1 9.876 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 9.876 * [taylor]: Taking taylor expansion of (log 2) in k 9.876 * [taylor]: Taking taylor expansion of 2 in k 9.876 * [backup-simplify]: Simplify 2 into 2 9.876 * [backup-simplify]: Simplify (log 2) into (log 2) 9.876 * [taylor]: Taking taylor expansion of (log n) in k 9.876 * [taylor]: Taking taylor expansion of n in k 9.876 * [backup-simplify]: Simplify n into n 9.876 * [backup-simplify]: Simplify (log n) into (log n) 9.877 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.877 * [backup-simplify]: Simplify (- 1/2) into -1/2 9.877 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 9.877 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.878 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 9.878 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 9.879 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 9.879 * [backup-simplify]: Simplify (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (pow k 1/4)) 9.880 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (pow k 1/4)) into (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 9.881 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 9.881 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 9.882 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 9.883 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 9.885 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 9.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.885 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 9.886 * [backup-simplify]: Simplify (- 0) into 0 9.886 * [backup-simplify]: Simplify (+ 0 0) into 0 9.887 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.888 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 9.889 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.890 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (* 0 (pow k 1/4))) into 0 9.890 * [taylor]: Taking taylor expansion of 0 in k 9.890 * [backup-simplify]: Simplify 0 into 0 9.890 * [backup-simplify]: Simplify 0 into 0 9.891 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 9.892 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.892 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 9.893 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 9.894 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 9.894 * [backup-simplify]: Simplify 0 into 0 9.895 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 9.896 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 9.897 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.901 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 9.901 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.902 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 9.903 * [backup-simplify]: Simplify (- 0) into 0 9.903 * [backup-simplify]: Simplify (+ 0 0) into 0 9.904 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.905 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 9.906 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.907 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 9.907 * [taylor]: Taking taylor expansion of 0 in k 9.907 * [backup-simplify]: Simplify 0 into 0 9.908 * [backup-simplify]: Simplify 0 into 0 9.908 * [backup-simplify]: Simplify 0 into 0 9.910 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 9.910 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 9.911 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 9.913 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.914 * [backup-simplify]: Simplify (+ (* (pow k 1/4) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 9.914 * [backup-simplify]: Simplify 0 into 0 9.916 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow k 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow k 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow k 1)))) 6) into 0 9.918 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 9.919 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.920 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.926 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 9.926 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.928 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 9.928 * [backup-simplify]: Simplify (- 0) into 0 9.929 * [backup-simplify]: Simplify (+ 0 0) into 0 9.929 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 9.931 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 9.933 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.934 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 9.934 * [taylor]: Taking taylor expansion of 0 in k 9.934 * [backup-simplify]: Simplify 0 into 0 9.934 * [backup-simplify]: Simplify 0 into 0 9.935 * [backup-simplify]: Simplify (* (pow (/ 1 k) 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))) into (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow (/ 1 k) 1/4)) 9.935 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 9.935 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 9.935 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in k 9.935 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 9.935 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 9.935 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.935 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.935 * [taylor]: Taking taylor expansion of -1 in k 9.935 * [backup-simplify]: Simplify -1 into -1 9.935 * [taylor]: Taking taylor expansion of k in k 9.935 * [backup-simplify]: Simplify 0 into 0 9.935 * [backup-simplify]: Simplify 1 into 1 9.936 * [backup-simplify]: Simplify (/ -1 1) into -1 9.936 * [backup-simplify]: Simplify (sqrt 0) into 0 9.938 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.939 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 9.939 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 9.940 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.943 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.945 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.947 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 9.947 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 9.947 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 9.947 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 9.947 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.947 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.947 * [taylor]: Taking taylor expansion of 1/2 in k 9.947 * [backup-simplify]: Simplify 1/2 into 1/2 9.947 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.947 * [taylor]: Taking taylor expansion of k in k 9.947 * [backup-simplify]: Simplify 0 into 0 9.947 * [backup-simplify]: Simplify 1 into 1 9.948 * [backup-simplify]: Simplify (/ 1 1) into 1 9.948 * [taylor]: Taking taylor expansion of 1/2 in k 9.948 * [backup-simplify]: Simplify 1/2 into 1/2 9.948 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 9.948 * [taylor]: Taking taylor expansion of (/ -2 n) in k 9.948 * [taylor]: Taking taylor expansion of -2 in k 9.948 * [backup-simplify]: Simplify -2 into -2 9.948 * [taylor]: Taking taylor expansion of n in k 9.948 * [backup-simplify]: Simplify n into n 9.948 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 9.948 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 9.949 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.949 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.949 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 9.949 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 9.950 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 9.950 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 9.950 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 9.950 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 9.950 * [taylor]: Taking taylor expansion of (/ -1 k) in n 9.950 * [taylor]: Taking taylor expansion of -1 in n 9.950 * [backup-simplify]: Simplify -1 into -1 9.950 * [taylor]: Taking taylor expansion of k in n 9.950 * [backup-simplify]: Simplify k into k 9.950 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 9.950 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 9.950 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 9.950 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 9.950 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 9.950 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 9.951 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 9.951 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 9.951 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 9.951 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 9.951 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 9.951 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 9.951 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.951 * [taylor]: Taking taylor expansion of 1/2 in n 9.951 * [backup-simplify]: Simplify 1/2 into 1/2 9.951 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.951 * [taylor]: Taking taylor expansion of k in n 9.951 * [backup-simplify]: Simplify k into k 9.951 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.951 * [taylor]: Taking taylor expansion of 1/2 in n 9.951 * [backup-simplify]: Simplify 1/2 into 1/2 9.951 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 9.951 * [taylor]: Taking taylor expansion of (/ -2 n) in n 9.951 * [taylor]: Taking taylor expansion of -2 in n 9.951 * [backup-simplify]: Simplify -2 into -2 9.951 * [taylor]: Taking taylor expansion of n in n 9.951 * [backup-simplify]: Simplify 0 into 0 9.951 * [backup-simplify]: Simplify 1 into 1 9.952 * [backup-simplify]: Simplify (/ -2 1) into -2 9.952 * [backup-simplify]: Simplify (log -2) into (log -2) 9.952 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.952 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 9.953 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.954 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 9.954 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.954 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 9.954 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 9.954 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 9.954 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 9.954 * [taylor]: Taking taylor expansion of (/ -1 k) in n 9.954 * [taylor]: Taking taylor expansion of -1 in n 9.954 * [backup-simplify]: Simplify -1 into -1 9.954 * [taylor]: Taking taylor expansion of k in n 9.955 * [backup-simplify]: Simplify k into k 9.955 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 9.955 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 9.955 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 9.955 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 9.955 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 9.955 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 9.955 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 9.955 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 9.955 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 9.955 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 9.956 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 9.956 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 9.956 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 9.956 * [taylor]: Taking taylor expansion of 1/2 in n 9.956 * [backup-simplify]: Simplify 1/2 into 1/2 9.956 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.956 * [taylor]: Taking taylor expansion of k in n 9.956 * [backup-simplify]: Simplify k into k 9.956 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.956 * [taylor]: Taking taylor expansion of 1/2 in n 9.956 * [backup-simplify]: Simplify 1/2 into 1/2 9.956 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 9.956 * [taylor]: Taking taylor expansion of (/ -2 n) in n 9.956 * [taylor]: Taking taylor expansion of -2 in n 9.956 * [backup-simplify]: Simplify -2 into -2 9.956 * [taylor]: Taking taylor expansion of n in n 9.956 * [backup-simplify]: Simplify 0 into 0 9.956 * [backup-simplify]: Simplify 1 into 1 9.956 * [backup-simplify]: Simplify (/ -2 1) into -2 9.957 * [backup-simplify]: Simplify (log -2) into (log -2) 9.957 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 9.957 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 9.958 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.958 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 9.959 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.960 * [backup-simplify]: Simplify (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 9.960 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) in k 9.960 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 9.960 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 9.960 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.960 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.960 * [taylor]: Taking taylor expansion of -1 in k 9.960 * [backup-simplify]: Simplify -1 into -1 9.960 * [taylor]: Taking taylor expansion of k in k 9.960 * [backup-simplify]: Simplify 0 into 0 9.960 * [backup-simplify]: Simplify 1 into 1 9.960 * [backup-simplify]: Simplify (/ -1 1) into -1 9.961 * [backup-simplify]: Simplify (sqrt 0) into 0 9.962 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.962 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 9.963 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 9.963 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.965 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.970 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.972 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 9.972 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 9.972 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 9.972 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 9.972 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 9.972 * [taylor]: Taking taylor expansion of 1/2 in k 9.972 * [backup-simplify]: Simplify 1/2 into 1/2 9.972 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.972 * [taylor]: Taking taylor expansion of k in k 9.972 * [backup-simplify]: Simplify 0 into 0 9.972 * [backup-simplify]: Simplify 1 into 1 9.972 * [backup-simplify]: Simplify (/ 1 1) into 1 9.972 * [taylor]: Taking taylor expansion of 1/2 in k 9.972 * [backup-simplify]: Simplify 1/2 into 1/2 9.972 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 9.972 * [taylor]: Taking taylor expansion of (log -2) in k 9.972 * [taylor]: Taking taylor expansion of -2 in k 9.972 * [backup-simplify]: Simplify -2 into -2 9.972 * [backup-simplify]: Simplify (log -2) into (log -2) 9.972 * [taylor]: Taking taylor expansion of (log n) in k 9.972 * [taylor]: Taking taylor expansion of n in k 9.973 * [backup-simplify]: Simplify n into n 9.973 * [backup-simplify]: Simplify (log n) into (log n) 9.973 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 9.973 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 9.973 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.973 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 9.974 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 9.974 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 9.975 * [backup-simplify]: Simplify (* (sqrt +nan.0) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) 9.975 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) 9.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 9.977 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 9.977 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.978 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 9.978 * [backup-simplify]: Simplify (+ 0 0) into 0 9.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.979 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 9.980 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.980 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into 0 9.980 * [taylor]: Taking taylor expansion of 0 in k 9.980 * [backup-simplify]: Simplify 0 into 0 9.980 * [backup-simplify]: Simplify 0 into 0 9.981 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +nan.0)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) 9.982 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) 9.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.984 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 9.984 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.985 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 9.985 * [backup-simplify]: Simplify (+ 0 0) into 0 9.986 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 9.986 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 9.987 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.987 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.988 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 9.988 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 9.989 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 9.989 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (sqrt (/ -1 k)))) 0) (+ (* 0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) into 0 9.989 * [taylor]: Taking taylor expansion of 0 in k 9.989 * [backup-simplify]: Simplify 0 into 0 9.989 * [backup-simplify]: Simplify 0 into 0 9.989 * [backup-simplify]: Simplify 0 into 0 9.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.992 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.994 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.998 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 10.003 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))))) 10.006 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)))))) 10.011 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow (sqrt +nan.0) 3)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0)))) (* (/ 1 (- k)) 1)) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0)))) into (- (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 10.011 * * * [progress]: simplifying candidates 10.011 * * * * [progress]: [ 1 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 2 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 3 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 4 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 5 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 6 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 7 / 1137 ] simplifiying candidate # 10.012 * * * * [progress]: [ 8 / 1137 ] 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] simplifiying candidate # 10.021 * * * * [progress]: [ 113 / 1137 ] simplifiying candidate # 10.021 * * * * [progress]: [ 114 / 1137 ] simplifiying candidate # 10.021 * * * * [progress]: [ 115 / 1137 ] simplifiying candidate # 10.021 * * * * [progress]: [ 116 / 1137 ] simplifiying candidate # 10.021 * * * * [progress]: [ 117 / 1137 ] simplifiying candidate # 10.021 * * * * [progress]: [ 118 / 1137 ] simplifiying candidate # 10.021 * * * * [progress]: [ 119 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 120 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 121 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 122 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 123 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 124 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 125 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 126 / 1137 ] simplifiying candidate # 10.022 * * * * [progress]: [ 127 / 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k))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 10.221 * * [simplify]: iteration 1: (1350 enodes) 11.062 * * [simplify]: Extracting #0: cost 711 inf + 0 11.068 * * [simplify]: Extracting #1: cost 1108 inf + 84 11.075 * * [simplify]: Extracting #2: cost 1293 inf + 655 11.085 * * [simplify]: Extracting #3: cost 1351 inf + 5737 11.112 * * [simplify]: Extracting #4: cost 1180 inf + 64608 11.140 * * [simplify]: Extracting #5: cost 825 inf + 221246 11.207 * * [simplify]: Extracting #6: cost 492 inf + 398473 11.289 * * [simplify]: Extracting #7: cost 189 inf + 604783 11.427 * * [simplify]: Extracting #8: cost 39 inf + 723397 11.564 * * [simplify]: Extracting #9: cost 1 inf + 753461 11.691 * * [simplify]: Extracting #10: cost 0 inf + 754075 11.880 * [simplify]: Simplified to: (expm1 (pow (* n 2) (- 1/2 (/ k 2)))) (log1p (pow (* n 2) (- 1/2 (/ k 2)))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* 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1/2)))) (* k (sqrt +nan.0))) (- (* (/ (/ (pow PI (- 1/2 (* k 1/2))) (* k k)) (* (* (sqrt +nan.0) (sqrt +nan.0)) (sqrt +nan.0))) +nan.0) (* +nan.0 (/ (pow PI (- 1/2 (* k 1/2))) (* (* k k) (sqrt +nan.0))))))) (- (fma 1/8 (* (exp (* (log (* n 2)) 1/2)) (* (* (log n) (log n)) (pow (pow k 7) 1/4))) (fma 1/8 (* (* (exp (* (log (* n 2)) 1/2)) (* (log 2) (log 2))) (pow (pow k 7) 1/4)) (fma (exp (* (log (* n 2)) 1/2)) (pow (/ 1 k) 1/4) (* (* 1/4 (* (* (exp (* (log (* n 2)) 1/2)) (log 2)) (log n))) (pow (pow k 7) 1/4))))) (* 1/2 (+ (* (* (exp (* (log (* n 2)) 1/2)) (log 2)) (pow (* (* k k) k) 1/4)) (* (pow (* (* k k) k) 1/4) (* (log n) (exp (* (log (* n 2)) 1/2))))))) (* (exp (* (- 1/2 (* k 1/2)) (- (log 2) (- (log n))))) (pow (/ 1 k) 1/4)) (- (* (sqrt +nan.0) (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) (- (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) (* (* k k) (sqrt +nan.0))) (- (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n))))) (* k (sqrt +nan.0))) +nan.0) (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))))) (* (* (* (sqrt +nan.0) (sqrt +nan.0)) (sqrt +nan.0)) (* k k)))))) 12.339 * * * [progress]: adding candidates to table 20.532 * * [progress]: iteration 3 / 4 20.533 * * * [progress]: picking best candidate 20.556 * * * * [pick]: Picked # 20.556 * * * [progress]: localizing error 20.607 * * * [progress]: generating rewritten candidates 20.607 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 20.617 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1) 20.623 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 20.636 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 20.890 * * * [progress]: generating series expansions 20.890 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 20.890 * [backup-simplify]: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 20.890 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 20.890 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 20.890 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 20.890 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 20.890 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.890 * [taylor]: Taking taylor expansion of 1/2 in k 20.890 * [backup-simplify]: Simplify 1/2 into 1/2 20.890 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.890 * [taylor]: Taking taylor expansion of 1/2 in k 20.891 * [backup-simplify]: Simplify 1/2 into 1/2 20.891 * [taylor]: Taking taylor expansion of k in k 20.891 * [backup-simplify]: Simplify 0 into 0 20.891 * [backup-simplify]: Simplify 1 into 1 20.891 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 20.891 * [taylor]: Taking taylor expansion of (* 2 n) in k 20.891 * [taylor]: Taking taylor expansion of 2 in k 20.891 * [backup-simplify]: Simplify 2 into 2 20.891 * [taylor]: Taking taylor expansion of n in k 20.891 * [backup-simplify]: Simplify n into n 20.891 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 20.891 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 20.892 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.892 * [backup-simplify]: Simplify (- 0) into 0 20.893 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.893 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 20.893 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 20.893 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 20.893 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 20.893 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 20.893 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.893 * [taylor]: Taking taylor expansion of 1/2 in n 20.893 * [backup-simplify]: Simplify 1/2 into 1/2 20.893 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.893 * [taylor]: Taking taylor expansion of 1/2 in n 20.893 * [backup-simplify]: Simplify 1/2 into 1/2 20.893 * [taylor]: Taking taylor expansion of k in n 20.893 * [backup-simplify]: Simplify k into k 20.893 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 20.893 * [taylor]: Taking taylor expansion of (* 2 n) in n 20.893 * [taylor]: Taking taylor expansion of 2 in n 20.893 * [backup-simplify]: Simplify 2 into 2 20.893 * [taylor]: Taking taylor expansion of n in n 20.893 * [backup-simplify]: Simplify 0 into 0 20.893 * [backup-simplify]: Simplify 1 into 1 20.894 * [backup-simplify]: Simplify (* 2 0) into 0 20.894 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 20.895 * [backup-simplify]: Simplify (log 2) into (log 2) 20.895 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.895 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.895 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.896 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 20.896 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 20.897 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 20.897 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 20.897 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 20.897 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 20.897 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 20.897 * [taylor]: Taking taylor expansion of 1/2 in n 20.897 * [backup-simplify]: Simplify 1/2 into 1/2 20.897 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 20.897 * [taylor]: Taking taylor expansion of 1/2 in n 20.897 * [backup-simplify]: Simplify 1/2 into 1/2 20.897 * [taylor]: Taking taylor expansion of k in n 20.897 * [backup-simplify]: Simplify k into k 20.897 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 20.897 * [taylor]: Taking taylor expansion of (* 2 n) in n 20.897 * [taylor]: Taking taylor expansion of 2 in n 20.897 * [backup-simplify]: Simplify 2 into 2 20.897 * [taylor]: Taking taylor expansion of n in n 20.897 * [backup-simplify]: Simplify 0 into 0 20.897 * [backup-simplify]: Simplify 1 into 1 20.898 * [backup-simplify]: Simplify (* 2 0) into 0 20.899 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 20.899 * [backup-simplify]: Simplify (log 2) into (log 2) 20.899 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 20.899 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 20.899 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 20.900 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 20.901 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 20.901 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 20.901 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 20.901 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 20.901 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 20.901 * [taylor]: Taking taylor expansion of (log 2) in k 20.901 * [taylor]: Taking taylor expansion of 2 in k 20.901 * [backup-simplify]: Simplify 2 into 2 20.902 * [backup-simplify]: Simplify (log 2) into (log 2) 20.902 * [taylor]: Taking taylor expansion of (log n) in k 20.902 * [taylor]: Taking taylor expansion of n in k 20.902 * [backup-simplify]: Simplify n into n 20.902 * [backup-simplify]: Simplify (log n) into (log n) 20.902 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 20.902 * [taylor]: Taking taylor expansion of 1/2 in k 20.902 * [backup-simplify]: Simplify 1/2 into 1/2 20.902 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 20.902 * [taylor]: Taking taylor expansion of 1/2 in k 20.902 * [backup-simplify]: Simplify 1/2 into 1/2 20.902 * [taylor]: Taking taylor expansion of k in k 20.902 * [backup-simplify]: Simplify 0 into 0 20.902 * [backup-simplify]: Simplify 1 into 1 20.902 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 20.903 * [backup-simplify]: Simplify (* 1/2 0) into 0 20.903 * [backup-simplify]: Simplify (- 0) into 0 20.904 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.904 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 20.905 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 20.905 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 20.906 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 20.908 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 20.908 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 20.909 * [backup-simplify]: Simplify (- 0) into 0 20.909 * [backup-simplify]: Simplify (+ 0 0) into 0 20.910 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 20.911 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 20.912 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.912 * [taylor]: Taking taylor expansion of 0 in k 