41.579 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.214 * * * [progress]: [2/2] Setting up program. 0.217 * [progress]: [Phase 2 of 3] Improving. 0.217 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.217 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.217 * * [simplify]: iteration 1: (13 enodes) 0.221 * * [simplify]: iteration 2: (29 enodes) 0.228 * * [simplify]: iteration 3: (60 enodes) 0.241 * * [simplify]: iteration 4: (123 enodes) 0.325 * * [simplify]: iteration 5: (322 enodes) 0.522 * * [simplify]: iteration 6: (821 enodes) 2.002 * * [simplify]: Extracting #0: cost 1 inf + 0 2.002 * * [simplify]: Extracting #1: cost 58 inf + 0 2.003 * * [simplify]: Extracting #2: cost 184 inf + 1 2.004 * * [simplify]: Extracting #3: cost 251 inf + 46 2.006 * * [simplify]: Extracting #4: cost 228 inf + 1879 2.010 * * [simplify]: Extracting #5: cost 157 inf + 21169 2.034 * * [simplify]: Extracting #6: cost 45 inf + 113683 2.092 * * [simplify]: Extracting #7: cost 0 inf + 157567 2.122 * * [simplify]: Extracting #8: cost 0 inf + 157407 2.177 * [simplify]: Simplified to: (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)) 2.189 * * [progress]: iteration 1 / 4 2.189 * * * [progress]: picking best candidate 2.200 * * * * [pick]: Picked # 2.201 * * * [progress]: localizing error 2.238 * * * [progress]: generating rewritten candidates 2.238 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1) 2.254 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 2.277 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 2.330 * * * [progress]: generating series expansions 2.330 * * * * [progress]: [ 1 / 3 ] generating series at (2 1) 2.331 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 2.331 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 2.331 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.331 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.331 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.331 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.331 * [taylor]: Taking taylor expansion of 1/2 in k 2.331 * [backup-simplify]: Simplify 1/2 into 1/2 2.331 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.331 * [taylor]: Taking taylor expansion of 1/2 in k 2.331 * [backup-simplify]: Simplify 1/2 into 1/2 2.331 * [taylor]: Taking taylor expansion of k in k 2.331 * [backup-simplify]: Simplify 0 into 0 2.331 * [backup-simplify]: Simplify 1 into 1 2.331 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.331 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.331 * [taylor]: Taking taylor expansion of 2 in k 2.331 * [backup-simplify]: Simplify 2 into 2 2.331 * [taylor]: Taking taylor expansion of (* n PI) in k 2.331 * [taylor]: Taking taylor expansion of n in k 2.331 * [backup-simplify]: Simplify n into n 2.331 * [taylor]: Taking taylor expansion of PI in k 2.331 * [backup-simplify]: Simplify PI into PI 2.331 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.331 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.331 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.332 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.332 * [backup-simplify]: Simplify (- 0) into 0 2.333 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.333 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.333 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.333 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.333 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.333 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.333 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.333 * [taylor]: Taking taylor expansion of 1/2 in n 2.333 * [backup-simplify]: Simplify 1/2 into 1/2 2.333 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.333 * [taylor]: Taking taylor expansion of 1/2 in n 2.333 * [backup-simplify]: Simplify 1/2 into 1/2 2.333 * [taylor]: Taking taylor expansion of k in n 2.333 * [backup-simplify]: Simplify k into k 2.333 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.333 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.333 * [taylor]: Taking taylor expansion of 2 in n 2.333 * [backup-simplify]: Simplify 2 into 2 2.333 * [taylor]: Taking taylor expansion of (* n PI) in n 2.333 * [taylor]: Taking taylor expansion of n in n 2.333 * [backup-simplify]: Simplify 0 into 0 2.333 * [backup-simplify]: Simplify 1 into 1 2.333 * [taylor]: Taking taylor expansion of PI in n 2.333 * [backup-simplify]: Simplify PI into PI 2.334 * [backup-simplify]: Simplify (* 0 PI) into 0 2.334 * [backup-simplify]: Simplify (* 2 0) into 0 2.336 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.337 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.338 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.338 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.339 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.339 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.340 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.341 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.342 * [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))))) 2.342 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.342 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.342 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.342 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.342 * [taylor]: Taking taylor expansion of 1/2 in n 2.342 * [backup-simplify]: Simplify 1/2 into 1/2 2.342 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.342 * [taylor]: Taking taylor expansion of 1/2 in n 2.342 * [backup-simplify]: Simplify 1/2 into 1/2 2.342 * [taylor]: Taking taylor expansion of k in n 2.342 * [backup-simplify]: Simplify k into k 2.342 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.342 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.342 * [taylor]: Taking taylor expansion of 2 in n 2.342 * [backup-simplify]: Simplify 2 into 2 2.342 * [taylor]: Taking taylor expansion of (* n PI) in n 2.342 * [taylor]: Taking taylor expansion of n in n 2.342 * [backup-simplify]: Simplify 0 into 0 2.342 * [backup-simplify]: Simplify 1 into 1 2.342 * [taylor]: Taking taylor expansion of PI in n 2.342 * [backup-simplify]: Simplify PI into PI 2.343 * [backup-simplify]: Simplify (* 0 PI) into 0 2.343 * [backup-simplify]: Simplify (* 2 0) into 0 2.344 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.346 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.346 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.347 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.347 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.347 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.348 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.348 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.349 * [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))))) 2.349 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.349 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.349 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.349 * [taylor]: Taking taylor expansion of 1/2 in k 2.349 * [backup-simplify]: Simplify 1/2 into 1/2 2.349 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.349 * [taylor]: Taking taylor expansion of 1/2 in k 2.349 * [backup-simplify]: Simplify 1/2 into 1/2 2.349 * [taylor]: Taking taylor expansion of k in k 2.349 * [backup-simplify]: Simplify 0 into 0 2.349 * [backup-simplify]: Simplify 1 into 1 2.349 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.349 * [taylor]: Taking taylor expansion of (log n) in k 2.349 * [taylor]: Taking taylor expansion of n in k 2.349 * [backup-simplify]: Simplify n into n 2.349 * [backup-simplify]: Simplify (log n) into (log n) 2.349 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.349 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.349 * [taylor]: Taking taylor expansion of 2 in k 2.349 * [backup-simplify]: Simplify 2 into 2 2.349 * [taylor]: Taking taylor expansion of PI in k 2.349 * [backup-simplify]: Simplify PI into PI 2.350 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.350 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.351 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.351 * [backup-simplify]: Simplify (- 0) into 0 2.351 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.352 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.352 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.353 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.354 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.354 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.355 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.356 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.356 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.357 * [backup-simplify]: Simplify (- 0) into 0 2.357 * [backup-simplify]: Simplify (+ 0 0) into 0 2.358 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.358 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.359 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.359 * [taylor]: Taking taylor expansion of 0 in k 2.360 * [backup-simplify]: Simplify 0 into 0 2.360 * [backup-simplify]: Simplify 0 into 0 2.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.360 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.362 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.362 * [backup-simplify]: Simplify (+ 0 0) into 0 2.362 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.363 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.363 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.364 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.365 * [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))))))) 2.367 * [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))))))) 2.368 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.369 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.371 * [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 2.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.371 * [backup-simplify]: Simplify (- 0) into 0 2.372 * [backup-simplify]: Simplify (+ 0 0) into 0 2.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.373 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.375 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.375 * [taylor]: Taking taylor expansion of 0 in k 2.375 * [backup-simplify]: Simplify 0 into 0 2.375 * [backup-simplify]: Simplify 0 into 0 2.375 * [backup-simplify]: Simplify 0 into 0 2.376 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.377 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.379 * [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 2.379 * [backup-simplify]: Simplify (+ 0 0) into 0 2.380 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.380 * [backup-simplify]: Simplify (- 0) into 0 2.381 * [backup-simplify]: Simplify (+ 0 0) into 0 2.383 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.386 * [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))))) 2.390 * [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))))) 2.399 * [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))))) 2.399 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 2.400 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 2.400 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.400 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.400 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.400 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.400 * [taylor]: Taking taylor expansion of 1/2 in k 2.400 * [backup-simplify]: Simplify 1/2 into 1/2 2.400 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.400 * [taylor]: Taking taylor expansion of 1/2 in k 2.400 * [backup-simplify]: Simplify 1/2 into 1/2 2.400 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.400 * [taylor]: Taking taylor expansion of k in k 2.400 * [backup-simplify]: Simplify 0 into 0 2.400 * [backup-simplify]: Simplify 1 into 1 2.400 * [backup-simplify]: Simplify (/ 1 1) into 1 2.400 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.400 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.400 * [taylor]: Taking taylor expansion of 2 in k 2.400 * [backup-simplify]: Simplify 2 into 2 2.400 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.400 * [taylor]: Taking taylor expansion of PI in k 2.400 * [backup-simplify]: Simplify PI into PI 2.400 * [taylor]: Taking taylor expansion of n in k 2.401 * [backup-simplify]: Simplify n into n 2.401 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.401 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.401 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.401 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.401 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.402 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.402 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.402 * [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)))) 2.402 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.402 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.402 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.402 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.402 * [taylor]: Taking taylor expansion of 1/2 in n 2.402 * [backup-simplify]: Simplify 1/2 into 1/2 2.402 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.402 * [taylor]: Taking taylor expansion of 1/2 in n 2.402 * [backup-simplify]: Simplify 1/2 into 1/2 2.403 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.403 * [taylor]: Taking taylor expansion of k in n 2.403 * [backup-simplify]: Simplify k into k 2.403 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.403 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.403 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.403 * [taylor]: Taking taylor expansion of 2 in n 2.403 * [backup-simplify]: Simplify 2 into 2 2.403 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.403 * [taylor]: Taking taylor expansion of PI in n 2.403 * [backup-simplify]: Simplify PI into PI 2.403 * [taylor]: Taking taylor expansion of n in n 2.403 * [backup-simplify]: Simplify 0 into 0 2.403 * [backup-simplify]: Simplify 1 into 1 2.403 * [backup-simplify]: Simplify (/ PI 1) into PI 2.404 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.405 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.405 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.405 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.405 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.413 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.414 * [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))) 2.416 * [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)))) 2.416 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.416 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.416 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.416 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.416 * [taylor]: Taking taylor expansion of 1/2 in n 2.416 * [backup-simplify]: Simplify 1/2 into 1/2 2.416 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.416 * [taylor]: Taking taylor expansion of 1/2 in n 2.416 * [backup-simplify]: Simplify 1/2 into 1/2 2.416 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.416 * [taylor]: Taking taylor expansion of k in n 2.416 * [backup-simplify]: Simplify k into k 2.416 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.416 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.416 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.416 * [taylor]: Taking taylor expansion of 2 in n 2.416 * [backup-simplify]: Simplify 2 into 2 2.416 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.416 * [taylor]: Taking taylor expansion of PI in n 2.416 * [backup-simplify]: Simplify PI into PI 2.416 * [taylor]: Taking taylor expansion of n in n 2.416 * [backup-simplify]: Simplify 0 into 0 2.416 * [backup-simplify]: Simplify 1 into 1 2.417 * [backup-simplify]: Simplify (/ PI 1) into PI 2.417 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.418 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.418 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.418 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.418 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.420 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.421 * [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))) 2.422 * [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)))) 2.422 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.422 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.422 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.422 * [taylor]: Taking taylor expansion of 1/2 in k 2.422 * [backup-simplify]: Simplify 1/2 into 1/2 2.422 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.422 * [taylor]: Taking taylor expansion of 1/2 in k 2.422 * [backup-simplify]: Simplify 1/2 into 1/2 2.422 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.422 * [taylor]: Taking taylor expansion of k in k 2.422 * [backup-simplify]: Simplify 0 into 0 2.422 * [backup-simplify]: Simplify 1 into 1 2.423 * [backup-simplify]: Simplify (/ 1 1) into 1 2.423 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.423 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.423 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.423 * [taylor]: Taking taylor expansion of 2 in k 2.423 * [backup-simplify]: Simplify 2 into 2 2.423 * [taylor]: Taking taylor expansion of PI in k 2.423 * [backup-simplify]: Simplify PI into PI 2.423 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.424 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.424 * [taylor]: Taking taylor expansion of (log n) in k 2.424 * [taylor]: Taking taylor expansion of n in k 2.424 * [backup-simplify]: Simplify n into n 2.424 * [backup-simplify]: Simplify (log n) into (log n) 2.425 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.425 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.425 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.425 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.426 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.427 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.428 * [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)))) 2.430 * [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)))) 2.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.431 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.433 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.433 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.433 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.434 * [backup-simplify]: Simplify (- 0) into 0 2.434 * [backup-simplify]: Simplify (+ 0 0) into 0 2.435 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.436 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.438 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.438 * [taylor]: Taking taylor expansion of 0 in k 2.438 * [backup-simplify]: Simplify 0 into 0 2.438 * [backup-simplify]: Simplify 0 into 0 2.438 * [backup-simplify]: Simplify 0 into 0 2.439 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.440 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.443 * [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 2.443 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.444 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.444 * [backup-simplify]: Simplify (- 0) into 0 2.445 * [backup-simplify]: Simplify (+ 0 0) into 0 2.446 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.448 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.450 * [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 2.450 * [taylor]: Taking taylor expansion of 0 in k 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 0 into 0 2.451 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.452 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.457 * [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 2.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.459 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.459 * [backup-simplify]: Simplify (- 0) into 0 2.459 * [backup-simplify]: Simplify (+ 0 0) into 0 2.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.462 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.463 * [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 2.463 * [taylor]: Taking taylor expansion of 0 in k 2.463 * [backup-simplify]: Simplify 0 into 0 2.463 * [backup-simplify]: Simplify 0 into 0 2.464 * [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))))) 2.464 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 2.464 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 2.464 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.464 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.464 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.464 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.464 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.464 * [taylor]: Taking taylor expansion of 1/2 in k 2.464 * [backup-simplify]: Simplify 1/2 into 1/2 2.464 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.464 * [taylor]: Taking taylor expansion of k in k 2.464 * [backup-simplify]: Simplify 0 into 0 2.464 * [backup-simplify]: Simplify 1 into 1 2.465 * [backup-simplify]: Simplify (/ 1 1) into 1 2.465 * [taylor]: Taking taylor expansion of 1/2 in k 2.465 * [backup-simplify]: Simplify 1/2 into 1/2 2.465 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.465 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.465 * [taylor]: Taking taylor expansion of -2 in k 2.465 * [backup-simplify]: Simplify -2 into -2 2.465 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.465 * [taylor]: Taking taylor expansion of PI in k 2.465 * [backup-simplify]: Simplify PI into PI 2.465 * [taylor]: Taking taylor expansion of n in k 2.465 * [backup-simplify]: Simplify n into n 2.465 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.465 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.465 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.465 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.466 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.466 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.466 * [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))) 2.466 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.466 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.466 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.466 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.466 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.466 * [taylor]: Taking taylor expansion of 1/2 in n 2.466 * [backup-simplify]: Simplify 1/2 into 1/2 2.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.466 * [taylor]: Taking taylor expansion of k in n 2.466 * [backup-simplify]: Simplify k into k 2.466 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.466 * [taylor]: Taking taylor expansion of 1/2 in n 2.466 * [backup-simplify]: Simplify 1/2 into 1/2 2.466 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.466 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.466 * [taylor]: Taking taylor expansion of -2 in n 2.466 * [backup-simplify]: Simplify -2 into -2 2.466 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.466 * [taylor]: Taking taylor expansion of PI in n 2.466 * [backup-simplify]: Simplify PI into PI 2.466 * [taylor]: Taking taylor expansion of n in n 2.466 * [backup-simplify]: Simplify 0 into 0 2.466 * [backup-simplify]: Simplify 1 into 1 2.467 * [backup-simplify]: Simplify (/ PI 1) into PI 2.467 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.468 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.468 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.468 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.469 * [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))) 2.470 * [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)))) 2.470 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.470 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.470 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.470 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.470 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.470 * [taylor]: Taking taylor expansion of 1/2 in n 2.470 * [backup-simplify]: Simplify 1/2 into 1/2 2.470 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.470 * [taylor]: Taking taylor expansion of k in n 2.470 * [backup-simplify]: Simplify k into k 2.470 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.470 * [taylor]: Taking taylor expansion of 1/2 in n 2.470 * [backup-simplify]: Simplify 1/2 into 1/2 2.470 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.470 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.470 * [taylor]: Taking taylor expansion of -2 in n 2.470 * [backup-simplify]: Simplify -2 into -2 2.470 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.470 * [taylor]: Taking taylor expansion of PI in n 2.470 * [backup-simplify]: Simplify PI into PI 2.470 * [taylor]: Taking taylor expansion of n in n 2.470 * [backup-simplify]: Simplify 0 into 0 2.470 * [backup-simplify]: Simplify 1 into 1 2.471 * [backup-simplify]: Simplify (/ PI 1) into PI 2.471 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.472 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.472 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.472 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.474 * [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))) 2.474 * [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)))) 2.474 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.475 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.475 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.475 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.475 * [taylor]: Taking taylor expansion of 1/2 in k 2.475 * [backup-simplify]: Simplify 1/2 into 1/2 2.475 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.475 * [taylor]: Taking taylor expansion of k in k 2.475 * [backup-simplify]: Simplify 0 into 0 2.475 * [backup-simplify]: Simplify 1 into 1 2.475 * [backup-simplify]: Simplify (/ 1 1) into 1 2.475 * [taylor]: Taking taylor expansion of 1/2 in k 2.475 * [backup-simplify]: Simplify 1/2 into 1/2 2.475 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.475 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.475 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.475 * [taylor]: Taking taylor expansion of -2 in k 2.475 * [backup-simplify]: Simplify -2 into -2 2.475 * [taylor]: Taking taylor expansion of PI in k 2.475 * [backup-simplify]: Simplify PI into PI 2.475 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.476 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.476 * [taylor]: Taking taylor expansion of (log n) in k 2.476 * [taylor]: Taking taylor expansion of n in k 2.476 * [backup-simplify]: Simplify n into n 2.476 * [backup-simplify]: Simplify (log n) into (log n) 2.477 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.477 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.477 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.478 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.478 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.479 * [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)))) 2.480 * [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)))) 2.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.481 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.482 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.482 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.482 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.482 * [backup-simplify]: Simplify (+ 0 0) into 0 2.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.484 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.485 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.485 * [taylor]: Taking taylor expansion of 0 in k 2.485 * [backup-simplify]: Simplify 0 into 0 2.485 * [backup-simplify]: Simplify 0 into 0 2.485 * [backup-simplify]: Simplify 0 into 0 2.486 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.486 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.488 * [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 2.488 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.489 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.489 * [backup-simplify]: Simplify (+ 0 0) into 0 2.490 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.491 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.493 * [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 2.493 * [taylor]: Taking taylor expansion of 0 in k 2.493 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify 0 into 0 2.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.494 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.498 * [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 2.498 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.499 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.499 * [backup-simplify]: Simplify (+ 0 0) into 0 2.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.501 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 2.503 * [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 2.503 * [taylor]: Taking taylor expansion of 0 in k 2.503 * [backup-simplify]: Simplify 0 into 0 2.503 * [backup-simplify]: Simplify 0 into 0 2.504 * [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))))) 2.505 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 2.505 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 2.505 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 2.505 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.505 * [taylor]: Taking taylor expansion of 2 in n 2.505 * [backup-simplify]: Simplify 2 into 2 2.505 * [taylor]: Taking taylor expansion of (* n PI) in n 2.505 * [taylor]: Taking taylor expansion of n in n 2.505 * [backup-simplify]: Simplify 0 into 0 2.505 * [backup-simplify]: Simplify 1 into 1 2.505 * [taylor]: Taking taylor expansion of PI in n 2.505 * [backup-simplify]: Simplify PI into PI 2.505 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.505 * [taylor]: Taking taylor expansion of 2 in n 2.505 * [backup-simplify]: Simplify 2 into 2 2.505 * [taylor]: Taking taylor expansion of (* n PI) in n 2.505 * [taylor]: Taking taylor expansion of n in n 2.505 * [backup-simplify]: Simplify 0 into 0 2.505 * [backup-simplify]: Simplify 1 into 1 2.505 * [taylor]: Taking taylor expansion of PI in n 2.505 * [backup-simplify]: Simplify PI into PI 2.506 * [backup-simplify]: Simplify (* 0 PI) into 0 2.506 * [backup-simplify]: Simplify (* 2 0) into 0 2.506 * [backup-simplify]: Simplify 0 into 0 2.508 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.510 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.510 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.511 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.512 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.512 * [backup-simplify]: Simplify 0 into 0 2.513 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.515 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.515 * [backup-simplify]: Simplify 0 into 0 2.516 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.518 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.518 * [backup-simplify]: Simplify 0 into 0 2.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.521 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.521 * [backup-simplify]: Simplify 0 into 0 2.523 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.524 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.524 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.530 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.530 * [backup-simplify]: Simplify 0 into 0 2.531 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 2.531 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 2.531 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 2.531 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.531 * [taylor]: Taking taylor expansion of 2 in n 2.531 * [backup-simplify]: Simplify 2 into 2 2.531 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.531 * [taylor]: Taking taylor expansion of PI in n 2.531 * [backup-simplify]: Simplify PI into PI 2.531 * [taylor]: Taking taylor expansion of n in n 2.531 * [backup-simplify]: Simplify 0 into 0 2.531 * [backup-simplify]: Simplify 1 into 1 2.532 * [backup-simplify]: Simplify (/ PI 1) into PI 2.532 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) 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 (/ PI n) in n 2.532 * [taylor]: Taking taylor expansion of PI in n 2.532 * [backup-simplify]: Simplify PI into PI 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 * [backup-simplify]: Simplify (/ PI 1) into PI 2.533 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.533 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.535 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.535 * [backup-simplify]: Simplify 0 into 0 2.536 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.536 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.536 * [backup-simplify]: Simplify 0 into 0 2.537 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.538 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.538 * [backup-simplify]: Simplify 0 into 0 2.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.541 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.541 * [backup-simplify]: Simplify 0 into 0 2.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.543 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.543 * [backup-simplify]: Simplify 0 into 0 2.544 * [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 2.546 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.546 * [backup-simplify]: Simplify 0 into 0 2.547 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 2.547 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 2.547 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 2.547 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.547 * [taylor]: Taking taylor expansion of -2 in n 2.547 * [backup-simplify]: Simplify -2 into -2 2.547 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.547 * [taylor]: Taking taylor expansion of PI in n 2.547 * [backup-simplify]: Simplify PI into PI 2.547 * [taylor]: Taking taylor expansion of n in n 2.547 * [backup-simplify]: Simplify 0 into 0 2.547 * [backup-simplify]: Simplify 1 into 1 2.548 * [backup-simplify]: Simplify (/ PI 1) into PI 2.548 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.548 * [taylor]: Taking taylor expansion of -2 in n 2.548 * [backup-simplify]: Simplify -2 into -2 2.548 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.548 * [taylor]: Taking taylor expansion of PI in n 2.548 * [backup-simplify]: Simplify PI into PI 2.548 * [taylor]: Taking taylor expansion of n in n 2.548 * [backup-simplify]: Simplify 0 into 0 2.548 * [backup-simplify]: Simplify 1 into 1 2.548 * [backup-simplify]: Simplify (/ PI 1) into PI 2.549 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.549 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.550 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.551 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.551 * [backup-simplify]: Simplify 0 into 0 2.552 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.553 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.553 * [backup-simplify]: Simplify 0 into 0 2.554 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.556 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.556 * [backup-simplify]: Simplify 0 into 0 2.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.559 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.559 * [backup-simplify]: Simplify 0 into 0 2.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.561 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.561 * [backup-simplify]: Simplify 0 into 0 2.563 * [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 2.564 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.564 * [backup-simplify]: Simplify 0 into 0 2.565 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 2.565 * * * * [progress]: [ 3 / 3 ] generating series at (2) 2.565 * [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)))) 2.566 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 2.566 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 2.566 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.566 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.566 * [taylor]: Taking taylor expansion of k in k 2.566 * [backup-simplify]: Simplify 0 into 0 2.566 * [backup-simplify]: Simplify 1 into 1 2.566 * [backup-simplify]: Simplify (/ 1 1) into 1 2.567 * [backup-simplify]: Simplify (sqrt 0) into 0 2.568 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.568 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 2.569 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 2.569 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 2.569 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.569 * [taylor]: Taking taylor expansion of 1/2 in k 2.569 * [backup-simplify]: Simplify 1/2 into 1/2 2.569 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.569 * [taylor]: Taking taylor expansion of 1/2 in k 2.569 * [backup-simplify]: Simplify 1/2 into 1/2 2.569 * [taylor]: Taking taylor expansion of k in k 2.569 * [backup-simplify]: Simplify 0 into 0 2.569 * [backup-simplify]: Simplify 1 into 1 2.569 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 2.569 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 2.569 * [taylor]: Taking taylor expansion of 2 in k 2.569 * [backup-simplify]: Simplify 2 into 2 2.569 * [taylor]: Taking taylor expansion of (* n PI) in k 2.569 * [taylor]: Taking taylor expansion of n in k 2.569 * [backup-simplify]: Simplify n into n 2.569 * [taylor]: Taking taylor expansion of PI in k 2.569 * [backup-simplify]: Simplify PI into PI 2.569 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.569 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 2.569 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 2.570 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.570 * [backup-simplify]: Simplify (- 0) into 0 2.571 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.571 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 2.571 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 2.571 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.571 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.571 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.571 * [taylor]: Taking taylor expansion of k in n 2.571 * [backup-simplify]: Simplify k into k 2.571 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.571 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.571 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.571 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.571 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.571 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.571 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.571 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.571 * [taylor]: Taking taylor expansion of 1/2 in n 2.571 * [backup-simplify]: Simplify 1/2 into 1/2 2.572 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.572 * [taylor]: Taking taylor expansion of 1/2 in n 2.572 * [backup-simplify]: Simplify 1/2 into 1/2 2.572 * [taylor]: Taking taylor expansion of k in n 2.572 * [backup-simplify]: Simplify k into k 2.572 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.572 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.572 * [taylor]: Taking taylor expansion of 2 in n 2.572 * [backup-simplify]: Simplify 2 into 2 2.572 * [taylor]: Taking taylor expansion of (* n PI) in n 2.572 * [taylor]: Taking taylor expansion of n in n 2.572 * [backup-simplify]: Simplify 0 into 0 2.572 * [backup-simplify]: Simplify 1 into 1 2.572 * [taylor]: Taking taylor expansion of PI in n 2.572 * [backup-simplify]: Simplify PI into PI 2.572 * [backup-simplify]: Simplify (* 0 PI) into 0 2.573 * [backup-simplify]: Simplify (* 2 0) into 0 2.574 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.576 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.577 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.577 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.577 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.577 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.579 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.580 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.581 * [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))))) 2.581 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 2.581 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.581 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.581 * [taylor]: Taking taylor expansion of k in n 2.581 * [backup-simplify]: Simplify k into k 2.581 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.581 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.581 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.582 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.582 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 2.582 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 2.582 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 2.582 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 2.582 * [taylor]: Taking taylor expansion of 1/2 in n 2.582 * [backup-simplify]: Simplify 1/2 into 1/2 2.582 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 2.582 * [taylor]: Taking taylor expansion of 1/2 in n 2.582 * [backup-simplify]: Simplify 1/2 into 1/2 2.582 * [taylor]: Taking taylor expansion of k in n 2.582 * [backup-simplify]: Simplify k into k 2.582 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 2.582 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 2.582 * [taylor]: Taking taylor expansion of 2 in n 2.582 * [backup-simplify]: Simplify 2 into 2 2.582 * [taylor]: Taking taylor expansion of (* n PI) in n 2.582 * [taylor]: Taking taylor expansion of n in n 2.582 * [backup-simplify]: Simplify 0 into 0 2.582 * [backup-simplify]: Simplify 1 into 1 2.582 * [taylor]: Taking taylor expansion of PI in n 2.582 * [backup-simplify]: Simplify PI into PI 2.583 * [backup-simplify]: Simplify (* 0 PI) into 0 2.583 * [backup-simplify]: Simplify (* 2 0) into 0 2.585 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.586 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 2.587 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.587 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 2.588 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 2.588 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 2.