20.912 * [backup-simplify]: Simplify 0 into 0 20.912 * [backup-simplify]: Simplify 0 into 0 20.913 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 20.913 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.914 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.916 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 20.916 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 20.917 * [backup-simplify]: Simplify (+ 0 0) into 0 20.918 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 20.919 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 20.921 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 20.922 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 20.924 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 20.925 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 20.926 * [backup-simplify]: Simplify (- 0) into 0 20.926 * [backup-simplify]: Simplify (+ 0 0) into 0 20.927 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 20.928 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 20.930 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.930 * [taylor]: Taking taylor expansion of 0 in k 20.930 * [backup-simplify]: Simplify 0 into 0 20.930 * [backup-simplify]: Simplify 0 into 0 20.930 * [backup-simplify]: Simplify 0 into 0 20.949 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 20.950 * [backup-simplify]: Simplify (- 0) into 0 20.951 * [backup-simplify]: Simplify (+ 0 0) into 0 20.954 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 20.955 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 20.955 * [backup-simplify]: Simplify (+ 0 0) into 0 20.956 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 20.958 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 20.959 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 20.962 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 20.962 * [backup-simplify]: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 20.962 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 20.963 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 20.963 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 20.963 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 20.963 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.963 * [taylor]: Taking taylor expansion of 1/2 in k 20.963 * [backup-simplify]: Simplify 1/2 into 1/2 20.963 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.963 * [taylor]: Taking taylor expansion of 1/2 in k 20.963 * [backup-simplify]: Simplify 1/2 into 1/2 20.963 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.963 * [taylor]: Taking taylor expansion of k in k 20.963 * [backup-simplify]: Simplify 0 into 0 20.963 * [backup-simplify]: Simplify 1 into 1 20.963 * [backup-simplify]: Simplify (/ 1 1) into 1 20.963 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 20.963 * [taylor]: Taking taylor expansion of (/ 2 n) in k 20.963 * [taylor]: Taking taylor expansion of 2 in k 20.963 * [backup-simplify]: Simplify 2 into 2 20.963 * [taylor]: Taking taylor expansion of n in k 20.963 * [backup-simplify]: Simplify n into n 20.963 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 20.963 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 20.963 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.964 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.964 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.964 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 20.964 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 20.964 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.964 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 20.964 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 20.964 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.964 * [taylor]: Taking taylor expansion of 1/2 in n 20.964 * [backup-simplify]: Simplify 1/2 into 1/2 20.964 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.964 * [taylor]: Taking taylor expansion of 1/2 in n 20.964 * [backup-simplify]: Simplify 1/2 into 1/2 20.964 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.964 * [taylor]: Taking taylor expansion of k in n 20.964 * [backup-simplify]: Simplify k into k 20.964 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.964 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 20.964 * [taylor]: Taking taylor expansion of (/ 2 n) in n 20.964 * [taylor]: Taking taylor expansion of 2 in n 20.964 * [backup-simplify]: Simplify 2 into 2 20.964 * [taylor]: Taking taylor expansion of n in n 20.964 * [backup-simplify]: Simplify 0 into 0 20.964 * [backup-simplify]: Simplify 1 into 1 20.965 * [backup-simplify]: Simplify (/ 2 1) into 2 20.965 * [backup-simplify]: Simplify (log 2) into (log 2) 20.965 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.965 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.965 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.966 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 20.966 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 20.966 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 20.966 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 20.966 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 20.966 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 20.966 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 20.966 * [taylor]: Taking taylor expansion of 1/2 in n 20.966 * [backup-simplify]: Simplify 1/2 into 1/2 20.966 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.966 * [taylor]: Taking taylor expansion of 1/2 in n 20.966 * [backup-simplify]: Simplify 1/2 into 1/2 20.966 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.967 * [taylor]: Taking taylor expansion of k in n 20.967 * [backup-simplify]: Simplify k into k 20.967 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.967 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 20.967 * [taylor]: Taking taylor expansion of (/ 2 n) in n 20.967 * [taylor]: Taking taylor expansion of 2 in n 20.967 * [backup-simplify]: Simplify 2 into 2 20.967 * [taylor]: Taking taylor expansion of n in n 20.967 * [backup-simplify]: Simplify 0 into 0 20.967 * [backup-simplify]: Simplify 1 into 1 20.967 * [backup-simplify]: Simplify (/ 2 1) into 2 20.967 * [backup-simplify]: Simplify (log 2) into (log 2) 20.967 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.967 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 20.967 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 20.968 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 20.968 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 20.969 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 20.969 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 20.969 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 20.969 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 20.969 * [taylor]: Taking taylor expansion of 1/2 in k 20.969 * [backup-simplify]: Simplify 1/2 into 1/2 20.969 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.969 * [taylor]: Taking taylor expansion of 1/2 in k 20.969 * [backup-simplify]: Simplify 1/2 into 1/2 20.969 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.969 * [taylor]: Taking taylor expansion of k in k 20.969 * [backup-simplify]: Simplify 0 into 0 20.969 * [backup-simplify]: Simplify 1 into 1 20.969 * [backup-simplify]: Simplify (/ 1 1) into 1 20.969 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 20.969 * [taylor]: Taking taylor expansion of (log 2) in k 20.969 * [taylor]: Taking taylor expansion of 2 in k 20.969 * [backup-simplify]: Simplify 2 into 2 20.969 * [backup-simplify]: Simplify (log 2) into (log 2) 20.969 * [taylor]: Taking taylor expansion of (log n) in k 20.969 * [taylor]: Taking taylor expansion of n in k 20.969 * [backup-simplify]: Simplify n into n 20.969 * [backup-simplify]: Simplify (log n) into (log n) 20.970 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.970 * [backup-simplify]: Simplify (- 1/2) into -1/2 20.970 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 20.970 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 20.971 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 20.971 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 20.971 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 20.972 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 20.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 20.973 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 20.973 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 20.973 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 20.974 * [backup-simplify]: Simplify (- 0) into 0 20.974 * [backup-simplify]: Simplify (+ 0 0) into 0 20.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 20.975 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 20.975 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 20.975 * [taylor]: Taking taylor expansion of 0 in k 20.975 * [backup-simplify]: Simplify 0 into 0 20.976 * [backup-simplify]: Simplify 0 into 0 20.976 * [backup-simplify]: Simplify 0 into 0 20.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.978 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 20.978 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.978 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 20.979 * [backup-simplify]: Simplify (- 0) into 0 20.979 * [backup-simplify]: Simplify (+ 0 0) into 0 20.980 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 20.980 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 20.981 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 20.981 * [taylor]: Taking taylor expansion of 0 in k 20.981 * [backup-simplify]: Simplify 0 into 0 20.981 * [backup-simplify]: Simplify 0 into 0 20.981 * [backup-simplify]: Simplify 0 into 0 20.981 * [backup-simplify]: Simplify 0 into 0 20.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 20.987 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 20.987 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 20.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 20.989 * [backup-simplify]: Simplify (- 0) into 0 20.989 * [backup-simplify]: Simplify (+ 0 0) into 0 20.990 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 20.991 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 20.994 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 20.994 * [taylor]: Taking taylor expansion of 0 in k 20.994 * [backup-simplify]: Simplify 0 into 0 20.994 * [backup-simplify]: Simplify 0 into 0 20.994 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 20.995 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 20.995 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 20.995 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 20.995 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 20.995 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 20.995 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 20.995 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 20.995 * [taylor]: Taking taylor expansion of 1/2 in k 20.995 * [backup-simplify]: Simplify 1/2 into 1/2 20.995 * [taylor]: Taking taylor expansion of (/ 1 k) in k 20.995 * [taylor]: Taking taylor expansion of k in k 20.995 * [backup-simplify]: Simplify 0 into 0 20.995 * [backup-simplify]: Simplify 1 into 1 20.995 * [backup-simplify]: Simplify (/ 1 1) into 1 20.995 * [taylor]: Taking taylor expansion of 1/2 in k 20.996 * [backup-simplify]: Simplify 1/2 into 1/2 20.996 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 20.996 * [taylor]: Taking taylor expansion of (/ -2 n) in k 20.996 * [taylor]: Taking taylor expansion of -2 in k 20.996 * [backup-simplify]: Simplify -2 into -2 20.996 * [taylor]: Taking taylor expansion of n in k 20.996 * [backup-simplify]: Simplify n into n 20.996 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 20.996 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 20.996 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 20.997 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 20.997 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 20.997 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 20.997 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 20.997 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 20.997 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 20.997 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 20.997 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 20.997 * [taylor]: Taking taylor expansion of 1/2 in n 20.997 * [backup-simplify]: Simplify 1/2 into 1/2 20.997 * [taylor]: Taking taylor expansion of (/ 1 k) in n 20.997 * [taylor]: Taking taylor expansion of k in n 20.997 * [backup-simplify]: Simplify k into k 20.997 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 20.997 * [taylor]: Taking taylor expansion of 1/2 in n 20.997 * [backup-simplify]: Simplify 1/2 into 1/2 20.997 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 20.997 * [taylor]: Taking taylor expansion of (/ -2 n) in n 20.998 * [taylor]: Taking taylor expansion of -2 in n 20.998 * [backup-simplify]: Simplify -2 into -2 20.998 * [taylor]: Taking taylor expansion of n in n 20.998 * [backup-simplify]: Simplify 0 into 0 20.998 * [backup-simplify]: Simplify 1 into 1 20.998 * [backup-simplify]: Simplify (/ -2 1) into -2 20.999 * [backup-simplify]: Simplify (log -2) into (log -2) 20.999 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 20.999 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.000 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.001 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.001 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 21.001 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 21.001 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 21.001 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 21.001 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.001 * [taylor]: Taking taylor expansion of 1/2 in n 21.001 * [backup-simplify]: Simplify 1/2 into 1/2 21.001 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.001 * [taylor]: Taking taylor expansion of k in n 21.001 * [backup-simplify]: Simplify k into k 21.001 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.001 * [taylor]: Taking taylor expansion of 1/2 in n 21.001 * [backup-simplify]: Simplify 1/2 into 1/2 21.001 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 21.001 * [taylor]: Taking taylor expansion of (/ -2 n) in n 21.001 * [taylor]: Taking taylor expansion of -2 in n 21.001 * [backup-simplify]: Simplify -2 into -2 21.001 * [taylor]: Taking taylor expansion of n in n 21.001 * [backup-simplify]: Simplify 0 into 0 21.001 * [backup-simplify]: Simplify 1 into 1 21.002 * [backup-simplify]: Simplify (/ -2 1) into -2 21.002 * [backup-simplify]: Simplify (log -2) into (log -2) 21.002 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.002 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.003 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.004 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.004 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.004 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 21.004 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 21.004 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.004 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.005 * [taylor]: Taking taylor expansion of 1/2 in k 21.005 * [backup-simplify]: Simplify 1/2 into 1/2 21.005 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.005 * [taylor]: Taking taylor expansion of k in k 21.005 * [backup-simplify]: Simplify 0 into 0 21.005 * [backup-simplify]: Simplify 1 into 1 21.005 * [backup-simplify]: Simplify (/ 1 1) into 1 21.005 * [taylor]: Taking taylor expansion of 1/2 in k 21.005 * [backup-simplify]: Simplify 1/2 into 1/2 21.005 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 21.005 * [taylor]: Taking taylor expansion of (log -2) in k 21.005 * [taylor]: Taking taylor expansion of -2 in k 21.005 * [backup-simplify]: Simplify -2 into -2 21.006 * [backup-simplify]: Simplify (log -2) into (log -2) 21.006 * [taylor]: Taking taylor expansion of (log n) in k 21.006 * [taylor]: Taking taylor expansion of n in k 21.006 * [backup-simplify]: Simplify n into n 21.006 * [backup-simplify]: Simplify (log n) into (log n) 21.006 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.007 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.007 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 21.007 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 21.008 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 21.008 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.009 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.010 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 21.011 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 21.012 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 21.012 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 21.013 * [backup-simplify]: Simplify (+ 0 0) into 0 21.013 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.014 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 21.015 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 21.016 * [taylor]: Taking taylor expansion of 0 in k 21.016 * [backup-simplify]: Simplify 0 into 0 21.016 * [backup-simplify]: Simplify 0 into 0 21.016 * [backup-simplify]: Simplify 0 into 0 21.017 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.020 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 21.020 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 21.021 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 21.022 * [backup-simplify]: Simplify (+ 0 0) into 0 21.023 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.023 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 21.025 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.025 * [taylor]: Taking taylor expansion of 0 in k 21.025 * [backup-simplify]: Simplify 0 into 0 21.025 * [backup-simplify]: Simplify 0 into 0 21.025 * [backup-simplify]: Simplify 0 into 0 21.025 * [backup-simplify]: Simplify 0 into 0 21.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.031 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 21.032 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 21.033 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 21.033 * [backup-simplify]: Simplify (+ 0 0) into 0 21.033 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.034 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 21.036 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 21.036 * [taylor]: Taking taylor expansion of 0 in k 21.036 * [backup-simplify]: Simplify 0 into 0 21.036 * [backup-simplify]: Simplify 0 into 0 21.036 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 21.036 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1) 21.036 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 21.036 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 21.036 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 21.036 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 21.036 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 21.036 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 21.036 * [taylor]: Taking taylor expansion of 1/2 in k 21.037 * [backup-simplify]: Simplify 1/2 into 1/2 21.037 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 21.037 * [taylor]: Taking taylor expansion of 1/2 in k 21.037 * [backup-simplify]: Simplify 1/2 into 1/2 21.037 * [taylor]: Taking taylor expansion of k in k 21.037 * [backup-simplify]: Simplify 0 into 0 21.037 * [backup-simplify]: Simplify 1 into 1 21.037 * [taylor]: Taking taylor expansion of (log PI) in k 21.037 * [taylor]: Taking taylor expansion of PI in k 21.037 * [backup-simplify]: Simplify PI into PI 21.038 * [backup-simplify]: Simplify (log PI) into (log PI) 21.038 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.038 * [backup-simplify]: Simplify (- 0) into 0 21.039 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.039 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.040 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 21.040 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 21.040 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 21.041 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 21.041 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 21.041 * [taylor]: Taking taylor expansion of 1/2 in k 21.041 * [backup-simplify]: Simplify 1/2 into 1/2 21.041 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 21.041 * [taylor]: Taking taylor expansion of 1/2 in k 21.041 * [backup-simplify]: Simplify 1/2 into 1/2 21.041 * [taylor]: Taking taylor expansion of k in k 21.041 * [backup-simplify]: Simplify 0 into 0 21.041 * [backup-simplify]: Simplify 1 into 1 21.041 * [taylor]: Taking taylor expansion of (log PI) in k 21.041 * [taylor]: Taking taylor expansion of PI in k 21.041 * [backup-simplify]: Simplify PI into PI 21.041 * [backup-simplify]: Simplify (log PI) into (log PI) 21.041 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.042 * [backup-simplify]: Simplify (- 0) into 0 21.042 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.042 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.043 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 21.044 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 21.045 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 21.045 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 21.046 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.046 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.047 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 21.054 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 21.056 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 21.058 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 21.058 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 21.059 * [backup-simplify]: Simplify (- 0) into 0 21.059 * [backup-simplify]: Simplify (+ 0 0) into 0 21.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 21.073 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 21.076 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 21.083 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 21.083 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 21.083 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 21.083 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 21.084 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 21.084 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 21.084 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 21.084 * [taylor]: Taking taylor expansion of 1/2 in k 21.084 * [backup-simplify]: Simplify 1/2 into 1/2 21.084 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.084 * [taylor]: Taking taylor expansion of 1/2 in k 21.084 * [backup-simplify]: Simplify 1/2 into 1/2 21.084 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.084 * [taylor]: Taking taylor expansion of k in k 21.084 * [backup-simplify]: Simplify 0 into 0 21.084 * [backup-simplify]: Simplify 1 into 1 21.084 * [backup-simplify]: Simplify (/ 1 1) into 1 21.084 * [taylor]: Taking taylor expansion of (log PI) in k 21.084 * [taylor]: Taking taylor expansion of PI in k 21.084 * [backup-simplify]: Simplify PI into PI 21.085 * [backup-simplify]: Simplify (log PI) into (log PI) 21.085 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.086 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.086 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.087 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 21.088 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 21.088 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 21.088 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 21.088 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 21.088 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 21.088 * [taylor]: Taking taylor expansion of 1/2 in k 21.088 * [backup-simplify]: Simplify 1/2 into 1/2 21.088 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.088 * [taylor]: Taking taylor expansion of 1/2 in k 21.088 * [backup-simplify]: Simplify 1/2 into 1/2 21.088 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.088 * [taylor]: Taking taylor expansion of k in k 21.088 * [backup-simplify]: Simplify 0 into 0 21.088 * [backup-simplify]: Simplify 1 into 1 21.088 * [backup-simplify]: Simplify (/ 1 1) into 1 21.089 * [taylor]: Taking taylor expansion of (log PI) in k 21.089 * [taylor]: Taking taylor expansion of PI in k 21.089 * [backup-simplify]: Simplify PI into PI 21.089 * [backup-simplify]: Simplify (log PI) into (log PI) 21.089 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.090 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.091 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.091 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 21.092 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 21.092 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 21.092 * [backup-simplify]: Simplify 0 into 0 21.092 * [backup-simplify]: Simplify 0 into 0 21.092 * [backup-simplify]: Simplify 0 into 0 21.092 * [backup-simplify]: Simplify 0 into 0 21.092 * [backup-simplify]: Simplify 0 into 0 21.093 * [backup-simplify]: Simplify 0 into 0 21.093 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 21.093 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 21.093 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 21.093 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 21.093 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 21.093 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 21.093 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.093 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.093 * [taylor]: Taking taylor expansion of 1/2 in k 21.093 * [backup-simplify]: Simplify 1/2 into 1/2 21.093 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.093 * [taylor]: Taking taylor expansion of k in k 21.093 * [backup-simplify]: Simplify 0 into 0 21.093 * [backup-simplify]: Simplify 1 into 1 21.094 * [backup-simplify]: Simplify (/ 1 1) into 1 21.094 * [taylor]: Taking taylor expansion of 1/2 in k 21.094 * [backup-simplify]: Simplify 1/2 into 1/2 21.094 * [taylor]: Taking taylor expansion of (log PI) in k 21.094 * [taylor]: Taking taylor expansion of PI in k 21.094 * [backup-simplify]: Simplify PI into PI 21.094 * [backup-simplify]: Simplify (log PI) into (log PI) 21.095 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.095 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.096 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.097 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 21.097 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 21.097 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 21.097 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 21.097 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.097 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.097 * [taylor]: Taking taylor expansion of 1/2 in k 21.097 * [backup-simplify]: Simplify 1/2 into 1/2 21.097 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.097 * [taylor]: Taking taylor expansion of k in k 21.097 * [backup-simplify]: Simplify 0 into 0 21.097 * [backup-simplify]: Simplify 1 into 1 21.097 * [backup-simplify]: Simplify (/ 1 1) into 1 21.097 * [taylor]: Taking taylor expansion of 1/2 in k 21.097 * [backup-simplify]: Simplify 1/2 into 1/2 21.097 * [taylor]: Taking taylor expansion of (log PI) in k 21.097 * [taylor]: Taking taylor expansion of PI in k 21.097 * [backup-simplify]: Simplify PI into PI 21.098 * [backup-simplify]: Simplify (log PI) into (log PI) 21.098 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.099 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.100 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.100 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 21.101 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 21.101 * [backup-simplify]: Simplify 0 into 0 21.101 * [backup-simplify]: Simplify 0 into 0 21.101 * [backup-simplify]: Simplify 0 into 0 21.101 * [backup-simplify]: Simplify 0 into 0 21.101 * [backup-simplify]: Simplify 0 into 0 21.101 * [backup-simplify]: Simplify 0 into 0 21.101 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 21.101 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 21.101 * [backup-simplify]: Simplify (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))) into (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) 21.101 * [approximate]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) in (k) around 0 21.101 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) in k 21.101 