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.590 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 2.591 * [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))))) 2.593 * [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))) 2.593 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 2.593 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 2.593 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 2.593 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 2.593 * [taylor]: Taking taylor expansion of 1/2 in k 2.593 * [backup-simplify]: Simplify 1/2 into 1/2 2.593 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 2.593 * [taylor]: Taking taylor expansion of 1/2 in k 2.593 * [backup-simplify]: Simplify 1/2 into 1/2 2.593 * [taylor]: Taking taylor expansion of k in k 2.593 * [backup-simplify]: Simplify 0 into 0 2.593 * [backup-simplify]: Simplify 1 into 1 2.593 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 2.593 * [taylor]: Taking taylor expansion of (log n) in k 2.593 * [taylor]: Taking taylor expansion of n in k 2.593 * [backup-simplify]: Simplify n into n 2.593 * [backup-simplify]: Simplify (log n) into (log n) 2.593 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.593 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.593 * [taylor]: Taking taylor expansion of 2 in k 2.593 * [backup-simplify]: Simplify 2 into 2 2.593 * [taylor]: Taking taylor expansion of PI in k 2.593 * [backup-simplify]: Simplify PI into PI 2.594 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.595 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.595 * [backup-simplify]: Simplify (* 1/2 0) into 0 2.596 * [backup-simplify]: Simplify (- 0) into 0 2.596 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.597 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.598 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 2.599 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 2.599 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.599 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.599 * [taylor]: Taking taylor expansion of k in k 2.599 * [backup-simplify]: Simplify 0 into 0 2.599 * [backup-simplify]: Simplify 1 into 1 2.600 * [backup-simplify]: Simplify (/ 1 1) into 1 2.600 * [backup-simplify]: Simplify (sqrt 0) into 0 2.601 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.603 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 2.603 * [backup-simplify]: Simplify 0 into 0 2.604 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.605 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 2.606 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.607 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 2.608 * [backup-simplify]: Simplify (- 0) into 0 2.608 * [backup-simplify]: Simplify (+ 0 0) into 0 2.609 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.611 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 2.613 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.614 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 2.614 * [taylor]: Taking taylor expansion of 0 in k 2.614 * [backup-simplify]: Simplify 0 into 0 2.615 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.616 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.617 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.618 * [backup-simplify]: Simplify (+ 0 0) into 0 2.619 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 2.619 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.619 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.621 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2.624 * [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))))))) 2.628 * [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))))))) 2.629 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 2.631 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.632 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.635 * [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 2.637 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 2.637 * [backup-simplify]: Simplify (- 0) into 0 2.637 * [backup-simplify]: Simplify (+ 0 0) into 0 2.639 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.641 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.644 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.645 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 2.648 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 2.648 * [taylor]: Taking taylor expansion of 0 in k 2.648 * [backup-simplify]: Simplify 0 into 0 2.648 * [backup-simplify]: Simplify 0 into 0 2.649 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.652 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.655 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.656 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.660 * [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 2.660 * [backup-simplify]: Simplify (+ 0 0) into 0 2.661 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 2.662 * [backup-simplify]: Simplify (- 0) into 0 2.662 * [backup-simplify]: Simplify (+ 0 0) into 0 2.664 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 2.669 * [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))))) 2.684 * [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)))))))) 2.689 * [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)))))))) 2.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.691 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.697 * [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 2.698 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 2.699 * [backup-simplify]: Simplify (- 0) into 0 2.699 * [backup-simplify]: Simplify (+ 0 0) into 0 2.700 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 2.701 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.703 * [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 2.703 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.703 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 2.705 * [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 2.705 * [taylor]: Taking taylor expansion of 0 in k 2.705 * [backup-simplify]: Simplify 0 into 0 2.705 * [backup-simplify]: Simplify 0 into 0 2.705 * [backup-simplify]: Simplify 0 into 0 2.705 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.708 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.710 * [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 2.711 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.714 * [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 2.714 * [backup-simplify]: Simplify (+ 0 0) into 0 2.715 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 2.715 * [backup-simplify]: Simplify (- 0) into 0 2.715 * [backup-simplify]: Simplify (+ 0 0) into 0 2.717 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 2.723 * [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))))))) 2.740 * [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)))))))))))))) 2.752 * [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)))))))))))))) 2.773 * [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)))))))))))))))))))))) 2.773 * [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))))) 2.773 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 2.773 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 2.773 * [taylor]: Taking taylor expansion of (sqrt 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 2.774 * [backup-simplify]: Simplify (sqrt 0) into 0 2.775 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.775 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 2.776 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 2.776 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 2.776 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.776 * [taylor]: Taking taylor expansion of 1/2 in k 2.776 * [backup-simplify]: Simplify 1/2 into 1/2 2.776 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.776 * [taylor]: Taking taylor expansion of 1/2 in k 2.776 * [backup-simplify]: Simplify 1/2 into 1/2 2.776 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.776 * [taylor]: Taking taylor expansion of k in k 2.776 * [backup-simplify]: Simplify 0 into 0 2.776 * [backup-simplify]: Simplify 1 into 1 2.776 * [backup-simplify]: Simplify (/ 1 1) into 1 2.776 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 2.776 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 2.776 * [taylor]: Taking taylor expansion of 2 in k 2.776 * [backup-simplify]: Simplify 2 into 2 2.776 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.777 * [taylor]: Taking taylor expansion of PI in k 2.777 * [backup-simplify]: Simplify PI into PI 2.777 * [taylor]: Taking taylor expansion of n in k 2.777 * [backup-simplify]: Simplify n into n 2.777 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.777 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 2.777 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 2.777 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.778 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.778 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.778 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 2.779 * [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)))) 2.779 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.779 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.779 * [taylor]: Taking taylor expansion of k in n 2.779 * [backup-simplify]: Simplify k into k 2.779 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.779 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.779 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.779 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.779 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.779 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 2.779 * [taylor]: Taking taylor expansion of 1/2 in n 2.779 * [backup-simplify]: Simplify 1/2 into 1/2 2.779 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.779 * [taylor]: Taking taylor expansion of 1/2 in n 2.779 * [backup-simplify]: Simplify 1/2 into 1/2 2.779 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.779 * [taylor]: Taking taylor expansion of k in n 2.779 * [backup-simplify]: Simplify k into k 2.779 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.779 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.779 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.779 * [taylor]: Taking taylor expansion of 2 in n 2.779 * [backup-simplify]: Simplify 2 into 2 2.779 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.780 * [taylor]: Taking taylor expansion of PI in n 2.780 * [backup-simplify]: Simplify PI into PI 2.780 * [taylor]: Taking taylor expansion of n in n 2.780 * [backup-simplify]: Simplify 0 into 0 2.780 * [backup-simplify]: Simplify 1 into 1 2.780 * [backup-simplify]: Simplify (/ PI 1) into PI 2.781 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.782 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.782 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.782 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.782 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.784 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.785 * [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))) 2.786 * [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)))) 2.786 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 2.786 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt k) into (sqrt k) 2.786 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.786 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 2.786 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 2.786 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 2.786 * [taylor]: Taking taylor expansion of (- 1/2 (* 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 (* 1/2 (/ 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) 2.787 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 2.787 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 2.787 * [taylor]: Taking taylor expansion of 2 in n 2.787 * [backup-simplify]: Simplify 2 into 2 2.787 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.787 * [taylor]: Taking taylor expansion of PI in n 2.787 * [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 2.787 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.788 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.788 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.788 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 2.788 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 2.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.790 * [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))) 2.791 * [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)))) 2.792 * [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)) 2.792 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 2.792 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 2.792 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 2.792 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 2.792 * [taylor]: Taking taylor expansion of 1/2 in k 2.792 * [backup-simplify]: Simplify 1/2 into 1/2 2.792 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.792 * [taylor]: Taking taylor expansion of 1/2 in k 2.792 * [backup-simplify]: Simplify 1/2 into 1/2 2.792 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.792 * [taylor]: Taking taylor expansion of k in k 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [backup-simplify]: Simplify (/ 1 1) into 1 2.792 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 2.792 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 2.792 * [taylor]: Taking taylor expansion of (* 2 PI) in k 2.792 * [taylor]: Taking taylor expansion of 2 in k 2.792 * [backup-simplify]: Simplify 2 into 2 2.792 * [taylor]: Taking taylor expansion of PI in k 2.792 * [backup-simplify]: Simplify PI into PI 2.792 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 2.793 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 2.793 * [taylor]: Taking taylor expansion of (log n) in k 2.793 * [taylor]: Taking taylor expansion of n in k 2.793 * [backup-simplify]: Simplify n into n 2.793 * [backup-simplify]: Simplify (log n) into (log n) 2.793 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.794 * [backup-simplify]: Simplify (- 1/2) into -1/2 2.794 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 2.794 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.795 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 2.795 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 2.796 * [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)))) 2.796 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.796 * [taylor]: Taking taylor expansion of k in k 2.796 * [backup-simplify]: Simplify 0 into 0 2.796 * [backup-simplify]: Simplify 1 into 1 2.796 * [backup-simplify]: Simplify (sqrt 0) into 0 2.797 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.798 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 2.798 * [backup-simplify]: Simplify 0 into 0 2.799 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.799 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 2.800 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 2.800 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.800 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.801 * [backup-simplify]: Simplify (- 0) into 0 2.801 * [backup-simplify]: Simplify (+ 0 0) into 0 2.804 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.804 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 2.806 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.806 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 2.806 * [taylor]: Taking taylor expansion of 0 in k 2.807 * [backup-simplify]: Simplify 0 into 0 2.807 * [backup-simplify]: Simplify 0 into 0 2.808 * [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)))))) 2.808 * [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)))))) 2.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.810 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 2.811 * [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 2.811 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.812 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.812 * [backup-simplify]: Simplify (- 0) into 0 2.813 * [backup-simplify]: Simplify (+ 0 0) into 0 2.813 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.814 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 2.816 * [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 2.816 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 2.817 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 2.817 * [taylor]: Taking taylor expansion of 0 in k 2.817 * [backup-simplify]: Simplify 0 into 0 2.817 * [backup-simplify]: Simplify 0 into 0 2.817 * [backup-simplify]: Simplify 0 into 0 2.820 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.821 * [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)))))) 2.821 * [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)))))) 2.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.824 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.830 * [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 2.830 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.832 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 2.832 * [backup-simplify]: Simplify (- 0) into 0 2.833 * [backup-simplify]: Simplify (+ 0 0) into 0 2.834 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 2.836 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 2.839 * [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 2.840 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 2.843 * [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 2.843 * [taylor]: Taking taylor expansion of 0 in k 2.843 * [backup-simplify]: Simplify 0 into 0 2.843 * [backup-simplify]: Simplify 0 into 0 2.843 * [backup-simplify]: Simplify 0 into 0 2.843 * [backup-simplify]: Simplify 0 into 0 2.848 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.851 * [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)))))) 2.852 * [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)))))) 2.857 * [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)))))))) 2.857 * [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))) 2.857 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 2.857 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 2.857 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 2.857 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 2.857 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 2.857 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.857 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.857 * [taylor]: Taking taylor expansion of 1/2 in k 2.857 * [backup-simplify]: Simplify 1/2 into 1/2 2.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.857 * [taylor]: Taking taylor expansion of k in k 2.857 * [backup-simplify]: Simplify 0 into 0 2.857 * [backup-simplify]: Simplify 1 into 1 2.858 * [backup-simplify]: Simplify (/ 1 1) into 1 2.858 * [taylor]: Taking taylor expansion of 1/2 in k 2.858 * [backup-simplify]: Simplify 1/2 into 1/2 2.858 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 2.858 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 2.858 * [taylor]: Taking taylor expansion of -2 in k 2.858 * [backup-simplify]: Simplify -2 into -2 2.858 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.858 * [taylor]: Taking taylor expansion of PI in k 2.858 * [backup-simplify]: Simplify PI into PI 2.858 * [taylor]: Taking taylor expansion of n in k 2.858 * [backup-simplify]: Simplify n into n 2.858 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.858 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 2.859 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 2.859 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.860 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.860 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 2.860 * [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))) 2.860 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.860 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.860 * [taylor]: Taking taylor expansion of -1 in k 2.860 * [backup-simplify]: Simplify -1 into -1 2.860 * [taylor]: Taking taylor expansion of k in k 2.860 * [backup-simplify]: Simplify 0 into 0 2.860 * [backup-simplify]: Simplify 1 into 1 2.861 * [backup-simplify]: Simplify (/ -1 1) into -1 2.861 * [backup-simplify]: Simplify (sqrt 0) into 0 2.863 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.863 * [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)))) 2.863 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.863 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.863 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.863 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.863 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.863 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.863 * [taylor]: Taking taylor expansion of 1/2 in n 2.863 * [backup-simplify]: Simplify 1/2 into 1/2 2.863 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.863 * [taylor]: Taking taylor expansion of k in n 2.863 * [backup-simplify]: Simplify k into k 2.863 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.863 * [taylor]: Taking taylor expansion of 1/2 in n 2.863 * [backup-simplify]: Simplify 1/2 into 1/2 2.863 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.863 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.863 * [taylor]: Taking taylor expansion of -2 in n 2.863 * [backup-simplify]: Simplify -2 into -2 2.864 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.864 * [taylor]: Taking taylor expansion of PI in n 2.864 * [backup-simplify]: Simplify PI into PI 2.864 * [taylor]: Taking taylor expansion of n in n 2.864 * [backup-simplify]: Simplify 0 into 0 2.864 * [backup-simplify]: Simplify 1 into 1 2.864 * [backup-simplify]: Simplify (/ PI 1) into PI 2.865 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.866 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.866 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.866 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.869 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.870 * [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))) 2.872 * [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)))) 2.872 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.872 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.872 * [taylor]: Taking taylor expansion of -1 in n 2.872 * [backup-simplify]: Simplify -1 into -1 2.872 * [taylor]: Taking taylor expansion of k in n 2.872 * [backup-simplify]: Simplify k into k 2.872 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.872 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.872 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.872 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.874 * [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))) 2.874 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 2.874 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 2.874 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 2.874 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 2.874 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 2.874 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 2.874 * [taylor]: Taking taylor expansion of 1/2 in n 2.874 * [backup-simplify]: Simplify 1/2 into 1/2 2.874 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.874 * [taylor]: Taking taylor expansion of k in n 2.874 * [backup-simplify]: Simplify k into k 2.874 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.874 * [taylor]: Taking taylor expansion of 1/2 in n 2.874 * [backup-simplify]: Simplify 1/2 into 1/2 2.874 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 2.874 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 2.874 * [taylor]: Taking taylor expansion of -2 in n 2.874 * [backup-simplify]: Simplify -2 into -2 2.875 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.875 * [taylor]: Taking taylor expansion of PI in n 2.875 * [backup-simplify]: Simplify PI into PI 2.875 * [taylor]: Taking taylor expansion of n in n 2.875 * [backup-simplify]: Simplify 0 into 0 2.875 * [backup-simplify]: Simplify 1 into 1 2.875 * [backup-simplify]: Simplify (/ PI 1) into PI 2.876 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.877 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.877 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 2.877 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 2.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.880 * [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))) 2.881 * [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)))) 2.881 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.881 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.881 * [taylor]: Taking taylor expansion of -1 in n 2.881 * [backup-simplify]: Simplify -1 into -1 2.881 * [taylor]: Taking taylor expansion of k in n 2.881 * [backup-simplify]: Simplify k into k 2.881 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.881 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.881 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.882 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.883 * [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))) 2.883 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 2.883 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 2.883 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 2.883 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 2.883 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 2.883 * [taylor]: Taking taylor expansion of 1/2 in k 2.883 * [backup-simplify]: Simplify 1/2 into 1/2 2.883 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.883 * [taylor]: Taking taylor expansion of k in k 2.883 * [backup-simplify]: Simplify 0 into 0 2.883 * [backup-simplify]: Simplify 1 into 1 2.884 * [backup-simplify]: Simplify (/ 1 1) into 1 2.884 * [taylor]: Taking taylor expansion of 1/2 in k 2.884 * [backup-simplify]: Simplify 1/2 into 1/2 2.884 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 2.884 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 2.884 * [taylor]: Taking taylor expansion of (* -2 PI) in k 2.884 * [taylor]: Taking taylor expansion of -2 in k 2.884 * [backup-simplify]: Simplify -2 into -2 2.884 * [taylor]: Taking taylor expansion of PI in k 2.884 * [backup-simplify]: Simplify PI into PI 2.884 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 2.885 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 2.885 * [taylor]: Taking taylor expansion of (log n) in k 2.885 * [taylor]: Taking taylor expansion of n in k 2.885 * [backup-simplify]: Simplify n into n 2.886 * [backup-simplify]: Simplify (log n) into (log n) 2.886 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 2.886 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 2.887 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.888 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 2.889 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 2.890 * [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)))) 2.890 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.890 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.890 * [taylor]: Taking taylor expansion of -1 in k 2.890 * [backup-simplify]: Simplify -1 into -1 2.890 * [taylor]: Taking taylor expansion of k in k 2.890 * [backup-simplify]: Simplify 0 into 0 2.890 * [backup-simplify]: Simplify 1 into 1 2.890 * [backup-simplify]: Simplify (/ -1 1) into -1 2.891 * [backup-simplify]: Simplify (sqrt 0) into 0 2.892 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.893 * [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))))) 2.895 * [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))))) 2.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.896 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 2.898 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 2.898 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.899 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 2.899 * [backup-simplify]: Simplify (+ 0 0) into 0 2.901 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.902 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 2.904 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.905 * [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 2.905 * [taylor]: Taking taylor expansion of 0 in k 2.905 * [backup-simplify]: Simplify 0 into 0 2.905 * [backup-simplify]: Simplify 0 into 0 2.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.909 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.911 * [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)))))) 2.913 * [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)))))) 2.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.914 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 2.916 * [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 2.917 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.917 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 2.917 * [backup-simplify]: Simplify (+ 0 0) into 0 2.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 2.919 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 2.921 * [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 2.921 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.921 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 2.922 * [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 2.922 * [taylor]: Taking taylor expansion of 0 in k 2.922 * [backup-simplify]: Simplify 0 into 0 2.922 * [backup-simplify]: Simplify 0 into 0 2.922 * [backup-simplify]: Simplify 0 into 0 2.923 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.926 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.928 * [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)))))) 2.929 * [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)))))) 2.933 * [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))))))))))) 2.933 * * * [progress]: simplifying candidates 2.933 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 2.933 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 11 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 12 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 13 / 445 ] simplifiying candidate # 2.934 * * * * [progress]: [ 14 / 445 ] simplifiying candidate # 2.934 * * * * 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candidate # 2.968 * * * * [progress]: [ 443 / 445 ] simplifiying candidate # 2.968 * * * * [progress]: [ 444 / 445 ] simplifiying candidate # 2.968 * * * * [progress]: [ 445 / 445 ] simplifiying candidate # 2.983 * [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) 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(- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) 3.008 * * [simplify]: iteration 1: (698 enodes) 3.402 * * [simplify]: iteration 2: (1515 enodes) 4.655 * * [simplify]: Extracting #0: cost 212 inf + 0 4.657 * * [simplify]: Extracting #1: cost 835 inf + 1 4.661 * * [simplify]: Extracting #2: cost 1371 inf + 2843 4.672 * * [simplify]: Extracting #3: cost 1490 inf + 50740 4.695 * * [simplify]: Extracting #4: cost 1165 inf + 173880 4.747 * * [simplify]: Extracting #5: cost 717 inf + 363097 4.856 * * [simplify]: Extracting #6: cost 398 inf + 548093 5.068 * * [simplify]: Extracting #7: cost 79 inf + 764685 5.277 * * [simplify]: Extracting #8: cost 2 inf + 822930 5.527 * * [simplify]: Extracting #9: cost 0 inf + 824546 5.716 * * [simplify]: Extracting #10: cost 0 inf + 824451 5.896 * * [simplify]: Extracting #11: cost 0 inf + 824426 6.076 * [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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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) (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)))))))) 6.185 * * * [progress]: adding candidates to table 12.857 * * [progress]: iteration 2 / 4 12.857 * * * [progress]: picking best candidate 12.896 * * * * [pick]: Picked # 12.896 * * * [progress]: localizing error 12.945 * * * [progress]: generating rewritten candidates 12.945 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 12.978 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 13.007 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 13.038 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 13.216 * * * [progress]: generating series expansions 13.216 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 13.216 * [backup-simplify]: Simplify (pow (* PI (* n 2)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 13.216 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 13.216 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.216 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.216 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.216 * [taylor]: Taking taylor expansion of 1/2 in k 13.216 * [backup-simplify]: Simplify 1/2 into 1/2 13.216 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.216 * [taylor]: Taking taylor expansion of 1/2 in k 13.216 * [backup-simplify]: Simplify 1/2 into 1/2 13.216 * [taylor]: Taking taylor expansion of k in k 13.216 * [backup-simplify]: Simplify 0 into 0 13.216 * [backup-simplify]: Simplify 1 into 1 13.217 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.217 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.217 * [taylor]: Taking taylor expansion of 2 in k 13.217 * [backup-simplify]: Simplify 2 into 2 13.217 * [taylor]: Taking taylor expansion of (* n PI) in k 13.217 * [taylor]: Taking taylor expansion of n in k 13.217 * [backup-simplify]: Simplify n into n 13.217 * [taylor]: Taking taylor expansion of PI in k 13.217 * [backup-simplify]: Simplify PI into PI 13.217 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.217 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.217 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.218 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.218 * [backup-simplify]: Simplify (- 0) into 0 13.219 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.219 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.219 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.219 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.219 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.219 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.219 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.219 * [taylor]: Taking taylor expansion of 1/2 in n 13.219 * [backup-simplify]: Simplify 1/2 into 1/2 13.219 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.219 * [taylor]: Taking taylor expansion of 1/2 in n 13.219 * [backup-simplify]: Simplify 1/2 into 1/2 13.219 * [taylor]: Taking taylor expansion of k in n 13.219 * [backup-simplify]: Simplify k into k 13.219 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.219 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.219 * [taylor]: Taking taylor expansion of 2 in n 13.219 * [backup-simplify]: Simplify 2 into 2 13.220 * [taylor]: Taking taylor expansion of (* n PI) in n 13.220 * [taylor]: Taking taylor expansion of n in n 13.220 * [backup-simplify]: Simplify 0 into 0 13.220 * [backup-simplify]: Simplify 1 into 1 13.220 * [taylor]: Taking taylor expansion of PI in n 13.220 * [backup-simplify]: Simplify PI into PI 13.220 * [backup-simplify]: Simplify (* 0 PI) into 0 13.221 * [backup-simplify]: Simplify (* 2 0) into 0 13.222 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.224 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.225 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.225 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.225 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.225 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.227 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.228 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.229 * [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))))) 13.229 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.229 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.229 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.229 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.229 * [taylor]: Taking taylor expansion of 1/2 in n 13.230 * [backup-simplify]: Simplify 1/2 into 1/2 13.230 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.230 * [taylor]: Taking taylor expansion of 1/2 in n 13.230 * [backup-simplify]: Simplify 1/2 into 1/2 13.230 * [taylor]: Taking taylor expansion of k in n 13.230 * [backup-simplify]: Simplify k into k 13.230 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.230 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.230 * [taylor]: Taking taylor expansion of 2 in n 13.230 * [backup-simplify]: Simplify 2 into 2 13.230 * [taylor]: Taking taylor expansion of (* n PI) in n 13.230 * [taylor]: Taking taylor expansion of n in n 13.230 * [backup-simplify]: Simplify 0 into 0 13.230 * [backup-simplify]: Simplify 1 into 1 13.230 * [taylor]: Taking taylor expansion of PI in n 13.230 * [backup-simplify]: Simplify PI into PI 13.231 * [backup-simplify]: Simplify (* 0 PI) into 0 13.231 * [backup-simplify]: Simplify (* 2 0) into 0 13.233 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.234 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.235 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.235 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.235 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.236 