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 21.101 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 21.102 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 21.102 * [taylor]: Taking taylor expansion of 1/4 in k 21.102 * [backup-simplify]: Simplify 1/4 into 1/4 21.102 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 21.102 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.102 * [taylor]: Taking taylor expansion of k in k 21.102 * [backup-simplify]: Simplify 0 into 0 21.102 * [backup-simplify]: Simplify 1 into 1 21.102 * [backup-simplify]: Simplify (/ 1 1) into 1 21.102 * [backup-simplify]: Simplify (log 1) into 0 21.103 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.103 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 21.103 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 21.103 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 21.103 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 21.103 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 21.103 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 21.103 * [taylor]: Taking taylor expansion of 1/2 in k 21.103 * [backup-simplify]: Simplify 1/2 into 1/2 21.103 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 21.103 * [taylor]: Taking taylor expansion of 1/2 in k 21.103 * [backup-simplify]: Simplify 1/2 into 1/2 21.103 * [taylor]: Taking taylor expansion of k in k 21.103 * [backup-simplify]: Simplify 0 into 0 21.103 * [backup-simplify]: Simplify 1 into 1 21.103 * [taylor]: Taking taylor expansion of (log PI) in k 21.104 * [taylor]: Taking taylor expansion of PI in k 21.104 * [backup-simplify]: Simplify PI into PI 21.104 * [backup-simplify]: Simplify (log PI) into (log PI) 21.104 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.105 * [backup-simplify]: Simplify (- 0) into 0 21.105 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.106 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.108 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 21.108 * [taylor]: Taking taylor expansion of (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) in k 21.108 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 21.108 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 21.108 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 21.108 * [taylor]: Taking taylor expansion of 1/4 in k 21.108 * [backup-simplify]: Simplify 1/4 into 1/4 21.108 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 21.108 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.108 * [taylor]: Taking taylor expansion of k in k 21.108 * [backup-simplify]: Simplify 0 into 0 21.108 * [backup-simplify]: Simplify 1 into 1 21.109 * [backup-simplify]: Simplify (/ 1 1) into 1 21.109 * [backup-simplify]: Simplify (log 1) into 0 21.109 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.110 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 21.110 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 21.110 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 21.110 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 21.110 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 21.110 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 21.110 * [taylor]: Taking taylor expansion of 1/2 in k 21.110 * [backup-simplify]: Simplify 1/2 into 1/2 21.110 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 21.110 * [taylor]: Taking taylor expansion of 1/2 in k 21.110 * [backup-simplify]: Simplify 1/2 into 1/2 21.110 * [taylor]: Taking taylor expansion of k in k 21.110 * [backup-simplify]: Simplify 0 into 0 21.110 * [backup-simplify]: Simplify 1 into 1 21.110 * [taylor]: Taking taylor expansion of (log PI) in k 21.110 * [taylor]: Taking taylor expansion of PI in k 21.110 * [backup-simplify]: Simplify PI into PI 21.110 * [backup-simplify]: Simplify (log PI) into (log PI) 21.111 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.111 * [backup-simplify]: Simplify (- 0) into 0 21.112 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.113 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.115 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 21.115 * [backup-simplify]: Simplify (* (pow k -1/4) (pow PI 1/2)) into (* (sqrt PI) (pow (/ 1 k) 1/4)) 21.116 * [backup-simplify]: Simplify (* (sqrt PI) (pow (/ 1 k) 1/4)) into (* (sqrt PI) (pow (/ 1 k) 1/4)) 21.117 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 21.118 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 21.118 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.119 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 21.131 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 21.132 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 21.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 21.133 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.133 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 21.134 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 21.136 * [backup-simplify]: Simplify (+ (* (pow k -1/4) (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2))) into (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) 21.136 * [backup-simplify]: Simplify (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) into (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) 21.138 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 21.139 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 21.139 * [backup-simplify]: Simplify (- 0) into 0 21.139 * [backup-simplify]: Simplify (+ 0 0) into 0 21.140 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 21.148 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 21.149 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.151 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 21.151 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.152 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 21.152 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.156 * [backup-simplify]: Simplify (+ (* (pow k -1/4) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* 0 (* -1/2 (* (log PI) (sqrt PI)))) (* 0 (pow PI 1/2)))) into (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) 21.157 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) into (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) 21.160 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (/ 1 k) 1/4)))) (pow k 2)) (+ (* (- (* 1/2 (* (log PI) (* (sqrt PI) (pow (/ 1 k) 1/4))))) k) (* (sqrt PI) (pow (/ 1 k) 1/4)))) into (- (+ (* (sqrt PI) (pow (/ 1 k) 1/4)) (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (pow k 7) 1/4))))) (* 1/2 (* (log PI) (* (sqrt PI) (pow (pow k 3) 1/4))))) 21.160 * [backup-simplify]: Simplify (/ (pow PI (- 1/2 (/ (/ 1 k) 2))) (sqrt (sqrt (/ 1 k)))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 21.160 * [approximate]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in (k) around 0 21.160 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 21.160 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 21.160 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 21.160 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 21.160 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 21.160 * [taylor]: Taking taylor expansion of 1/2 in k 21.160 * [backup-simplify]: Simplify 1/2 into 1/2 21.160 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.160 * [taylor]: Taking taylor expansion of 1/2 in k 21.160 * [backup-simplify]: Simplify 1/2 into 1/2 21.160 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.161 * [taylor]: Taking taylor expansion of k in k 21.161 * [backup-simplify]: Simplify 0 into 0 21.161 * [backup-simplify]: Simplify 1 into 1 21.161 * [backup-simplify]: Simplify (/ 1 1) into 1 21.161 * [taylor]: Taking taylor expansion of (log PI) in k 21.161 * [taylor]: Taking taylor expansion of PI in k 21.161 * [backup-simplify]: Simplify PI into PI 21.162 * [backup-simplify]: Simplify (log PI) into (log PI) 21.162 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.162 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.163 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.164 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 21.164 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 21.165 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 21.165 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 21.165 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 21.165 * [taylor]: Taking taylor expansion of 1/4 in k 21.165 * [backup-simplify]: Simplify 1/4 into 1/4 21.165 * [taylor]: Taking taylor expansion of (log k) in k 21.165 * [taylor]: Taking taylor expansion of k in k 21.165 * [backup-simplify]: Simplify 0 into 0 21.165 * [backup-simplify]: Simplify 1 into 1 21.165 * [backup-simplify]: Simplify (log 1) into 0 21.166 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.166 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 21.166 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 21.166 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 21.166 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 21.166 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 21.166 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 21.166 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 21.167 * [taylor]: Taking taylor expansion of 1/2 in k 21.167 * [backup-simplify]: Simplify 1/2 into 1/2 21.167 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.167 * [taylor]: Taking taylor expansion of 1/2 in k 21.167 * [backup-simplify]: Simplify 1/2 into 1/2 21.167 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.167 * [taylor]: Taking taylor expansion of k in k 21.167 * [backup-simplify]: Simplify 0 into 0 21.167 * [backup-simplify]: Simplify 1 into 1 21.167 * [backup-simplify]: Simplify (/ 1 1) into 1 21.167 * [taylor]: Taking taylor expansion of (log PI) in k 21.167 * [taylor]: Taking taylor expansion of PI in k 21.167 * [backup-simplify]: Simplify PI into PI 21.168 * [backup-simplify]: Simplify (log PI) into (log PI) 21.168 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.169 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.169 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.170 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 21.171 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 21.171 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 21.171 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 21.171 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 21.171 * [taylor]: Taking taylor expansion of 1/4 in k 21.171 * [backup-simplify]: Simplify 1/4 into 1/4 21.171 * [taylor]: Taking taylor expansion of (log k) in k 21.171 * [taylor]: Taking taylor expansion of k in k 21.171 * [backup-simplify]: Simplify 0 into 0 21.171 * [backup-simplify]: Simplify 1 into 1 21.171 * [backup-simplify]: Simplify (log 1) into 0 21.172 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.172 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 21.172 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 21.172 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 21.173 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 21.174 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 21.174 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.175 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 21.176 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 21.176 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow k 1/4))) into 0 21.176 * [backup-simplify]: Simplify 0 into 0 21.179 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 21.179 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.180 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 21.182 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.182 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 21.182 * [backup-simplify]: Simplify 0 into 0 21.188 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 21.188 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.190 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 21.191 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 21.192 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 21.193 * [backup-simplify]: Simplify 0 into 0 21.205 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 21.206 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.207 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 21.209 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.209 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0 21.209 * [backup-simplify]: Simplify 0 into 0 21.219 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 21.219 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.221 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 21.223 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 21.224 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0 21.224 * [backup-simplify]: Simplify 0 into 0 21.251 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 21.252 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.255 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 21.262 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.264 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0 21.264 * [backup-simplify]: Simplify 0 into 0 21.265 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (pow (/ 1 k) 1/4)) into (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) 21.265 * [backup-simplify]: Simplify (/ (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (sqrt (/ 1 (- k))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 21.265 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in (k) around 0 21.265 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 21.265 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 21.265 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 21.265 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 21.265 * [taylor]: Taking taylor expansion of (/ -1 k) in k 21.265 * [taylor]: Taking taylor expansion of -1 in k 21.265 * [backup-simplify]: Simplify -1 into -1 21.265 * [taylor]: Taking taylor expansion of k in k 21.265 * [backup-simplify]: Simplify 0 into 0 21.265 * [backup-simplify]: Simplify 1 into 1 21.266 * [backup-simplify]: Simplify (/ -1 1) into -1 21.266 * [backup-simplify]: Simplify (sqrt 0) into 0 21.268 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 21.268 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 21.269 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.270 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 21.273 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 21.275 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 21.278 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 21.278 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 21.278 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 21.278 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 21.278 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.278 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.278 * [taylor]: Taking taylor expansion of 1/2 in k 21.278 * [backup-simplify]: Simplify 1/2 into 1/2 21.278 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.278 * [taylor]: Taking taylor expansion of k in k 21.278 * [backup-simplify]: Simplify 0 into 0 21.278 * [backup-simplify]: Simplify 1 into 1 21.278 * [backup-simplify]: Simplify (/ 1 1) into 1 21.278 * [taylor]: Taking taylor expansion of 1/2 in k 21.278 * [backup-simplify]: Simplify 1/2 into 1/2 21.278 * [taylor]: Taking taylor expansion of (log PI) in k 21.278 * [taylor]: Taking taylor expansion of PI in k 21.278 * [backup-simplify]: Simplify PI into PI 21.279 * [backup-simplify]: Simplify (log PI) into (log PI) 21.279 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.280 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.281 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.282 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 21.282 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 21.282 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 21.282 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 21.282 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 21.282 * [taylor]: Taking taylor expansion of (/ -1 k) in k 21.282 * [taylor]: Taking taylor expansion of -1 in k 21.282 * [backup-simplify]: Simplify -1 into -1 21.282 * [taylor]: Taking taylor expansion of k in k 21.282 * [backup-simplify]: Simplify 0 into 0 21.282 * [backup-simplify]: Simplify 1 into 1 21.282 * [backup-simplify]: Simplify (/ -1 1) into -1 21.283 * [backup-simplify]: Simplify (sqrt 0) into 0 21.284 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 21.285 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 21.285 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.286 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 21.290 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 21.292 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 21.294 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 21.294 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 21.294 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 21.294 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 21.294 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.295 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.295 * [taylor]: Taking taylor expansion of 1/2 in k 21.295 * [backup-simplify]: Simplify 1/2 into 1/2 21.295 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.295 * [taylor]: Taking taylor expansion of k in k 21.295 * [backup-simplify]: Simplify 0 into 0 21.295 * [backup-simplify]: Simplify 1 into 1 21.295 * [backup-simplify]: Simplify (/ 1 1) into 1 21.295 * [taylor]: Taking taylor expansion of 1/2 in k 21.295 * [backup-simplify]: Simplify 1/2 into 1/2 21.295 * [taylor]: Taking taylor expansion of (log PI) in k 21.295 * [taylor]: Taking taylor expansion of PI in k 21.295 * [backup-simplify]: Simplify PI into PI 21.296 * [backup-simplify]: Simplify (log PI) into (log PI) 21.296 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.296 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.297 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 21.298 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 21.299 * [backup-simplify]: Simplify (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 21.299 * [backup-simplify]: Simplify (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 21.301 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +nan.0)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) 21.302 * [backup-simplify]: Simplify (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) into (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) 21.303 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.307 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 21.311 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 21.316 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 21.327 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) 21.329 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) into (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) 21.341 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (sqrt +nan.0)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) (sqrt +nan.0)))) (/ 1 (- k))) (* (sqrt +nan.0) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) into (- (* (sqrt +nan.0) (pow PI (- 1/2 (* 1/2 k)))) (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* k (sqrt +nan.0)))) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* (pow k 2) (pow (sqrt +nan.0) 3)))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* (pow k 2) (sqrt +nan.0))))))))) 21.341 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 21.341 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2))))) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) 21.341 * [approximate]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in (k n) around 0 21.341 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in n 21.341 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 21.341 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 21.341 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 21.341 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 21.341 * [taylor]: Taking taylor expansion of 1/2 in n 21.341 * [backup-simplify]: Simplify 1/2 into 1/2 21.342 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 21.342 * [taylor]: Taking taylor expansion of 1/2 in n 21.342 * [backup-simplify]: Simplify 1/2 into 1/2 21.342 * [taylor]: Taking taylor expansion of k in n 21.342 * [backup-simplify]: Simplify k into k 21.342 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 21.342 * [taylor]: Taking taylor expansion of (* 2 n) in n 21.342 * [taylor]: Taking taylor expansion of 2 in n 21.342 * [backup-simplify]: Simplify 2 into 2 21.342 * [taylor]: Taking taylor expansion of n in n 21.342 * [backup-simplify]: Simplify 0 into 0 21.342 * [backup-simplify]: Simplify 1 into 1 21.342 * [backup-simplify]: Simplify (* 2 0) into 0 21.343 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 21.344 * [backup-simplify]: Simplify (log 2) into (log 2) 21.344 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 21.344 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 21.344 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 21.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 21.345 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 21.346 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 21.346 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 21.346 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 21.346 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 21.346 * [taylor]: Taking taylor expansion of 1/4 in n 21.346 * [backup-simplify]: Simplify 1/4 into 1/4 21.346 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 21.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.346 * [taylor]: Taking taylor expansion of k in n 21.346 * [backup-simplify]: Simplify k into k 21.346 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.346 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 21.346 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 21.346 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 21.346 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in k 21.346 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 21.346 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 21.346 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 21.346 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 21.346 * [taylor]: Taking taylor expansion of 1/2 in k 21.346 * [backup-simplify]: Simplify 1/2 into 1/2 21.346 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 21.346 * [taylor]: Taking taylor expansion of 1/2 in k 21.347 * [backup-simplify]: Simplify 1/2 into 1/2 21.347 * [taylor]: Taking taylor expansion of k in k 21.347 * [backup-simplify]: Simplify 0 into 0 21.347 * [backup-simplify]: Simplify 1 into 1 21.347 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 21.347 * [taylor]: Taking taylor expansion of (* 2 n) in k 21.347 * [taylor]: Taking taylor expansion of 2 in k 21.347 * [backup-simplify]: Simplify 2 into 2 21.347 * [taylor]: Taking taylor expansion of n in k 21.347 * [backup-simplify]: Simplify n into n 21.347 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 21.347 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 21.347 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.348 * [backup-simplify]: Simplify (- 0) into 0 21.348 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.348 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 21.348 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 21.348 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 21.348 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 21.348 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 21.348 * [taylor]: Taking taylor expansion of 1/4 in k 21.348 * [backup-simplify]: Simplify 1/4 into 1/4 21.348 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 21.348 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.348 * [taylor]: Taking taylor expansion of k in k 21.348 * [backup-simplify]: Simplify 0 into 0 21.348 * [backup-simplify]: Simplify 1 into 1 21.349 * [backup-simplify]: Simplify (/ 1 1) into 1 21.349 * [backup-simplify]: Simplify (log 1) into 0 21.350 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.350 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 21.350 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 21.350 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (/ 1 k) 1/4)) in k 21.350 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 21.350 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 21.350 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 21.350 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 21.350 * [taylor]: Taking taylor expansion of 1/2 in k 21.350 * [backup-simplify]: Simplify 1/2 into 1/2 21.350 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 21.350 * [taylor]: Taking taylor expansion of 1/2 in k 21.350 * [backup-simplify]: Simplify 1/2 into 1/2 21.350 * [taylor]: Taking taylor expansion of k in k 21.350 * [backup-simplify]: Simplify 0 into 0 21.350 * [backup-simplify]: Simplify 1 into 1 21.350 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 21.350 * [taylor]: Taking taylor expansion of (* 2 n) in k 21.350 * [taylor]: Taking taylor expansion of 2 in k 21.350 * [backup-simplify]: Simplify 2 into 2 21.350 * [taylor]: Taking taylor expansion of n in k 21.350 * [backup-simplify]: Simplify n into n 21.350 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 21.350 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 21.351 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.351 * [backup-simplify]: Simplify (- 0) into 0 21.352 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.352 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 21.352 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 21.352 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k 21.352 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k 21.352 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k 21.352 * [taylor]: Taking taylor expansion of 1/4 in k 21.352 * [backup-simplify]: Simplify 1/4 into 1/4 21.352 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 21.352 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.352 * [taylor]: Taking taylor expansion of k in k 21.352 * [backup-simplify]: Simplify 0 into 0 21.352 * [backup-simplify]: Simplify 1 into 1 21.352 * [backup-simplify]: Simplify (/ 1 1) into 1 21.353 * [backup-simplify]: Simplify (log 1) into 0 21.353 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.353 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k)) 21.353 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4) 21.354 * [backup-simplify]: Simplify (* (pow (* 2 n) 1/2) (pow k -1/4)) into (* (sqrt (* n 2)) (pow (/ 1 k) 1/4)) 21.355 * [taylor]: Taking taylor expansion of (* (sqrt (* n 2)) (pow (/ 1 k) 1/4)) in n 21.355 * [taylor]: Taking taylor expansion of (sqrt (* n 2)) in n 21.355 * [taylor]: Taking taylor expansion of (* n 2) in n 21.355 * [taylor]: Taking taylor expansion of n in n 21.355 * [backup-simplify]: Simplify 0 into 0 21.355 * [backup-simplify]: Simplify 1 into 1 21.355 * [taylor]: Taking taylor expansion of 2 in n 21.355 * [backup-simplify]: Simplify 2 into 2 21.355 * [backup-simplify]: Simplify (* 0 2) into 0 21.356 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 2)) into 2 21.357 * [backup-simplify]: Simplify (sqrt 0) into 0 21.358 * [backup-simplify]: Simplify (/ 2 (* 2 (sqrt 0))) into +nan.0 21.358 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 21.358 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 21.359 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 21.359 * [taylor]: Taking taylor expansion of 1/4 in n 21.359 * [backup-simplify]: Simplify 1/4 into 1/4 21.359 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 21.