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.237 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.238 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.261 * [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))))) 13.261 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 13.261 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 13.261 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.261 * [taylor]: Taking taylor expansion of 1/2 in k 13.261 * [backup-simplify]: Simplify 1/2 into 1/2 13.261 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.261 * [taylor]: Taking taylor expansion of 1/2 in k 13.261 * [backup-simplify]: Simplify 1/2 into 1/2 13.261 * [taylor]: Taking taylor expansion of k in k 13.261 * [backup-simplify]: Simplify 0 into 0 13.261 * [backup-simplify]: Simplify 1 into 1 13.261 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 13.262 * [taylor]: Taking taylor expansion of (log n) in k 13.262 * [taylor]: Taking taylor expansion of n in k 13.262 * [backup-simplify]: Simplify n into n 13.262 * [backup-simplify]: Simplify (log n) into (log n) 13.262 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.262 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.262 * [taylor]: Taking taylor expansion of 2 in k 13.262 * [backup-simplify]: Simplify 2 into 2 13.262 * [taylor]: Taking taylor expansion of PI in k 13.262 * [backup-simplify]: Simplify PI into PI 13.262 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.263 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.264 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.264 * [backup-simplify]: Simplify (- 0) into 0 13.265 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.266 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.268 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 13.269 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 13.270 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 13.272 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.273 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.275 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.275 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 13.276 * [backup-simplify]: Simplify (- 0) into 0 13.276 * [backup-simplify]: Simplify (+ 0 0) into 0 13.277 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.279 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 13.281 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.281 * [taylor]: Taking taylor expansion of 0 in k 13.281 * [backup-simplify]: Simplify 0 into 0 13.281 * [backup-simplify]: Simplify 0 into 0 13.282 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.283 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.285 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.285 * [backup-simplify]: Simplify (+ 0 0) into 0 13.286 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.286 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.287 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.288 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 13.291 * [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))))))) 13.294 * [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))))))) 13.296 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.297 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.300 * [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 13.301 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 13.302 * [backup-simplify]: Simplify (- 0) into 0 13.302 * [backup-simplify]: Simplify (+ 0 0) into 0 13.304 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.305 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 13.308 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.308 * [taylor]: Taking taylor expansion of 0 in k 13.308 * [backup-simplify]: Simplify 0 into 0 13.308 * [backup-simplify]: Simplify 0 into 0 13.308 * [backup-simplify]: Simplify 0 into 0 13.310 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.311 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.316 * [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 13.317 * [backup-simplify]: Simplify (+ 0 0) into 0 13.318 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.319 * [backup-simplify]: Simplify (- 0) into 0 13.319 * [backup-simplify]: Simplify (+ 0 0) into 0 13.322 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 13.326 * [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))))) 13.329 * [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))))) 13.335 * [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))))) 13.335 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 13.335 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 13.335 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.335 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.335 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.335 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.335 * [taylor]: Taking taylor expansion of 1/2 in k 13.335 * [backup-simplify]: Simplify 1/2 into 1/2 13.335 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.335 * [taylor]: Taking taylor expansion of 1/2 in k 13.335 * [backup-simplify]: Simplify 1/2 into 1/2 13.335 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.335 * [taylor]: Taking taylor expansion of k in k 13.335 * [backup-simplify]: Simplify 0 into 0 13.335 * [backup-simplify]: Simplify 1 into 1 13.335 * [backup-simplify]: Simplify (/ 1 1) into 1 13.336 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.336 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.336 * [taylor]: Taking taylor expansion of 2 in k 13.336 * [backup-simplify]: Simplify 2 into 2 13.336 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.336 * [taylor]: Taking taylor expansion of PI in k 13.336 * [backup-simplify]: Simplify PI into PI 13.336 * [taylor]: Taking taylor expansion of n in k 13.336 * [backup-simplify]: Simplify n into n 13.336 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.336 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.336 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.336 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.336 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.337 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.337 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.337 * [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)))) 13.337 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.337 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.337 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.337 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.337 * [taylor]: Taking taylor expansion of 1/2 in n 13.337 * [backup-simplify]: Simplify 1/2 into 1/2 13.337 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.337 * [taylor]: Taking taylor expansion of 1/2 in n 13.337 * [backup-simplify]: Simplify 1/2 into 1/2 13.337 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.337 * [taylor]: Taking taylor expansion of k in n 13.337 * [backup-simplify]: Simplify k into k 13.337 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.337 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.337 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.337 * [taylor]: Taking taylor expansion of 2 in n 13.337 * [backup-simplify]: Simplify 2 into 2 13.337 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.337 * [taylor]: Taking taylor expansion of PI in n 13.337 * [backup-simplify]: Simplify PI into PI 13.337 * [taylor]: Taking taylor expansion of n in n 13.337 * [backup-simplify]: Simplify 0 into 0 13.337 * [backup-simplify]: Simplify 1 into 1 13.338 * [backup-simplify]: Simplify (/ PI 1) into PI 13.338 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.338 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.338 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.339 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.339 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.340 * [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))) 13.341 * [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)))) 13.341 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.341 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.341 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.341 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.341 * [taylor]: Taking taylor expansion of 1/2 in n 13.341 * [backup-simplify]: Simplify 1/2 into 1/2 13.341 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.341 * [taylor]: Taking taylor expansion of 1/2 in n 13.341 * [backup-simplify]: Simplify 1/2 into 1/2 13.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.341 * [taylor]: Taking taylor expansion of k in n 13.341 * [backup-simplify]: Simplify k into k 13.341 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.341 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.341 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.341 * [taylor]: Taking taylor expansion of 2 in n 13.341 * [backup-simplify]: Simplify 2 into 2 13.341 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.341 * [taylor]: Taking taylor expansion of PI in n 13.341 * [backup-simplify]: Simplify PI into PI 13.341 * [taylor]: Taking taylor expansion of n in n 13.341 * [backup-simplify]: Simplify 0 into 0 13.341 * [backup-simplify]: Simplify 1 into 1 13.342 * [backup-simplify]: Simplify (/ PI 1) into PI 13.342 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.343 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.343 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.343 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.343 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.346 * [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))) 13.347 * [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)))) 13.347 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 13.347 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 13.347 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.347 * [taylor]: Taking taylor expansion of 1/2 in k 13.347 * [backup-simplify]: Simplify 1/2 into 1/2 13.347 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.347 * [taylor]: Taking taylor expansion of 1/2 in k 13.347 * [backup-simplify]: Simplify 1/2 into 1/2 13.347 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.347 * [taylor]: Taking taylor expansion of k in k 13.347 * [backup-simplify]: Simplify 0 into 0 13.347 * [backup-simplify]: Simplify 1 into 1 13.348 * [backup-simplify]: Simplify (/ 1 1) into 1 13.348 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 13.348 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 13.348 * [taylor]: Taking taylor expansion of (* 2 PI) in k 13.348 * [taylor]: Taking taylor expansion of 2 in k 13.348 * [backup-simplify]: Simplify 2 into 2 13.348 * [taylor]: Taking taylor expansion of PI in k 13.348 * [backup-simplify]: Simplify PI into PI 13.348 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.349 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.349 * [taylor]: Taking taylor expansion of (log n) in k 13.350 * [taylor]: Taking taylor expansion of n in k 13.350 * [backup-simplify]: Simplify n into n 13.350 * [backup-simplify]: Simplify (log n) into (log n) 13.350 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.351 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.351 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.351 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.353 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 13.354 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 13.355 * [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)))) 13.357 * [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)))) 13.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.358 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.360 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.361 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.361 * [backup-simplify]: Simplify (- 0) into 0 13.361 * [backup-simplify]: Simplify (+ 0 0) into 0 13.363 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.363 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 13.364 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.364 * [taylor]: Taking taylor expansion of 0 in k 13.364 * [backup-simplify]: Simplify 0 into 0 13.364 * [backup-simplify]: Simplify 0 into 0 13.365 * [backup-simplify]: Simplify 0 into 0 13.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.366 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.368 * [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 13.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.368 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.368 * [backup-simplify]: Simplify (- 0) into 0 13.369 * [backup-simplify]: Simplify (+ 0 0) into 0 13.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.370 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 13.372 * [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 13.372 * [taylor]: Taking taylor expansion of 0 in k 13.372 * [backup-simplify]: Simplify 0 into 0 13.372 * [backup-simplify]: Simplify 0 into 0 13.372 * [backup-simplify]: Simplify 0 into 0 13.372 * [backup-simplify]: Simplify 0 into 0 13.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.373 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.376 * [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 13.377 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.377 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 13.378 * [backup-simplify]: Simplify (- 0) into 0 13.378 * [backup-simplify]: Simplify (+ 0 0) into 0 13.379 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.380 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 13.382 * [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 13.382 * [taylor]: Taking taylor expansion of 0 in k 13.382 * [backup-simplify]: Simplify 0 into 0 13.382 * [backup-simplify]: Simplify 0 into 0 13.383 * [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))))) 13.383 * [backup-simplify]: Simplify (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 13.383 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 13.383 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.383 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.383 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.383 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.383 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.383 * [taylor]: Taking taylor expansion of 1/2 in k 13.383 * [backup-simplify]: Simplify 1/2 into 1/2 13.383 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.383 * [taylor]: Taking taylor expansion of k in k 13.383 * [backup-simplify]: Simplify 0 into 0 13.383 * [backup-simplify]: Simplify 1 into 1 13.383 * [backup-simplify]: Simplify (/ 1 1) into 1 13.383 * [taylor]: Taking taylor expansion of 1/2 in k 13.383 * [backup-simplify]: Simplify 1/2 into 1/2 13.383 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.383 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.383 * [taylor]: Taking taylor expansion of -2 in k 13.383 * [backup-simplify]: Simplify -2 into -2 13.383 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.383 * [taylor]: Taking taylor expansion of PI in k 13.383 * [backup-simplify]: Simplify PI into PI 13.383 * [taylor]: Taking taylor expansion of n in k 13.383 * [backup-simplify]: Simplify n into n 13.383 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.383 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.383 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.384 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.388 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.388 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.388 * [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))) 13.388 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.388 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.388 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.388 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.388 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.388 * [taylor]: Taking taylor expansion of 1/2 in n 13.388 * [backup-simplify]: Simplify 1/2 into 1/2 13.388 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.388 * [taylor]: Taking taylor expansion of k in n 13.388 * [backup-simplify]: Simplify k into k 13.388 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.388 * [taylor]: Taking taylor expansion of 1/2 in n 13.388 * [backup-simplify]: Simplify 1/2 into 1/2 13.388 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.388 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.388 * [taylor]: Taking taylor expansion of -2 in n 13.388 * [backup-simplify]: Simplify -2 into -2 13.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.388 * [taylor]: Taking taylor expansion of PI in n 13.388 * [backup-simplify]: Simplify PI into PI 13.388 * [taylor]: Taking taylor expansion of n in n 13.388 * [backup-simplify]: Simplify 0 into 0 13.388 * [backup-simplify]: Simplify 1 into 1 13.389 * [backup-simplify]: Simplify (/ PI 1) into PI 13.389 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.390 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.390 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.390 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.391 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.392 * [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))) 13.392 * [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)))) 13.392 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.392 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.392 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.392 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.392 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.392 * [taylor]: Taking taylor expansion of 1/2 in n 13.392 * [backup-simplify]: Simplify 1/2 into 1/2 13.393 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.393 * [taylor]: Taking taylor expansion of k in n 13.393 * [backup-simplify]: Simplify k into k 13.393 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.393 * [taylor]: Taking taylor expansion of 1/2 in n 13.393 * [backup-simplify]: Simplify 1/2 into 1/2 13.393 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.393 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.393 * [taylor]: Taking taylor expansion of -2 in n 13.393 * [backup-simplify]: Simplify -2 into -2 13.393 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.393 * [taylor]: Taking taylor expansion of PI in n 13.393 * [backup-simplify]: Simplify PI into PI 13.393 * [taylor]: Taking taylor expansion of n in n 13.393 * [backup-simplify]: Simplify 0 into 0 13.393 * [backup-simplify]: Simplify 1 into 1 13.393 * [backup-simplify]: Simplify (/ PI 1) into PI 13.393 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.394 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.394 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.394 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.396 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.397 * [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))) 13.398 * [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)))) 13.398 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 13.398 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 13.398 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.398 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.398 * [taylor]: Taking taylor expansion of 1/2 in k 13.398 * [backup-simplify]: Simplify 1/2 into 1/2 13.398 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.398 * [taylor]: Taking taylor expansion of k in k 13.398 * [backup-simplify]: Simplify 0 into 0 13.398 * [backup-simplify]: Simplify 1 into 1 13.398 * [backup-simplify]: Simplify (/ 1 1) into 1 13.398 * [taylor]: Taking taylor expansion of 1/2 in k 13.399 * [backup-simplify]: Simplify 1/2 into 1/2 13.399 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 13.399 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 13.399 * [taylor]: Taking taylor expansion of (* -2 PI) in k 13.399 * [taylor]: Taking taylor expansion of -2 in k 13.399 * [backup-simplify]: Simplify -2 into -2 13.399 * [taylor]: Taking taylor expansion of PI in k 13.399 * [backup-simplify]: Simplify PI into PI 13.399 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.400 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.400 * [taylor]: Taking taylor expansion of (log n) in k 13.400 * [taylor]: Taking taylor expansion of n in k 13.400 * [backup-simplify]: Simplify n into n 13.400 * [backup-simplify]: Simplify (log n) into (log n) 13.401 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.401 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.401 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.402 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 13.403 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 13.404 * [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)))) 13.405 * [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)))) 13.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.407 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.408 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 13.408 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.409 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.409 * [backup-simplify]: Simplify (+ 0 0) into 0 13.411 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.412 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 13.413 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.413 * [taylor]: Taking taylor expansion of 0 in k 13.413 * [backup-simplify]: Simplify 0 into 0 13.413 * [backup-simplify]: Simplify 0 into 0 13.413 * [backup-simplify]: Simplify 0 into 0 13.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.415 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 13.419 * [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 13.419 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.420 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 13.420 * [backup-simplify]: Simplify (+ 0 0) into 0 13.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.423 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 13.425 * [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 13.425 * [taylor]: Taking taylor expansion of 0 in k 13.425 * [backup-simplify]: Simplify 0 into 0 13.425 * [backup-simplify]: Simplify 0 into 0 13.425 * [backup-simplify]: Simplify 0 into 0 13.425 * [backup-simplify]: Simplify 0 into 0 13.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.427 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.434 * [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 13.434 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.435 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 13.436 * [backup-simplify]: Simplify (+ 0 0) into 0 13.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.439 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 13.442 * [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 13.442 * [taylor]: Taking taylor expansion of 0 in k 13.442 * [backup-simplify]: Simplify 0 into 0 13.442 * [backup-simplify]: Simplify 0 into 0 13.443 * [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))))) 13.443 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 13.444 * [backup-simplify]: Simplify (* PI (* n 2)) into (* 2 (* n PI)) 13.444 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 13.444 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.444 * [taylor]: Taking taylor expansion of 2 in n 13.444 * [backup-simplify]: Simplify 2 into 2 13.444 * [taylor]: Taking taylor expansion of (* n PI) in n 13.444 * [taylor]: Taking taylor expansion of n in n 13.444 * [backup-simplify]: Simplify 0 into 0 13.444 * [backup-simplify]: Simplify 1 into 1 13.444 * [taylor]: Taking taylor expansion of PI in n 13.444 * [backup-simplify]: Simplify PI into PI 13.444 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.444 * [taylor]: Taking taylor expansion of 2 in n 13.444 * [backup-simplify]: Simplify 2 into 2 13.444 * [taylor]: Taking taylor expansion of (* n PI) in n 13.444 * [taylor]: Taking taylor expansion of n in n 13.444 * [backup-simplify]: Simplify 0 into 0 13.444 * [backup-simplify]: Simplify 1 into 1 13.444 * [taylor]: Taking taylor expansion of PI in n 13.444 * [backup-simplify]: Simplify PI into PI 13.445 * [backup-simplify]: Simplify (* 0 PI) into 0 13.445 * [backup-simplify]: Simplify (* 2 0) into 0 13.445 * [backup-simplify]: Simplify 0 into 0 13.446 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.447 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.447 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.448 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.449 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.449 * [backup-simplify]: Simplify 0 into 0 13.449 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.450 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.450 * [backup-simplify]: Simplify 0 into 0 13.451 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.452 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.452 * [backup-simplify]: Simplify 0 into 0 13.453 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.453 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.454 * [backup-simplify]: Simplify 0 into 0 13.454 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.455 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.455 * [backup-simplify]: Simplify 0 into 0 13.456 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.457 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.458 * [backup-simplify]: Simplify 0 into 0 13.458 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 13.458 * [backup-simplify]: Simplify (* PI (* (/ 1 n) 2)) into (* 2 (/ PI n)) 13.458 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 13.458 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.458 * [taylor]: Taking taylor expansion of 2 in n 13.458 * [backup-simplify]: Simplify 2 into 2 13.458 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.458 * [taylor]: Taking taylor expansion of PI in n 13.458 * [backup-simplify]: Simplify PI into PI 13.458 * [taylor]: Taking taylor expansion of n in n 13.458 * [backup-simplify]: Simplify 0 into 0 13.458 * [backup-simplify]: Simplify 1 into 1 13.458 * [backup-simplify]: Simplify (/ PI 1) into PI 13.458 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.458 * [taylor]: Taking taylor expansion of 2 in n 13.458 * [backup-simplify]: Simplify 2 into 2 13.458 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.459 * [taylor]: Taking taylor expansion of PI in n 13.459 * [backup-simplify]: Simplify PI into PI 13.459 * [taylor]: Taking taylor expansion of n in n 13.459 * [backup-simplify]: Simplify 0 into 0 13.459 * [backup-simplify]: Simplify 1 into 1 13.459 * [backup-simplify]: Simplify (/ PI 1) into PI 13.459 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.459 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.460 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.460 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.460 * [backup-simplify]: Simplify 0 into 0 13.461 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.462 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 13.462 * [backup-simplify]: Simplify 0 into 0 13.462 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.463 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.463 * [backup-simplify]: Simplify 0 into 0 13.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.464 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.464 * [backup-simplify]: Simplify 0 into 0 13.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.466 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.466 * [backup-simplify]: Simplify 0 into 0 13.467 * [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 13.468 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.468 * [backup-simplify]: Simplify 0 into 0 13.468 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 13.468 * [backup-simplify]: Simplify (* PI (* (/ 1 (- n)) 2)) into (* -2 (/ PI n)) 13.468 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 13.468 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.468 * [taylor]: Taking taylor expansion of -2 in n 13.468 * [backup-simplify]: Simplify -2 into -2 13.468 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.468 * [taylor]: Taking taylor expansion of PI in n 13.468 * [backup-simplify]: Simplify PI into PI 13.468 * [taylor]: Taking taylor expansion of n in n 13.468 * [backup-simplify]: Simplify 0 into 0 13.468 * [backup-simplify]: Simplify 1 into 1 13.469 * [backup-simplify]: Simplify (/ PI 1) into PI 13.469 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.469 * [taylor]: Taking taylor expansion of -2 in n 13.469 * [backup-simplify]: Simplify -2 into -2 13.469 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.469 * [taylor]: Taking taylor expansion of PI in n 13.469 * [backup-simplify]: Simplify PI into PI 13.469 * [taylor]: Taking taylor expansion of n in n 13.469 * [backup-simplify]: Simplify 0 into 0 13.469 * [backup-simplify]: Simplify 1 into 1 13.469 * [backup-simplify]: Simplify (/ PI 1) into PI 13.470 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.470 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.470 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.471 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.471 * [backup-simplify]: Simplify 0 into 0 13.472 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.472 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 13.472 * [backup-simplify]: Simplify 0 into 0 13.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.473 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.473 * [backup-simplify]: Simplify 0 into 0 13.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.475 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.476 * [backup-simplify]: Simplify 0 into 0 13.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.478 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.478 * [backup-simplify]: Simplify 0 into 0 13.479 * [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 13.481 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.481 * [backup-simplify]: Simplify 0 into 0 13.482 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 13.482 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 13.482 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 13.482 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 13.482 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 13.482 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 13.482 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.482 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.482 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.482 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.482 * [taylor]: Taking taylor expansion of 1/2 in n 13.482 * [backup-simplify]: Simplify 1/2 into 1/2 13.482 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.482 * [taylor]: Taking taylor expansion of 1/2 in n 13.482 * [backup-simplify]: Simplify 1/2 into 1/2 13.482 * [taylor]: Taking taylor expansion of k in n 13.482 * [backup-simplify]: Simplify k into k 13.482 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.482 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.482 * [taylor]: Taking taylor expansion of 2 in n 13.482 * [backup-simplify]: Simplify 2 into 2 13.483 * [taylor]: Taking taylor expansion of (* n PI) in n 13.483 * [taylor]: Taking taylor expansion of n in n 13.483 * [backup-simplify]: Simplify 0 into 0 13.483 * [backup-simplify]: Simplify 1 into 1 13.483 * [taylor]: Taking taylor expansion of PI in n 13.483 * [backup-simplify]: Simplify PI into PI 13.483 * [backup-simplify]: Simplify (* 0 PI) into 0 13.484 * [backup-simplify]: Simplify (* 2 0) into 0 13.485 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.487 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.488 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.488 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.488 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.488 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.489 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.490 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.492 * [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))))) 13.493 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 13.493 * [taylor]: Taking taylor expansion of (sqrt k) in n 13.493 * [taylor]: Taking taylor expansion of k in n 13.493 * [backup-simplify]: Simplify k into k 13.493 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 13.493 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 13.493 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 13.493 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.493 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.493 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.493 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.493 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.493 * [taylor]: Taking taylor expansion of 1/2 in k 13.493 * [backup-simplify]: Simplify 1/2 into 1/2 13.493 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.493 * [taylor]: Taking taylor expansion of 1/2 in k 13.493 * [backup-simplify]: Simplify 1/2 into 1/2 13.493 * [taylor]: Taking taylor expansion of k in k 13.493 * [backup-simplify]: Simplify 0 into 0 13.493 * [backup-simplify]: Simplify 1 into 1 13.493 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.493 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.493 * [taylor]: Taking taylor expansion of 2 in k 13.493 * [backup-simplify]: Simplify 2 into 2 13.493 * [taylor]: Taking taylor expansion of (* n PI) in k 13.493 * [taylor]: Taking taylor expansion of n in k 13.494 * [backup-simplify]: Simplify n into n 13.494 * [taylor]: Taking taylor expansion of PI in k 13.494 * [backup-simplify]: Simplify PI into PI 13.494 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.494 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.494 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.494 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.495 * [backup-simplify]: Simplify (- 0) into 0 13.495 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.495 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.495 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.495 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 13.495 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.495 * [taylor]: Taking taylor expansion of k in k 13.495 * [backup-simplify]: Simplify 0 into 0 13.495 * [backup-simplify]: Simplify 1 into 1 13.496 * [backup-simplify]: Simplify (sqrt 0) into 0 13.497 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.497 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 13.497 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.497 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.497 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.498 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.498 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.498 * [taylor]: Taking taylor expansion of 1/2 in k 13.498 * [backup-simplify]: Simplify 1/2 into 1/2 13.498 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.498 * [taylor]: Taking taylor expansion of 1/2 in k 13.498 * [backup-simplify]: Simplify 1/2 into 1/2 13.498 * [taylor]: Taking taylor expansion of k in k 13.498 * [backup-simplify]: Simplify 0 into 0 13.498 * [backup-simplify]: Simplify 1 into 1 13.498 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.498 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.498 * [taylor]: Taking taylor expansion of 2 in k 13.498 * [backup-simplify]: Simplify 2 into 2 13.498 * [taylor]: Taking taylor expansion of (* n PI) in k 13.498 * [taylor]: Taking taylor expansion of n in k 13.498 * [backup-simplify]: Simplify n into n 13.498 * [taylor]: Taking taylor expansion of PI in k 13.498 * [backup-simplify]: Simplify PI into PI 13.498 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.498 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.498 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.498 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.499 * [backup-simplify]: Simplify (- 0) into 0 13.499 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.499 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.499 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.499 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 13.499 * [taylor]: Taking taylor expansion of (sqrt k) in k 13.499 * [taylor]: Taking taylor expansion of k in k 13.499 * [backup-simplify]: Simplify 0 into 0 13.499 * [backup-simplify]: Simplify 1 into 1 13.499 * [backup-simplify]: Simplify (sqrt 0) into 0 13.500 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.500 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 13.500 * [taylor]: Taking taylor expansion of 0 in n 13.500 * [backup-simplify]: Simplify 0 into 0 13.501 * [backup-simplify]: Simplify 0 into 0 13.501 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 13.501 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 13.502 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 13.502 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.502 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.503 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.503 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 13.503 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 13.504 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 13.505 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) 13.505 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 13.505 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 13.505 * [taylor]: Taking taylor expansion of +nan.0 in n 13.505 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.505 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 13.505 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 13.505 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 13.505 * [taylor]: Taking taylor expansion of (* n PI) in n 13.505 * [taylor]: Taking taylor expansion of n in n 13.505 * [backup-simplify]: Simplify 0 into 0 13.505 * [backup-simplify]: Simplify 1 into 1 13.505 * [taylor]: Taking taylor expansion of PI in n 13.505 * [backup-simplify]: Simplify PI into PI 13.509 * [backup-simplify]: Simplify (* 0 PI) into 0 13.510 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.510 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 13.511 * [backup-simplify]: Simplify (sqrt 0) into 0 13.512 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 13.512 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 13.512 * [taylor]: Taking taylor expansion of 1/2 in n 13.512 * [backup-simplify]: Simplify 1/2 into 1/2 13.512 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 13.513 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 13.515 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.515 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 13.518 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.520 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.521 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.521 * [backup-simplify]: Simplify 0 into 0 13.523 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.524 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 13.524 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 13.525 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 13.526 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.526 * [backup-simplify]: Simplify (- 0) into 0 13.527 * [backup-simplify]: Simplify (+ 0 0) into 0 13.528 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 13.529 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 13.532 * [backup-simplify]: Simplify (- (+ (* (sqrt (/ 1 (* PI (* n 2)))) (/ (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) (pow (* 2 (* n PI)) 1/2))) (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (/ (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) (pow (* 2 (* n PI)) 1/2))))) into (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 13.538 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 (* PI (* n 2)))) +nan.0) (+ (* (* 1/2 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) +nan.0) (* (- (* 1/4 (* (* (pow (sqrt 2) 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 3))) (sqrt (/ 1 (* n PI))))) (* 1/8 (* (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) 13.538 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))))) in n 13.538 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))))) in n 13.538 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 13.538 * [taylor]: Taking taylor expansion of +nan.0 in n 13.538 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.538 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 13.538 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 13.538 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.538 * [taylor]: Taking taylor expansion of 2 in n 13.538 * [backup-simplify]: Simplify 2 into 2 13.538 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.539 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.539 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 13.539 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.539 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.539 * [taylor]: Taking taylor expansion of 2 in n 13.539 * [backup-simplify]: Simplify 2 into 2 13.539 * [taylor]: Taking taylor expansion of (* n PI) in n 13.539 * [taylor]: Taking taylor expansion of n in n 13.539 * [backup-simplify]: Simplify 0 into 0 13.539 * [backup-simplify]: Simplify 1 into 1 13.539 * [taylor]: Taking taylor expansion of PI in n 13.539 * [backup-simplify]: Simplify PI into PI 13.540 * [backup-simplify]: Simplify (* 0 PI) into 0 13.540 * [backup-simplify]: Simplify (* 2 0) into 0 13.542 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.543 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.544 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.544 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 13.544 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 13.544 * [taylor]: Taking taylor expansion of 1/2 in n 13.544 * [backup-simplify]: Simplify 1/2 into 1/2 13.545 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 13.545 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 13.545 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 13.546 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 13.546 * [taylor]: Taking taylor expansion of (* n PI) in n 13.546 * [taylor]: Taking taylor expansion of n in n 13.546 * [backup-simplify]: Simplify 0 into 0 13.546 * [backup-simplify]: Simplify 1 into 1 13.546 * [taylor]: Taking taylor expansion of PI in n 13.546 * [backup-simplify]: Simplify PI into PI 13.546 * [backup-simplify]: Simplify (* 0 PI) into 0 13.547 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.548 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 13.548 * [backup-simplify]: Simplify (sqrt 0) into 0 13.550 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 13.550 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 13.550 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 13.550 * [taylor]: Taking taylor expansion of +nan.0 in n 13.550 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.550 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 13.550 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 13.550 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 13.550 * [taylor]: Taking taylor expansion of (* n PI) in n 13.550 * [taylor]: Taking taylor expansion of n in n 13.550 * [backup-simplify]: Simplify 0 into 0 13.551 * [backup-simplify]: Simplify 1 into 1 13.551 * [taylor]: Taking taylor expansion of PI in n 13.551 * [backup-simplify]: Simplify PI into PI 13.551 * [backup-simplify]: Simplify (* 0 PI) into 0 13.553 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.553 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 13.554 * [backup-simplify]: Simplify (sqrt 0) into 0 13.556 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 13.556 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 13.556 * [taylor]: Taking taylor expansion of 1/2 in n 13.556 * [backup-simplify]: Simplify 1/2 into 1/2 13.556 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 13.557 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 13.558 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.559 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 13.561 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 13.564 * [backup-simplify]: Simplify (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) into (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 13.566 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.567 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 13.568 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.569 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.571 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.573 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 13.576 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 13.579 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) (/ +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 13.582 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 13.595 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))) (* 0 0)) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) 13.598 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.599 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 13.604 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.608 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 13.621 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))) (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 13.648 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI)))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 13.668 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) 13.669 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 13.670 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.671 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 13.676 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 13.683 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* (/ +nan.0 PI) 0) (* (/ +nan.0 (pow PI 2)) (sqrt 1/2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.692 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.698 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.702 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 13.730 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) (* n k)) (+ (* (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log n))) PI)) (- (+ (* +nan.0 (/ (sqrt 1/2) PI)) (- (* +nan.0 (/ (* (sqrt 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI)))) PI))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (/ (sqrt 1/2) PI))) (* 1 k)))) into (- (+ (* +nan.0 (/ (* (sqrt 2) (* (pow k 2) (* (pow (sqrt 1/2) 2) (log (* 2 PI))))) PI)) (- (+ (* +nan.0 (/ (* (sqrt 1/2) (pow k 2)) PI)) (- (+ (* +nan.0 (/ (* n (* (sqrt 1/2) k)) (pow PI 2))) (- (+ (* +nan.0 (/ (* (log n) (* (sqrt 2) (* (pow (sqrt 1/2) 2) (pow k 2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) 13.730 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 13.730 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 13.730 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 13.730 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.730 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.730 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.730 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.731 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.731 * [taylor]: Taking taylor expansion of 1/2 in n 13.731 * [backup-simplify]: Simplify 1/2 into 1/2 13.731 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.731 * [taylor]: Taking taylor expansion of 1/2 in n 13.731 * [backup-simplify]: Simplify 1/2 into 1/2 13.731 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.731 * [taylor]: Taking taylor expansion of k in n 13.731 * [backup-simplify]: Simplify k into k 13.731 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.731 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.731 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.731 * [taylor]: Taking taylor expansion of 2 in n 13.731 * [backup-simplify]: Simplify 2 into 2 13.731 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.731 * [taylor]: Taking taylor expansion of PI in n 13.731 * [backup-simplify]: Simplify PI into PI 13.731 * [taylor]: Taking taylor expansion of n in n 13.731 * [backup-simplify]: Simplify 0 into 0 13.731 * [backup-simplify]: Simplify 1 into 1 13.732 * [backup-simplify]: Simplify (/ PI 1) into PI 13.732 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.733 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.733 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.733 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.734 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.735 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.735 * [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))) 13.736 * [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)))) 13.737 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.737 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 13.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.737 * [taylor]: Taking taylor expansion of k in n 13.737 * [backup-simplify]: Simplify k into k 13.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.737 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 13.737 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.737 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 13.737 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 13.737 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 13.737 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.737 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.737 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.737 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.737 * [taylor]: Taking taylor expansion of 1/2 in k 13.737 * [backup-simplify]: Simplify 1/2 into 1/2 13.737 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.737 * [taylor]: Taking taylor expansion of 1/2 in k 13.737 * [backup-simplify]: Simplify 1/2 into 1/2 13.737 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.737 * [taylor]: Taking taylor expansion of k in k 13.737 * [backup-simplify]: Simplify 0 into 0 13.737 * [backup-simplify]: Simplify 1 into 1 13.738 * [backup-simplify]: Simplify (/ 1 1) into 1 13.738 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.738 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.738 * [taylor]: Taking taylor expansion of 2 in k 13.738 * [backup-simplify]: Simplify 2 into 2 13.738 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.738 * [taylor]: Taking taylor expansion of PI in k 13.738 * [backup-simplify]: Simplify PI into PI 13.738 * [taylor]: Taking taylor expansion of n in k 13.738 * [backup-simplify]: Simplify n into n 13.738 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.738 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.738 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.738 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.739 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.739 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.739 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.739 * [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)))) 13.739 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 13.739 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.739 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.739 * [taylor]: Taking taylor expansion of k in k 13.739 * [backup-simplify]: Simplify 0 into 0 13.739 * [backup-simplify]: Simplify 1 into 1 13.739 * [backup-simplify]: Simplify (/ 1 1) into 1 13.740 * [backup-simplify]: Simplify (sqrt 0) into 0 13.741 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.741 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 13.741 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 13.741 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 13.741 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 13.741 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 13.741 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 13.741 * [taylor]: Taking taylor expansion of 1/2 in k 13.741 * [backup-simplify]: Simplify 1/2 into 1/2 13.741 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.741 * [taylor]: Taking taylor expansion of 1/2 in k 13.741 * [backup-simplify]: Simplify 1/2 into 1/2 13.741 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.741 * [taylor]: Taking taylor expansion of k in k 13.741 * [backup-simplify]: Simplify 0 into 0 13.741 * [backup-simplify]: Simplify 1 into 1 13.741 * [backup-simplify]: Simplify (/ 1 1) into 1 13.741 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 13.741 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 13.741 * [taylor]: Taking taylor expansion of 2 in k 13.741 * [backup-simplify]: Simplify 2 into 2 13.741 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.741 * [taylor]: Taking taylor expansion of PI in k 13.741 * [backup-simplify]: Simplify PI into PI 13.741 * [taylor]: Taking taylor expansion of n in k 13.741 * [backup-simplify]: Simplify n into n 13.741 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.741 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 13.741 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 13.742 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.742 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.742 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.742 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 13.742 * [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)))) 13.743 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 13.743 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.743 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.743 * [taylor]: Taking taylor expansion of k in k 13.743 * [backup-simplify]: Simplify 0 into 0 13.743 * [backup-simplify]: Simplify 1 into 1 13.743 * [backup-simplify]: Simplify (/ 1 1) into 1 13.743 * [backup-simplify]: Simplify (sqrt 0) into 0 13.744 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.744 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 13.744 * [taylor]: Taking taylor expansion of 0 in n 13.744 * [backup-simplify]: Simplify 0 into 0 13.744 * [backup-simplify]: Simplify 0 into 0 13.744 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 13.745 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 13.745 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 13.745 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 13.745 * [taylor]: Taking taylor expansion of +nan.0 in n 13.745 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.745 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.745 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.745 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.745 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.745 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.745 * [taylor]: Taking taylor expansion of 1/2 in n 13.745 * [backup-simplify]: Simplify 1/2 into 1/2 13.745 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.745 * [taylor]: Taking taylor expansion of 1/2 in n 13.745 * [backup-simplify]: Simplify 1/2 into 1/2 13.745 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.745 * [taylor]: Taking taylor expansion of k in n 13.745 * [backup-simplify]: Simplify k into k 13.745 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.745 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.745 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.745 * [taylor]: Taking taylor expansion of 2 in n 13.745 * [backup-simplify]: Simplify 2 into 2 13.745 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.745 * [taylor]: Taking taylor expansion of PI in n 13.745 * [backup-simplify]: Simplify PI into PI 13.745 * [taylor]: Taking taylor expansion of n in n 13.745 * [backup-simplify]: Simplify 0 into 0 13.745 * [backup-simplify]: Simplify 1 into 1 13.746 * [backup-simplify]: Simplify (/ PI 1) into PI 13.746 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.747 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.747 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.747 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.747 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.748 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.748 * [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))) 13.749 * [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)))) 13.750 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.751 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))) 13.751 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.752 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.752 * [backup-simplify]: Simplify 0 into 0 13.753 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.755 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.755 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 13.756 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 13.756 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 13.756 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 13.756 * [taylor]: Taking taylor expansion of +nan.0 in n 13.756 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.756 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.756 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.756 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.756 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.756 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.756 * [taylor]: Taking taylor expansion of 1/2 in n 13.756 * [backup-simplify]: Simplify 1/2 into 1/2 13.756 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.756 * [taylor]: Taking taylor expansion of 1/2 in n 13.756 * [backup-simplify]: Simplify 1/2 into 1/2 13.756 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.756 * [taylor]: Taking taylor expansion of k in n 13.756 * [backup-simplify]: Simplify k into k 13.757 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.757 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.757 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.757 * [taylor]: Taking taylor expansion of 2 in n 13.757 * [backup-simplify]: Simplify 2 into 2 13.757 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.757 * [taylor]: Taking taylor expansion of PI in n 13.757 * [backup-simplify]: Simplify PI into PI 13.757 * [taylor]: Taking taylor expansion of n in n 13.757 * [backup-simplify]: Simplify 0 into 0 13.757 * [backup-simplify]: Simplify 1 into 1 13.757 * [backup-simplify]: Simplify (/ PI 1) into PI 13.758 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.759 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.759 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.759 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.759 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.760 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.761 * [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))) 13.763 * [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)))) 13.764 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.765 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))) 13.766 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.768 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.770 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 13.771 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.772 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.772 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.773 * [backup-simplify]: Simplify (- 0) into 0 13.773 * [backup-simplify]: Simplify (+ 0 0) into 0 13.775 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.776 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 13.786 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.789 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 13.790 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 13.791 * [backup-simplify]: Simplify (- 0) into 0 13.791 * [backup-simplify]: Simplify 0 into 0 13.791 * [backup-simplify]: Simplify 0 into 0 13.792 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.796 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.797 * [backup-simplify]: Simplify (- (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) (* 0 (/ 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 13.798 * [backup-simplify]: Simplify (+ (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) 13.798 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 13.798 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 13.798 * [taylor]: Taking taylor expansion of +nan.0 in n 13.798 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.798 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 13.798 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 13.798 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 13.798 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 13.798 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 13.798 * [taylor]: Taking taylor expansion of 1/2 in n 13.798 * [backup-simplify]: Simplify 1/2 into 1/2 13.798 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.798 * [taylor]: Taking taylor expansion of 1/2 in n 13.798 * [backup-simplify]: Simplify 1/2 into 1/2 13.798 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.798 * [taylor]: Taking taylor expansion of k in n 13.798 * [backup-simplify]: Simplify k into k 13.798 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.798 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 13.798 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 13.798 * [taylor]: Taking taylor expansion of 2 in n 13.798 * [backup-simplify]: Simplify 2 into 2 13.798 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.798 * [taylor]: Taking taylor expansion of PI in n 13.798 * [backup-simplify]: Simplify PI into PI 13.798 * [taylor]: Taking taylor expansion of n in n 13.798 * [backup-simplify]: Simplify 0 into 0 13.798 * [backup-simplify]: Simplify 1 into 1 13.799 * [backup-simplify]: Simplify (/ PI 1) into PI 13.799 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 13.800 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.800 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.800 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 13.800 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 13.801 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 13.801 * [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))) 13.802 * [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)))) 13.803 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 13.804 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))) 13.804 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.805 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) 13.807 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) 13.808 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 13.808 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 13.808 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.808 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 13.808 * [taylor]: Taking taylor expansion of (/ -1 k) in n 13.808 * [taylor]: Taking taylor expansion of -1 in n 13.808 * [backup-simplify]: Simplify -1 into -1 13.808 * [taylor]: Taking taylor expansion of k in n 13.808 * [backup-simplify]: Simplify k into k 13.808 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 13.808 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 13.808 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 13.808 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 13.808 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.808 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 13.808 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 13.808 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.808 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.808 * [taylor]: Taking taylor expansion of 1/2 in n 13.808 * [backup-simplify]: Simplify 1/2 into 1/2 13.808 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.808 * [taylor]: Taking taylor expansion of k in n 13.808 * [backup-simplify]: Simplify k into k 13.808 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.808 * [taylor]: Taking taylor expansion of 1/2 in n 13.808 * [backup-simplify]: Simplify 1/2 into 1/2 13.808 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.808 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.808 * [taylor]: Taking taylor expansion of -2 in n 13.808 * [backup-simplify]: Simplify -2 into -2 13.808 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.808 * [taylor]: Taking taylor expansion of PI in n 13.808 * [backup-simplify]: Simplify PI into PI 13.808 * [taylor]: Taking taylor expansion of n in n 13.808 * [backup-simplify]: Simplify 0 into 0 13.808 * [backup-simplify]: Simplify 1 into 1 13.809 * [backup-simplify]: Simplify (/ PI 1) into PI 13.809 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.810 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.810 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.810 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.811 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.811 * [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))) 13.812 * [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)))) 13.813 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ (sqrt (/ -1 k)) (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.813 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 13.813 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.813 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.813 * [taylor]: Taking taylor expansion of -1 in k 13.813 * [backup-simplify]: Simplify -1 into -1 13.813 * [taylor]: Taking taylor expansion of k in k 13.813 * [backup-simplify]: Simplify 0 into 0 13.813 * [backup-simplify]: Simplify 1 into 1 13.813 * [backup-simplify]: Simplify (/ -1 1) into -1 13.813 * [backup-simplify]: Simplify (sqrt 0) into 0 13.814 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.814 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.814 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.814 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.814 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.814 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.814 * [taylor]: Taking taylor expansion of 1/2 in k 13.814 * [backup-simplify]: Simplify 1/2 into 1/2 13.815 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.815 * [taylor]: Taking taylor expansion of k in k 13.815 * [backup-simplify]: Simplify 0 into 0 13.815 * [backup-simplify]: Simplify 1 into 1 13.815 * [backup-simplify]: Simplify (/ 1 1) into 1 13.815 * [taylor]: Taking taylor expansion of 1/2 in k 13.815 * [backup-simplify]: Simplify 1/2 into 1/2 13.815 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.815 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.815 * [taylor]: Taking taylor expansion of -2 in k 13.815 * [backup-simplify]: Simplify -2 into -2 13.815 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.815 * [taylor]: Taking taylor expansion of PI in k 13.815 * [backup-simplify]: Simplify PI into PI 13.815 * [taylor]: Taking taylor expansion of n in k 13.815 * [backup-simplify]: Simplify n into n 13.815 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.815 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.815 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.815 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.816 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.816 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.816 * [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))) 13.816 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 13.816 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 13.816 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.816 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.816 * [taylor]: Taking taylor expansion of -1 in k 13.816 * [backup-simplify]: Simplify -1 into -1 13.816 * [taylor]: Taking taylor expansion of k in k 13.816 * [backup-simplify]: Simplify 0 into 0 13.816 * [backup-simplify]: Simplify 1 into 1 13.816 * [backup-simplify]: Simplify (/ -1 1) into -1 13.817 * [backup-simplify]: Simplify (sqrt 0) into 0 13.818 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.818 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 13.818 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 13.818 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 13.818 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 13.818 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 13.818 * [taylor]: Taking taylor expansion of 1/2 in k 13.818 * [backup-simplify]: Simplify 1/2 into 1/2 13.818 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.818 * [taylor]: Taking taylor expansion of k in k 13.818 * [backup-simplify]: Simplify 0 into 0 13.818 * [backup-simplify]: Simplify 1 into 1 13.818 * [backup-simplify]: Simplify (/ 1 1) into 1 13.818 * [taylor]: Taking taylor expansion of 1/2 in k 13.818 * [backup-simplify]: Simplify 1/2 into 1/2 13.818 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 13.818 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 13.818 * [taylor]: Taking taylor expansion of -2 in k 13.818 * [backup-simplify]: Simplify -2 into -2 13.818 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.818 * [taylor]: Taking taylor expansion of PI in k 13.818 * [backup-simplify]: Simplify PI into PI 13.818 * [taylor]: Taking taylor expansion of n in k 13.818 * [backup-simplify]: Simplify n into n 13.818 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.818 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 13.818 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 13.819 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 13.819 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.819 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 13.819 * [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))) 13.819 * [backup-simplify]: Simplify (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 13.819 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 13.819 * [taylor]: Taking taylor expansion of +nan.0 in n 13.819 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.819 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.819 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.819 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.819 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.819 * [taylor]: Taking taylor expansion of -2 in n 13.819 * [backup-simplify]: Simplify -2 into -2 13.819 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.819 * [taylor]: Taking taylor expansion of PI in n 13.820 * [backup-simplify]: Simplify PI into PI 13.820 * [taylor]: Taking taylor expansion of n in n 13.820 * [backup-simplify]: Simplify 0 into 0 13.820 * [backup-simplify]: Simplify 1 into 1 13.820 * [backup-simplify]: Simplify (/ PI 1) into PI 13.820 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.821 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.821 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.821 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.821 * [taylor]: Taking taylor expansion of 1/2 in n 13.821 * [backup-simplify]: Simplify 1/2 into 1/2 13.821 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.821 * [taylor]: Taking taylor expansion of k in n 13.821 * [backup-simplify]: Simplify k into k 13.821 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.821 * [taylor]: Taking taylor expansion of 1/2 in n 13.821 * [backup-simplify]: Simplify 1/2 into 1/2 13.822 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.822 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.822 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.823 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 13.823 * [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)))) 13.824 * [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))))) 13.825 * [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))))) 13.825 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.827 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.827 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 13.828 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 13.828 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 13.828 * [taylor]: Taking taylor expansion of +nan.0 in n 13.828 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.828 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 13.828 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.828 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.828 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.828 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.828 * [taylor]: Taking taylor expansion of -2 in n 13.828 * [backup-simplify]: Simplify -2 into -2 13.828 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.828 * [taylor]: Taking taylor expansion of PI in n 13.828 * [backup-simplify]: Simplify PI into PI 13.828 * [taylor]: Taking taylor expansion of n in n 13.828 * [backup-simplify]: Simplify 0 into 0 13.828 * [backup-simplify]: Simplify 1 into 1 13.828 * [backup-simplify]: Simplify (/ PI 1) into PI 13.828 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.829 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.829 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.829 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.829 * [taylor]: Taking taylor expansion of 1/2 in n 13.829 * [backup-simplify]: Simplify 1/2 into 1/2 13.829 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.829 * [taylor]: Taking taylor expansion of k in n 13.829 * [backup-simplify]: Simplify k into k 13.829 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.829 * [taylor]: Taking taylor expansion of 1/2 in n 13.829 * [backup-simplify]: Simplify 1/2 into 1/2 13.830 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.830 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.830 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.832 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 13.833 * [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)))) 13.834 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.835 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))) 13.836 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.836 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.837 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.837 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.838 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 13.838 * [backup-simplify]: Simplify (+ 0 0) into 0 13.838 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.839 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 13.840 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 13.841 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 13.842 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 13.844 * [backup-simplify]: Simplify (- (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 13.844 * [backup-simplify]: Simplify 0 into 0 13.844 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.847 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.848 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (+ (* (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (* (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) 13.848 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 13.848 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 13.848 * [taylor]: Taking taylor expansion of +nan.0 in n 13.848 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.848 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 13.848 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 13.848 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 13.848 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 13.848 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 13.848 * [taylor]: Taking taylor expansion of -2 in n 13.848 * [backup-simplify]: Simplify -2 into -2 13.848 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.848 * [taylor]: Taking taylor expansion of PI in n 13.848 * [backup-simplify]: Simplify PI into PI 13.848 * [taylor]: Taking taylor expansion of n in n 13.848 * [backup-simplify]: Simplify 0 into 0 13.848 * [backup-simplify]: Simplify 1 into 1 13.848 * [backup-simplify]: Simplify (/ PI 1) into PI 13.848 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 13.849 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 13.849 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 13.849 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 13.849 * [taylor]: Taking taylor expansion of 1/2 in n 13.849 * [backup-simplify]: Simplify 1/2 into 1/2 13.849 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.849 * [taylor]: Taking taylor expansion of k in n 13.849 * [backup-simplify]: Simplify k into k 13.849 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.849 * [taylor]: Taking taylor expansion of 1/2 in n 13.849 * [backup-simplify]: Simplify 1/2 into 1/2 13.850 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 13.850 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 13.850 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 13.851 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 13.852 * [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)))) 13.852 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) 13.853 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))) 13.854 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.855 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) 13.857 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) 13.857 * * * * [progress]: [ 4 / 4 ] generating series at (2) 13.857 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* PI (* n 2)) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 13.857 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 13.857 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 13.857 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 13.858 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.858 * [taylor]: Taking taylor expansion of k in n 13.858 * [backup-simplify]: Simplify k into k 13.858 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.858 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 13.858 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.858 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 13.858 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 13.858 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 13.858 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 13.858 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 13.858 * [taylor]: Taking taylor expansion of 1/2 in n 13.858 * [backup-simplify]: Simplify 1/2 into 1/2 13.858 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 13.858 * [taylor]: Taking taylor expansion of 1/2 in n 13.858 * [backup-simplify]: Simplify 1/2 into 1/2 13.858 * [taylor]: Taking taylor expansion of k in n 13.858 * [backup-simplify]: Simplify k into k 13.858 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.858 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.858 * [taylor]: Taking taylor expansion of 2 in n 13.858 * [backup-simplify]: Simplify 2 into 2 13.858 * [taylor]: Taking taylor expansion of (* n PI) in n 13.858 * [taylor]: Taking taylor expansion of n in n 13.858 * [backup-simplify]: Simplify 0 into 0 13.858 * [backup-simplify]: Simplify 1 into 1 13.858 * [taylor]: Taking taylor expansion of PI in n 13.858 * [backup-simplify]: Simplify PI into PI 13.859 * [backup-simplify]: Simplify (* 0 PI) into 0 13.859 * [backup-simplify]: Simplify (* 2 0) into 0 13.860 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.861 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.861 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.861 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 13.861 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 13.862 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 13.862 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.863 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 13.864 * [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))))) 13.864 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.864 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.864 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.864 * [taylor]: Taking taylor expansion of k in k 13.864 * [backup-simplify]: Simplify 0 into 0 13.864 * [backup-simplify]: Simplify 1 into 1 13.864 * [backup-simplify]: Simplify (/ 1 1) into 1 13.864 * [backup-simplify]: Simplify (sqrt 0) into 0 13.865 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.865 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.865 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.865 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.865 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.865 * [taylor]: Taking taylor expansion of 1/2 in k 13.865 * [backup-simplify]: Simplify 1/2 into 1/2 13.865 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.865 * [taylor]: Taking taylor expansion of 1/2 in k 13.865 * [backup-simplify]: Simplify 1/2 into 1/2 13.865 * [taylor]: Taking taylor expansion of k in k 13.865 * [backup-simplify]: Simplify 0 into 0 13.865 * [backup-simplify]: Simplify 1 into 1 13.865 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.865 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.866 * [taylor]: Taking taylor expansion of 2 in k 13.866 * [backup-simplify]: Simplify 2 into 2 13.866 * [taylor]: Taking taylor expansion of (* n PI) in k 13.866 * [taylor]: Taking taylor expansion of n in k 13.866 * [backup-simplify]: Simplify n into n 13.866 * [taylor]: Taking taylor expansion of PI in k 13.866 * [backup-simplify]: Simplify PI into PI 13.866 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.866 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.866 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.866 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.866 * [backup-simplify]: Simplify (- 0) into 0 13.867 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.867 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.867 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.867 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 13.867 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 13.