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.359 * [taylor]: Taking taylor expansion of k in n 21.359 * [backup-simplify]: Simplify k into k 21.359 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.359 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 21.359 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 21.359 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 21.359 * [backup-simplify]: Simplify (* 0 (pow (/ 1 k) 1/4)) into 0 21.359 * [backup-simplify]: Simplify 0 into 0 21.360 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 21.361 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 21.362 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.362 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0 21.363 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 21.363 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 n)) into 0 21.364 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 21.364 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 21.365 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.365 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.365 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 21.365 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1)))) into (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 21.366 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) 0) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow k -1/4))) into (- (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (* (sqrt n) (pow (/ 1 k) 1/4))))) 21.366 * [taylor]: Taking taylor expansion of (- (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (* (sqrt n) (pow (/ 1 k) 1/4))))) in n 21.366 * [taylor]: Taking taylor expansion of (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (* (sqrt n) (pow (/ 1 k) 1/4)))) in n 21.366 * [taylor]: Taking taylor expansion of 1/2 in n 21.366 * [backup-simplify]: Simplify 1/2 into 1/2 21.366 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (* (sqrt n) (pow (/ 1 k) 1/4))) in n 21.366 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 21.366 * [taylor]: Taking taylor expansion of (sqrt 2) in n 21.366 * [taylor]: Taking taylor expansion of 2 in n 21.366 * [backup-simplify]: Simplify 2 into 2 21.366 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 21.366 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 21.366 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 21.366 * [taylor]: Taking taylor expansion of (* 2 n) in n 21.366 * [taylor]: Taking taylor expansion of 2 in n 21.367 * [backup-simplify]: Simplify 2 into 2 21.367 * [taylor]: Taking taylor expansion of n in n 21.367 * [backup-simplify]: Simplify 0 into 0 21.367 * [backup-simplify]: Simplify 1 into 1 21.367 * [backup-simplify]: Simplify (* 2 0) into 0 21.367 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 21.367 * [backup-simplify]: Simplify (log 2) into (log 2) 21.368 * [taylor]: Taking taylor expansion of (* (sqrt n) (pow (/ 1 k) 1/4)) in n 21.368 * [taylor]: Taking taylor expansion of (sqrt n) in n 21.368 * [taylor]: Taking taylor expansion of n in n 21.368 * [backup-simplify]: Simplify 0 into 0 21.368 * [backup-simplify]: Simplify 1 into 1 21.368 * [backup-simplify]: Simplify (sqrt 0) into 0 21.369 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 21.369 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 21.369 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 21.369 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 21.369 * [taylor]: Taking taylor expansion of 1/4 in n 21.369 * [backup-simplify]: Simplify 1/4 into 1/4 21.369 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 21.369 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.369 * [taylor]: Taking taylor expansion of k in n 21.369 * [backup-simplify]: Simplify k into k 21.369 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.369 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 21.369 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 21.369 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 21.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 21.370 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 21.370 * [backup-simplify]: Simplify (* 0 (pow (/ 1 k) 1/4)) into 0 21.371 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 21.371 * [backup-simplify]: Simplify (* 1/2 0) into 0 21.371 * [backup-simplify]: Simplify (- 0) into 0 21.371 * [backup-simplify]: Simplify 0 into 0 21.371 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 21.372 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 21.372 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 21.373 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 21.373 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (/ 1 k) 1/4))) into (- (* +nan.0 (pow (/ 1 k) 1/4))) 21.373 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 k) 1/4))) into (- (* +nan.0 (pow (/ 1 k) 1/4))) 21.374 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.376 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 21.376 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 21.376 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 21.377 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.378 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 21.379 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 21.379 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 21.380 * [backup-simplify]: Simplify (- 0) into 0 21.380 * [backup-simplify]: Simplify (+ 0 0) into 0 21.380 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 21.381 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) 21.381 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) 0) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) 0) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow k -1/4)))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (* (sqrt n) (pow (/ 1 k) 1/4)))) 21.382 * [taylor]: Taking taylor expansion of (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (* (sqrt n) (pow (/ 1 k) 1/4)))) in n 21.382 * [taylor]: Taking taylor expansion of 1/8 in n 21.382 * [backup-simplify]: Simplify 1/8 into 1/8 21.382 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (* (sqrt n) (pow (/ 1 k) 1/4))) in n 21.382 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 n)) 2)) in n 21.382 * [taylor]: Taking taylor expansion of (sqrt 2) in n 21.382 * [taylor]: Taking taylor expansion of 2 in n 21.382 * [backup-simplify]: Simplify 2 into 2 21.382 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 21.382 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 21.382 * [taylor]: Taking taylor expansion of (pow (log (* 2 n)) 2) in n 21.382 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 21.382 * [taylor]: Taking taylor expansion of (* 2 n) in n 21.382 * [taylor]: Taking taylor expansion of 2 in n 21.382 * [backup-simplify]: Simplify 2 into 2 21.382 * [taylor]: Taking taylor expansion of n in n 21.382 * [backup-simplify]: Simplify 0 into 0 21.382 * [backup-simplify]: Simplify 1 into 1 21.383 * [backup-simplify]: Simplify (* 2 0) into 0 21.383 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 21.383 * [backup-simplify]: Simplify (log 2) into (log 2) 21.384 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 21.384 * [taylor]: Taking taylor expansion of (* (sqrt n) (pow (/ 1 k) 1/4)) in n 21.384 * [taylor]: Taking taylor expansion of (sqrt n) in n 21.384 * [taylor]: Taking taylor expansion of n in n 21.384 * [backup-simplify]: Simplify 0 into 0 21.384 * [backup-simplify]: Simplify 1 into 1 21.384 * [backup-simplify]: Simplify (sqrt 0) into 0 21.385 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 21.385 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in n 21.385 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in n 21.385 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in n 21.385 * [taylor]: Taking taylor expansion of 1/4 in n 21.385 * [backup-simplify]: Simplify 1/4 into 1/4 21.385 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in n 21.385 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.385 * [taylor]: Taking taylor expansion of k in n 21.385 * [backup-simplify]: Simplify k into k 21.385 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.385 * [backup-simplify]: Simplify (log (/ 1 k)) into (log (/ 1 k)) 21.385 * [backup-simplify]: Simplify (* 1/4 (log (/ 1 k))) into (* 1/4 (log (/ 1 k))) 21.385 * [backup-simplify]: Simplify (exp (* 1/4 (log (/ 1 k)))) into (pow (/ 1 k) 1/4) 21.386 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 21.386 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 21.387 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) (+ (log 2) (log n))) into (pow (+ (log 2) (log n)) 2) 21.387 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log 2) (log n)) 2)) into (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 21.388 * [backup-simplify]: Simplify (* 0 (pow (/ 1 k) 1/4)) into 0 21.388 * [backup-simplify]: Simplify (* (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 0) into 0 21.388 * [backup-simplify]: Simplify (* 1/8 0) into 0 21.388 * [backup-simplify]: Simplify 0 into 0 21.388 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 21.389 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (/ 1 k) 1)))) 1) into 0 21.389 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log (/ 1 k)))) into 0 21.390 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 21.390 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (/ 1 k) 1/4))) into (- (* +nan.0 (pow (/ 1 k) 1/4))) 21.391 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 21.392 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 21.392 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 21.393 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log 2) (log n)))) into 0 21.394 * [backup-simplify]: Simplify (+ (* (* (+ (log 2) (log n)) (sqrt 2)) (- (* +nan.0 (pow (/ 1 k) 1/4)))) (* 0 0)) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4)))))) 21.396 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4))))))) (* 0 0)) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4)))))) 21.398 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4))))))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4)))))) 21.400 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4)))))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4)))))) 21.401 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 21.402 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (/ 1 k) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (/ 1 k) 1)))) 2) into 0 21.403 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log (/ 1 k))))) into 0 21.404 * [backup-simplify]: Simplify (* (exp (* 1/4 (log (/ 1 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.405 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 2))) into 0 21.408 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 21.409 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (/ 1 k) 1/4)))) into (- (* +nan.0 (pow (/ 1 k) 1/4))) 21.409 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 k) 1/4))) into (- (* +nan.0 (pow (/ 1 k) 1/4))) 21.413 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (/ 1 k) 1/4))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (pow (/ 1 k) 1/4)))))) (* n k)) (* (- (* +nan.0 (pow (/ 1 k) 1/4))) (* n 1)))) into (- (+ (* +nan.0 (* (pow n 2) (pow (/ 1 k) 1/4))) (- (+ (* +nan.0 (* n (pow (/ 1 k) 1/4))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) n)) (pow (pow k 3) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (* n (log n))) (pow (pow k 3) 1/4)))))))))) 21.413 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (sqrt (/ 1 k))) (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 21.413 * [approximate]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in (k n) around 0 21.413 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in n 21.413 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 21.413 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 21.414 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 21.414 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 21.414 * [taylor]: Taking taylor expansion of 1/2 in n 21.414 * [backup-simplify]: Simplify 1/2 into 1/2 21.414 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.414 * [taylor]: Taking taylor expansion of 1/2 in n 21.414 * [backup-simplify]: Simplify 1/2 into 1/2 21.414 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.414 * [taylor]: Taking taylor expansion of k in n 21.414 * [backup-simplify]: Simplify k into k 21.414 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.414 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 21.414 * [taylor]: Taking taylor expansion of (/ 2 n) in n 21.414 * [taylor]: Taking taylor expansion of 2 in n 21.414 * [backup-simplify]: Simplify 2 into 2 21.414 * [taylor]: Taking taylor expansion of n in n 21.414 * [backup-simplify]: Simplify 0 into 0 21.414 * [backup-simplify]: Simplify 1 into 1 21.415 * [backup-simplify]: Simplify (/ 2 1) into 2 21.415 * [backup-simplify]: Simplify (log 2) into (log 2) 21.415 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.415 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 21.415 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 21.416 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 21.417 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 21.417 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 21.417 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 21.417 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 21.417 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 21.417 * [taylor]: Taking taylor expansion of 1/4 in n 21.417 * [backup-simplify]: Simplify 1/4 into 1/4 21.417 * [taylor]: Taking taylor expansion of (log k) in n 21.417 * [taylor]: Taking taylor expansion of k in n 21.417 * [backup-simplify]: Simplify k into k 21.417 * [backup-simplify]: Simplify (log k) into (log k) 21.417 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 21.418 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 21.418 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 21.418 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 21.418 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 21.418 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 21.418 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 21.418 * [taylor]: Taking taylor expansion of 1/2 in k 21.418 * [backup-simplify]: Simplify 1/2 into 1/2 21.418 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.418 * [taylor]: Taking taylor expansion of 1/2 in k 21.418 * [backup-simplify]: Simplify 1/2 into 1/2 21.418 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.418 * [taylor]: Taking taylor expansion of k in k 21.418 * [backup-simplify]: Simplify 0 into 0 21.418 * [backup-simplify]: Simplify 1 into 1 21.418 * [backup-simplify]: Simplify (/ 1 1) into 1 21.418 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 21.418 * [taylor]: Taking taylor expansion of (/ 2 n) in k 21.418 * [taylor]: Taking taylor expansion of 2 in k 21.418 * [backup-simplify]: Simplify 2 into 2 21.418 * [taylor]: Taking taylor expansion of n in k 21.418 * [backup-simplify]: Simplify n into n 21.418 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 21.419 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 21.419 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.419 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.420 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.420 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 21.420 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 21.420 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 21.420 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 21.420 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 21.420 * [taylor]: Taking taylor expansion of 1/4 in k 21.420 * [backup-simplify]: Simplify 1/4 into 1/4 21.420 * [taylor]: Taking taylor expansion of (log k) in k 21.420 * [taylor]: Taking taylor expansion of k in k 21.420 * [backup-simplify]: Simplify 0 into 0 21.420 * [backup-simplify]: Simplify 1 into 1 21.421 * [backup-simplify]: Simplify (log 1) into 0 21.421 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.421 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 21.421 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 21.421 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in k 21.421 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 21.421 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 21.421 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 21.421 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 21.421 * [taylor]: Taking taylor expansion of 1/2 in k 21.421 * [backup-simplify]: Simplify 1/2 into 1/2 21.421 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.421 * [taylor]: Taking taylor expansion of 1/2 in k 21.421 * [backup-simplify]: Simplify 1/2 into 1/2 21.421 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.421 * [taylor]: Taking taylor expansion of k in k 21.422 * [backup-simplify]: Simplify 0 into 0 21.422 * [backup-simplify]: Simplify 1 into 1 21.422 * [backup-simplify]: Simplify (/ 1 1) into 1 21.422 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 21.422 * [taylor]: Taking taylor expansion of (/ 2 n) in k 21.422 * [taylor]: Taking taylor expansion of 2 in k 21.422 * [backup-simplify]: Simplify 2 into 2 21.422 * [taylor]: Taking taylor expansion of n in k 21.422 * [backup-simplify]: Simplify n into n 21.422 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 21.422 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 21.423 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.423 * [backup-simplify]: Simplify (- 1/2) into -1/2 21.424 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 21.424 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 21.424 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 21.424 * [taylor]: Taking taylor expansion of (pow k 1/4) in k 21.424 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k 21.424 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k 21.424 * [taylor]: Taking taylor expansion of 1/4 in k 21.424 * [backup-simplify]: Simplify 1/4 into 1/4 21.424 * [taylor]: Taking taylor expansion of (log k) in k 21.424 * [taylor]: Taking taylor expansion of k in k 21.424 * [backup-simplify]: Simplify 0 into 0 21.424 * [backup-simplify]: Simplify 1 into 1 21.425 * [backup-simplify]: Simplify (log 1) into 0 21.425 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.425 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 21.425 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 21.425 * [backup-simplify]: Simplify (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) 21.426 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (pow k 1/4)) in n 21.426 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 21.426 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 21.426 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 21.426 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 21.426 * [taylor]: Taking taylor expansion of 1/2 in n 21.426 * [backup-simplify]: Simplify 1/2 into 1/2 21.426 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.426 * [taylor]: Taking taylor expansion of 1/2 in n 21.426 * [backup-simplify]: Simplify 1/2 into 1/2 21.426 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.426 * [taylor]: Taking taylor expansion of k in n 21.426 * [backup-simplify]: Simplify k into k 21.426 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.426 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 21.426 * [taylor]: Taking taylor expansion of (/ 2 n) in n 21.426 * [taylor]: Taking taylor expansion of 2 in n 21.426 * [backup-simplify]: Simplify 2 into 2 21.426 * [taylor]: Taking taylor expansion of n in n 21.426 * [backup-simplify]: Simplify 0 into 0 21.426 * [backup-simplify]: Simplify 1 into 1 21.427 * [backup-simplify]: Simplify (/ 2 1) into 2 21.427 * [backup-simplify]: Simplify (log 2) into (log 2) 21.427 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.427 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 21.427 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 21.428 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 21.429 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 21.429 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 21.429 * [taylor]: Taking taylor expansion of (pow k 1/4) in n 21.429 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in n 21.429 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in n 21.429 * [taylor]: Taking taylor expansion of 1/4 in n 21.429 * [backup-simplify]: Simplify 1/4 into 1/4 21.430 * [taylor]: Taking taylor expansion of (log k) in n 21.430 * [taylor]: Taking taylor expansion of k in n 21.430 * [backup-simplify]: Simplify k into k 21.430 * [backup-simplify]: Simplify (log k) into (log k) 21.430 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k)) 21.430 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4) 21.430 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (pow k 1/4)) into (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 21.431 * [backup-simplify]: Simplify (* (pow k 1/4) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (pow k 1/4)) 21.432 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 21.433 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.433 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 21.434 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 21.434 * [backup-simplify]: Simplify (+ (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow k 1/4))) into 0 21.434 * [taylor]: Taking taylor expansion of 0 in n 21.434 * [backup-simplify]: Simplify 0 into 0 21.434 * [backup-simplify]: Simplify 0 into 0 21.435 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow k 1)))) 1) into 0 21.436 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0 21.436 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 21.437 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 21.439 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 21.439 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 21.439 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 21.439 * [backup-simplify]: Simplify (- 0) into 0 21.440 * [backup-simplify]: Simplify (+ 0 0) into 0 21.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 21.441 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 21.442 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 21.443 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (* 0 (pow k 1/4))) into 0 21.443 * [backup-simplify]: Simplify 0 into 0 21.446 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 21.446 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.447 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 21.448 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.448 * [backup-simplify]: Simplify (+ (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 21.448 * [taylor]: Taking taylor expansion of 0 in n 21.448 * [backup-simplify]: Simplify 0 into 0 21.448 * [backup-simplify]: Simplify 0 into 0 21.448 * [backup-simplify]: Simplify 0 into 0 21.449 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow k 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow k 1)))) 2) into 0 21.450 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0 21.450 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.451 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.453 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 21.453 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 21.453 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 21.453 * [backup-simplify]: Simplify (- 0) into 0 21.454 * [backup-simplify]: Simplify (+ 0 0) into 0 21.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 21.455 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 21.456 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 21.457 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0 21.457 * [backup-simplify]: Simplify 0 into 0 21.465 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 21.466 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 21.467 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 21.468 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 21.468 * [backup-simplify]: Simplify (+ (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0 21.468 * [taylor]: Taking taylor expansion of 0 in n 21.469 * [backup-simplify]: Simplify 0 into 0 21.469 * [backup-simplify]: Simplify 0 into 0 21.469 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) (pow (/ 1 k) 1/4)) into (* (pow (/ 1 k) 1/4) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) 21.469 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (sqrt (/ 1 (- k)))) (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))))) into (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 21.469 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 21.469 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in n 21.469 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in n 21.469 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in n 21.469 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 21.469 * [taylor]: Taking taylor expansion of (/ -1 k) in n 21.469 * [taylor]: Taking taylor expansion of -1 in n 21.469 * [backup-simplify]: Simplify -1 into -1 21.469 * [taylor]: Taking taylor expansion of k in n 21.469 * [backup-simplify]: Simplify k into k 21.469 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 21.469 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 21.470 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 21.470 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 21.470 * [backup-simplify]: Simplify (/ 1 (sqrt (/ -1 k))) into (/ 1 (sqrt (/ -1 k))) 21.470 * [backup-simplify]: Simplify (sqrt (/ 1 (sqrt (/ -1 k)))) into (sqrt (/ 1 (sqrt (/ -1 k)))) 21.470 * [backup-simplify]: Simplify (- (+ (* (/ 1 (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 21.470 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 (sqrt (/ -1 k)))))) into 0 21.470 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 21.470 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 21.470 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 21.470 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 21.470 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.470 * [taylor]: Taking taylor expansion of 1/2 in n 21.470 * [backup-simplify]: Simplify 1/2 into 1/2 21.470 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.470 * [taylor]: Taking taylor expansion of k in n 21.470 * [backup-simplify]: Simplify k into k 21.470 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.470 * [taylor]: Taking taylor expansion of 1/2 in n 21.470 * [backup-simplify]: Simplify 1/2 into 1/2 21.470 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 21.470 * [taylor]: Taking taylor expansion of (/ -2 n) in n 21.470 * [taylor]: Taking taylor expansion of -2 in n 21.470 * [backup-simplify]: Simplify -2 into -2 21.470 * [taylor]: Taking taylor expansion of n in n 21.470 * [backup-simplify]: Simplify 0 into 0 21.470 * [backup-simplify]: Simplify 1 into 1 21.470 * [backup-simplify]: Simplify (/ -2 1) into -2 21.471 * [backup-simplify]: Simplify (log -2) into (log -2) 21.471 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.471 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.472 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.472 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.472 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in k 21.472 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 21.472 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 21.472 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 21.472 * [taylor]: Taking taylor expansion of (/ -1 k) in k 21.472 * [taylor]: Taking taylor expansion of -1 in k 21.472 * [backup-simplify]: Simplify -1 into -1 21.472 * [taylor]: Taking taylor expansion of k in k 21.472 * [backup-simplify]: Simplify 0 into 0 21.472 * [backup-simplify]: Simplify 1 into 1 21.473 * [backup-simplify]: Simplify (/ -1 1) into -1 21.473 * [backup-simplify]: Simplify (sqrt 0) into 0 21.474 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 21.474 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 21.475 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.475 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 21.477 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 21.479 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 21.481 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 21.481 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 21.481 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 21.481 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 21.482 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.482 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.482 * [taylor]: Taking taylor expansion of 1/2 in k 21.482 * [backup-simplify]: Simplify 1/2 into 1/2 21.482 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.482 * [taylor]: Taking taylor expansion of k in k 21.482 * [backup-simplify]: Simplify 0 into 0 21.482 * [backup-simplify]: Simplify 1 into 1 21.482 * [backup-simplify]: Simplify (/ 1 1) into 1 21.482 * [taylor]: Taking taylor expansion of 1/2 in k 21.482 * [backup-simplify]: Simplify 1/2 into 1/2 21.482 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 21.482 * [taylor]: Taking taylor expansion of (/ -2 n) in k 21.482 * [taylor]: Taking taylor expansion of -2 in k 21.482 * [backup-simplify]: Simplify -2 into -2 21.482 * [taylor]: Taking taylor expansion of n in k 21.482 * [backup-simplify]: Simplify n into n 21.482 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 21.483 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 21.483 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.484 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.484 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 21.484 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 21.484 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (sqrt (/ -1 k)))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) in k 21.484 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k 21.484 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 21.484 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 21.484 * [taylor]: Taking taylor expansion of (/ -1 k) in k 21.484 * [taylor]: Taking taylor expansion of -1 in k 21.484 * [backup-simplify]: Simplify -1 into -1 21.484 * [taylor]: Taking taylor expansion of k in k 21.484 * [backup-simplify]: Simplify 0 into 0 21.484 * [backup-simplify]: Simplify 1 into 1 21.485 * [backup-simplify]: Simplify (/ -1 1) into -1 21.485 * [backup-simplify]: Simplify (sqrt 0) into 0 21.487 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 21.487 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 21.487 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 21.491 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 21.493 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 21.495 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0)) 21.495 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 21.495 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 21.495 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 21.495 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 21.495 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 21.495 * [taylor]: Taking taylor expansion of 1/2 in k 21.495 * [backup-simplify]: Simplify 1/2 into 1/2 21.495 * [taylor]: Taking taylor expansion of (/ 1 k) in k 21.495 * [taylor]: Taking taylor expansion of k in k 21.495 * [backup-simplify]: Simplify 0 into 0 21.495 * [backup-simplify]: Simplify 1 into 1 21.496 * [backup-simplify]: Simplify (/ 1 1) into 1 21.496 * [taylor]: Taking taylor expansion of 1/2 in k 21.496 * [backup-simplify]: Simplify 1/2 into 1/2 21.496 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 21.496 * [taylor]: Taking taylor expansion of (/ -2 n) in k 21.496 * [taylor]: Taking taylor expansion of -2 in k 21.496 * [backup-simplify]: Simplify -2 into -2 21.496 * [taylor]: Taking taylor expansion of n in k 21.496 * [backup-simplify]: Simplify n into n 21.496 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 21.496 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 21.496 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 21.496 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 21.496 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 21.496 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 21.497 * [backup-simplify]: Simplify (* (sqrt +nan.0) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)) 21.497 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)) in n 21.497 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 21.497 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 21.497 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 21.497 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 21.497 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.497 * [taylor]: Taking taylor expansion of 1/2 in n 21.497 * [backup-simplify]: Simplify 1/2 into 1/2 21.497 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.497 * [taylor]: Taking taylor expansion of k in n 21.497 * [backup-simplify]: Simplify k into k 21.497 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.497 * [taylor]: Taking taylor expansion of 1/2 in n 21.497 * [backup-simplify]: Simplify 1/2 into 1/2 21.497 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 21.497 * [taylor]: Taking taylor expansion of (/ -2 n) in n 21.497 * [taylor]: Taking taylor expansion of -2 in n 21.497 * [backup-simplify]: Simplify -2 into -2 21.497 * [taylor]: Taking taylor expansion of n in n 21.497 * [backup-simplify]: Simplify 0 into 0 21.497 * [backup-simplify]: Simplify 1 into 1 21.497 * [backup-simplify]: Simplify (/ -2 1) into -2 21.498 * [backup-simplify]: Simplify (log -2) into (log -2) 21.498 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.498 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.499 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.499 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.499 * [taylor]: Taking taylor expansion of (sqrt +nan.0) in n 21.499 * [taylor]: Taking taylor expansion of +nan.0 in n 21.499 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.499 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.500 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0 21.500 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) 21.501 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) 21.502 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (* (/ +nan.0 (sqrt +nan.0)) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)))) into (- (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) 21.502 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) in n 21.502 * [taylor]: Taking taylor expansion of (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0))) in n 21.502 * [taylor]: Taking taylor expansion of +nan.0 in n 21.502 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.502 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)) in n 21.502 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 21.502 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 21.502 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 21.502 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 21.502 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.502 * [taylor]: Taking taylor expansion of 1/2 in n 21.502 * [backup-simplify]: Simplify 1/2 into 1/2 21.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.502 * [taylor]: Taking taylor expansion of k in n 21.502 * [backup-simplify]: Simplify k into k 21.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.502 * [taylor]: Taking taylor expansion of 1/2 in n 21.502 * [backup-simplify]: Simplify 1/2 into 1/2 21.502 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 21.502 * [taylor]: Taking taylor expansion of (/ -2 n) in n 21.502 * [taylor]: Taking taylor expansion of -2 in n 21.502 * [backup-simplify]: Simplify -2 into -2 21.502 * [taylor]: Taking taylor expansion of n in n 21.502 * [backup-simplify]: Simplify 0 into 0 21.502 * [backup-simplify]: Simplify 1 into 1 21.503 * [backup-simplify]: Simplify (/ -2 1) into -2 21.503 * [backup-simplify]: Simplify (log -2) into (log -2) 21.503 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.503 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.504 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.504 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.504 * [taylor]: Taking taylor expansion of (sqrt +nan.0) in n 21.504 * [taylor]: Taking taylor expansion of +nan.0 in n 21.504 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.504 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.505 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0 21.505 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) 21.506 * [backup-simplify]: Simplify (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) into (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) 21.507 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) 21.507 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) 21.508 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 21.509 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 21.509 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 21.509 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 21.509 * [backup-simplify]: Simplify (+ 0 0) into 0 21.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.510 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 21.511 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 21.512 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (sqrt +nan.0))) into 0 21.512 * [backup-simplify]: Simplify 0 into 0 21.512 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 21.515 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 21.517 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 21.520 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) 21.527 * [backup-simplify]: Simplify (+ (* (sqrt +nan.0) 0) (+ (* (/ +nan.0 (sqrt +nan.0)) 0) (* (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (+ (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) 21.527 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))))) in n 21.527 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0))))) in n 21.527 * [taylor]: Taking taylor expansion of (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3))) in n 21.528 * [taylor]: Taking taylor expansion of +nan.0 in n 21.528 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.528 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow (sqrt +nan.0) 3)) in n 21.528 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 21.528 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 21.528 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 21.528 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 21.528 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.528 * [taylor]: Taking taylor expansion of 1/2 in n 21.528 * [backup-simplify]: Simplify 1/2 into 1/2 21.528 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.528 * [taylor]: Taking taylor expansion of k in n 21.528 * [backup-simplify]: Simplify k into k 21.528 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.528 * [taylor]: Taking taylor expansion of 1/2 in n 21.528 * [backup-simplify]: Simplify 1/2 into 1/2 21.528 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 21.528 * [taylor]: Taking taylor expansion of (/ -2 n) in n 21.528 * [taylor]: Taking taylor expansion of -2 in n 21.528 * [backup-simplify]: Simplify -2 into -2 21.528 * [taylor]: Taking taylor expansion of n in n 21.528 * [backup-simplify]: Simplify 0 into 0 21.528 * [backup-simplify]: Simplify 1 into 1 21.529 * [backup-simplify]: Simplify (/ -2 1) into -2 21.529 * [backup-simplify]: Simplify (log -2) into (log -2) 21.529 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.529 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.530 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.531 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.531 * [taylor]: Taking taylor expansion of (pow (sqrt +nan.0) 3) in n 21.531 * [taylor]: Taking taylor expansion of (sqrt +nan.0) in n 21.531 * [taylor]: Taking taylor expansion of +nan.0 in n 21.531 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.531 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.532 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0 21.534 * [backup-simplify]: Simplify (* (sqrt +nan.0) (sqrt +nan.0)) into (pow (sqrt +nan.0) 2) 21.536 * [backup-simplify]: Simplify (* (sqrt +nan.0) (pow (sqrt +nan.0) 2)) into (pow (sqrt +nan.0) 3) 21.537 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)) 21.538 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)))) in n 21.538 * [taylor]: Taking taylor expansion of (* +nan.0 (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0))) in n 21.538 * [taylor]: Taking taylor expansion of +nan.0 in n 21.538 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.538 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt +nan.0)) in n 21.538 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 21.538 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 21.538 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 21.538 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 21.538 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 21.538 * [taylor]: Taking taylor expansion of 1/2 in n 21.538 * [backup-simplify]: Simplify 1/2 into 1/2 21.538 * [taylor]: Taking taylor expansion of (/ 1 k) in n 21.538 * [taylor]: Taking taylor expansion of k in n 21.538 * [backup-simplify]: Simplify k into k 21.538 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 21.538 * [taylor]: Taking taylor expansion of 1/2 in n 21.538 * [backup-simplify]: Simplify 1/2 into 1/2 21.538 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 21.538 * [taylor]: Taking taylor expansion of (/ -2 n) in n 21.538 * [taylor]: Taking taylor expansion of -2 in n 21.538 * [backup-simplify]: Simplify -2 into -2 21.538 * [taylor]: Taking taylor expansion of n in n 21.538 * [backup-simplify]: Simplify 0 into 0 21.538 * [backup-simplify]: Simplify 1 into 1 21.539 * [backup-simplify]: Simplify (/ -2 1) into -2 21.539 * [backup-simplify]: Simplify (log -2) into (log -2) 21.539 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 21.539 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 21.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 21.541 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 21.541 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 21.541 * [taylor]: Taking taylor expansion of (sqrt +nan.0) in n 21.541 * [taylor]: Taking taylor expansion of +nan.0 in n 21.541 * [backup-simplify]: Simplify +nan.0 into +nan.0 21.542 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0) 21.542 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt +nan.0))) into 0 21.543 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)) 21.545 * [backup-simplify]: Simplify (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3))) into (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3))) 21.545 * [backup-simplify]: Simplify (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) into (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) 21.546 * [backup-simplify]: Simplify (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) into (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0)))) 21.548 * [backup-simplify]: Simplify (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)))))) 21.551 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3))))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)))))) 21.553 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow (sqrt +nan.0) 3)))))) 21.556 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0))) (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow (sqrt +nan.0) 3)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0)))) (* 1 (/ 1 (- k)))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (sqrt +nan.0)))) into (- (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 21.556 * * * [progress]: simplifying candidates 21.557 * * * * [progress]: [ 1 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 2 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 3 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 4 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 5 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 6 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 7 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 8 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 9 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 10 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 11 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 12 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 13 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 14 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 15 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 16 / 2361 ] simplifiying candidate # 21.557 * * * * [progress]: [ 17 / 2361 ] simplifiying candidate # 21.557 * * * * 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[progress]: [ 63 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 64 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 65 / 2361 ] simplifiying candidate #real (real->posit16 (pow (* n 2) (- 1/2 (/ k 2)))))))))> 21.560 * * * * [progress]: [ 66 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 67 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 68 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 69 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 70 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 71 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 72 / 2361 ] simplifiying candidate # 21.560 * * * * [progress]: [ 73 / 2361 ] simplifiying candidate # 21.561 * * * * [progress]: [ 74 / 2361 ] simplifiying candidate # 21.561 * * * * [progress]: [ 75 / 2361 ] simplifiying candidate # 21.561 * * * * [progress]: [ 76 / 2361 ] simplifiying candidate # 21.561 * * * * [progress]: [ 77 / 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simplifiying candidate # 21.562 * * * * [progress]: [ 108 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 109 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 110 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 111 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 112 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 113 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 114 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 115 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 116 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 117 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 118 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 119 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 120 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 121 / 2361 ] simplifiying candidate # 21.563 * * * * [progress]: [ 122 / 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2361 ] simplifiying candidate # 21.740 * * * * [progress]: [ 1892 / 2361 ] simplifiying candidate # 21.740 * * * * [progress]: [ 1893 / 2361 ] simplifiying candidate # 21.740 * * * * [progress]: [ 1894 / 2361 ] simplifiying candidate # 21.740 * * * * [progress]: [ 1895 / 2361 ] simplifiying candidate # 21.740 * * * * [progress]: [ 1896 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1897 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1898 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1899 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1900 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1901 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1902 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1903 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1904 / 2361 ] simplifiying candidate # 21.741 * * * * [progress]: [ 1905 / 2361 ] simplifiying candidate # 21.741 * * * * 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2361 ] simplifiying candidate # 21.744 * * * * [progress]: [ 1936 / 2361 ] simplifiying candidate # 21.744 * * * * [progress]: [ 1937 / 2361 ] simplifiying candidate # 21.744 * * * * [progress]: [ 1938 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1939 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1940 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1941 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1942 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1943 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1944 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1945 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1946 / 2361 ] simplifiying candidate # 21.745 * * * * [progress]: [ 1947 / 2361 ] simplifiying candidate # 21.746 * * * * [progress]: [ 1948 / 2361 ] simplifiying candidate # 21.746 * * * * [progress]: [ 1949 / 2361 ] simplifiying candidate # 21.746 * * * * 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candidate # 21.747 * * * * [progress]: [ 1965 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1966 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1967 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1968 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1969 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1970 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1971 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1972 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1973 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1974 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1975 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1976 / 2361 ] simplifiying candidate # 21.748 * * * * [progress]: [ 1977 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1978 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1979 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1980 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1981 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1982 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1983 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1984 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1985 / 2361 ] simplifiying candidate # 21.749 * * * * [progress]: [ 1986 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1987 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1988 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1989 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1990 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1991 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1992 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1993 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1994 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1995 / 2361 ] simplifiying candidate # 21.750 * * * * [progress]: [ 1996 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 1997 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 1998 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 1999 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2000 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2001 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2002 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2003 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2004 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2005 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2006 / 2361 ] simplifiying candidate # 21.751 * * * * [progress]: [ 2007 / 2361 ] simplifiying candidate # 21.752 * * * * [progress]: [ 2008 / 2361 ] simplifiying 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2361 ] simplifiying candidate # 21.789 * * * * [progress]: [ 2332 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2333 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2334 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2335 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2336 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2337 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2338 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2339 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2340 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2341 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2342 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2343 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2344 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2345 / 2361 ] simplifiying candidate # 21.790 * * * * [progress]: [ 2346 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2347 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2348 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2349 / 2361 ] simplifiying candidate #real (real->posit16 (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))))))> 21.791 * * * * [progress]: [ 2350 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2351 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2352 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2353 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2354 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2355 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2356 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2357 / 2361 ] simplifiying candidate # 21.791 * * * * [progress]: [ 2358 / 2361 ] simplifiying candidate # 21.792 * * * * [progress]: [ 2359 / 2361 ] simplifiying candidate # 21.792 * * * * [progress]: [ 2360 / 2361 ] simplifiying candidate # 21.792 * * * * [progress]: [ 2361 / 2361 ] simplifiying candidate # 21.894 * [simplify]: Simplifying: (expm1 (pow (* n 2) (- 1/2 (/ k 2)))) (log1p (pow (* n 2) (- 1/2 (/ k 2)))) (* (+ (log n) (log 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (* 1 (- 1/2 (/ k 2))) (pow (* n 2) 1/2) (pow (* n 2) (/ k 2)) (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (pow (* n 2) 1) (pow (* n 2) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* n 2) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* n 2) 1) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (pow (* n 2) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ 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PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (- (+ (* (sqrt PI) (pow (/ 1 k) 1/4)) (* 1/8 (* (pow (log PI) 2) (* (sqrt PI) (pow (pow k 7) 1/4))))) (* 1/2 (* (log PI) (* (sqrt PI) (pow (pow k 3) 1/4))))) (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* 1/2 k)))) (- (* (sqrt +nan.0) (pow PI (- 1/2 (* 1/2 k)))) (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* k (sqrt +nan.0)))) (- (+ (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* (pow k 2) (pow (sqrt +nan.0) 3)))) (- (* +nan.0 (/ (pow PI (- 1/2 (* 1/2 k))) (* (pow k 2) (sqrt +nan.0))))))))) (- (+ (* +nan.0 (* (pow n 2) (pow (/ 1 k) 1/4))) (- (+ (* +nan.0 (* n (pow (/ 1 k) 1/4))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) n)) (pow (pow k 3) 1/4))) (- (* +nan.0 (* (* (sqrt 2) (* n (log n))) (pow (pow k 3) 1/4)))))))))) (* (pow (/ 1 k) 1/4) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (- (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (sqrt +nan.0)) (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (sqrt +nan.0) k))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* (pow (sqrt +nan.0) 3) (pow k 2))))))))) 22.032 * * [simplify]: iteration 1: (2609 enodes) 185.245 * * [simplify]: Extracting #0: cost 706 inf + 0 185.250 * * [simplify]: Extracting #1: cost 2275 inf + 3 185.260 * * [simplify]: Extracting #2: cost 2373 inf + 6140 185.269 * * [simplify]: Extracting #3: cost 2429 inf + 12384 185.284 * * [simplify]: Extracting #4: cost 2173 inf + 82813 185.324 * * [simplify]: Extracting #5: cost 1482 inf + 338232 185.398 * * [simplify]: Extracting #6: cost 794 inf + 645950 185.515 * * [simplify]: Extracting #7: cost 302 inf + 990092 185.664 * * [simplify]: Extracting #8: cost 45 inf + 1183406 185.818 * * [simplify]: Extracting #9: cost 5 inf + 1214372 185.973 * * [simplify]: Extracting #10: cost 1 inf + 1218460 186.128 * * [simplify]: Extracting #11: cost 0 inf + 1219912 186.311 * [simplify]: Simplified to: (expm1 (pow (* n 2) (- 1/2 (/ k 2)))) (log1p (pow (* n 2) (- 1/2 (/ k 2)))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* n 2)) (pow (* n 2) (/ k 2)) (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* n 2) (sqrt (- 1/2 (/ k 2)))) (* n 2) (pow (* n 2) (+ (sqrt (/ k 2)) (sqrt 1/2))) (pow (* n 2) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2))) (* n 2) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (pow (* n 2) (+ (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))) (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* n 2) (+ (/ (- k) 2) (/ k 2))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) 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(pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (sqrt k) (sqrt k)) 2))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* k 1/2)))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (- (/ (cbrt k) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k)))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (- (sqrt k)) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (sqrt k) (sqrt k)) 2))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* k 1/2))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (* (- (/ (cbrt k) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (* (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (+ 1/2 (* (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (* (/ (- (sqrt