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.867 * [taylor]: Taking taylor expansion of k in k 13.867 * [backup-simplify]: Simplify 0 into 0 13.867 * [backup-simplify]: Simplify 1 into 1 13.868 * [backup-simplify]: Simplify (/ 1 1) into 1 13.868 * [backup-simplify]: Simplify (sqrt 0) into 0 13.870 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 13.870 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 13.870 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 13.870 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 13.870 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 13.870 * [taylor]: Taking taylor expansion of 1/2 in k 13.870 * [backup-simplify]: Simplify 1/2 into 1/2 13.870 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 13.870 * [taylor]: Taking taylor expansion of 1/2 in k 13.870 * [backup-simplify]: Simplify 1/2 into 1/2 13.870 * [taylor]: Taking taylor expansion of k in k 13.870 * [backup-simplify]: Simplify 0 into 0 13.870 * [backup-simplify]: Simplify 1 into 1 13.870 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 13.870 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 13.870 * [taylor]: Taking taylor expansion of 2 in k 13.870 * [backup-simplify]: Simplify 2 into 2 13.870 * [taylor]: Taking taylor expansion of (* n PI) in k 13.870 * [taylor]: Taking taylor expansion of n in k 13.870 * [backup-simplify]: Simplify n into n 13.870 * [taylor]: Taking taylor expansion of PI in k 13.870 * [backup-simplify]: Simplify PI into PI 13.870 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.870 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 13.871 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 13.871 * [backup-simplify]: Simplify (* 1/2 0) into 0 13.872 * [backup-simplify]: Simplify (- 0) into 0 13.872 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 13.872 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 13.872 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 13.873 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 13.873 * [taylor]: Taking taylor expansion of 0 in n 13.873 * [backup-simplify]: Simplify 0 into 0 13.873 * [backup-simplify]: Simplify 0 into 0 13.873 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 13.874 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 13.875 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 13.876 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 13.876 * [backup-simplify]: Simplify (- 1/2) into -1/2 13.876 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 13.877 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 13.877 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 13.878 * [backup-simplify]: Simplify (+ (* 0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 13.878 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 13.878 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 13.878 * [taylor]: Taking taylor expansion of +nan.0 in n 13.878 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.878 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 13.878 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.878 * [taylor]: Taking taylor expansion of 2 in n 13.878 * [backup-simplify]: Simplify 2 into 2 13.879 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.879 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.879 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.879 * [taylor]: Taking taylor expansion of (* n PI) in n 13.879 * [taylor]: Taking taylor expansion of n in n 13.879 * [backup-simplify]: Simplify 0 into 0 13.879 * [backup-simplify]: Simplify 1 into 1 13.879 * [taylor]: Taking taylor expansion of PI in n 13.880 * [backup-simplify]: Simplify PI into PI 13.880 * [backup-simplify]: Simplify (* 0 PI) into 0 13.882 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.882 * [backup-simplify]: Simplify (sqrt 0) into 0 13.884 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.884 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 13.885 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.885 * [backup-simplify]: Simplify (- 0) into 0 13.885 * [backup-simplify]: Simplify 0 into 0 13.885 * [backup-simplify]: Simplify 0 into 0 13.886 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 13.887 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 13.889 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0 13.895 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 13.896 * [backup-simplify]: Simplify (- 0) into 0 13.896 * [backup-simplify]: Simplify (+ 0 0) into 0 13.897 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 13.898 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 13.899 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.902 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.903 * [backup-simplify]: Simplify (+ (* 0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) 13.903 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 13.903 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 13.903 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 13.903 * [taylor]: Taking taylor expansion of +nan.0 in n 13.903 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.903 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 13.903 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 13.903 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.903 * [taylor]: Taking taylor expansion of 2 in n 13.903 * [backup-simplify]: Simplify 2 into 2 13.903 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.904 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.904 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.904 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.904 * [taylor]: Taking taylor expansion of 2 in n 13.904 * [backup-simplify]: Simplify 2 into 2 13.904 * [taylor]: Taking taylor expansion of (* n PI) in n 13.904 * [taylor]: Taking taylor expansion of n in n 13.904 * [backup-simplify]: Simplify 0 into 0 13.904 * [backup-simplify]: Simplify 1 into 1 13.904 * [taylor]: Taking taylor expansion of PI in n 13.904 * [backup-simplify]: Simplify PI into PI 13.905 * [backup-simplify]: Simplify (* 0 PI) into 0 13.905 * [backup-simplify]: Simplify (* 2 0) into 0 13.906 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.908 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.909 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.909 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.909 * [taylor]: Taking taylor expansion of (* n PI) in n 13.909 * [taylor]: Taking taylor expansion of n in n 13.909 * [backup-simplify]: Simplify 0 into 0 13.909 * [backup-simplify]: Simplify 1 into 1 13.909 * [taylor]: Taking taylor expansion of PI in n 13.909 * [backup-simplify]: Simplify PI into PI 13.910 * [backup-simplify]: Simplify (* 0 PI) into 0 13.911 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.912 * [backup-simplify]: Simplify (sqrt 0) into 0 13.913 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.913 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 13.913 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 13.913 * [taylor]: Taking taylor expansion of +nan.0 in n 13.913 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.913 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 13.913 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.913 * [taylor]: Taking taylor expansion of 2 in n 13.913 * [backup-simplify]: Simplify 2 into 2 13.914 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.914 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.914 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.914 * [taylor]: Taking taylor expansion of (* n PI) in n 13.914 * [taylor]: Taking taylor expansion of n in n 13.914 * [backup-simplify]: Simplify 0 into 0 13.914 * [backup-simplify]: Simplify 1 into 1 13.914 * [taylor]: Taking taylor expansion of PI in n 13.915 * [backup-simplify]: Simplify PI into PI 13.915 * [backup-simplify]: Simplify (* 0 PI) into 0 13.917 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.917 * [backup-simplify]: Simplify (sqrt 0) into 0 13.918 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.920 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.921 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 13.922 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 13.923 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.923 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 13.924 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.924 * [backup-simplify]: Simplify (- 0) into 0 13.925 * [backup-simplify]: Simplify (+ 0 0) into 0 13.925 * [backup-simplify]: Simplify (- 0) into 0 13.925 * [backup-simplify]: Simplify 0 into 0 13.928 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.933 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.937 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 13.939 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 13.939 * [backup-simplify]: Simplify 0 into 0 13.940 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.942 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 13.944 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0 13.946 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 13.946 * [backup-simplify]: Simplify (- 0) into 0 13.946 * [backup-simplify]: Simplify (+ 0 0) into 0 13.947 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 13.949 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 13.950 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.954 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.955 * [backup-simplify]: Simplify (+ (* 0 (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))) (+ (* +nan.0 (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))) (+ (* +nan.0 (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))) (* +nan.0 (pow (* 2 (* n PI)) 1/2))))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) 13.955 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))))) in n 13.955 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))) in n 13.955 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 13.955 * [taylor]: Taking taylor expansion of +nan.0 in n 13.955 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.955 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 13.955 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 13.955 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.955 * [taylor]: Taking taylor expansion of 2 in n 13.955 * [backup-simplify]: Simplify 2 into 2 13.956 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.956 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.956 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.956 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.956 * [taylor]: Taking taylor expansion of 2 in n 13.957 * [backup-simplify]: Simplify 2 into 2 13.957 * [taylor]: Taking taylor expansion of (* n PI) in n 13.957 * [taylor]: Taking taylor expansion of n in n 13.957 * [backup-simplify]: Simplify 0 into 0 13.957 * [backup-simplify]: Simplify 1 into 1 13.957 * [taylor]: Taking taylor expansion of PI in n 13.957 * [backup-simplify]: Simplify PI into PI 13.957 * [backup-simplify]: Simplify (* 0 PI) into 0 13.958 * [backup-simplify]: Simplify (* 2 0) into 0 13.959 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.961 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.962 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.962 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.962 * [taylor]: Taking taylor expansion of (* n PI) in n 13.962 * [taylor]: Taking taylor expansion of n in n 13.962 * [backup-simplify]: Simplify 0 into 0 13.962 * [backup-simplify]: Simplify 1 into 1 13.962 * [taylor]: Taking taylor expansion of PI in n 13.962 * [backup-simplify]: Simplify PI into PI 13.962 * [backup-simplify]: Simplify (* 0 PI) into 0 13.963 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.963 * [backup-simplify]: Simplify (sqrt 0) into 0 13.964 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.964 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n 13.964 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n 13.964 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 13.964 * [taylor]: Taking taylor expansion of +nan.0 in n 13.964 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.964 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 13.964 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 13.964 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.964 * [taylor]: Taking taylor expansion of 2 in n 13.964 * [backup-simplify]: Simplify 2 into 2 13.965 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.965 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.965 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 13.965 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 13.965 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 13.965 * [taylor]: Taking taylor expansion of 2 in n 13.965 * [backup-simplify]: Simplify 2 into 2 13.965 * [taylor]: Taking taylor expansion of (* n PI) in n 13.965 * [taylor]: Taking taylor expansion of n in n 13.965 * [backup-simplify]: Simplify 0 into 0 13.965 * [backup-simplify]: Simplify 1 into 1 13.965 * [taylor]: Taking taylor expansion of PI in n 13.965 * [backup-simplify]: Simplify PI into PI 13.966 * [backup-simplify]: Simplify (* 0 PI) into 0 13.966 * [backup-simplify]: Simplify (* 2 0) into 0 13.967 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.968 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 13.968 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 13.969 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.969 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.969 * [taylor]: Taking taylor expansion of (* n PI) in n 13.969 * [taylor]: Taking taylor expansion of n in n 13.969 * [backup-simplify]: Simplify 0 into 0 13.969 * [backup-simplify]: Simplify 1 into 1 13.969 * [taylor]: Taking taylor expansion of PI in n 13.969 * [backup-simplify]: Simplify PI into PI 13.970 * [backup-simplify]: Simplify (* 0 PI) into 0 13.971 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.971 * [backup-simplify]: Simplify (sqrt 0) into 0 13.972 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.972 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 13.972 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 13.972 * [taylor]: Taking taylor expansion of +nan.0 in n 13.972 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.972 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 13.972 * [taylor]: Taking taylor expansion of (sqrt 2) in n 13.972 * [taylor]: Taking taylor expansion of 2 in n 13.972 * [backup-simplify]: Simplify 2 into 2 13.972 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 13.972 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 13.972 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 13.972 * [taylor]: Taking taylor expansion of (* n PI) in n 13.972 * [taylor]: Taking taylor expansion of n in n 13.972 * [backup-simplify]: Simplify 0 into 0 13.973 * [backup-simplify]: Simplify 1 into 1 13.973 * [taylor]: Taking taylor expansion of PI in n 13.973 * [backup-simplify]: Simplify PI into PI 13.973 * [backup-simplify]: Simplify (* 0 PI) into 0 13.974 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.974 * [backup-simplify]: Simplify (sqrt 0) into 0 13.975 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 13.976 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.977 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 13.977 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 13.978 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.979 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.979 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.981 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 13.982 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 13.982 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 13.983 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.983 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 13.983 * [backup-simplify]: Simplify (* +nan.0 0) into 0 13.984 * [backup-simplify]: Simplify (- 0) into 0 13.984 * [backup-simplify]: Simplify (+ 0 0) into 0 13.984 * [backup-simplify]: Simplify (- 0) into 0 13.984 * [backup-simplify]: Simplify (+ 0 0) into 0 13.985 * [backup-simplify]: Simplify (- 0) into 0 13.985 * [backup-simplify]: Simplify 0 into 0 13.985 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.986 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 13.987 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 13.988 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 13.989 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 13.990 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 13.994 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) 13.996 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 13.999 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 14.003 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 14.017 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))))) 14.025 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 14.032 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) 14.033 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 14.038 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 14.039 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 14.044 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.053 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.058 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.062 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 14.078 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) 14.078 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* PI (* (/ 1 n) 2)) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 14.078 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 14.078 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.078 * [taylor]: Taking taylor expansion of (sqrt k) in n 14.078 * [taylor]: Taking taylor expansion of k in n 14.078 * [backup-simplify]: Simplify k into k 14.078 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 14.078 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 14.078 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.078 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.079 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.079 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.079 * [taylor]: Taking taylor expansion of 1/2 in n 14.079 * [backup-simplify]: Simplify 1/2 into 1/2 14.079 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.079 * [taylor]: Taking taylor expansion of 1/2 in n 14.079 * [backup-simplify]: Simplify 1/2 into 1/2 14.079 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.079 * [taylor]: Taking taylor expansion of k in n 14.079 * [backup-simplify]: Simplify k into k 14.079 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.079 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.079 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.079 * [taylor]: Taking taylor expansion of 2 in n 14.079 * [backup-simplify]: Simplify 2 into 2 14.079 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.079 * [taylor]: Taking taylor expansion of PI in n 14.079 * [backup-simplify]: Simplify PI into PI 14.079 * [taylor]: Taking taylor expansion of n in n 14.079 * [backup-simplify]: Simplify 0 into 0 14.079 * [backup-simplify]: Simplify 1 into 1 14.080 * [backup-simplify]: Simplify (/ PI 1) into PI 14.080 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.081 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.081 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.081 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.081 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.083 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.083 * [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))) 14.084 * [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)))) 14.084 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 14.084 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.084 * [taylor]: Taking taylor expansion of k in k 14.084 * [backup-simplify]: Simplify 0 into 0 14.084 * [backup-simplify]: Simplify 1 into 1 14.084 * [backup-simplify]: Simplify (sqrt 0) into 0 14.085 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.085 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 14.085 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 14.085 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 14.085 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 14.086 * [taylor]: Taking taylor expansion of 1/2 in k 14.086 * [backup-simplify]: Simplify 1/2 into 1/2 14.086 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.086 * [taylor]: Taking taylor expansion of 1/2 in k 14.086 * [backup-simplify]: Simplify 1/2 into 1/2 14.086 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.086 * [taylor]: Taking taylor expansion of k in k 14.086 * [backup-simplify]: Simplify 0 into 0 14.086 * [backup-simplify]: Simplify 1 into 1 14.086 * [backup-simplify]: Simplify (/ 1 1) into 1 14.086 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 14.086 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 14.086 * [taylor]: Taking taylor expansion of 2 in k 14.086 * [backup-simplify]: Simplify 2 into 2 14.086 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.086 * [taylor]: Taking taylor expansion of PI in k 14.086 * [backup-simplify]: Simplify PI into PI 14.086 * [taylor]: Taking taylor expansion of n in k 14.086 * [backup-simplify]: Simplify n into n 14.086 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.086 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 14.086 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 14.086 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.087 * [backup-simplify]: Simplify (- 1/2) into -1/2 14.087 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 14.087 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 14.087 * [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)))) 14.087 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 14.087 * [taylor]: Taking taylor expansion of (sqrt k) in k 14.087 * [taylor]: Taking taylor expansion of k in k 14.087 * [backup-simplify]: Simplify 0 into 0 14.087 * [backup-simplify]: Simplify 1 into 1 14.088 * [backup-simplify]: Simplify (sqrt 0) into 0 14.088 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 14.088 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 14.088 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 14.088 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 14.088 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 14.088 * [taylor]: Taking taylor expansion of 1/2 in k 14.088 * [backup-simplify]: Simplify 1/2 into 1/2 14.089 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.089 * [taylor]: Taking taylor expansion of 1/2 in k 14.089 * [backup-simplify]: Simplify 1/2 into 1/2 14.089 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.089 * [taylor]: Taking taylor expansion of k in k 14.089 * [backup-simplify]: Simplify 0 into 0 14.089 * [backup-simplify]: Simplify 1 into 1 14.089 * [backup-simplify]: Simplify (/ 1 1) into 1 14.089 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 14.089 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 14.089 * [taylor]: Taking taylor expansion of 2 in k 14.089 * [backup-simplify]: Simplify 2 into 2 14.089 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.089 * [taylor]: Taking taylor expansion of PI in k 14.089 * [backup-simplify]: Simplify PI into PI 14.089 * [taylor]: Taking taylor expansion of n in k 14.089 * [backup-simplify]: Simplify n into n 14.089 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.089 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 14.089 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 14.089 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.090 * [backup-simplify]: Simplify (- 1/2) into -1/2 14.090 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 14.090 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 14.090 * [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)))) 14.090 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 14.090 * [taylor]: Taking taylor expansion of 0 in n 14.090 * [backup-simplify]: Simplify 0 into 0 14.090 * [backup-simplify]: Simplify 0 into 0 14.091 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 14.091 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 14.091 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.091 * [taylor]: Taking taylor expansion of +nan.0 in n 14.091 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.091 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.091 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.091 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.091 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.091 * [taylor]: Taking taylor expansion of 1/2 in n 14.091 * [backup-simplify]: Simplify 1/2 into 1/2 14.091 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.091 * [taylor]: Taking taylor expansion of 1/2 in n 14.091 * [backup-simplify]: Simplify 1/2 into 1/2 14.091 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.091 * [taylor]: Taking taylor expansion of k in n 14.091 * [backup-simplify]: Simplify k into k 14.091 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.091 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.091 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.091 * [taylor]: Taking taylor expansion of 2 in n 14.091 * [backup-simplify]: Simplify 2 into 2 14.091 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.091 * [taylor]: Taking taylor expansion of PI in n 14.091 * [backup-simplify]: Simplify PI into PI 14.091 * [taylor]: Taking taylor expansion of n in n 14.091 * [backup-simplify]: Simplify 0 into 0 14.091 * [backup-simplify]: Simplify 1 into 1 14.092 * [backup-simplify]: Simplify (/ PI 1) into PI 14.092 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.092 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.093 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.093 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.093 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.094 * [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))) 14.095 * [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)))) 14.096 * [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))))) 14.096 * [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)))))) 14.097 * [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)))))) 14.097 * [backup-simplify]: Simplify 0 into 0 14.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.100 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 14.100 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 14.100 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.100 * [taylor]: Taking taylor expansion of +nan.0 in n 14.100 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.100 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.100 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.100 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.100 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.100 * [taylor]: Taking taylor expansion of 1/2 in n 14.100 * [backup-simplify]: Simplify 1/2 into 1/2 14.100 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.100 * [taylor]: Taking taylor expansion of 1/2 in n 14.100 * [backup-simplify]: Simplify 1/2 into 1/2 14.100 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.100 * [taylor]: Taking taylor expansion of k in n 14.100 * [backup-simplify]: Simplify k into k 14.100 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.100 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.100 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.100 * [taylor]: Taking taylor expansion of 2 in n 14.100 * [backup-simplify]: Simplify 2 into 2 14.100 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.100 * [taylor]: Taking taylor expansion of PI in n 14.100 * [backup-simplify]: Simplify PI into PI 14.100 * [taylor]: Taking taylor expansion of n in n 14.100 * [backup-simplify]: Simplify 0 into 0 14.100 * [backup-simplify]: Simplify 1 into 1 14.100 * [backup-simplify]: Simplify (/ PI 1) into PI 14.101 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.101 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.101 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.101 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.101 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.103 * [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))) 14.104 * [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)))) 14.104 * [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))))) 14.105 * [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)))))) 14.106 * [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)))))) 14.106 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.107 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 14.108 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 14.108 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.108 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 14.108 * [backup-simplify]: Simplify (- 0) into 0 14.109 * [backup-simplify]: Simplify (+ 0 0) into 0 14.110 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.110 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 14.111 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 14.112 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 14.113 * [backup-simplify]: Simplify (- 0) into 0 14.113 * [backup-simplify]: Simplify 0 into 0 14.113 * [backup-simplify]: Simplify 0 into 0 14.115 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.116 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 14.116 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 14.116 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 14.116 * [taylor]: Taking taylor expansion of +nan.0 in n 14.116 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.116 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 14.116 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 14.116 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 14.116 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 14.116 * [taylor]: Taking taylor expansion of 1/2 in n 14.116 * [backup-simplify]: Simplify 1/2 into 1/2 14.116 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.116 * [taylor]: Taking taylor expansion of 1/2 in n 14.116 * [backup-simplify]: Simplify 1/2 into 1/2 14.116 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.116 * [taylor]: Taking taylor expansion of k in n 14.116 * [backup-simplify]: Simplify k into k 14.116 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.116 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 14.116 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 14.116 * [taylor]: Taking taylor expansion of 2 in n 14.116 * [backup-simplify]: Simplify 2 into 2 14.116 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.116 * [taylor]: Taking taylor expansion of PI in n 14.116 * [backup-simplify]: Simplify PI into PI 14.116 * [taylor]: Taking taylor expansion of n in n 14.116 * [backup-simplify]: Simplify 0 into 0 14.116 * [backup-simplify]: Simplify 1 into 1 14.117 * [backup-simplify]: Simplify (/ PI 1) into PI 14.117 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 14.118 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 14.118 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.118 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 14.118 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 14.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 14.119 * [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))) 14.120 * [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)))) 14.121 * [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))))) 14.122 * [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)))))) 14.122 * [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)))))) 14.125 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* 1 (/ 1 k))))) 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)))))))) 14.125 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* PI (* (/ 1 (- n)) 2)) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 14.125 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 14.125 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 14.125 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.125 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 14.125 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 14.125 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.125 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.125 * [taylor]: Taking taylor expansion of 1/2 in n 14.125 * [backup-simplify]: Simplify 1/2 into 1/2 14.125 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.125 * [taylor]: Taking taylor expansion of k in n 14.125 * [backup-simplify]: Simplify k into k 14.125 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.125 * [taylor]: Taking taylor expansion of 1/2 in n 14.125 * [backup-simplify]: Simplify 1/2 into 1/2 14.125 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.125 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.125 * [taylor]: Taking taylor expansion of -2 in n 14.125 * [backup-simplify]: Simplify -2 into -2 14.125 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.125 * [taylor]: Taking taylor expansion of PI in n 14.125 * [backup-simplify]: Simplify PI into PI 14.125 * [taylor]: Taking taylor expansion of n in n 14.125 * [backup-simplify]: Simplify 0 into 0 14.125 * [backup-simplify]: Simplify 1 into 1 14.126 * [backup-simplify]: Simplify (/ PI 1) into PI 14.126 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.131 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.131 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.131 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.132 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.133 * [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))) 14.133 * [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)))) 14.133 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 14.133 * [taylor]: Taking taylor expansion of (/ -1 k) in n 14.133 * [taylor]: Taking taylor expansion of -1 in n 14.134 * [backup-simplify]: Simplify -1 into -1 14.134 * [taylor]: Taking taylor expansion of k in n 14.134 * [backup-simplify]: Simplify k into k 14.134 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 14.134 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 14.134 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 14.134 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 14.135 * [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))) 14.135 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 14.135 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 14.135 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 14.135 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 14.135 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 14.135 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.135 * [taylor]: Taking taylor expansion of 1/2 in k 14.135 * [backup-simplify]: Simplify 1/2 into 1/2 14.135 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.135 * [taylor]: Taking taylor expansion of k in k 14.135 * [backup-simplify]: Simplify 0 into 0 14.135 * [backup-simplify]: Simplify 1 into 1 14.136 * [backup-simplify]: Simplify (/ 1 1) into 1 14.136 * [taylor]: Taking taylor expansion of 1/2 in k 14.136 * [backup-simplify]: Simplify 1/2 into 1/2 14.136 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 14.136 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 14.136 * [taylor]: Taking taylor expansion of -2 in k 14.136 * [backup-simplify]: Simplify -2 into -2 14.136 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.136 * [taylor]: Taking taylor expansion of PI in k 14.136 * [backup-simplify]: Simplify PI into PI 14.136 * [taylor]: Taking taylor expansion of n in k 14.136 * [backup-simplify]: Simplify n into n 14.136 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.136 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 14.136 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 14.137 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.137 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 14.137 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 14.138 * [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))) 14.138 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.138 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.138 * [taylor]: Taking taylor expansion of -1 in k 14.138 * [backup-simplify]: Simplify -1 into -1 14.138 * [taylor]: Taking taylor expansion of k in k 14.138 * [backup-simplify]: Simplify 0 into 0 14.138 * [backup-simplify]: Simplify 1 into 1 14.138 * [backup-simplify]: Simplify (/ -1 1) into -1 14.139 * [backup-simplify]: Simplify (sqrt 0) into 0 14.140 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.140 * [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)))) 14.140 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 14.141 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 14.141 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 14.141 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 14.141 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 14.141 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 14.141 * [taylor]: Taking taylor expansion of 1/2 in k 14.141 * [backup-simplify]: Simplify 1/2 into 1/2 14.141 * [taylor]: Taking taylor expansion of (/ 1 k) in k 14.141 * [taylor]: Taking taylor expansion of k in k 14.141 * [backup-simplify]: Simplify 0 into 0 14.141 * [backup-simplify]: Simplify 1 into 1 14.141 * [backup-simplify]: Simplify (/ 1 1) into 1 14.141 * [taylor]: Taking taylor expansion of 1/2 in k 14.141 * [backup-simplify]: Simplify 1/2 into 1/2 14.141 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 14.141 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 14.141 * [taylor]: Taking taylor expansion of -2 in k 14.141 * [backup-simplify]: Simplify -2 into -2 14.141 * [taylor]: Taking taylor expansion of (/ PI n) in k 14.142 * [taylor]: Taking taylor expansion of PI in k 14.142 * [backup-simplify]: Simplify PI into PI 14.142 * [taylor]: Taking taylor expansion of n in k 14.142 * [backup-simplify]: Simplify n into n 14.142 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 14.142 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 14.142 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 14.142 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 14.143 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 14.143 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 14.143 * [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))) 14.143 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 14.143 * [taylor]: Taking taylor expansion of (/ -1 k) in k 14.143 * [taylor]: Taking taylor expansion of -1 in k 14.143 * [backup-simplify]: Simplify -1 into -1 14.143 * [taylor]: Taking taylor expansion of k in k 14.143 * [backup-simplify]: Simplify 0 into 0 14.143 * [backup-simplify]: Simplify 1 into 1 14.144 * [backup-simplify]: Simplify (/ -1 1) into -1 14.144 * [backup-simplify]: Simplify (sqrt 0) into 0 14.146 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 14.146 * [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)))) 14.146 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 14.146 * [taylor]: Taking taylor expansion of +nan.0 in n 14.146 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.146 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 14.146 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.146 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.146 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.146 * [taylor]: Taking taylor expansion of -2 in n 14.146 * [backup-simplify]: Simplify -2 into -2 14.146 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.146 * [taylor]: Taking taylor expansion of PI in n 14.146 * [backup-simplify]: Simplify PI into PI 14.146 * [taylor]: Taking taylor expansion of n in n 14.146 * [backup-simplify]: Simplify 0 into 0 14.146 * [backup-simplify]: Simplify 1 into 1 14.147 * [backup-simplify]: Simplify (/ PI 1) into PI 14.147 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.148 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.148 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.148 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.148 * [taylor]: Taking taylor expansion of 1/2 in n 14.149 * [backup-simplify]: Simplify 1/2 into 1/2 14.149 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.149 * [taylor]: Taking taylor expansion of k in n 14.149 * [backup-simplify]: Simplify k into k 14.149 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.149 * [taylor]: Taking taylor expansion of 1/2 in n 14.149 * [backup-simplify]: Simplify 1/2 into 1/2 14.