k)) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (+ 1/2 (- (/ (* (sqrt k) (sqrt k)) 2)))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (+ 1/2 (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (+ 1/2 (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow (* n 2) (- 1/2 (* k 1/2)))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (sqrt (* n 2)))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (sqrt (* n 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (pow n (- 1/2 (/ k 2)))) (* (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2)))))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (sqrt (pow (* n 2) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (/ (sqrt (sqrt (sqrt k))) (pow (* n 2) (- 1/4 (/ (/ k 2) 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (/ (cbrt k) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (- (sqrt k)) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (sqrt k) (sqrt k)) 2)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* k 1/2)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (- (/ (cbrt k) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (- (sqrt k)) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (sqrt k) (sqrt k)) 2)))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* n 2) (fma (sqrt 1/2) (sqrt 1/2) (- (* k 1/2)))) (pow (* n 2) (+ 1/2 (- (* (* (cbrt (/ k 2)) (cbrt (/ k 2))) (cbrt (/ k 2)))))) (pow (* n 2) (+ 1/2 (/ (- k) 2))) (pow (* n 2) (+ 1/2 (* (- (/ (cbrt k) (cbrt 2))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow (* n 2) (+ 1/2 (* (/ (- (cbrt k)) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n 2) (+ 1/2 (* (- (/ (cbrt k) 2)) (* (cbrt k) (cbrt k))))) (pow (* n 2) (+ 1/2 (* (/ (- (sqrt k)) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (+ 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n 2) (+ 1/2 (- (/ (* (sqrt k) (sqrt k)) 2)))) (pow (* n 2) (+ 1/2 (- (/ (* (/ k (cbrt 2)) 1) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* n 2) (+ 1/2 (/ (- k) 2))) (pow (* n 2) (+ 1/2 (/ (- k) 2))) (pow (* n 2) (- 1/2 (* k 1/2))) (sqrt (* n 2)) (sqrt (* n 2)) (pow n (- 1/2 (/ k 2))) (* (cbrt (pow (* n 2) (- 1/2 (/ k 2)))) (cbrt (pow (* n 2) (- 1/2 (/ k 2))))) (sqrt (pow (* n 2) (- 1/2 (/ k 2)))) 1 (pow (* n 2) (- 1/4 (/ (/ k 2) 2))) 1 (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (sqrt (* n 2))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (sqrt (sqrt k))) (real->posit16 (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))) (+ (exp (* (log (* n 2)) 1/2)) (- (fma 1/8 (* (* (* k k) (exp (* (log (* n 2)) 1/2))) (* (log 2) (log 2))) (fma 1/4 (* (* (exp (* (log (* n 2)) 1/2)) (* (log n) (* k k))) (log 2)) (* (* 1/8 (exp (* (log (* n 2)) 1/2))) (* (* (log n) (log n)) (* k k))))) (* 1/2 (+ (* (exp (* (log (* n 2)) 1/2)) (* k (log n))) (* (log 2) (* k (exp (* (log (* n 2)) 1/2)))))))) (exp (* (- 1/2 (* k 1/2)) (- (log 2) (- (log n))))) (exp (* (- (log -2) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (+ (sqrt PI) (- (* 1/8 (* (* (log PI) (log PI)) (* (* k k) (sqrt PI)))) (* (* (log PI) (* k (sqrt PI))) 1/2))) (pow PI (- 1/2 (* k 1/2))) (pow PI (- 1/2 (* k 1/2))) (- (fma (sqrt PI) (pow (/ 1 k) 1/4) (* 1/8 (* (* (* (log PI) (log PI)) (sqrt PI)) (pow (pow k 7) 1/4)))) (* (* (* (log PI) (sqrt PI)) (pow (* k (* k k)) 1/4)) 1/2)) (* (pow (/ 1 k) 1/4) (pow PI (- 1/2 (* k 1/2)))) (- (* (pow PI (- 1/2 (* k 1/2))) (sqrt +nan.0)) (- (/ (* +nan.0 (pow PI (- 1/2 (* k 1/2)))) (* k (sqrt +nan.0))) (- (* +nan.0 (/ (/ (pow PI (- 1/2 (* k 1/2))) (* k k)) (* (sqrt +nan.0) (* (sqrt +nan.0) (sqrt +nan.0))))) (* +nan.0 (/ (pow PI (- 1/2 (* k 1/2))) (* (sqrt +nan.0) (* k k))))))) (- (- (* +nan.0 (* (* n n) (pow (/ 1 k) 1/4))) (- (* +nan.0 (* (pow (/ 1 k) 1/4) n)) (- (* (* (pow (* k (* k k)) 1/4) (* (log 2) (* (sqrt 2) n))) +nan.0) (* (* +nan.0 (* (* (sqrt 2) n) (log n))) (pow (* k (* k k)) 1/4)))))) (* (exp (* (- 1/2 (* k 1/2)) (- (log 2) (- (log n))))) (pow (/ 1 k) 1/4)) (- (* (exp (* (- (log -2) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (sqrt +nan.0)) (- (* +nan.0 (/ (/ (exp (* (- (log -2) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (sqrt +nan.0)) (* k k))) (- (* (/ (exp (* (- (log -2) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k (sqrt +nan.0))) +nan.0) (* +nan.0 (/ (exp (* (- (log -2) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* (* (sqrt +nan.0) (* (sqrt +nan.0) (sqrt +nan.0))) (* k k))))))) 186.890 * * * [progress]: adding candidates to table 195.702 * * [progress]: iteration 4 / 4 195.702 * * * [progress]: picking best candidate 195.721 * * * * [pick]: Picked # 195.722 * * * [progress]: localizing error 195.771 * * * [progress]: generating rewritten candidates 195.772 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 195.781 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1 1) 195.781 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 2 1 1) 195.782 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1) 195.791 * * * [progress]: generating series expansions 195.791 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 195.791 * [backup-simplify]: Simplify (pow (* n 2) (- 1/2 (/ k 2))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 195.791 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 195.791 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 195.791 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 195.791 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 195.791 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 195.791 * [taylor]: Taking taylor expansion of 1/2 in k 195.791 * [backup-simplify]: Simplify 1/2 into 1/2 195.791 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 195.791 * [taylor]: Taking taylor expansion of 1/2 in k 195.791 * [backup-simplify]: Simplify 1/2 into 1/2 195.791 * [taylor]: Taking taylor expansion of k in k 195.791 * [backup-simplify]: Simplify 0 into 0 195.791 * [backup-simplify]: Simplify 1 into 1 195.791 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 195.791 * [taylor]: Taking taylor expansion of (* 2 n) in k 195.791 * [taylor]: Taking taylor expansion of 2 in k 195.791 * [backup-simplify]: Simplify 2 into 2 195.791 * [taylor]: Taking taylor expansion of n in k 195.791 * [backup-simplify]: Simplify n into n 195.791 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 195.791 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 195.792 * [backup-simplify]: Simplify (* 1/2 0) into 0 195.792 * [backup-simplify]: Simplify (- 0) into 0 195.792 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 195.792 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 195.792 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 195.792 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 195.793 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 195.793 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 195.793 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 195.793 * [taylor]: Taking taylor expansion of 1/2 in n 195.793 * [backup-simplify]: Simplify 1/2 into 1/2 195.793 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 195.793 * [taylor]: Taking taylor expansion of 1/2 in n 195.793 * [backup-simplify]: Simplify 1/2 into 1/2 195.793 * [taylor]: Taking taylor expansion of k in n 195.793 * [backup-simplify]: Simplify k into k 195.793 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 195.793 * [taylor]: Taking taylor expansion of (* 2 n) in n 195.793 * [taylor]: Taking taylor expansion of 2 in n 195.793 * [backup-simplify]: Simplify 2 into 2 195.793 * [taylor]: Taking taylor expansion of n in n 195.793 * [backup-simplify]: Simplify 0 into 0 195.793 * [backup-simplify]: Simplify 1 into 1 195.793 * [backup-simplify]: Simplify (* 2 0) into 0 195.793 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 195.794 * [backup-simplify]: Simplify (log 2) into (log 2) 195.794 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 195.794 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 195.794 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 195.794 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 195.795 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 195.795 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 195.795 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 195.795 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 195.795 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 195.795 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 195.795 * [taylor]: Taking taylor expansion of 1/2 in n 195.795 * [backup-simplify]: Simplify 1/2 into 1/2 195.795 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 195.795 * [taylor]: Taking taylor expansion of 1/2 in n 195.795 * [backup-simplify]: Simplify 1/2 into 1/2 195.795 * [taylor]: Taking taylor expansion of k in n 195.795 * [backup-simplify]: Simplify k into k 195.795 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 195.795 * [taylor]: Taking taylor expansion of (* 2 n) in n 195.795 * [taylor]: Taking taylor expansion of 2 in n 195.795 * [backup-simplify]: Simplify 2 into 2 195.795 * [taylor]: Taking taylor expansion of n in n 195.795 * [backup-simplify]: Simplify 0 into 0 195.795 * [backup-simplify]: Simplify 1 into 1 195.795 * [backup-simplify]: Simplify (* 2 0) into 0 195.796 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 195.796 * [backup-simplify]: Simplify (log 2) into (log 2) 195.796 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 195.796 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 195.796 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 195.797 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 195.797 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 195.797 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 195.797 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 195.797 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 195.797 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 195.797 * [taylor]: Taking taylor expansion of (log 2) in k 195.797 * [taylor]: Taking taylor expansion of 2 in k 195.797 * [backup-simplify]: Simplify 2 into 2 195.798 * [backup-simplify]: Simplify (log 2) into (log 2) 195.798 * [taylor]: Taking taylor expansion of (log n) in k 195.798 * [taylor]: Taking taylor expansion of n in k 195.798 * [backup-simplify]: Simplify n into n 195.798 * [backup-simplify]: Simplify (log n) into (log n) 195.798 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 195.798 * [taylor]: Taking taylor expansion of 1/2 in k 195.798 * [backup-simplify]: Simplify 1/2 into 1/2 195.798 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 195.798 * [taylor]: Taking taylor expansion of 1/2 in k 195.798 * [backup-simplify]: Simplify 1/2 into 1/2 195.798 * [taylor]: Taking taylor expansion of k in k 195.798 * [backup-simplify]: Simplify 0 into 0 195.798 * [backup-simplify]: Simplify 1 into 1 195.798 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 195.798 * [backup-simplify]: Simplify (* 1/2 0) into 0 195.799 * [backup-simplify]: Simplify (- 0) into 0 195.799 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 195.799 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 195.799 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 195.800 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 195.800 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 195.801 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 195.801 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 195.802 * [backup-simplify]: Simplify (- 0) into 0 195.802 * [backup-simplify]: Simplify (+ 0 0) into 0 195.802 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 195.803 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 195.803 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 195.803 * [taylor]: Taking taylor expansion of 0 in k 195.803 * [backup-simplify]: Simplify 0 into 0 195.803 * [backup-simplify]: Simplify 0 into 0 195.804 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 195.804 * [backup-simplify]: Simplify (- 1/2) into -1/2 195.804 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 195.805 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 195.805 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 195.806 * [backup-simplify]: Simplify (+ 0 0) into 0 195.806 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 195.807 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 195.808 * [backup-simplify]: Simplify (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) into (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 195.809 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 195.810 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 195.811 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 195.811 * [backup-simplify]: Simplify (- 0) into 0 195.811 * [backup-simplify]: Simplify (+ 0 0) into 0 195.811 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 195.812 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 195.813 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.813 * [taylor]: Taking taylor expansion of 0 in k 195.813 * [backup-simplify]: Simplify 0 into 0 195.813 * [backup-simplify]: Simplify 0 into 0 195.813 * [backup-simplify]: Simplify 0 into 0 195.814 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 195.814 * [backup-simplify]: Simplify (- 0) into 0 195.814 * [backup-simplify]: Simplify (+ 0 0) into 0 195.815 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 195.816 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 195.817 * [backup-simplify]: Simplify (+ 0 0) into 0 195.817 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 195.819 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 195.820 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) into (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) 195.823 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log 2) (log n))) (* 1/8 (pow (log 2) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* k 1)) (exp (* 1/2 (+ (log 2) (log n)))))) into (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) 195.823 * [backup-simplify]: Simplify (pow (* (/ 1 n) 2) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 195.823 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 195.823 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 195.823 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 195.823 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 195.823 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 195.823 * [taylor]: Taking taylor expansion of 1/2 in k 195.823 * [backup-simplify]: Simplify 1/2 into 1/2 195.823 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 195.823 * [taylor]: Taking taylor expansion of 1/2 in k 195.823 * [backup-simplify]: Simplify 1/2 into 1/2 195.823 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.823 * [taylor]: Taking taylor expansion of k in k 195.823 * [backup-simplify]: Simplify 0 into 0 195.823 * [backup-simplify]: Simplify 1 into 1 195.824 * [backup-simplify]: Simplify (/ 1 1) into 1 195.824 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 195.824 * [taylor]: Taking taylor expansion of (/ 2 n) in k 195.824 * [taylor]: Taking taylor expansion of 2 in k 195.824 * [backup-simplify]: Simplify 2 into 2 195.824 * [taylor]: Taking taylor expansion of n in k 195.824 * [backup-simplify]: Simplify n into n 195.824 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 195.824 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 195.824 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 195.824 * [backup-simplify]: Simplify (- 1/2) into -1/2 195.825 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 195.825 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 195.825 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 195.825 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 195.825 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 195.825 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 195.825 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 195.825 * [taylor]: Taking taylor expansion of 1/2 in n 195.825 * [backup-simplify]: Simplify 1/2 into 1/2 195.825 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 195.825 * [taylor]: Taking taylor expansion of 1/2 in n 195.825 * [backup-simplify]: Simplify 1/2 into 1/2 195.825 * [taylor]: Taking taylor expansion of (/ 1 k) in n 195.825 * [taylor]: Taking taylor expansion of k in n 195.825 * [backup-simplify]: Simplify k into k 195.825 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 195.825 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 195.825 * [taylor]: Taking taylor expansion of (/ 2 n) in n 195.825 * [taylor]: Taking taylor expansion of 2 in n 195.825 * [backup-simplify]: Simplify 2 into 2 195.825 * [taylor]: Taking taylor expansion of n in n 195.825 * [backup-simplify]: Simplify 0 into 0 195.825 * [backup-simplify]: Simplify 1 into 1 195.825 * [backup-simplify]: Simplify (/ 2 1) into 2 195.826 * [backup-simplify]: Simplify (log 2) into (log 2) 195.826 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 195.826 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 195.826 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 195.826 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 195.830 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 195.831 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 195.831 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 195.831 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 195.831 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 195.831 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 195.831 * [taylor]: Taking taylor expansion of 1/2 in n 195.831 * [backup-simplify]: Simplify 1/2 into 1/2 195.831 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 195.831 * [taylor]: Taking taylor expansion of 1/2 in n 195.831 * [backup-simplify]: Simplify 1/2 into 1/2 195.831 * [taylor]: Taking taylor expansion of (/ 1 k) in n 195.831 * [taylor]: Taking taylor expansion of k in n 195.831 * [backup-simplify]: Simplify k into k 195.831 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 195.831 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 195.831 * [taylor]: Taking taylor expansion of (/ 2 n) in n 195.831 * [taylor]: Taking taylor expansion of 2 in n 195.831 * [backup-simplify]: Simplify 2 into 2 195.831 * [taylor]: Taking taylor expansion of n in n 195.831 * [backup-simplify]: Simplify 0 into 0 195.831 * [backup-simplify]: Simplify 1 into 1 195.832 * [backup-simplify]: Simplify (/ 2 1) into 2 195.832 * [backup-simplify]: Simplify (log 2) into (log 2) 195.832 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 195.832 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 195.832 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 195.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 195.833 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 195.833 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 195.833 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 195.833 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 195.833 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 195.833 * [taylor]: Taking taylor expansion of 1/2 in k 195.833 * [backup-simplify]: Simplify 1/2 into 1/2 195.833 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 195.833 * [taylor]: Taking taylor expansion of 1/2 in k 195.833 * [backup-simplify]: Simplify 1/2 into 1/2 195.833 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.833 * [taylor]: Taking taylor expansion of k in k 195.833 * [backup-simplify]: Simplify 0 into 0 195.833 * [backup-simplify]: Simplify 1 into 1 195.834 * [backup-simplify]: Simplify (/ 1 1) into 1 195.834 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 195.834 * [taylor]: Taking taylor expansion of (log 2) in k 195.834 * [taylor]: Taking taylor expansion of 2 in k 195.834 * [backup-simplify]: Simplify 2 into 2 195.834 * [backup-simplify]: Simplify (log 2) into (log 2) 195.834 * [taylor]: Taking taylor expansion of (log n) in k 195.834 * [taylor]: Taking taylor expansion of n in k 195.834 * [backup-simplify]: Simplify n into n 195.834 * [backup-simplify]: Simplify (log n) into (log n) 195.834 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 195.834 * [backup-simplify]: Simplify (- 1/2) into -1/2 195.835 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 195.835 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 195.835 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 195.835 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 195.836 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 195.836 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 195.836 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 195.837 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 195.837 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 195.837 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 195.838 * [backup-simplify]: Simplify (- 0) into 0 195.838 * [backup-simplify]: Simplify (+ 0 0) into 0 195.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 195.839 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 195.839 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 195.839 * [taylor]: Taking taylor expansion of 0 in k 195.839 * [backup-simplify]: Simplify 0 into 0 195.839 * [backup-simplify]: Simplify 0 into 0 195.840 * [backup-simplify]: Simplify 0 into 0 195.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.841 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 195.842 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 195.842 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 195.842 * [backup-simplify]: Simplify (- 0) into 0 195.843 * [backup-simplify]: Simplify (+ 0 0) into 0 195.843 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 195.844 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 195.844 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.845 * [taylor]: Taking taylor expansion of 0 in k 195.845 * [backup-simplify]: Simplify 0 into 0 195.845 * [backup-simplify]: Simplify 0 into 0 195.845 * [backup-simplify]: Simplify 0 into 0 195.845 * [backup-simplify]: Simplify 0 into 0 195.845 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.848 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0 195.848 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 195.849 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 195.849 * [backup-simplify]: Simplify (- 0) into 0 195.849 * [backup-simplify]: Simplify (+ 0 0) into 0 195.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 195.850 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 195.851 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 195.851 * [taylor]: Taking taylor expansion of 0 in k 195.851 * [backup-simplify]: Simplify 0 into 0 195.851 * [backup-simplify]: Simplify 0 into 0 195.852 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))) into (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) 195.852 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) 2) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 195.852 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 195.852 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 195.852 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 195.852 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 195.852 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 195.852 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 195.852 * [taylor]: Taking taylor expansion of 1/2 in k 195.852 * [backup-simplify]: Simplify 1/2 into 1/2 195.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.852 * [taylor]: Taking taylor expansion of k in k 195.852 * [backup-simplify]: Simplify 0 into 0 195.852 * [backup-simplify]: Simplify 1 into 1 195.852 * [backup-simplify]: Simplify (/ 1 1) into 1 195.852 * [taylor]: Taking taylor expansion of 1/2 in k 195.852 * [backup-simplify]: Simplify 1/2 into 1/2 195.852 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 195.852 * [taylor]: Taking taylor expansion of (/ -2 n) in k 195.852 * [taylor]: Taking taylor expansion of -2 in k 195.852 * [backup-simplify]: Simplify -2 into -2 195.852 * [taylor]: Taking taylor expansion of n in k 195.852 * [backup-simplify]: Simplify n into n 195.852 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 195.853 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 195.853 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 195.853 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 195.853 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 195.853 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 195.853 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 195.853 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 195.853 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 195.853 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 195.853 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 195.853 * [taylor]: Taking taylor expansion of 1/2 in n 195.853 * [backup-simplify]: Simplify 1/2 into 1/2 195.853 * [taylor]: Taking taylor expansion of (/ 1 k) in n 195.853 * [taylor]: Taking taylor expansion of k in n 195.853 * [backup-simplify]: Simplify k into k 195.853 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 195.853 * [taylor]: Taking taylor expansion of 1/2 in n 195.853 * [backup-simplify]: Simplify 1/2 into 1/2 195.853 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 195.853 * [taylor]: Taking taylor expansion of (/ -2 n) in n 195.853 * [taylor]: Taking taylor expansion of -2 in n 195.853 * [backup-simplify]: Simplify -2 into -2 195.853 * [taylor]: Taking taylor expansion of n in n 195.853 * [backup-simplify]: Simplify 0 into 0 195.854 * [backup-simplify]: Simplify 1 into 1 195.854 * [backup-simplify]: Simplify (/ -2 1) into -2 195.854 * [backup-simplify]: Simplify (log -2) into (log -2) 195.854 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 195.854 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 195.855 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 195.855 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 195.855 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 195.855 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 195.855 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 195.855 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 195.855 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 195.855 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 195.855 * [taylor]: Taking taylor expansion of 1/2 in n 195.855 * [backup-simplify]: Simplify 1/2 into 1/2 195.855 * [taylor]: Taking taylor expansion of (/ 1 k) in n 195.855 * [taylor]: Taking taylor expansion of k in n 195.855 * [backup-simplify]: Simplify k into k 195.855 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 195.855 * [taylor]: Taking taylor expansion of 1/2 in n 195.855 * [backup-simplify]: Simplify 1/2 into 1/2 195.855 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 195.855 * [taylor]: Taking taylor expansion of (/ -2 n) in n 195.855 * [taylor]: Taking taylor expansion of -2 in n 195.855 * [backup-simplify]: Simplify -2 into -2 195.856 * [taylor]: Taking taylor expansion of n in n 195.856 * [backup-simplify]: Simplify 0 into 0 195.856 * [backup-simplify]: Simplify 1 into 1 195.856 * [backup-simplify]: Simplify (/ -2 1) into -2 195.856 * [backup-simplify]: Simplify (log -2) into (log -2) 195.856 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 195.856 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 195.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 195.857 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 195.857 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 195.857 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 195.857 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 195.857 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 195.857 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 195.857 * [taylor]: Taking taylor expansion of 1/2 in k 195.857 * [backup-simplify]: Simplify 1/2 into 1/2 195.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.857 * [taylor]: Taking taylor expansion of k in k 195.857 * [backup-simplify]: Simplify 0 into 0 195.857 * [backup-simplify]: Simplify 1 into 1 195.858 * [backup-simplify]: Simplify (/ 1 1) into 1 195.858 * [taylor]: Taking taylor expansion of 1/2 in k 195.858 * [backup-simplify]: Simplify 1/2 into 1/2 195.858 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 195.858 * [taylor]: Taking taylor expansion of (log -2) in k 195.858 * [taylor]: Taking taylor expansion of -2 in k 195.858 * [backup-simplify]: Simplify -2 into -2 195.858 * [backup-simplify]: Simplify (log -2) into (log -2) 195.858 * [taylor]: Taking taylor expansion of (log n) in k 195.858 * [taylor]: Taking taylor expansion of n in k 195.858 * [backup-simplify]: Simplify n into n 195.858 * [backup-simplify]: Simplify (log n) into (log n) 195.858 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 195.859 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 195.859 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 195.859 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 195.859 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 195.859 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 195.860 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 195.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 195.861 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 195.861 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 195.861 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 195.862 * [backup-simplify]: Simplify (+ 0 0) into 0 195.862 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 195.862 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 195.863 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 195.863 * [taylor]: Taking taylor expansion of 0 in k 195.863 * [backup-simplify]: Simplify 0 into 0 195.863 * [backup-simplify]: Simplify 0 into 0 195.863 * [backup-simplify]: Simplify 0 into 0 195.864 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.865 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 195.865 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 195.866 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 195.866 * [backup-simplify]: Simplify (+ 0 0) into 0 195.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 195.867 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 195.868 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.868 * [taylor]: Taking taylor expansion of 0 in k 195.868 * [backup-simplify]: Simplify 0 into 0 195.868 * [backup-simplify]: Simplify 0 into 0 195.868 * [backup-simplify]: Simplify 0 into 0 195.868 * [backup-simplify]: Simplify 0 into 0 195.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.872 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0 195.872 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 195.873 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 195.873 * [backup-simplify]: Simplify (+ 0 0) into 0 195.873 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 195.874 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 195.875 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 195.875 * [taylor]: Taking taylor expansion of 0 in k 195.875 * [backup-simplify]: Simplify 0 into 0 195.875 * [backup-simplify]: Simplify 0 into 0 195.875 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) 195.876 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1 1) 195.876 * [backup-simplify]: Simplify (cbrt k) into (pow k 1/3) 195.876 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 195.876 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 195.876 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 195.876 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 195.876 * [taylor]: Taking taylor expansion of 1/3 in k 195.876 * [backup-simplify]: Simplify 1/3 into 1/3 195.876 * [taylor]: Taking taylor expansion of (log k) in k 195.876 * [taylor]: Taking taylor expansion of k in k 195.876 * [backup-simplify]: Simplify 0 into 0 195.876 * [backup-simplify]: Simplify 1 into 1 195.876 * [backup-simplify]: Simplify (log 1) into 0 195.876 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.876 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 195.876 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 195.876 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 195.876 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 195.876 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 195.876 * [taylor]: Taking taylor expansion of 1/3 in k 195.876 * [backup-simplify]: Simplify 1/3 into 1/3 195.876 * [taylor]: Taking taylor expansion of (log k) in k 195.876 * [taylor]: Taking taylor expansion of k in k 195.876 * [backup-simplify]: Simplify 0 into 0 195.876 * [backup-simplify]: Simplify 1 into 1 195.877 * [backup-simplify]: Simplify (log 1) into 0 195.877 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.877 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 195.877 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 195.877 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 195.878 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 195.878 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.878 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log k))) into 0 195.879 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 195.879 * [backup-simplify]: Simplify 0 into 0 195.880 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 195.881 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.881 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log k)))) into 0 195.882 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.882 * [backup-simplify]: Simplify 0 into 0 195.884 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 195.885 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.885 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 195.886 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 195.886 * [backup-simplify]: Simplify 0 into 0 195.891 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 195.892 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.893 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 195.894 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.894 * [backup-simplify]: Simplify 0 into 0 195.902 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 195.903 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.904 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 195.906 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 195.906 * [backup-simplify]: Simplify 0 into 0 195.925 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 195.926 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 195.927 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 195.930 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.930 * [backup-simplify]: Simplify 0 into 0 195.930 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 195.930 * [backup-simplify]: Simplify (cbrt (/ 1 k)) into (pow (/ 1 k) 1/3) 195.930 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 195.930 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 195.930 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 195.930 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 195.930 * [taylor]: Taking taylor expansion of 1/3 in k 195.930 * [backup-simplify]: Simplify 1/3 into 1/3 195.930 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 195.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.930 * [taylor]: Taking taylor expansion of k in k 195.930 * [backup-simplify]: Simplify 0 into 0 195.930 * [backup-simplify]: Simplify 1 into 1 195.930 * [backup-simplify]: Simplify (/ 1 1) into 1 195.931 * [backup-simplify]: Simplify (log 1) into 0 195.931 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.931 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 195.931 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 195.931 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 195.931 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 195.931 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 195.931 * [taylor]: Taking taylor expansion of 1/3 in k 195.931 * [backup-simplify]: Simplify 1/3 into 1/3 195.931 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 195.931 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.931 * [taylor]: Taking taylor expansion of k in k 195.931 * [backup-simplify]: Simplify 0 into 0 195.931 * [backup-simplify]: Simplify 1 into 1 195.931 * [backup-simplify]: Simplify (/ 1 1) into 1 195.932 * [backup-simplify]: Simplify (log 1) into 0 195.932 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.932 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 195.932 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 195.932 * [backup-simplify]: Simplify (pow k -1/3) into (pow k -1/3) 195.933 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 195.933 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 195.934 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.934 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 195.934 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 195.934 * [backup-simplify]: Simplify 0 into 0 195.935 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.936 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 195.937 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.937 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 195.938 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.938 * [backup-simplify]: Simplify 0 into 0 195.938 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.941 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 195.941 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.942 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 195.943 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 195.943 * [backup-simplify]: Simplify 0 into 0 195.943 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.949 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 195.949 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.950 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 195.951 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.951 * [backup-simplify]: Simplify 0 into 0 195.952 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.960 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 195.960 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.961 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 195.963 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 195.963 * [backup-simplify]: Simplify 0 into 0 195.964 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.980 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 195.980 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.981 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 195.984 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 195.984 * [backup-simplify]: Simplify 0 into 0 195.984 * [backup-simplify]: Simplify (pow (/ 1 k) -1/3) into (pow (/ 1 k) -1/3) 195.985 * [backup-simplify]: Simplify (cbrt (/ 1 (- k))) into (* (cbrt -1) (pow (/ 1 k) 1/3)) 195.985 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 k) 1/3)) in (k) around 0 195.985 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 k) 1/3)) in k 195.985 * [taylor]: Taking taylor expansion of (cbrt -1) in k 195.985 * [taylor]: Taking taylor expansion of -1 in k 195.985 * [backup-simplify]: Simplify -1 into -1 195.985 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 195.986 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 195.986 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 195.986 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 195.986 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 195.986 * [taylor]: Taking taylor expansion of 1/3 in k 195.986 * [backup-simplify]: Simplify 1/3 into 1/3 195.986 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 195.986 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.986 * [taylor]: Taking taylor expansion of k in k 195.986 * [backup-simplify]: Simplify 0 into 0 195.986 * [backup-simplify]: Simplify 1 into 1 195.986 * [backup-simplify]: Simplify (/ 1 1) into 1 195.986 * [backup-simplify]: Simplify (log 1) into 0 195.986 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.986 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 195.986 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 195.987 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 k) 1/3)) in k 195.987 * [taylor]: Taking taylor expansion of (cbrt -1) in k 195.987 * [taylor]: Taking taylor expansion of -1 in k 195.987 * [backup-simplify]: Simplify -1 into -1 195.987 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 195.991 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 195.991 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 195.991 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 195.991 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 195.991 * [taylor]: Taking taylor expansion of 1/3 in k 195.991 * [backup-simplify]: Simplify 1/3 into 1/3 195.991 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 195.991 * [taylor]: Taking taylor expansion of (/ 1 k) in k 195.991 * [taylor]: Taking taylor expansion of k in k 195.991 * [backup-simplify]: Simplify 0 into 0 195.991 * [backup-simplify]: Simplify 1 into 1 195.992 * [backup-simplify]: Simplify (/ 1 1) into 1 195.992 * [backup-simplify]: Simplify (log 1) into 0 195.992 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.992 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 195.992 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 195.993 * [backup-simplify]: Simplify (* (cbrt -1) (pow k -1/3)) into (* (cbrt -1) (pow (/ 1 k) 1/3)) 195.993 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 k) 1/3)) into (* (cbrt -1) (pow (/ 1 k) 1/3)) 195.994 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 195.994 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 195.994 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.995 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 195.995 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 195.996 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow k -1/3))) into 0 195.996 * [backup-simplify]: Simplify 0 into 0 195.996 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 195.998 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 195.998 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 195.998 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 195.999 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.000 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 196.001 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow k -1/3)))) into 0 196.001 * [backup-simplify]: Simplify 0 into 0 196.001 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.004 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 196.004 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.005 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 196.006 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.006 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 196.007 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3))))) into 0 196.007 * [backup-simplify]: Simplify 0 into 0 196.008 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.013 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 196.013 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.014 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 196.015 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.016 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 196.017 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3)))))) into 0 196.017 * [backup-simplify]: Simplify 0 into 0 196.018 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.027 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 196.027 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.028 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 196.030 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.031 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 196.032 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3))))))) into 0 196.032 * [backup-simplify]: Simplify 0 into 0 196.033 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.048 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 196.049 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.050 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 196.053 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.054 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 196.055 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3)))))))) into 0 196.055 * [backup-simplify]: Simplify 0 into 0 196.056 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- k))) 1/3)) into (* (pow (* k -1) 1/3) (cbrt -1)) 196.056 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 2 1 1) 196.056 * [backup-simplify]: Simplify (cbrt k) into (pow k 1/3) 196.056 * [approximate]: Taking taylor expansion of (pow k 1/3) in (k) around 0 196.056 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 196.056 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 196.056 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 196.056 * [taylor]: Taking taylor expansion of 1/3 in k 196.056 * [backup-simplify]: Simplify 1/3 into 1/3 196.056 * [taylor]: Taking taylor expansion of (log k) in k 196.056 * [taylor]: Taking taylor expansion of k in k 196.056 * [backup-simplify]: Simplify 0 into 0 196.056 * [backup-simplify]: Simplify 1 into 1 196.056 * [backup-simplify]: Simplify (log 1) into 0 196.056 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.056 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 196.057 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 196.057 * [taylor]: Taking taylor expansion of (pow k 1/3) in k 196.057 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log k))) in k 196.057 * [taylor]: Taking taylor expansion of (* 1/3 (log k)) in k 196.057 * [taylor]: Taking taylor expansion of 1/3 in k 196.057 * [backup-simplify]: Simplify 1/3 into 1/3 196.057 * [taylor]: Taking taylor expansion of (log k) in k 196.057 * [taylor]: Taking taylor expansion of k in k 196.057 * [backup-simplify]: Simplify 0 into 0 196.057 * [backup-simplify]: Simplify 1 into 1 196.057 * [backup-simplify]: Simplify (log 1) into 0 196.057 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.057 * [backup-simplify]: Simplify (* 1/3 (log k)) into (* 1/3 (log k)) 196.057 * [backup-simplify]: Simplify (exp (* 1/3 (log k))) into (pow k 1/3) 196.057 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 196.058 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 196.058 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.059 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log k))) into 0 196.059 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 196.059 * [backup-simplify]: Simplify 0 into 0 196.060 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 196.061 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.061 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log k)))) into 0 196.062 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.062 * [backup-simplify]: Simplify 0 into 0 196.065 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 196.069 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.070 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0 196.071 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.071 * [backup-simplify]: Simplify 0 into 0 196.076 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 196.076 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.077 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0 196.079 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.079 * [backup-simplify]: Simplify 0 into 0 196.087 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 196.087 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.089 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0 196.090 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.090 * [backup-simplify]: Simplify 0 into 0 196.106 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 196.106 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k) 196.107 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0 196.110 * [backup-simplify]: Simplify (* (exp (* 1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.110 * [backup-simplify]: Simplify 0 into 0 196.110 * [backup-simplify]: Simplify (pow k 1/3) into (pow k 1/3) 196.111 * [backup-simplify]: Simplify (cbrt (/ 1 k)) into (pow (/ 1 k) 1/3) 196.111 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/3) in (k) around 0 196.111 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 196.111 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 196.111 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 196.111 * [taylor]: Taking taylor expansion of 1/3 in k 196.111 * [backup-simplify]: Simplify 1/3 into 1/3 196.111 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 196.111 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.111 * [taylor]: Taking taylor expansion of k in k 196.111 * [backup-simplify]: Simplify 0 into 0 196.111 * [backup-simplify]: Simplify 1 into 1 196.111 * [backup-simplify]: Simplify (/ 1 1) into 1 196.111 * [backup-simplify]: Simplify (log 1) into 0 196.111 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.112 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 196.112 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 196.112 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 196.112 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 196.112 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 196.112 * [taylor]: Taking taylor expansion of 1/3 in k 196.112 * [backup-simplify]: Simplify 1/3 into 1/3 196.112 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 196.112 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.112 * [taylor]: Taking taylor expansion of k in k 196.112 * [backup-simplify]: Simplify 0 into 0 196.112 * [backup-simplify]: Simplify 1 into 1 196.112 * [backup-simplify]: Simplify (/ 1 1) into 1 196.112 * [backup-simplify]: Simplify (log 1) into 0 196.112 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.112 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 196.113 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 196.113 * [backup-simplify]: Simplify (pow k -1/3) into (pow k -1/3) 196.113 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 196.114 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 196.114 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.114 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 196.115 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 196.115 * [backup-simplify]: Simplify 0 into 0 196.115 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.117 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 196.117 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.118 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 196.118 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.118 * [backup-simplify]: Simplify 0 into 0 196.119 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.121 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 196.122 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.122 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 196.123 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.123 * [backup-simplify]: Simplify 0 into 0 196.124 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.129 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 196.129 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.130 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 196.132 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.132 * [backup-simplify]: Simplify 0 into 0 196.132 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.145 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 196.145 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.146 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 196.148 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.148 * [backup-simplify]: Simplify 0 into 0 196.149 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.164 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 196.164 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.166 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 196.169 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.169 * [backup-simplify]: Simplify 0 into 0 196.169 * [backup-simplify]: Simplify (pow (/ 1 k) -1/3) into (pow (/ 1 k) -1/3) 196.169 * [backup-simplify]: Simplify (cbrt (/ 1 (- k))) into (* (cbrt -1) (pow (/ 1 k) 1/3)) 196.169 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 k) 1/3)) in (k) around 0 196.169 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 k) 1/3)) in k 196.169 * [taylor]: Taking taylor expansion of (cbrt -1) in k 196.169 * [taylor]: Taking taylor expansion of -1 in k 196.169 * [backup-simplify]: Simplify -1 into -1 196.169 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 196.170 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 196.170 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 196.170 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 196.170 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 196.170 * [taylor]: Taking taylor expansion of 1/3 in k 196.170 * [backup-simplify]: Simplify 1/3 into 1/3 196.170 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 196.170 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.170 * [taylor]: Taking taylor expansion of k in k 196.170 * [backup-simplify]: Simplify 0 into 0 196.170 * [backup-simplify]: Simplify 1 into 1 196.170 * [backup-simplify]: Simplify (/ 1 1) into 1 196.170 * [backup-simplify]: Simplify (log 1) into 0 196.171 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.171 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 196.171 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 196.171 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 k) 1/3)) in k 196.171 * [taylor]: Taking taylor expansion of (cbrt -1) in k 196.171 * [taylor]: Taking taylor expansion of -1 in k 196.171 * [backup-simplify]: Simplify -1 into -1 196.171 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 196.171 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 196.172 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/3) in k 196.172 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 k)))) in k 196.172 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 k))) in k 196.172 * [taylor]: Taking taylor expansion of 1/3 in k 196.172 * [backup-simplify]: Simplify 1/3 into 1/3 196.172 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k 196.172 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.172 * [taylor]: Taking taylor expansion of k in k 196.172 * [backup-simplify]: Simplify 0 into 0 196.172 * [backup-simplify]: Simplify 1 into 1 196.172 * [backup-simplify]: Simplify (/ 1 1) into 1 196.172 * [backup-simplify]: Simplify (log 1) into 0 196.172 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.172 * [backup-simplify]: Simplify (* 1/3 (- (log k))) into (* -1/3 (log k)) 196.172 * [backup-simplify]: Simplify (exp (* -1/3 (log k))) into (pow k -1/3) 196.173 * [backup-simplify]: Simplify (* (cbrt -1) (pow k -1/3)) into (* (cbrt -1) (pow (/ 1 k) 1/3)) 196.173 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 k) 1/3)) into (* (cbrt -1) (pow (/ 1 k) 1/3)) 196.174 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 196.175 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 196.175 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.175 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log k)))) into 0 196.176 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0 196.176 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow k -1/3))) into 0 196.176 * [backup-simplify]: Simplify 0 into 0 196.177 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.178 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 196.178 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.179 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log k))))) into 0 196.179 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.180 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 196.181 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow k -1/3)))) into 0 196.181 * [backup-simplify]: Simplify 0 into 0 196.181 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.184 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 196.184 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.185 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0 196.186 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.187 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 196.187 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3))))) into 0 196.187 * [backup-simplify]: Simplify 0 into 0 196.188 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.193 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 196.193 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.194 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0 196.196 