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.150 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.150 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.151 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 14.152 * [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)))) 14.154 * [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))))) 14.155 * [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))))) 14.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 14.159 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 14.160 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 14.160 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 14.160 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 14.160 * [taylor]: Taking taylor expansion of +nan.0 in n 14.160 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.160 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 14.160 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.160 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.160 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.160 * [taylor]: Taking taylor expansion of -2 in n 14.160 * [backup-simplify]: Simplify -2 into -2 14.160 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.160 * [taylor]: Taking taylor expansion of PI in n 14.160 * [backup-simplify]: Simplify PI into PI 14.160 * [taylor]: Taking taylor expansion of n in n 14.160 * [backup-simplify]: Simplify 0 into 0 14.160 * [backup-simplify]: Simplify 1 into 1 14.161 * [backup-simplify]: Simplify (/ PI 1) into PI 14.161 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.162 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.162 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.162 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.162 * [taylor]: Taking taylor expansion of 1/2 in n 14.162 * [backup-simplify]: Simplify 1/2 into 1/2 14.162 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.162 * [taylor]: Taking taylor expansion of k in n 14.162 * [backup-simplify]: Simplify k into k 14.162 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.162 * [taylor]: Taking taylor expansion of 1/2 in n 14.162 * [backup-simplify]: Simplify 1/2 into 1/2 14.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.163 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.163 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.164 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 14.165 * [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)))) 14.165 * [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))))) 14.166 * [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)))))) 14.167 * [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)))))) 14.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.168 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 14.168 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 14.168 * [backup-simplify]: Simplify (+ 0 0) into 0 14.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 14.169 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 14.170 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 14.171 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 14.172 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 14.173 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 14.173 * [backup-simplify]: Simplify 0 into 0 14.174 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.176 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 14.177 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) 14.177 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 14.177 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 14.177 * [taylor]: Taking taylor expansion of +nan.0 in n 14.177 * [backup-simplify]: Simplify +nan.0 into +nan.0 14.177 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 14.177 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 14.177 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 14.177 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 14.177 * [taylor]: Taking taylor expansion of -2 in n 14.177 * [backup-simplify]: Simplify -2 into -2 14.177 * [taylor]: Taking taylor expansion of (/ PI n) in n 14.177 * [taylor]: Taking taylor expansion of PI in n 14.177 * [backup-simplify]: Simplify PI into PI 14.177 * [taylor]: Taking taylor expansion of n in n 14.177 * [backup-simplify]: Simplify 0 into 0 14.177 * [backup-simplify]: Simplify 1 into 1 14.178 * [backup-simplify]: Simplify (/ PI 1) into PI 14.178 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 14.179 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 14.179 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 14.179 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 14.179 * [taylor]: Taking taylor expansion of 1/2 in n 14.179 * [backup-simplify]: Simplify 1/2 into 1/2 14.179 * [taylor]: Taking taylor expansion of (/ 1 k) in n 14.179 * [taylor]: Taking taylor expansion of k in n 14.179 * [backup-simplify]: Simplify k into k 14.179 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 14.179 * [taylor]: Taking taylor expansion of 1/2 in n 14.179 * [backup-simplify]: Simplify 1/2 into 1/2 14.180 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 14.180 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 14.180 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 14.180 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) 14.181 * [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)))) 14.182 * [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))))) 14.183 * [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)))))) 14.183 * [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)))))) 14.186 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* 1 (/ 1 (- k)))) (* +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))))))))))) 14.186 * * * [progress]: simplifying candidates 14.186 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 14.186 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 14.186 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 14.186 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 14.186 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 14.186 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 14.186 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 8 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 9 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 10 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 11 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 12 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 13 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 14 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 15 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 16 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 17 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 18 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 19 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 20 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 21 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 22 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 23 / 1611 ] simplifiying candidate # 14.187 * * * * [progress]: [ 24 / 1611 ] simplifiying candidate # 14.187 * * * * 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(- 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 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2)))) PI)) (- (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k))) (- (* +nan.0 (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))) (- (+ (* +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))))))))))) 14.428 * * [simplify]: iteration 1: (1731 enodes) 191.632 * * [simplify]: Extracting #0: cost 587 inf + 0 191.638 * * [simplify]: Extracting #1: cost 1621 inf + 43 191.645 * * [simplify]: Extracting #2: cost 1682 inf + 4606 191.654 * * [simplify]: Extracting #3: cost 1540 inf + 38528 191.679 * * [simplify]: Extracting #4: cost 1106 inf + 156846 191.752 * * [simplify]: Extracting #5: cost 745 inf + 324268 191.839 * * [simplify]: Extracting #6: cost 439 inf + 522409 191.948 * * [simplify]: Extracting #7: cost 164 inf + 722627 192.092 * * [simplify]: Extracting #8: cost 45 inf + 801756 192.261 * * [simplify]: Extracting #9: cost 17 inf + 817147 192.422 * * [simplify]: Extracting #10: cost 8 inf + 824150 192.572 * * [simplify]: Extracting #11: cost 2 inf + 829901 192.708 * * [simplify]: Extracting #12: cost 0 inf + 832303 192.842 * * [simplify]: Extracting #13: cost 0 inf + 832273 193.007 * [simplify]: Simplified to: (expm1 (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (log1p (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (* (log (* (* 2 n) PI)) (- 1/2 (/ k 2))) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (- 1/2 (/ k 2)) (sqrt (* (* 2 n) PI)) (pow (* (* 2 n) PI) (/ k 2)) (pow (* (* 2 n) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (pow (* (* 2 n) PI) (sqrt (- 1/2 (/ k 2)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (pow (* (* 2 n) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (* (* 2 n) PI) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 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1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- 1/2) k))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) 2) (- (sqrt k)))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2)))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- 1/2) k))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) 2) (- (sqrt k)))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2))))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2))))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))))) (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (- 1/2 (* k 1/2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (* (* 2 n) PI))) (* (/ 1 (sqrt (sqrt k))) (sqrt (* (* 2 n) PI))) (/ 1 (/ (sqrt (sqrt k)) (pow PI (- 1/2 (/ k 2))))) (* (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 n) PI) (- 1/4 (/ (/ k 2) 2)))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* (- 1/2) k))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (/ (- k) 2))) (pow (* (* 2 n) PI) (fma (sqrt 1/2) (sqrt 1/2) (* (- 1/2) k))) (pow (* (* 2 n) PI) (+ 1/2 (* (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (cbrt 2)) (- (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) (sqrt 2)) (- (/ (cbrt k) (/ (sqrt 2) (cbrt k))))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (cbrt k) 2) (- (* (cbrt k) (cbrt k)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (cbrt 2)) (- (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) (sqrt 2)) (- (/ (sqrt k) (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ (sqrt k) 2) (- (sqrt k))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (cbrt 2)) (- (/ (/ 1 (cbrt 2)) (cbrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (* (/ k (sqrt 2)) (- (/ 1 (sqrt 2)))))) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))) (pow (* (* 2 n) PI) (+ 1/2 (/ (- k) 2))) (pow (* (* 2 n) PI) (- 1/2 (* k 1/2))) (sqrt (* (* 2 n) PI)) (sqrt (* (* 2 n) PI)) (pow PI (- 1/2 (/ k 2))) (* (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2))))) (sqrt (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) 1 (pow (* (* 2 n) PI) (- 1/4 (/ (/ k 2) 2))) 1 (/ 1 (sqrt k)) (/ 1 (/ (sqrt k) (sqrt (* (* 2 n) PI)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))) (/ 1 (sqrt k)) (real->posit16 (/ 1 (/ (sqrt k) (pow (* (* 2 n) PI) (- 1/2 (/ k 2)))))) (- (fma 1/4 (* (* (log (* PI 2)) (exp (* 1/2 (+ (log n) (log (* PI 2)))))) (* (* k k) (log n))) (fma 1/8 (* (* (* k k) (* (log n) (log n))) (exp (* 1/2 (+ (log n) (log (* PI 2)))))) (+ (exp (* 1/2 (+ (log n) (log (* PI 2))))) (* (* (* (exp (* 1/2 (+ (log n) (log (* PI 2))))) (* k k)) (* (log (* PI 2)) (log (* PI 2)))) 1/8)))) (* 1/2 (+ (* (* (exp (* 1/2 (+ (log n) (log (* PI 2))))) (log n)) k) (* (log (* PI 2)) (* (exp (* 1/2 (+ (log n) (log (* PI 2))))) k))))) (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (- (* +nan.0 (/ (* (* (sqrt 2) (* k k)) (* (log (* PI 2)) (* (sqrt 1/2) (sqrt 1/2)))) PI)) (- (* +nan.0 (/ (sqrt 1/2) (/ PI (* k k)))) (- (/ (* +nan.0 (* (* n (sqrt 1/2)) k)) (* PI PI)) (- (* (/ (log n) (/ PI (* (sqrt 2) (* (* k k) (* (sqrt 1/2) (sqrt 1/2)))))) +nan.0) (* +nan.0 (/ (* (sqrt 1/2) k) PI))))))) (- (- (* (/ (exp (- (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2))))) k) +nan.0) (- (* (/ (exp (- (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2))))) (* k k)) +nan.0) (* (exp (- (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2))))) +nan.0)))) (- (- (* +nan.0 (/ (exp (- (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) (* k k))) (- (* (/ (exp (- (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) k) +nan.0) (* +nan.0 (exp (- (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))) (- (- (* (* +nan.0 (sqrt 2)) (* (* PI n) k)) (- (* +nan.0 (* (* PI n) (sqrt 2))) (- (* (* (log (* PI 2)) (* (* (* PI n) k) (sqrt 2))) +nan.0) (- (* (* (* (sqrt 2) n) (* PI (* (log n) k))) +nan.0) (* (* +nan.0 (sqrt 2)) (* (* n n) (* PI PI)))))))) (- (- (* (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (* k (* k k))) +nan.0) (- (* +nan.0 (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) k)) (* +nan.0 (/ (exp (* (- (log (* PI 2)) (- (log n))) (- 1/2 (* k 1/2)))) (* k k)))))) (- (- (/ (* +nan.0 (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) k) (- (* +nan.0 (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k))) (* +nan.0 (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))))) 193.434 * * * [progress]: adding candidates to table 213.994 * * [progress]: iteration 3 / 4 213.994 * * * [progress]: picking best candidate 214.018 * * * * [pick]: Picked # 214.018 * * * [progress]: localizing error 214.041 * * * [progress]: generating rewritten candidates 214.041 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 214.047 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 214.051 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 214.064 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 214.087 * * * [progress]: generating series expansions 214.087 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 214.087 * [backup-simplify]: Simplify (pow (* 2 n) (- 1/2 (* 1/2 k))) into (pow (* 2 n) (- 1/2 (* 1/2 k))) 214.087 * [approximate]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in (n k) around 0 214.087 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 214.087 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 214.087 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 214.087 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.087 * [taylor]: Taking taylor expansion of 1/2 in k 214.087 * [backup-simplify]: Simplify 1/2 into 1/2 214.087 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.087 * [taylor]: Taking taylor expansion of 1/2 in k 214.087 * [backup-simplify]: Simplify 1/2 into 1/2 214.087 * [taylor]: Taking taylor expansion of k in k 214.088 * [backup-simplify]: Simplify 0 into 0 214.088 * [backup-simplify]: Simplify 1 into 1 214.088 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 214.088 * [taylor]: Taking taylor expansion of (* 2 n) in k 214.088 * [taylor]: Taking taylor expansion of 2 in k 214.088 * [backup-simplify]: Simplify 2 into 2 214.088 * [taylor]: Taking taylor expansion of n in k 214.088 * [backup-simplify]: Simplify n into n 214.088 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 214.088 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 214.088 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.088 * [backup-simplify]: Simplify (- 0) into 0 214.089 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.089 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 214.089 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 214.089 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 214.089 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 214.089 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 214.089 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 214.089 * [taylor]: Taking taylor expansion of 1/2 in n 214.089 * [backup-simplify]: Simplify 1/2 into 1/2 214.089 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 214.089 * [taylor]: Taking taylor expansion of 1/2 in n 214.089 * [backup-simplify]: Simplify 1/2 into 1/2 214.089 * [taylor]: Taking taylor expansion of k in n 214.089 * [backup-simplify]: Simplify k into k 214.089 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.089 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.089 * [taylor]: Taking taylor expansion of 2 in n 214.089 * [backup-simplify]: Simplify 2 into 2 214.089 * [taylor]: Taking taylor expansion of n in n 214.089 * [backup-simplify]: Simplify 0 into 0 214.089 * [backup-simplify]: Simplify 1 into 1 214.089 * [backup-simplify]: Simplify (* 2 0) into 0 214.090 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.090 * [backup-simplify]: Simplify (log 2) into (log 2) 214.090 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 214.090 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 214.090 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 214.091 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.091 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 214.091 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 214.091 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 214.091 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 214.091 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 214.091 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 214.091 * [taylor]: Taking taylor expansion of 1/2 in n 214.091 * [backup-simplify]: Simplify 1/2 into 1/2 214.091 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 214.092 * [taylor]: Taking taylor expansion of 1/2 in n 214.092 * [backup-simplify]: Simplify 1/2 into 1/2 214.092 * [taylor]: Taking taylor expansion of k in n 214.092 * [backup-simplify]: Simplify k into k 214.092 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.092 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.092 * [taylor]: Taking taylor expansion of 2 in n 214.092 * [backup-simplify]: Simplify 2 into 2 214.092 * [taylor]: Taking taylor expansion of n in n 214.092 * [backup-simplify]: Simplify 0 into 0 214.092 * [backup-simplify]: Simplify 1 into 1 214.092 * [backup-simplify]: Simplify (* 2 0) into 0 214.092 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.093 * [backup-simplify]: Simplify (log 2) into (log 2) 214.093 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 214.093 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 214.093 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 214.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.094 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 214.094 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 214.094 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 214.094 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 214.094 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 214.094 * [taylor]: Taking taylor expansion of (log 2) in k 214.094 * [taylor]: Taking taylor expansion of 2 in k 214.094 * [backup-simplify]: Simplify 2 into 2 214.094 * [backup-simplify]: Simplify (log 2) into (log 2) 214.094 * [taylor]: Taking taylor expansion of (log n) in k 214.094 * [taylor]: Taking taylor expansion of n in k 214.094 * [backup-simplify]: Simplify n into n 214.094 * [backup-simplify]: Simplify (log n) into (log n) 214.094 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.094 * [taylor]: Taking taylor expansion of 1/2 in k 214.094 * [backup-simplify]: Simplify 1/2 into 1/2 214.094 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.094 * [taylor]: Taking taylor expansion of 1/2 in k 214.094 * [backup-simplify]: Simplify 1/2 into 1/2 214.094 * [taylor]: Taking taylor expansion of k in k 214.094 * [backup-simplify]: Simplify 0 into 0 214.094 * [backup-simplify]: Simplify 1 into 1 214.095 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 214.095 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.095 * [backup-simplify]: Simplify (- 0) into 0 214.095 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.096 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 214.096 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 214.096 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 214.097 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 214.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.098 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 214.098 * [backup-simplify]: Simplify (- 0) into 0 214.098 * [backup-simplify]: Simplify (+ 0 0) into 0 214.099 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.099 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 214.100 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.100 * [taylor]: Taking taylor expansion of 0 in k 214.100 * [backup-simplify]: Simplify 0 into 0 214.100 * [backup-simplify]: Simplify 0 into 0 214.100 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 214.101 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.101 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 214.102 * [backup-simplify]: Simplify (+ 0 0) into 0 214.103 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 214.104 * [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))))) 214.105 * [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))))) 214.105 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 214.107 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 214.107 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 214.108 * [backup-simplify]: Simplify (- 0) into 0 214.108 * [backup-simplify]: Simplify (+ 0 0) into 0 214.108 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.109 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 214.110 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 214.110 * [taylor]: Taking taylor expansion of 0 in k 214.110 * [backup-simplify]: Simplify 0 into 0 214.110 * [backup-simplify]: Simplify 0 into 0 214.110 * [backup-simplify]: Simplify 0 into 0 214.111 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 214.111 * [backup-simplify]: Simplify (- 0) into 0 214.111 * [backup-simplify]: Simplify (+ 0 0) into 0 214.113 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 214.113 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 214.114 * [backup-simplify]: Simplify (+ 0 0) into 0 214.114 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 214.116 * [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))))) 214.117 * [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))))) 214.120 * [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))))) 214.120 * [backup-simplify]: Simplify (pow (* 2 (/ 1 n)) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 214.120 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 214.120 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 214.120 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 214.120 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 214.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.120 * [taylor]: Taking taylor expansion of 1/2 in k 214.120 * [backup-simplify]: Simplify 1/2 into 1/2 214.120 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.120 * [taylor]: Taking taylor expansion of 1/2 in k 214.120 * [backup-simplify]: Simplify 1/2 into 1/2 214.121 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.121 * [taylor]: Taking taylor expansion of k in k 214.121 * [backup-simplify]: Simplify 0 into 0 214.121 * [backup-simplify]: Simplify 1 into 1 214.125 * [backup-simplify]: Simplify (/ 1 1) into 1 214.125 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 214.125 * [taylor]: Taking taylor expansion of (/ 2 n) in k 214.125 * [taylor]: Taking taylor expansion of 2 in k 214.125 * [backup-simplify]: Simplify 2 into 2 214.125 * [taylor]: Taking taylor expansion of n in k 214.125 * [backup-simplify]: Simplify n into n 214.125 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 214.125 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 214.126 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.126 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.126 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.126 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 214.126 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 214.126 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.126 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.127 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.127 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.127 * [taylor]: Taking taylor expansion of 1/2 in n 214.127 * [backup-simplify]: Simplify 1/2 into 1/2 214.127 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.127 * [taylor]: Taking taylor expansion of 1/2 in n 214.127 * [backup-simplify]: Simplify 1/2 into 1/2 214.127 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.127 * [taylor]: Taking taylor expansion of k in n 214.127 * [backup-simplify]: Simplify k into k 214.127 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.127 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.127 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.127 * [taylor]: Taking taylor expansion of 2 in n 214.127 * [backup-simplify]: Simplify 2 into 2 214.127 * [taylor]: Taking taylor expansion of n in n 214.127 * [backup-simplify]: Simplify 0 into 0 214.127 * [backup-simplify]: Simplify 1 into 1 214.127 * [backup-simplify]: Simplify (/ 2 1) into 2 214.127 * [backup-simplify]: Simplify (log 2) into (log 2) 214.127 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.127 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.127 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.128 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.128 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.129 * [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)))) 214.129 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.129 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.129 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.129 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.129 * [taylor]: Taking taylor expansion of 1/2 in n 214.129 * [backup-simplify]: Simplify 1/2 into 1/2 214.129 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.129 * [taylor]: Taking taylor expansion of 1/2 in n 214.129 * [backup-simplify]: Simplify 1/2 into 1/2 214.129 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.129 * [taylor]: Taking taylor expansion of k in n 214.129 * [backup-simplify]: Simplify k into k 214.129 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.129 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.129 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.129 * [taylor]: Taking taylor expansion of 2 in n 214.129 * [backup-simplify]: Simplify 2 into 2 214.129 * [taylor]: Taking taylor expansion of n in n 214.129 * [backup-simplify]: Simplify 0 into 0 214.129 * [backup-simplify]: Simplify 1 into 1 214.129 * [backup-simplify]: Simplify (/ 2 1) into 2 214.129 * [backup-simplify]: Simplify (log 2) into (log 2) 214.130 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.130 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.130 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.130 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.130 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.131 * [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)))) 214.131 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 214.131 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 214.131 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.131 * [taylor]: Taking taylor expansion of 1/2 in k 214.131 * [backup-simplify]: Simplify 1/2 into 1/2 214.131 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.131 * [taylor]: Taking taylor expansion of 1/2 in k 214.131 * [backup-simplify]: Simplify 1/2 into 1/2 214.131 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.131 * [taylor]: Taking taylor expansion of k in k 214.131 * [backup-simplify]: Simplify 0 into 0 214.131 * [backup-simplify]: Simplify 1 into 1 214.131 * [backup-simplify]: Simplify (/ 1 1) into 1 214.131 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 214.131 * [taylor]: Taking taylor expansion of (log 2) in k 214.131 * [taylor]: Taking taylor expansion of 2 in k 214.131 * [backup-simplify]: Simplify 2 into 2 214.132 * [backup-simplify]: Simplify (log 2) into (log 2) 214.132 * [taylor]: Taking taylor expansion of (log n) in k 214.132 * [taylor]: Taking taylor expansion of n in k 214.132 * [backup-simplify]: Simplify n into n 214.132 * [backup-simplify]: Simplify (log n) into (log n) 214.132 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.132 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.132 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.132 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 214.133 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 214.133 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 214.133 * [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)))) 214.134 * [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)))) 214.134 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 214.135 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.136 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.136 * [backup-simplify]: Simplify (- 0) into 0 214.136 * [backup-simplify]: Simplify (+ 0 0) into 0 214.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.137 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 214.138 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.138 * [taylor]: Taking taylor expansion of 0 in k 214.138 * [backup-simplify]: Simplify 0 into 0 214.138 * [backup-simplify]: Simplify 0 into 0 214.138 * [backup-simplify]: Simplify 0 into 0 214.138 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.140 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 214.140 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.140 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 214.141 * [backup-simplify]: Simplify (- 0) into 0 214.141 * [backup-simplify]: Simplify (+ 0 0) into 0 214.141 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.142 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 214.143 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 214.143 * [taylor]: Taking taylor expansion of 0 in k 214.143 * [backup-simplify]: Simplify 0 into 0 214.143 * [backup-simplify]: Simplify 0 into 0 214.143 * [backup-simplify]: Simplify 0 into 0 214.143 * [backup-simplify]: Simplify 0 into 0 214.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.146 * [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 0 214.146 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 214.147 * [backup-simplify]: Simplify (- 0) into 0 214.148 * [backup-simplify]: Simplify (+ 0 0) into 0 214.148 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.149 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 214.150 * [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 0 214.150 * [taylor]: Taking taylor expansion of 0 in k 214.150 * [backup-simplify]: Simplify 0 into 0 214.150 * [backup-simplify]: Simplify 0 into 0 214.150 * [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)))) 214.150 * [backup-simplify]: Simplify (pow (* 2 (/ 1 (- n))) (- 1/2 (* 1/2 (/ 1 (- k))))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 214.151 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 214.151 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.151 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 214.151 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 214.151 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.151 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.151 * [taylor]: Taking taylor expansion of 1/2 in k 214.151 * [backup-simplify]: Simplify 1/2 into 1/2 214.151 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.151 * [taylor]: Taking taylor expansion of k in k 214.151 * [backup-simplify]: Simplify 0 into 0 214.151 * [backup-simplify]: Simplify 1 into 1 214.151 * [backup-simplify]: Simplify (/ 1 1) into 1 214.151 * [taylor]: Taking taylor expansion of 1/2 in k 214.151 * [backup-simplify]: Simplify 1/2 into 1/2 214.151 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 214.151 * [taylor]: Taking taylor expansion of (/ -2 n) in k 214.151 * [taylor]: Taking taylor expansion of -2 in k 214.151 * [backup-simplify]: Simplify -2 into -2 214.151 * [taylor]: Taking taylor expansion of n in k 214.151 * [backup-simplify]: Simplify n into n 214.151 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 214.151 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 214.151 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.152 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.152 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 214.152 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 214.152 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.152 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.152 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.152 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.152 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.152 * [taylor]: Taking taylor expansion of 1/2 in n 214.152 * [backup-simplify]: Simplify 1/2 into 1/2 214.152 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.152 * [taylor]: Taking taylor expansion of k in n 214.152 * [backup-simplify]: Simplify k into k 214.152 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.152 * [taylor]: Taking taylor expansion of 1/2 in n 214.152 * [backup-simplify]: Simplify 1/2 into 1/2 214.152 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.152 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.152 * [taylor]: Taking taylor expansion of -2 in n 214.152 * [backup-simplify]: Simplify -2 into -2 214.152 * [taylor]: Taking taylor expansion of n in n 214.152 * [backup-simplify]: Simplify 0 into 0 214.152 * [backup-simplify]: Simplify 1 into 1 214.152 * [backup-simplify]: Simplify (/ -2 1) into -2 214.153 * [backup-simplify]: Simplify (log -2) into (log -2) 214.153 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.153 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.154 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.154 * [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)))) 214.154 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.154 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.154 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.154 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.154 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.154 * [taylor]: Taking taylor expansion of 1/2 in n 214.154 * [backup-simplify]: Simplify 1/2 into 1/2 214.154 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.154 * [taylor]: Taking taylor expansion of k in n 214.154 * [backup-simplify]: Simplify k into k 214.154 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.154 * [taylor]: Taking taylor expansion of 1/2 in n 214.154 * [backup-simplify]: Simplify 1/2 into 1/2 214.154 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.154 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.154 * [taylor]: Taking taylor expansion of -2 in n 214.154 * [backup-simplify]: Simplify -2 into -2 214.154 * [taylor]: Taking taylor expansion of n in n 214.154 * [backup-simplify]: Simplify 0 into 0 214.154 * [backup-simplify]: Simplify 1 into 1 214.155 * [backup-simplify]: Simplify (/ -2 1) into -2 214.155 * [backup-simplify]: Simplify (log -2) into (log -2) 214.155 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.155 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.155 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.156 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.156 * [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)))) 214.156 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 214.156 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 214.156 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.156 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.156 * [taylor]: Taking taylor expansion of 1/2 in k 214.156 * [backup-simplify]: Simplify 1/2 into 1/2 214.156 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.156 * [taylor]: Taking taylor expansion of k in k 214.156 * [backup-simplify]: Simplify 0 into 0 214.156 * [backup-simplify]: Simplify 1 into 1 214.157 * [backup-simplify]: Simplify (/ 1 1) into 1 214.157 * [taylor]: Taking taylor expansion of 1/2 in k 214.157 * [backup-simplify]: Simplify 1/2 into 1/2 214.157 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 214.157 * [taylor]: Taking taylor expansion of (log -2) in k 214.157 * [taylor]: Taking taylor expansion of -2 in k 214.157 * [backup-simplify]: Simplify -2 into -2 214.157 * [backup-simplify]: Simplify (log -2) into (log -2) 214.157 * [taylor]: Taking taylor expansion of (log n) in k 214.157 * [taylor]: Taking taylor expansion of n in k 214.157 * [backup-simplify]: Simplify n into n 214.157 * [backup-simplify]: Simplify (log n) into (log n) 214.157 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.158 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.158 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 214.158 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 214.158 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 214.158 * [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)))) 214.159 * [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)))) 214.159 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 214.160 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 214.160 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.160 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.161 * [backup-simplify]: Simplify (+ 0 0) into 0 214.161 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.162 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 214.162 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.162 * [taylor]: Taking taylor expansion of 0 in k 214.162 * [backup-simplify]: Simplify 0 into 0 214.162 * [backup-simplify]: Simplify 0 into 0 214.162 * [backup-simplify]: Simplify 0 into 0 214.