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.197 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 196.198 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3)))))) into 0 196.198 * [backup-simplify]: Simplify 0 into 0 196.198 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.207 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 196.207 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.208 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0 196.210 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 196.211 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 196.212 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3))))))) into 0 196.212 * [backup-simplify]: Simplify 0 into 0 196.213 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 196.233 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 196.233 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k)) 196.234 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0 196.237 * [backup-simplify]: Simplify (* (exp (* -1/3 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 196.238 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 196.240 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/3)))))))) into 0 196.240 * [backup-simplify]: Simplify 0 into 0 196.240 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- k))) 1/3)) into (* (pow (* k -1) 1/3) (cbrt -1)) 196.240 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1) 196.240 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ k 2))) into (pow PI (- 1/2 (* 1/2 k))) 196.240 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 196.240 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 196.240 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 196.240 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 196.240 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 196.240 * [taylor]: Taking taylor expansion of 1/2 in k 196.240 * [backup-simplify]: Simplify 1/2 into 1/2 196.240 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 196.240 * [taylor]: Taking taylor expansion of 1/2 in k 196.240 * [backup-simplify]: Simplify 1/2 into 1/2 196.240 * [taylor]: Taking taylor expansion of k in k 196.240 * [backup-simplify]: Simplify 0 into 0 196.240 * [backup-simplify]: Simplify 1 into 1 196.240 * [taylor]: Taking taylor expansion of (log PI) in k 196.240 * [taylor]: Taking taylor expansion of PI in k 196.240 * [backup-simplify]: Simplify PI into PI 196.241 * [backup-simplify]: Simplify (log PI) into (log PI) 196.241 * [backup-simplify]: Simplify (* 1/2 0) into 0 196.241 * [backup-simplify]: Simplify (- 0) into 0 196.242 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 196.242 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 196.243 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 196.243 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 196.243 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 196.243 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 196.243 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 196.243 * [taylor]: Taking taylor expansion of 1/2 in k 196.243 * [backup-simplify]: Simplify 1/2 into 1/2 196.243 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 196.243 * [taylor]: Taking taylor expansion of 1/2 in k 196.243 * [backup-simplify]: Simplify 1/2 into 1/2 196.243 * [taylor]: Taking taylor expansion of k in k 196.243 * [backup-simplify]: Simplify 0 into 0 196.243 * [backup-simplify]: Simplify 1 into 1 196.243 * [taylor]: Taking taylor expansion of (log PI) in k 196.243 * [taylor]: Taking taylor expansion of PI in k 196.243 * [backup-simplify]: Simplify PI into PI 196.243 * [backup-simplify]: Simplify (log PI) into (log PI) 196.244 * [backup-simplify]: Simplify (* 1/2 0) into 0 196.244 * [backup-simplify]: Simplify (- 0) into 0 196.244 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 196.245 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 196.246 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 196.246 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 196.247 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 196.247 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 196.248 * [backup-simplify]: Simplify (- 1/2) into -1/2 196.248 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 196.249 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 196.254 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 196.256 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 196.257 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 196.258 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 196.258 * [backup-simplify]: Simplify (- 0) into 0 196.258 * [backup-simplify]: Simplify (+ 0 0) into 0 196.259 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 196.265 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 196.267 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 196.270 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (pow (log PI) 2) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (log PI) (sqrt PI))) k) (pow PI 1/2))) into (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) 196.271 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 k) 2))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 196.271 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 196.271 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 196.271 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 196.271 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 196.271 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 196.271 * [taylor]: Taking taylor expansion of 1/2 in k 196.271 * [backup-simplify]: Simplify 1/2 into 1/2 196.271 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 196.271 * [taylor]: Taking taylor expansion of 1/2 in k 196.271 * [backup-simplify]: Simplify 1/2 into 1/2 196.271 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.271 * [taylor]: Taking taylor expansion of k in k 196.271 * [backup-simplify]: Simplify 0 into 0 196.271 * [backup-simplify]: Simplify 1 into 1 196.271 * [backup-simplify]: Simplify (/ 1 1) into 1 196.271 * [taylor]: Taking taylor expansion of (log PI) in k 196.271 * [taylor]: Taking taylor expansion of PI in k 196.271 * [backup-simplify]: Simplify PI into PI 196.271 * [backup-simplify]: Simplify (log PI) into (log PI) 196.272 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 196.272 * [backup-simplify]: Simplify (- 1/2) into -1/2 196.272 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 196.273 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 196.273 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 196.273 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 196.273 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 196.273 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 196.273 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 196.273 * [taylor]: Taking taylor expansion of 1/2 in k 196.273 * [backup-simplify]: Simplify 1/2 into 1/2 196.273 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 196.273 * [taylor]: Taking taylor expansion of 1/2 in k 196.273 * [backup-simplify]: Simplify 1/2 into 1/2 196.273 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.273 * [taylor]: Taking taylor expansion of k in k 196.273 * [backup-simplify]: Simplify 0 into 0 196.273 * [backup-simplify]: Simplify 1 into 1 196.273 * [backup-simplify]: Simplify (/ 1 1) into 1 196.273 * [taylor]: Taking taylor expansion of (log PI) in k 196.273 * [taylor]: Taking taylor expansion of PI in k 196.273 * [backup-simplify]: Simplify PI into PI 196.274 * [backup-simplify]: Simplify (log PI) into (log PI) 196.274 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 196.274 * [backup-simplify]: Simplify (- 1/2) into -1/2 196.274 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 196.275 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 196.275 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 196.275 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 196.276 * [backup-simplify]: Simplify (pow PI (- 1/2 (/ (/ 1 (- k)) 2))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 196.276 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 196.276 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 196.276 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 196.276 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 196.276 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 196.276 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 196.276 * [taylor]: Taking taylor expansion of 1/2 in k 196.276 * [backup-simplify]: Simplify 1/2 into 1/2 196.276 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.276 * [taylor]: Taking taylor expansion of k in k 196.276 * [backup-simplify]: Simplify 0 into 0 196.276 * [backup-simplify]: Simplify 1 into 1 196.276 * [backup-simplify]: Simplify (/ 1 1) into 1 196.276 * [taylor]: Taking taylor expansion of 1/2 in k 196.276 * [backup-simplify]: Simplify 1/2 into 1/2 196.276 * [taylor]: Taking taylor expansion of (log PI) in k 196.276 * [taylor]: Taking taylor expansion of PI in k 196.276 * [backup-simplify]: Simplify PI into PI 196.277 * [backup-simplify]: Simplify (log PI) into (log PI) 196.277 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 196.277 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 196.278 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 196.278 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 196.278 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 196.278 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 196.278 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 196.278 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 196.278 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 196.278 * [taylor]: Taking taylor expansion of 1/2 in k 196.278 * [backup-simplify]: Simplify 1/2 into 1/2 196.278 * [taylor]: Taking taylor expansion of (/ 1 k) in k 196.278 * [taylor]: Taking taylor expansion of k in k 196.278 * [backup-simplify]: Simplify 0 into 0 196.278 * [backup-simplify]: Simplify 1 into 1 196.278 * [backup-simplify]: Simplify (/ 1 1) into 1 196.278 * [taylor]: Taking taylor expansion of 1/2 in k 196.278 * [backup-simplify]: Simplify 1/2 into 1/2 196.278 * [taylor]: Taking taylor expansion of (log PI) in k 196.278 * [taylor]: Taking taylor expansion of PI in k 196.278 * [backup-simplify]: Simplify PI into PI 196.279 * [backup-simplify]: Simplify (log PI) into (log PI) 196.279 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 196.279 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 196.280 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 196.280 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 196.280 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 196.280 * [backup-simplify]: Simplify 0 into 0 196.280 * [backup-simplify]: Simplify 0 into 0 196.280 * [backup-simplify]: Simplify 0 into 0 196.280 * [backup-simplify]: Simplify 0 into 0 196.280 * [backup-simplify]: Simplify 0 into 0 196.280 * [backup-simplify]: Simplify 0 into 0 196.280 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 196.280 * * * [progress]: simplifying candidates 196.281 * * * * [progress]: [ 1 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 2 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 3 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 4 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 5 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 6 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 7 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 8 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 9 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 10 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 11 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 12 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 13 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 14 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 15 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 16 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 17 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 18 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 19 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 20 / 170 ] simplifiying candidate # 196.281 * * * * [progress]: [ 21 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 22 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 23 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 24 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 25 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 26 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 27 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 28 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 29 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 30 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 31 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 32 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 33 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 34 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 35 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 36 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 37 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 38 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 39 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 40 / 170 ] simplifiying candidate # 196.282 * * * * [progress]: [ 41 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 42 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 43 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 44 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 45 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 46 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 47 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 48 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 49 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 50 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 51 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 52 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 53 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 54 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 55 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 56 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 57 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 58 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 59 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 60 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 61 / 170 ] simplifiying candidate # 196.283 * * * * [progress]: [ 62 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 63 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 64 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 65 / 170 ] simplifiying candidate #real (real->posit16 (pow (* n 2) (- 1/2 (/ k 2)))))))))> 196.284 * * * * [progress]: [ 66 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 67 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 68 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 69 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 70 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 71 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 72 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 73 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 74 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 75 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 76 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 77 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 78 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 79 / 170 ] simplifiying candidate #real (real->posit16 (cbrt k)))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))))> 196.284 * * * * [progress]: [ 80 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 81 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 82 / 170 ] simplifiying candidate # 196.284 * * * * [progress]: [ 83 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 84 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 85 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 86 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 87 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 88 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 89 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 90 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 91 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 92 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 93 / 170 ] simplifiying candidate #real (real->posit16 (cbrt k)))))) (sqrt (sqrt (cbrt k)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))))> 196.285 * * * * [progress]: [ 94 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 95 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 96 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 97 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 98 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 99 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 100 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 101 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 102 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 103 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 104 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 105 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 106 / 170 ] simplifiying candidate # 196.285 * * * * [progress]: [ 107 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 108 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 109 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 110 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 111 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 112 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 113 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 114 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 115 / 170 ] simplifiying candidate # 196.286 * * * * [progress]: [ 116 / 170 ] simplifiying 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simplifiying candidate # 196.287 * * * * [progress]: [ 132 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 133 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 134 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 135 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 136 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 137 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 138 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 139 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 140 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 141 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 142 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 143 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 144 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 145 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 146 / 170 ] simplifiying candidate # 196.287 * * * * [progress]: [ 147 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 148 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 149 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 150 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 151 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 152 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 153 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 154 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 155 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 156 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 157 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 158 / 170 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (/ k 2))))) (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* n 2) (- 1/2 (/ k 2)))))))> 196.288 * * * * [progress]: [ 159 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 160 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 161 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 162 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 163 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 164 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 165 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 166 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 167 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 168 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 169 / 170 ] simplifiying candidate # 196.288 * * * * [progress]: [ 170 / 170 ] simplifiying candidate # 196.290 * [simplify]: Simplifying: (expm1 (pow (* n 2) (- 1/2 (/ k 2)))) (log1p (pow (* n 2) (- 1/2 (/ k 2)))) (* (+ (log n) (log 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 (/ k 2))) (* (log (* n 2)) (- 1/2 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(* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (pow (* n 2) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (pow (* n 2) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (pow (* n 2) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (pow (* n 2) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (pow (* n 2) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (pow (* n 2) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (pow (* n 2) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1))))) (pow (* n 2) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1)))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1)))) (pow (* n 2) (fma (- (/ k 2)) 1 (* (/ k 2) 1))) (pow (* n 2) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k)))) (pow (* n 2) (fma (- (/ 1 2)) k (* (/ 1 2) k))) 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(/ (- 1/2 (/ k 2)) 2)) (real->posit16 (pow PI (- 1/2 (/ k 2)))) (- (+ (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/8 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/4 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (* 1/8 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (* 1/2 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* k -1) 1/3) (cbrt -1)) (pow k 1/3) (pow (/ 1 k) -1/3) (* (pow (* k -1) 1/3) (cbrt -1)) (- (+ (pow PI 1/2) (* 1/8 (* (* (pow (log PI) 2) (pow k 2)) (sqrt PI)))) (* 1/2 (* (* (log PI) k) (sqrt PI)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) 196.294 * * [simplify]: iteration 1: (371 enodes) 196.414 * * [simplify]: iteration 2: (1131 enodes) 197.112 * * [simplify]: Extracting #0: cost 111 inf + 0 197.113 * * [simplify]: Extracting #1: cost 423 inf + 43 197.115 * * [simplify]: Extracting #2: cost 910 inf + 1607 197.122 * * [simplify]: Extracting #3: cost 1071 inf + 47353 197.139 * * [simplify]: Extracting #4: cost 692 inf + 151673 197.170 * * [simplify]: Extracting #5: cost 385 inf + 249456 197.211 * * [simplify]: Extracting #6: cost 148 inf + 347579 197.262 * * [simplify]: Extracting #7: cost 18 inf + 415944 197.315 * * [simplify]: Extracting #8: cost 0 inf + 424062 197.367 * * [simplify]: Extracting #9: cost 0 inf + 423692 197.420 * [simplify]: Simplified to: (expm1 (pow (* n 2) (- 1/2 (* 1/2 k)))) (log1p (pow (* n 2) (- 1/2 (* 1/2 k)))) (* (- 1/2 (* 1/2 k)) (log (* n 2))) (* (- 1/2 (* 1/2 k)) (log (* n 2))) (* (- 1/2 (* 1/2 k)) (log (* n 2))) (- 1/2 (* 1/2 k)) (- 1/2 (* 1/2 k)) (sqrt (* n 2)) (pow (* n 2) (* 1/2 k)) (pow (* n 2) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow (* n 2) (sqrt (- 1/2 (* 1/2 k)))) (* n 2) (pow (* n 2) (+ 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(- 1/2 (* 1/2 k)) (sqrt PI) (pow PI (* 1/2 k)) (pow PI (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow PI (sqrt (- 1/2 (* 1/2 k)))) PI (pow PI (+ (sqrt (* 1/2 k)) (sqrt 1/2))) (pow PI (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2))) PI (pow PI (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* k -1/2))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* k -1/2))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow PI (* (/ (cbrt k) (cbrt 2)) (+ (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (/ (/ (* (cbrt k) (* (cbrt k) (cbrt k))) (sqrt 2)) (sqrt 2)))) (pow PI (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2))))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2)))) (pow PI (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow PI (+ (- (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow PI (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow PI (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* k -1/2))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow PI (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow PI (- (* (cbrt 1/2) (* (cbrt 1/2) (cbrt 1/2))) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow PI (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow PI (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* k -1/2))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* k -1/2))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* k -1/2))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow PI (* (/ (cbrt k) (cbrt 2)) (+ (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow PI (- 1/2 (/ (/ (* (cbrt k) (* (cbrt k) (cbrt k))) (sqrt 2)) (sqrt 2)))) (pow PI (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2))))) (pow PI (- 1/2 (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2)))) (pow PI (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow PI (- 1/2 (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow PI (+ (- (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow PI (- 1/2 (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow PI (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow PI (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow PI (- 1/2 (/ (/ k (sqrt 2)) (sqrt 2)))) (pow PI (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow PI (* (/ (cbrt k) (cbrt 2)) (+ (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow PI (- 1/2 (/ (/ (* (cbrt k) (* (cbrt k) (cbrt k))) (sqrt 2)) (sqrt 2)))) (pow PI (* (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (+ (- (/ (cbrt k) (sqrt 2))) (/ (cbrt k) (sqrt 2))))) (pow PI (- 1/2 (* (* (cbrt k) (cbrt k)) (/ (cbrt k) 2)))) (pow PI (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow PI (- 1/2 (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow PI (+ (- (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2)))) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow PI (- 1/2 (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow PI (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow PI (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow PI (- 1/2 (/ (/ k (sqrt 2)) (sqrt 2)))) (pow PI (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (fma -1/2 k (* 1/2 k))) (sqrt PI) (pow PI (* k -1/2)) (sqrt PI) (pow PI (* k -1/2)) (pow (* (cbrt PI) (cbrt PI)) (- 1/2 (* 1/2 k))) (pow (cbrt PI) (- 1/2 (* 1/2 k))) (pow (sqrt PI) (- 1/2 (* 1/2 k))) (pow (sqrt PI) (- 1/2 (* 1/2 k))) 1 (pow PI (- 1/2 (* 1/2 k))) (* (- 1/2 (* 1/2 k)) (log PI)) (exp (pow PI (- 1/2 (* 1/2 k)))) (* (cbrt (pow PI (- 1/2 (* 1/2 k)))) (cbrt (pow PI (- 1/2 (* 1/2 k))))) (cbrt (pow PI (- 1/2 (* 1/2 k)))) (* (* (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (pow PI (- 1/2 (* 1/2 k)))) (sqrt (pow PI (- 1/2 (* 1/2 k)))) (pow PI (- 1/4 (/ k 4))) (pow PI (- 1/4 (/ k 4))) (real->posit16 (pow PI (- 1/2 (* 1/2 k)))) (+ (fma (* 1/8 (* (log 2) (log 2))) (* (sqrt (* n 2)) (* k k)) (fma 1/8 (* (* (* (log n) (sqrt (* n 2))) (log n)) (* k k)) (* (* 1/4 (log 2)) (* (* (log n) (sqrt (* n 2))) (* k k))))) (- (sqrt (* n 2)) (* 1/2 (* k (+ (* (log n) (sqrt (* n 2))) (* (sqrt (* n 2)) (log 2))))))) (exp (* (- 1/2 (* 1/2 k)) (log (* n 2)))) (exp (* (- (log -2) (log (/ -1 n))) (- 1/2 (* 1/2 k)))) (cbrt k) (pow (/ 1 k) -1/3) (* (cbrt -1) (cbrt (- k))) (cbrt k) (pow (/ 1 k) -1/3) (* (cbrt -1) (cbrt (- k))) (+ (* (sqrt PI) (- (* 1/8 (* (* (log PI) k) (* (log PI) k))) (* (* 1/2 k) (log PI)))) (sqrt PI)) (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) 197.453 * * * [progress]: adding candidates to table 198.397 * [progress]: [Phase 3 of 3] Extracting. 198.397 * * [regime]: Finding splitpoints for: (# # # # # # #) 198.398 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2 PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) n k) 198.399 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (# # # # # # #) 198.439 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (# # # # # # #) 198.482 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 198.522 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 198.563 * * * [regime]: Found split indices: #