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.164 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 214.165 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.165 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 214.165 * [backup-simplify]: Simplify (+ 0 0) into 0 214.166 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.166 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 214.167 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 214.167 * [taylor]: Taking taylor expansion of 0 in k 214.167 * [backup-simplify]: Simplify 0 into 0 214.167 * [backup-simplify]: Simplify 0 into 0 214.167 * [backup-simplify]: Simplify 0 into 0 214.168 * [backup-simplify]: Simplify 0 into 0 214.168 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.171 * [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 0 214.171 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.172 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 214.172 * [backup-simplify]: Simplify (+ 0 0) into 0 214.172 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.173 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0 214.174 * [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 0 214.174 * [taylor]: Taking taylor expansion of 0 in k 214.174 * [backup-simplify]: Simplify 0 into 0 214.174 * [backup-simplify]: Simplify 0 into 0 214.175 * [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))))) 214.175 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 214.175 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 k))) into (pow PI (- 1/2 (* 1/2 k))) 214.175 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 214.175 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 214.175 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 214.175 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 214.175 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.175 * [taylor]: Taking taylor expansion of 1/2 in k 214.175 * [backup-simplify]: Simplify 1/2 into 1/2 214.175 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.175 * [taylor]: Taking taylor expansion of 1/2 in k 214.175 * [backup-simplify]: Simplify 1/2 into 1/2 214.175 * [taylor]: Taking taylor expansion of k in k 214.175 * [backup-simplify]: Simplify 0 into 0 214.175 * [backup-simplify]: Simplify 1 into 1 214.175 * [taylor]: Taking taylor expansion of (log PI) in k 214.175 * [taylor]: Taking taylor expansion of PI in k 214.175 * [backup-simplify]: Simplify PI into PI 214.175 * [backup-simplify]: Simplify (log PI) into (log PI) 214.176 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.176 * [backup-simplify]: Simplify (- 0) into 0 214.176 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.177 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.178 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 214.178 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 214.178 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 214.178 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 214.178 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.178 * [taylor]: Taking taylor expansion of 1/2 in k 214.178 * [backup-simplify]: Simplify 1/2 into 1/2 214.178 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.178 * [taylor]: Taking taylor expansion of 1/2 in k 214.178 * [backup-simplify]: Simplify 1/2 into 1/2 214.178 * [taylor]: Taking taylor expansion of k in k 214.178 * [backup-simplify]: Simplify 0 into 0 214.178 * [backup-simplify]: Simplify 1 into 1 214.178 * [taylor]: Taking taylor expansion of (log PI) in k 214.178 * [taylor]: Taking taylor expansion of PI in k 214.178 * [backup-simplify]: Simplify PI into PI 214.178 * [backup-simplify]: Simplify (log PI) into (log PI) 214.178 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.179 * [backup-simplify]: Simplify (- 0) into 0 214.179 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.179 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.180 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 214.181 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 214.181 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 214.182 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 214.182 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.182 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.184 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 214.189 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 214.190 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 214.192 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 214.192 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 214.192 * [backup-simplify]: Simplify (- 0) into 0 214.193 * [backup-simplify]: Simplify (+ 0 0) into 0 214.193 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 214.199 * [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))) 214.201 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 214.204 * [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)))) 214.204 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.205 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 214.205 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 214.205 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 214.205 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 214.205 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.205 * [taylor]: Taking taylor expansion of 1/2 in k 214.205 * [backup-simplify]: Simplify 1/2 into 1/2 214.205 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.205 * [taylor]: Taking taylor expansion of 1/2 in k 214.205 * [backup-simplify]: Simplify 1/2 into 1/2 214.205 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.205 * [taylor]: Taking taylor expansion of k in k 214.205 * [backup-simplify]: Simplify 0 into 0 214.205 * [backup-simplify]: Simplify 1 into 1 214.205 * [backup-simplify]: Simplify (/ 1 1) into 1 214.205 * [taylor]: Taking taylor expansion of (log PI) in k 214.205 * [taylor]: Taking taylor expansion of PI in k 214.205 * [backup-simplify]: Simplify PI into PI 214.205 * [backup-simplify]: Simplify (log PI) into (log PI) 214.206 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.210 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.210 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.211 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 214.211 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.211 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 214.211 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 214.211 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 214.211 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.211 * [taylor]: Taking taylor expansion of 1/2 in k 214.211 * [backup-simplify]: Simplify 1/2 into 1/2 214.211 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.211 * [taylor]: Taking taylor expansion of 1/2 in k 214.211 * [backup-simplify]: Simplify 1/2 into 1/2 214.211 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.211 * [taylor]: Taking taylor expansion of k in k 214.211 * [backup-simplify]: Simplify 0 into 0 214.211 * [backup-simplify]: Simplify 1 into 1 214.211 * [backup-simplify]: Simplify (/ 1 1) into 1 214.211 * [taylor]: Taking taylor expansion of (log PI) in k 214.211 * [taylor]: Taking taylor expansion of PI in k 214.211 * [backup-simplify]: Simplify PI into PI 214.212 * [backup-simplify]: Simplify (log PI) into (log PI) 214.212 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.212 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.212 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.213 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 214.213 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.213 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.213 * [backup-simplify]: Simplify 0 into 0 214.213 * [backup-simplify]: Simplify 0 into 0 214.214 * [backup-simplify]: Simplify 0 into 0 214.214 * [backup-simplify]: Simplify 0 into 0 214.214 * [backup-simplify]: Simplify 0 into 0 214.214 * [backup-simplify]: Simplify 0 into 0 214.214 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 214.214 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (- k))))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.214 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 214.214 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.214 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 214.214 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 214.214 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.214 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.214 * [taylor]: Taking taylor expansion of 1/2 in k 214.214 * [backup-simplify]: Simplify 1/2 into 1/2 214.214 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.214 * [taylor]: Taking taylor expansion of k in k 214.214 * [backup-simplify]: Simplify 0 into 0 214.214 * [backup-simplify]: Simplify 1 into 1 214.214 * [backup-simplify]: Simplify (/ 1 1) into 1 214.214 * [taylor]: Taking taylor expansion of 1/2 in k 214.214 * [backup-simplify]: Simplify 1/2 into 1/2 214.214 * [taylor]: Taking taylor expansion of (log PI) in k 214.214 * [taylor]: Taking taylor expansion of PI in k 214.214 * [backup-simplify]: Simplify PI into PI 214.215 * [backup-simplify]: Simplify (log PI) into (log PI) 214.215 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.215 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.216 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.216 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.216 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.216 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 214.216 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 214.216 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.216 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.216 * [taylor]: Taking taylor expansion of 1/2 in k 214.216 * [backup-simplify]: Simplify 1/2 into 1/2 214.216 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.216 * [taylor]: Taking taylor expansion of k in k 214.216 * [backup-simplify]: Simplify 0 into 0 214.216 * [backup-simplify]: Simplify 1 into 1 214.216 * [backup-simplify]: Simplify (/ 1 1) into 1 214.216 * [taylor]: Taking taylor expansion of 1/2 in k 214.216 * [backup-simplify]: Simplify 1/2 into 1/2 214.216 * [taylor]: Taking taylor expansion of (log PI) in k 214.216 * [taylor]: Taking taylor expansion of PI in k 214.217 * [backup-simplify]: Simplify PI into PI 214.217 * [backup-simplify]: Simplify (log PI) into (log PI) 214.217 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.217 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.218 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.218 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.218 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.218 * [backup-simplify]: Simplify 0 into 0 214.218 * [backup-simplify]: Simplify 0 into 0 214.218 * [backup-simplify]: Simplify 0 into 0 214.218 * [backup-simplify]: Simplify 0 into 0 214.218 * [backup-simplify]: Simplify 0 into 0 214.218 * [backup-simplify]: Simplify 0 into 0 214.218 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 214.219 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 214.219 * [backup-simplify]: Simplify (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k)) into (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 214.219 * [approximate]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 214.219 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 214.219 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 214.219 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 214.219 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 214.219 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.219 * [taylor]: Taking taylor expansion of 1/2 in k 214.219 * [backup-simplify]: Simplify 1/2 into 1/2 214.219 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.219 * [taylor]: Taking taylor expansion of 1/2 in k 214.219 * [backup-simplify]: Simplify 1/2 into 1/2 214.219 * [taylor]: Taking taylor expansion of k in k 214.219 * [backup-simplify]: Simplify 0 into 0 214.219 * [backup-simplify]: Simplify 1 into 1 214.219 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 214.219 * [taylor]: Taking taylor expansion of (* 2 n) in k 214.219 * [taylor]: Taking taylor expansion of 2 in k 214.219 * [backup-simplify]: Simplify 2 into 2 214.219 * [taylor]: Taking taylor expansion of n in k 214.219 * [backup-simplify]: Simplify n into n 214.219 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 214.219 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 214.219 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.220 * [backup-simplify]: Simplify (- 0) into 0 214.220 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.220 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 214.220 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 214.220 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 214.220 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.220 * [taylor]: Taking taylor expansion of k in k 214.220 * [backup-simplify]: Simplify 0 into 0 214.220 * [backup-simplify]: Simplify 1 into 1 214.220 * [backup-simplify]: Simplify (/ 1 1) into 1 214.220 * [backup-simplify]: Simplify (sqrt 0) into 0 214.221 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.221 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 214.221 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 214.221 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 214.221 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 214.222 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 214.222 * [taylor]: Taking taylor expansion of 1/2 in n 214.222 * [backup-simplify]: Simplify 1/2 into 1/2 214.222 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 214.222 * [taylor]: Taking taylor expansion of 1/2 in n 214.222 * [backup-simplify]: Simplify 1/2 into 1/2 214.222 * [taylor]: Taking taylor expansion of k in n 214.222 * [backup-simplify]: Simplify k into k 214.222 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.222 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.222 * [taylor]: Taking taylor expansion of 2 in n 214.222 * [backup-simplify]: Simplify 2 into 2 214.222 * [taylor]: Taking taylor expansion of n in n 214.222 * [backup-simplify]: Simplify 0 into 0 214.222 * [backup-simplify]: Simplify 1 into 1 214.222 * [backup-simplify]: Simplify (* 2 0) into 0 214.222 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.223 * [backup-simplify]: Simplify (log 2) into (log 2) 214.223 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 214.223 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 214.223 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 214.223 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.224 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 214.224 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 214.224 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 214.224 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.224 * [taylor]: Taking taylor expansion of k in n 214.224 * [backup-simplify]: Simplify k into k 214.224 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.224 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 214.224 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.224 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 214.224 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 214.224 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 214.224 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 214.224 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 214.224 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 214.224 * [taylor]: Taking taylor expansion of 1/2 in n 214.224 * [backup-simplify]: Simplify 1/2 into 1/2 214.224 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 214.224 * [taylor]: Taking taylor expansion of 1/2 in n 214.224 * [backup-simplify]: Simplify 1/2 into 1/2 214.224 * [taylor]: Taking taylor expansion of k in n 214.224 * [backup-simplify]: Simplify k into k 214.224 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.224 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.224 * [taylor]: Taking taylor expansion of 2 in n 214.224 * [backup-simplify]: Simplify 2 into 2 214.224 * [taylor]: Taking taylor expansion of n in n 214.224 * [backup-simplify]: Simplify 0 into 0 214.224 * [backup-simplify]: Simplify 1 into 1 214.225 * [backup-simplify]: Simplify (* 2 0) into 0 214.225 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.225 * [backup-simplify]: Simplify (log 2) into (log 2) 214.225 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 214.226 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 214.226 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 214.226 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.226 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 214.227 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 214.227 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 214.227 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.227 * [taylor]: Taking taylor expansion of k in n 214.227 * [backup-simplify]: Simplify k into k 214.227 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.227 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 214.227 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.227 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 214.227 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) into (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 214.227 * [taylor]: Taking taylor expansion of (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 214.227 * [taylor]: Taking taylor expansion of (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k 214.227 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k 214.227 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k 214.227 * [taylor]: Taking taylor expansion of (log 2) in k 214.227 * [taylor]: Taking taylor expansion of 2 in k 214.227 * [backup-simplify]: Simplify 2 into 2 214.228 * [backup-simplify]: Simplify (log 2) into (log 2) 214.228 * [taylor]: Taking taylor expansion of (log n) in k 214.228 * [taylor]: Taking taylor expansion of n in k 214.228 * [backup-simplify]: Simplify n into n 214.228 * [backup-simplify]: Simplify (log n) into (log n) 214.228 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.228 * [taylor]: Taking taylor expansion of 1/2 in k 214.228 * [backup-simplify]: Simplify 1/2 into 1/2 214.228 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.228 * [taylor]: Taking taylor expansion of 1/2 in k 214.228 * [backup-simplify]: Simplify 1/2 into 1/2 214.228 * [taylor]: Taking taylor expansion of k in k 214.228 * [backup-simplify]: Simplify 0 into 0 214.228 * [backup-simplify]: Simplify 1 into 1 214.228 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n)) 214.228 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.229 * [backup-simplify]: Simplify (- 0) into 0 214.229 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.229 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n))) 214.230 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log 2) (log n)))) into (exp (* 1/2 (+ (log 2) (log n)))) 214.230 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 214.230 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.230 * [taylor]: Taking taylor expansion of k in k 214.230 * [backup-simplify]: Simplify 0 into 0 214.230 * [backup-simplify]: Simplify 1 into 1 214.230 * [backup-simplify]: Simplify (/ 1 1) into 1 214.230 * [backup-simplify]: Simplify (sqrt 0) into 0 214.231 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.231 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) 0) into 0 214.231 * [backup-simplify]: Simplify 0 into 0 214.232 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 214.233 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.233 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 214.233 * [backup-simplify]: Simplify (- 0) into 0 214.233 * [backup-simplify]: Simplify (+ 0 0) into 0 214.234 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.234 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log 2) (log n)))) into 0 214.235 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.235 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (* 0 (sqrt (/ 1 k)))) into 0 214.235 * [taylor]: Taking taylor expansion of 0 in k 214.235 * [backup-simplify]: Simplify 0 into 0 214.236 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 214.236 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.236 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.237 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.238 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 214.238 * [backup-simplify]: Simplify (+ 0 0) into 0 214.238 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 214.239 * [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))))) 214.240 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 214.241 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) into (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))) 214.241 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.241 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 214.242 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 214.243 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 214.244 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 214.244 * [backup-simplify]: Simplify (- 0) into 0 214.244 * [backup-simplify]: Simplify (+ 0 0) into 0 214.245 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.245 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0 214.246 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 214.247 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 214.247 * [taylor]: Taking taylor expansion of 0 in k 214.247 * [backup-simplify]: Simplify 0 into 0 214.247 * [backup-simplify]: Simplify 0 into 0 214.248 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 214.249 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 214.250 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 214.250 * [backup-simplify]: Simplify (- 0) into 0 214.250 * [backup-simplify]: Simplify (+ 0 0) into 0 214.252 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 214.253 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 214.253 * [backup-simplify]: Simplify (+ 0 0) into 0 214.254 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0 214.255 * [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))))) 214.258 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.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))))) 0))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 214.259 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) 214.259 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.260 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 214.260 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 1) (* 0 0))))) into 0 214.263 * [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 0 214.264 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 214.264 * [backup-simplify]: Simplify (- 0) into 0 214.264 * [backup-simplify]: Simplify (+ 0 0) into 0 214.265 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.265 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log 2) (log n)))))) into 0 214.267 * [backup-simplify]: Simplify (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 214.267 * [backup-simplify]: Simplify (+ (* (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 214.267 * [taylor]: Taking taylor expansion of 0 in k 214.267 * [backup-simplify]: Simplify 0 into 0 214.267 * [backup-simplify]: Simplify 0 into 0 214.267 * [backup-simplify]: Simplify 0 into 0 214.268 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.270 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 214.271 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 214.271 * [backup-simplify]: Simplify (- 0) into 0 214.271 * [backup-simplify]: Simplify (+ 0 0) into 0 214.274 * [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 0 214.276 * [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 0 214.276 * [backup-simplify]: Simplify (+ 0 0) into 0 214.277 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 0) (+ (* 0 -1/2) (* 0 1/2)))) into 0 214.279 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log 2)) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 214.284 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log 2) (log n)))) +nan.0) (+ (* (* -1 (* (exp (* 1/2 (+ (log 2) (log n)))) (+ (* 1/2 (log 2)) (* 1/2 (log n))))) +nan.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))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (log 2) (pow (log n) 2))) (+ (* 1/16 (* (pow (log 2) 2) (log n))) (* 1/48 (pow (log 2) 3))))) (exp (* 1/2 (+ (log 2) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 214.288 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) into (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) 214.297 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (pow (log 2) 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log 2) (exp (* 1/2 (+ (log 2) (log n)))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (log n))) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log 2) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (pow (log 2) 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) k)) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log 2) (log n))))) (- (+ (* +nan.0 (* (log 2) (* (exp (* 1/2 (+ (log 2) (log n)))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log 2) (log n)))) (pow k 2)))))))))))))))))))))) 214.297 * [backup-simplify]: Simplify (/ (pow (* 2 (/ 1 n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k))) into (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 214.297 * [approximate]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 214.297 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 214.298 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 214.298 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 214.298 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 214.298 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.298 * [taylor]: Taking taylor expansion of 1/2 in k 214.298 * [backup-simplify]: Simplify 1/2 into 1/2 214.298 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.298 * [taylor]: Taking taylor expansion of 1/2 in k 214.298 * [backup-simplify]: Simplify 1/2 into 1/2 214.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.298 * [taylor]: Taking taylor expansion of k in k 214.298 * [backup-simplify]: Simplify 0 into 0 214.298 * [backup-simplify]: Simplify 1 into 1 214.298 * [backup-simplify]: Simplify (/ 1 1) into 1 214.298 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 214.298 * [taylor]: Taking taylor expansion of (/ 2 n) in k 214.298 * [taylor]: Taking taylor expansion of 2 in k 214.298 * [backup-simplify]: Simplify 2 into 2 214.298 * [taylor]: Taking taylor expansion of n in k 214.298 * [backup-simplify]: Simplify n into n 214.298 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 214.298 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 214.298 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.299 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.299 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.299 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 214.299 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 214.299 * [taylor]: Taking taylor expansion of (sqrt k) in k 214.299 * [taylor]: Taking taylor expansion of k in k 214.299 * [backup-simplify]: Simplify 0 into 0 214.299 * [backup-simplify]: Simplify 1 into 1 214.299 * [backup-simplify]: Simplify (sqrt 0) into 0 214.300 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.300 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 214.300 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.300 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.300 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.300 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.300 * [taylor]: Taking taylor expansion of 1/2 in n 214.300 * [backup-simplify]: Simplify 1/2 into 1/2 214.300 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.300 * [taylor]: Taking taylor expansion of 1/2 in n 214.300 * [backup-simplify]: Simplify 1/2 into 1/2 214.300 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.300 * [taylor]: Taking taylor expansion of k in n 214.301 * [backup-simplify]: Simplify k into k 214.301 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.301 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.301 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.301 * [taylor]: Taking taylor expansion of 2 in n 214.301 * [backup-simplify]: Simplify 2 into 2 214.301 * [taylor]: Taking taylor expansion of n in n 214.301 * [backup-simplify]: Simplify 0 into 0 214.301 * [backup-simplify]: Simplify 1 into 1 214.301 * [backup-simplify]: Simplify (/ 2 1) into 2 214.301 * [backup-simplify]: Simplify (log 2) into (log 2) 214.301 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.301 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.301 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.302 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.302 * [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)))) 214.303 * [taylor]: Taking taylor expansion of (sqrt k) in n 214.303 * [taylor]: Taking taylor expansion of k in n 214.303 * [backup-simplify]: Simplify k into k 214.303 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 214.303 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 214.303 * [taylor]: Taking taylor expansion of (* (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 214.303 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.303 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.303 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.303 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.303 * [taylor]: Taking taylor expansion of 1/2 in n 214.303 * [backup-simplify]: Simplify 1/2 into 1/2 214.303 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.303 * [taylor]: Taking taylor expansion of 1/2 in n 214.303 * [backup-simplify]: Simplify 1/2 into 1/2 214.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.303 * [taylor]: Taking taylor expansion of k in n 214.303 * [backup-simplify]: Simplify k into k 214.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.303 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.303 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.303 * [taylor]: Taking taylor expansion of 2 in n 214.303 * [backup-simplify]: Simplify 2 into 2 214.303 * [taylor]: Taking taylor expansion of n in n 214.303 * [backup-simplify]: Simplify 0 into 0 214.303 * [backup-simplify]: Simplify 1 into 1 214.303 * [backup-simplify]: Simplify (/ 2 1) into 2 214.303 * [backup-simplify]: Simplify (log 2) into (log 2) 214.304 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.304 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.304 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.304 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.304 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.305 * [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)))) 214.305 * [taylor]: Taking taylor expansion of (sqrt k) in n 214.305 * [taylor]: Taking taylor expansion of k in n 214.305 * [backup-simplify]: Simplify k into k 214.305 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 214.305 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 214.305 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (sqrt k)) into (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 214.305 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k 214.305 * [taylor]: Taking taylor expansion of (sqrt k) in k 214.305 * [taylor]: Taking taylor expansion of k in k 214.305 * [backup-simplify]: Simplify 0 into 0 214.305 * [backup-simplify]: Simplify 1 into 1 214.306 * [backup-simplify]: Simplify (sqrt 0) into 0 214.306 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.306 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k 214.307 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k 214.307 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.307 * [taylor]: Taking taylor expansion of 1/2 in k 214.307 * [backup-simplify]: Simplify 1/2 into 1/2 214.307 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.307 * [taylor]: Taking taylor expansion of 1/2 in k 214.307 * [backup-simplify]: Simplify 1/2 into 1/2 214.307 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.307 * [taylor]: Taking taylor expansion of k in k 214.307 * [backup-simplify]: Simplify 0 into 0 214.307 * [backup-simplify]: Simplify 1 into 1 214.307 * [backup-simplify]: Simplify (/ 1 1) into 1 214.307 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k 214.307 * [taylor]: Taking taylor expansion of (log 2) in k 214.307 * [taylor]: Taking taylor expansion of 2 in k 214.307 * [backup-simplify]: Simplify 2 into 2 214.307 * [backup-simplify]: Simplify (log 2) into (log 2) 214.307 * [taylor]: Taking taylor expansion of (log n) in k 214.307 * [taylor]: Taking taylor expansion of n in k 214.307 * [backup-simplify]: Simplify n into n 214.307 * [backup-simplify]: Simplify (log n) into (log n) 214.308 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.308 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.308 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.308 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 214.308 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n)) 214.309 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n))) 214.309 * [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)))) 214.309 * [backup-simplify]: Simplify (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into 0 214.309 * [backup-simplify]: Simplify 0 into 0 214.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 214.311 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.311 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.311 * [backup-simplify]: Simplify (- 0) into 0 214.311 * [backup-simplify]: Simplify (+ 0 0) into 0 214.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.312 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 214.313 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.313 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (* 0 (sqrt k))) into 0 214.313 * [taylor]: Taking taylor expansion of 0 in k 214.313 * [backup-simplify]: Simplify 0 into 0 214.313 * [backup-simplify]: Simplify 0 into 0 214.314 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.314 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.315 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 214.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.317 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 214.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.318 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 214.318 * [backup-simplify]: Simplify (- 0) into 0 214.318 * [backup-simplify]: Simplify (+ 0 0) into 0 214.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.319 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0 214.320 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 214.321 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 214.321 * [taylor]: Taking taylor expansion of 0 in k 214.321 * [backup-simplify]: Simplify 0 into 0 214.321 * [backup-simplify]: Simplify 0 into 0 214.321 * [backup-simplify]: Simplify 0 into 0 214.322 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 214.323 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.324 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.324 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 214.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.327 * [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 0 214.327 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.328 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 214.328 * [backup-simplify]: Simplify (- 0) into 0 214.329 * [backup-simplify]: Simplify (+ 0 0) into 0 214.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.330 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0 214.331 * [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 0 214.332 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 214.332 * [taylor]: Taking taylor expansion of 0 in k 214.332 * [backup-simplify]: Simplify 0 into 0 214.332 * [backup-simplify]: Simplify 0 into 0 214.332 * [backup-simplify]: Simplify 0 into 0 214.332 * [backup-simplify]: Simplify 0 into 0 214.334 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 214.335 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.336 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.337 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 214.337 * [backup-simplify]: Simplify (/ (pow (* 2 (/ 1 (- n))) (- 1/2 (* 1/2 (/ 1 (- k))))) (sqrt (/ 1 (- k)))) into (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 214.337 * [approximate]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 214.337 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 214.337 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.337 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 214.337 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 214.337 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.338 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.338 * [taylor]: Taking taylor expansion of 1/2 in k 214.338 * [backup-simplify]: Simplify 1/2 into 1/2 214.338 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.338 * [taylor]: Taking taylor expansion of k in k 214.338 * [backup-simplify]: Simplify 0 into 0 214.338 * [backup-simplify]: Simplify 1 into 1 214.338 * [backup-simplify]: Simplify (/ 1 1) into 1 214.338 * [taylor]: Taking taylor expansion of 1/2 in k 214.338 * [backup-simplify]: Simplify 1/2 into 1/2 214.338 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 214.338 * [taylor]: Taking taylor expansion of (/ -2 n) in k 214.338 * [taylor]: Taking taylor expansion of -2 in k 214.338 * [backup-simplify]: Simplify -2 into -2 214.338 * [taylor]: Taking taylor expansion of n in k 214.338 * [backup-simplify]: Simplify n into n 214.338 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 214.338 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 214.338 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.339 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.339 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 214.339 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 214.339 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 214.339 * [taylor]: Taking taylor expansion of (/ -1 k) in k 214.339 * [taylor]: Taking taylor expansion of -1 in k 214.339 * [backup-simplify]: Simplify -1 into -1 214.339 * [taylor]: Taking taylor expansion of k in k 214.339 * [backup-simplify]: Simplify 0 into 0 214.339 * [backup-simplify]: Simplify 1 into 1 214.339 * [backup-simplify]: Simplify (/ -1 1) into -1 214.339 * [backup-simplify]: Simplify (sqrt 0) into 0 214.340 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 214.340 * [backup-simplify]: Simplify (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2))) 214.340 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 214.340 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.340 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.340 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.340 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.340 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.341 * [taylor]: Taking taylor expansion of 1/2 in n 214.341 * [backup-simplify]: Simplify 1/2 into 1/2 214.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.341 * [taylor]: Taking taylor expansion of k in n 214.341 * [backup-simplify]: Simplify k into k 214.341 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.341 * [taylor]: Taking taylor expansion of 1/2 in n 214.341 * [backup-simplify]: Simplify 1/2 into 1/2 214.341 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.341 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.341 * [taylor]: Taking taylor expansion of -2 in n 214.341 * [backup-simplify]: Simplify -2 into -2 214.341 * [taylor]: Taking taylor expansion of n in n 214.341 * [backup-simplify]: Simplify 0 into 0 214.341 * [backup-simplify]: Simplify 1 into 1 214.341 * [backup-simplify]: Simplify (/ -2 1) into -2 214.341 * [backup-simplify]: Simplify (log -2) into (log -2) 214.341 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.341 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.342 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.342 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.343 * [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)))) 214.343 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 214.343 * [taylor]: Taking taylor expansion of (/ -1 k) in n 214.343 * [taylor]: Taking taylor expansion of -1 in n 214.343 * [backup-simplify]: Simplify -1 into -1 214.343 * [taylor]: Taking taylor expansion of k in n 214.343 * [backup-simplify]: Simplify k into k 214.343 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 214.343 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 214.343 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 214.343 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 214.343 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 214.343 * [taylor]: Taking taylor expansion of (/ (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 214.343 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.343 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.343 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.343 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.343 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.343 * [taylor]: Taking taylor expansion of 1/2 in n 214.343 * [backup-simplify]: Simplify 1/2 into 1/2 214.343 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.343 * [taylor]: Taking taylor expansion of k in n 214.343 * [backup-simplify]: Simplify k into k 214.343 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.343 * [taylor]: Taking taylor expansion of 1/2 in n 214.343 * [backup-simplify]: Simplify 1/2 into 1/2 214.343 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.343 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.344 * [taylor]: Taking taylor expansion of -2 in n 214.344 * [backup-simplify]: Simplify -2 into -2 214.344 * [taylor]: Taking taylor expansion of n in n 214.344 * [backup-simplify]: Simplify 0 into 0 214.344 * [backup-simplify]: Simplify 1 into 1 214.344 * [backup-simplify]: Simplify (/ -2 1) into -2 214.344 * [backup-simplify]: Simplify (log -2) into (log -2) 214.344 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.344 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.345 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.345 * [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)))) 214.345 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 214.345 * [taylor]: Taking taylor expansion of (/ -1 k) in n 214.345 * [taylor]: Taking taylor expansion of -1 in n 214.345 * [backup-simplify]: Simplify -1 into -1 214.345 * [taylor]: Taking taylor expansion of k in n 214.345 * [backup-simplify]: Simplify k into k 214.345 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 214.346 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 214.346 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 214.346 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 214.346 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) 214.346 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) in k 214.346 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k 214.346 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k 214.346 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.346 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.346 * [taylor]: Taking taylor expansion of 1/2 in k 214.346 * [backup-simplify]: Simplify 1/2 into 1/2 214.346 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.346 * [taylor]: Taking taylor expansion of k in k 214.346 * [backup-simplify]: Simplify 0 into 0 214.346 * [backup-simplify]: Simplify 1 into 1 214.346 * [backup-simplify]: Simplify (/ 1 1) into 1 214.347 * [taylor]: Taking taylor expansion of 1/2 in k 214.347 * [backup-simplify]: Simplify 1/2 into 1/2 214.347 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k 214.347 * [taylor]: Taking taylor expansion of (log -2) in k 214.347 * [taylor]: Taking taylor expansion of -2 in k 214.347 * [backup-simplify]: Simplify -2 into -2 214.347 * [backup-simplify]: Simplify (log -2) into (log -2) 214.347 * [taylor]: Taking taylor expansion of (log n) in k 214.347 * [taylor]: Taking taylor expansion of n in k 214.347 * [backup-simplify]: Simplify n into n 214.347 * [backup-simplify]: Simplify (log n) into (log n) 214.347 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.347 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.348 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 214.348 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n)) 214.348 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n))) 214.348 * [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)))) 214.348 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 214.348 * [taylor]: Taking taylor expansion of (/ -1 k) in k 214.348 * [taylor]: Taking taylor expansion of -1 in k 214.348 * [backup-simplify]: Simplify -1 into -1 214.348 * [taylor]: Taking taylor expansion of k in k 214.348 * [backup-simplify]: Simplify 0 into 0 214.349 * [backup-simplify]: Simplify 1 into 1 214.349 * [backup-simplify]: Simplify (/ -1 1) into -1 214.349 * [backup-simplify]: Simplify (sqrt 0) into 0 214.350 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 214.350 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) 214.350 * [backup-simplify]: Simplify (* +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))))) 214.351 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 214.352 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 214.352 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.352 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.352 * [backup-simplify]: Simplify (+ 0 0) into 0 214.353 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.353 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 214.354 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.354 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 214.354 * [taylor]: Taking taylor expansion of 0 in k 214.354 * [backup-simplify]: Simplify 0 into 0 214.354 * [backup-simplify]: Simplify 0 into 0 214.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 214.357 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 214.358 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 214.358 * [backup-simplify]: Simplify (- (* +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)))))) 214.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.360 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0 214.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.361 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 214.361 * [backup-simplify]: Simplify (+ 0 0) into 0 214.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.362 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0 214.363 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 214.363 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 214.364 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 214.364 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 214.364 * [taylor]: Taking taylor expansion of 0 in k 214.364 * [backup-simplify]: Simplify 0 into 0 214.364 * [backup-simplify]: Simplify 0 into 0 214.364 * [backup-simplify]: Simplify 0 into 0 214.365 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.367 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 214.368 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))) 214.369 * [backup-simplify]: Simplify (- (* +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)))))) 214.370 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow k 2))) (- (+ (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k))))))) 214.370 * * * * [progress]: [ 4 / 4 ] generating series at (2) 214.370 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 k))) (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))) into (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) 214.370 * [approximate]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (k n) around 0 214.370 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n 214.370 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 214.370 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in n 214.370 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in n 214.370 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in n 214.370 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 214.370 * [taylor]: Taking taylor expansion of 1/2 in n 214.370 * [backup-simplify]: Simplify 1/2 into 1/2 214.370 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 214.370 * [taylor]: Taking taylor expansion of 1/2 in n 214.370 * [backup-simplify]: Simplify 1/2 into 1/2 214.370 * [taylor]: Taking taylor expansion of k in n 214.370 * [backup-simplify]: Simplify k into k 214.370 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.371 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.371 * [taylor]: Taking taylor expansion of 2 in n 214.371 * [backup-simplify]: Simplify 2 into 2 214.371 * [taylor]: Taking taylor expansion of n in n 214.371 * [backup-simplify]: Simplify 0 into 0 214.371 * [backup-simplify]: Simplify 1 into 1 214.371 * [backup-simplify]: Simplify (* 2 0) into 0 214.371 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.372 * [backup-simplify]: Simplify (log 2) into (log 2) 214.372 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 214.372 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 214.372 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 214.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.372 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) 214.373 * [backup-simplify]: Simplify (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) into (exp (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) 214.373 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 214.373 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 214.373 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 214.373 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 214.373 * [taylor]: Taking taylor expansion of 1/2 in n 214.373 * [backup-simplify]: Simplify 1/2 into 1/2 214.373 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 214.373 * [taylor]: Taking taylor expansion of 1/2 in n 214.373 * [backup-simplify]: Simplify 1/2 into 1/2 214.373 * [taylor]: Taking taylor expansion of k in n 214.373 * [backup-simplify]: Simplify k into k 214.373 * [taylor]: Taking taylor expansion of (log PI) in n 214.373 * [taylor]: Taking taylor expansion of PI in n 214.373 * [backup-simplify]: Simplify PI into PI 214.373 * [backup-simplify]: Simplify (log PI) into (log PI) 214.373 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 214.373 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 214.373 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 214.374 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 214.374 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 214.374 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 214.374 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.374 * [taylor]: Taking taylor expansion of k in n 214.374 * [backup-simplify]: Simplify k into k 214.374 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.374 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 214.374 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.374 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 214.374 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 214.374 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 214.374 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 214.374 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 214.374 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 214.374 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.374 * [taylor]: Taking taylor expansion of 1/2 in k 214.374 * [backup-simplify]: Simplify 1/2 into 1/2 214.374 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.374 * [taylor]: Taking taylor expansion of 1/2 in k 214.374 * [backup-simplify]: Simplify 1/2 into 1/2 214.374 * [taylor]: Taking taylor expansion of k in k 214.374 * [backup-simplify]: Simplify 0 into 0 214.374 * [backup-simplify]: Simplify 1 into 1 214.375 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 214.375 * [taylor]: Taking taylor expansion of (* 2 n) in k 214.375 * [taylor]: Taking taylor expansion of 2 in k 214.375 * [backup-simplify]: Simplify 2 into 2 214.375 * [taylor]: Taking taylor expansion of n in k 214.375 * [backup-simplify]: Simplify n into n 214.375 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 214.375 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 214.379 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.379 * [backup-simplify]: Simplify (- 0) into 0 214.379 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.379 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 214.379 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 214.379 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 214.379 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 214.379 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 214.379 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.379 * [taylor]: Taking taylor expansion of 1/2 in k 214.379 * [backup-simplify]: Simplify 1/2 into 1/2 214.380 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.380 * [taylor]: Taking taylor expansion of 1/2 in k 214.380 * [backup-simplify]: Simplify 1/2 into 1/2 214.380 * [taylor]: Taking taylor expansion of k in k 214.380 * [backup-simplify]: Simplify 0 into 0 214.380 * [backup-simplify]: Simplify 1 into 1 214.380 * [taylor]: Taking taylor expansion of (log PI) in k 214.380 * [taylor]: Taking taylor expansion of PI in k 214.380 * [backup-simplify]: Simplify PI into PI 214.380 * [backup-simplify]: Simplify (log PI) into (log PI) 214.380 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.380 * [backup-simplify]: Simplify (- 0) into 0 214.381 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.381 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.382 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 214.382 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 214.382 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.382 * [taylor]: Taking taylor expansion of k in k 214.382 * [backup-simplify]: Simplify 0 into 0 214.382 * [backup-simplify]: Simplify 1 into 1 214.382 * [backup-simplify]: Simplify (/ 1 1) into 1 214.383 * [backup-simplify]: Simplify (sqrt 0) into 0 214.383 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.383 * [taylor]: Taking taylor expansion of (* (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k 214.383 * [taylor]: Taking taylor expansion of (* (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 214.383 * [taylor]: Taking taylor expansion of (pow (* 2 n) (- 1/2 (* 1/2 k))) in k 214.384 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 n)))) in k 214.384 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 n))) in k 214.384 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.384 * [taylor]: Taking taylor expansion of 1/2 in k 214.384 * [backup-simplify]: Simplify 1/2 into 1/2 214.384 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.384 * [taylor]: Taking taylor expansion of 1/2 in k 214.384 * [backup-simplify]: Simplify 1/2 into 1/2 214.384 * [taylor]: Taking taylor expansion of k in k 214.384 * [backup-simplify]: Simplify 0 into 0 214.384 * [backup-simplify]: Simplify 1 into 1 214.384 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k 214.384 * [taylor]: Taking taylor expansion of (* 2 n) in k 214.384 * [taylor]: Taking taylor expansion of 2 in k 214.384 * [backup-simplify]: Simplify 2 into 2 214.384 * [taylor]: Taking taylor expansion of n in k 214.384 * [backup-simplify]: Simplify n into n 214.384 * [backup-simplify]: Simplify (* 2 n) into (* 2 n) 214.384 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n)) 214.384 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.384 * [backup-simplify]: Simplify (- 0) into 0 214.385 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.385 * [backup-simplify]: Simplify (* 1/2 (log (* 2 n))) into (* 1/2 (log (* 2 n))) 214.385 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 n)))) into (pow (* 2 n) 1/2) 214.385 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 214.385 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 214.385 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 214.385 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 214.385 * [taylor]: Taking taylor expansion of 1/2 in k 214.385 * [backup-simplify]: Simplify 1/2 into 1/2 214.385 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 214.385 * [taylor]: Taking taylor expansion of 1/2 in k 214.385 * [backup-simplify]: Simplify 1/2 into 1/2 214.385 * [taylor]: Taking taylor expansion of k in k 214.385 * [backup-simplify]: Simplify 0 into 0 214.385 * [backup-simplify]: Simplify 1 into 1 214.385 * [taylor]: Taking taylor expansion of (log PI) in k 214.385 * [taylor]: Taking taylor expansion of PI in k 214.385 * [backup-simplify]: Simplify PI into PI 214.385 * [backup-simplify]: Simplify (log PI) into (log PI) 214.385 * [backup-simplify]: Simplify (* 1/2 0) into 0 214.386 * [backup-simplify]: Simplify (- 0) into 0 214.386 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.387 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.388 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 214.388 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 214.388 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.388 * [taylor]: Taking taylor expansion of k in k 214.388 * [backup-simplify]: Simplify 0 into 0 214.388 * [backup-simplify]: Simplify 1 into 1 214.388 * [backup-simplify]: Simplify (/ 1 1) into 1 214.388 * [backup-simplify]: Simplify (sqrt 0) into 0 214.389 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.389 * [backup-simplify]: Simplify (* (pow (* 2 n) 1/2) (pow PI 1/2)) into (sqrt (* PI (* n 2))) 214.389 * [backup-simplify]: Simplify (* (sqrt (* PI (* n 2))) 0) into 0 214.389 * [taylor]: Taking taylor expansion of 0 in n 214.389 * [backup-simplify]: Simplify 0 into 0 214.390 * [backup-simplify]: Simplify 0 into 0 214.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 214.391 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 214.391 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.391 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 214.397 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 214.398 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 n)) into 0 214.398 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 n) 1)))) 1) into 0 214.399 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 214.399 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.399 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.399 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 n)))) into (- (* 1/2 (log (* 2 n)))) 214.400 * [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)))) 214.401 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 214.403 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 214.403 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 214.403 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 214.403 * [taylor]: Taking taylor expansion of +nan.0 in n 214.403 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.403 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 214.403 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.403 * [taylor]: Taking taylor expansion of 2 in n 214.403 * [backup-simplify]: Simplify 2 into 2 214.403 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.403 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.403 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 214.403 * [taylor]: Taking taylor expansion of (* n PI) in n 214.403 * [taylor]: Taking taylor expansion of n in n 214.403 * [backup-simplify]: Simplify 0 into 0 214.404 * [backup-simplify]: Simplify 1 into 1 214.404 * [taylor]: Taking taylor expansion of PI in n 214.404 * [backup-simplify]: Simplify PI into PI 214.404 * [backup-simplify]: Simplify (* 0 PI) into 0 214.405 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 214.405 * [backup-simplify]: Simplify (sqrt 0) into 0 214.406 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.406 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 214.406 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.407 * [backup-simplify]: Simplify (- 0) into 0 214.407 * [backup-simplify]: Simplify 0 into 0 214.407 * [backup-simplify]: Simplify 0 into 0 214.407 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 214.409 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 214.410 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 214.411 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 214.411 * [backup-simplify]: Simplify (- 0) into 0 214.411 * [backup-simplify]: Simplify (+ 0 0) into 0 214.412 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 214.418 * [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))) 214.419 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 n))) into 0 214.420 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 n) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 n) 1)))) 2) into 0 214.420 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 214.420 * [backup-simplify]: Simplify (- 0) into 0 214.421 * [backup-simplify]: Simplify (+ 0 0) into 0 214.421 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 n))))) into 0 214.422 * [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))) 214.425 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 214.429 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) 214.429 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 214.429 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 214.429 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 214.429 * [taylor]: Taking taylor expansion of +nan.0 in n 214.429 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.429 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 214.429 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 214.429 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.429 * [taylor]: Taking taylor expansion of 2 in n 214.429 * [backup-simplify]: Simplify 2 into 2 214.430 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.430 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.430 * [taylor]: Taking taylor expansion of (log PI) in n 214.430 * [taylor]: Taking taylor expansion of PI in n 214.430 * [backup-simplify]: Simplify PI into PI 214.430 * [backup-simplify]: Simplify (log PI) into (log PI) 214.430 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 214.430 * [taylor]: Taking taylor expansion of (* PI n) in n 214.430 * [taylor]: Taking taylor expansion of PI in n 214.430 * [backup-simplify]: Simplify PI into PI 214.430 * [taylor]: Taking taylor expansion of n in n 214.430 * [backup-simplify]: Simplify 0 into 0 214.430 * [backup-simplify]: Simplify 1 into 1 214.431 * [backup-simplify]: Simplify (* PI 0) into 0 214.432 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 214.432 * [backup-simplify]: Simplify (sqrt 0) into 0 214.433 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.433 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 214.433 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 214.433 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 214.433 * [taylor]: Taking taylor expansion of +nan.0 in n 214.433 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.433 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 214.433 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.433 * [taylor]: Taking taylor expansion of 2 in n 214.433 * [backup-simplify]: Simplify 2 into 2 214.433 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.433 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.433 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 214.433 * [taylor]: Taking taylor expansion of (* n PI) in n 214.433 * [taylor]: Taking taylor expansion of n in n 214.433 * [backup-simplify]: Simplify 0 into 0 214.433 * [backup-simplify]: Simplify 1 into 1 214.433 * [taylor]: Taking taylor expansion of PI in n 214.434 * [backup-simplify]: Simplify PI into PI 214.434 * [backup-simplify]: Simplify (* 0 PI) into 0 214.435 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 214.435 * [backup-simplify]: Simplify (sqrt 0) into 0 214.436 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.436 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 214.436 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 214.436 * [taylor]: Taking taylor expansion of +nan.0 in n 214.436 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.436 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 214.436 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 214.436 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.436 * [taylor]: Taking taylor expansion of 2 in n 214.436 * [backup-simplify]: Simplify 2 into 2 214.436 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.437 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.437 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.437 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.437 * [taylor]: Taking taylor expansion of 2 in n 214.437 * [backup-simplify]: Simplify 2 into 2 214.437 * [taylor]: Taking taylor expansion of n in n 214.437 * [backup-simplify]: Simplify 0 into 0 214.437 * [backup-simplify]: Simplify 1 into 1 214.437 * [backup-simplify]: Simplify (* 2 0) into 0 214.437 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.438 * [backup-simplify]: Simplify (log 2) into (log 2) 214.438 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 214.438 * [taylor]: Taking taylor expansion of (* PI n) in n 214.438 * [taylor]: Taking taylor expansion of PI in n 214.438 * [backup-simplify]: Simplify PI into PI 214.438 * [taylor]: Taking taylor expansion of n in n 214.438 * [backup-simplify]: Simplify 0 into 0 214.438 * [backup-simplify]: Simplify 1 into 1 214.438 * [backup-simplify]: Simplify (* PI 0) into 0 214.439 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 214.439 * [backup-simplify]: Simplify (sqrt 0) into 0 214.440 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.441 * [backup-simplify]: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 214.441 * [backup-simplify]: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 214.442 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.442 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 214.442 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.443 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.443 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 214.444 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 214.444 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.444 * [backup-simplify]: Simplify (- 0) into 0 214.444 * [backup-simplify]: Simplify (+ 0 0) into 0 214.445 * [backup-simplify]: Simplify (- 0) into 0 214.445 * [backup-simplify]: Simplify (+ 0 0) into 0 214.445 * [backup-simplify]: Simplify (- 0) into 0 214.445 * [backup-simplify]: Simplify 0 into 0 214.447 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 214.450 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 214.452 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 214.453 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 214.453 * [backup-simplify]: Simplify 0 into 0 214.454 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.456 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 214.463 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 214.464 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 214.464 * [backup-simplify]: Simplify (- 0) into 0 214.464 * [backup-simplify]: Simplify (+ 0 0) into 0 214.465 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 214.473 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 214.474 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 n)))) into 0 214.475 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 n) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 n) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 n) 1)))) 6) into 0 214.476 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 214.476 * [backup-simplify]: Simplify (- 0) into 0 214.476 * [backup-simplify]: Simplify (+ 0 0) into 0 214.477 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 n)))))) into 0 214.478 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 n)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 n)))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) 214.484 * [backup-simplify]: Simplify (+ (* (pow (* 2 n) 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (sqrt (* n 2)) (log (* 2 n)))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (sqrt (* n 2)) (pow (log (* 2 n)) 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (sqrt (* n 2)) (pow (log (* 2 n)) 3))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 214.492 * [backup-simplify]: Simplify (+ (* (sqrt (* PI (* n 2))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (+ (* 1/8 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (* 1/4 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (log PI))))))) +nan.0) (* (- (+ (* 1/48 (* (* (sqrt 2) (pow (log (* 2 n)) 3)) (sqrt (* PI n)))) (+ (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (log (* 2 n)) (pow (log PI) 2))))) (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))) (* 1/16 (* (sqrt (* PI n)) (* (sqrt 2) (* (pow (log (* 2 n)) 2) (log PI))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) 214.492 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))))) in n 214.492 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))))) in n 214.492 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 214.492 * [taylor]: Taking taylor expansion of +nan.0 in n 214.492 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.492 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 214.492 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 214.492 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.492 * [taylor]: Taking taylor expansion of 2 in n 214.492 * [backup-simplify]: Simplify 2 into 2 214.492 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.493 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.493 * [taylor]: Taking taylor expansion of (log PI) in n 214.493 * [taylor]: Taking taylor expansion of PI in n 214.493 * [backup-simplify]: Simplify PI into PI 214.493 * [backup-simplify]: Simplify (log PI) into (log PI) 214.493 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 214.493 * [taylor]: Taking taylor expansion of (* PI n) in n 214.493 * [taylor]: Taking taylor expansion of PI in n 214.493 * [backup-simplify]: Simplify PI into PI 214.493 * [taylor]: Taking taylor expansion of n in n 214.493 * [backup-simplify]: Simplify 0 into 0 214.493 * [backup-simplify]: Simplify 1 into 1 214.494 * [backup-simplify]: Simplify (* PI 0) into 0 214.494 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 214.495 * [backup-simplify]: Simplify (sqrt 0) into 0 214.496 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.496 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))))) in n 214.496 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))))) in n 214.496 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 214.496 * [taylor]: Taking taylor expansion of +nan.0 in n 214.496 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.496 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 214.496 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 214.496 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.496 * [taylor]: Taking taylor expansion of 2 in n 214.496 * [backup-simplify]: Simplify 2 into 2 214.496 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.496 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.496 * [taylor]: Taking taylor expansion of (pow (log PI) 2) in n 214.496 * [taylor]: Taking taylor expansion of (log PI) in n 214.496 * [taylor]: Taking taylor expansion of PI in n 214.496 * [backup-simplify]: Simplify PI into PI 214.497 * [backup-simplify]: Simplify (log PI) into (log PI) 214.497 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 214.497 * [taylor]: Taking taylor expansion of (* PI n) in n 214.497 * [taylor]: Taking taylor expansion of PI in n 214.497 * [backup-simplify]: Simplify PI into PI 214.497 * [taylor]: Taking taylor expansion of n in n 214.497 * [backup-simplify]: Simplify 0 into 0 214.497 * [backup-simplify]: Simplify 1 into 1 214.497 * [backup-simplify]: Simplify (* PI 0) into 0 214.498 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 214.498 * [backup-simplify]: Simplify (sqrt 0) into 0 214.499 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.499 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))))) in n 214.499 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))))) in n 214.499 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n)))) in n 214.499 * [taylor]: Taking taylor expansion of +nan.0 in n 214.499 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.499 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 n)) 2)) (sqrt (* PI n))) in n 214.499 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 n)) 2)) in n 214.499 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.499 * [taylor]: Taking taylor expansion of 2 in n 214.499 * [backup-simplify]: Simplify 2 into 2 214.499 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.500 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.500 * [taylor]: Taking taylor expansion of (pow (log (* 2 n)) 2) in n 214.500 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.500 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.500 * [taylor]: Taking taylor expansion of 2 in n 214.500 * [backup-simplify]: Simplify 2 into 2 214.500 * [taylor]: Taking taylor expansion of n in n 214.500 * [backup-simplify]: Simplify 0 into 0 214.500 * [backup-simplify]: Simplify 1 into 1 214.500 * [backup-simplify]: Simplify (* 2 0) into 0 214.501 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.501 * [backup-simplify]: Simplify (log 2) into (log 2) 214.501 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.501 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 214.501 * [taylor]: Taking taylor expansion of (* PI n) in n 214.501 * [taylor]: Taking taylor expansion of PI in n 214.501 * [backup-simplify]: Simplify PI into PI 214.501 * [taylor]: Taking taylor expansion of n in n 214.501 * [backup-simplify]: Simplify 0 into 0 214.501 * [backup-simplify]: Simplify 1 into 1 214.502 * [backup-simplify]: Simplify (* PI 0) into 0 214.503 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 214.503 * [backup-simplify]: Simplify (sqrt 0) into 0 214.504 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.504 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))))) in n 214.504 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))))) in n 214.504 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI)))) in n 214.504 * [taylor]: Taking taylor expansion of +nan.0 in n 214.504 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.504 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 n)) (log PI))) (sqrt (* n PI))) in n 214.504 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 n)) (log PI))) in n 214.504 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.504 * [taylor]: Taking taylor expansion of 2 in n 214.504 * [backup-simplify]: Simplify 2 into 2 214.504 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.504 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.504 * [taylor]: Taking taylor expansion of (* (log (* 2 n)) (log PI)) in n 214.504 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.504 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.505 * [taylor]: Taking taylor expansion of 2 in n 214.505 * [backup-simplify]: Simplify 2 into 2 214.505 * [taylor]: Taking taylor expansion of n in n 214.505 * [backup-simplify]: Simplify 0 into 0 214.505 * [backup-simplify]: Simplify 1 into 1 214.505 * [backup-simplify]: Simplify (* 2 0) into 0 214.505 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.505 * [backup-simplify]: Simplify (log 2) into (log 2) 214.506 * [taylor]: Taking taylor expansion of (log PI) in n 214.506 * [taylor]: Taking taylor expansion of PI in n 214.506 * [backup-simplify]: Simplify PI into PI 214.506 * [backup-simplify]: Simplify (log PI) into (log PI) 214.506 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 214.506 * [taylor]: Taking taylor expansion of (* n PI) in n 214.506 * [taylor]: Taking taylor expansion of n in n 214.506 * [backup-simplify]: Simplify 0 into 0 214.506 * [backup-simplify]: Simplify 1 into 1 214.506 * [taylor]: Taking taylor expansion of PI in n 214.506 * [backup-simplify]: Simplify PI into PI 214.506 * [backup-simplify]: Simplify (* 0 PI) into 0 214.507 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 214.507 * [backup-simplify]: Simplify (sqrt 0) into 0 214.508 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.508 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))))) in n 214.508 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))))) in n 214.508 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 214.508 * [taylor]: Taking taylor expansion of +nan.0 in n 214.508 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.508 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 214.508 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.508 * [taylor]: Taking taylor expansion of 2 in n 214.508 * [backup-simplify]: Simplify 2 into 2 214.508 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.509 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.509 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 214.509 * [taylor]: Taking taylor expansion of (* n PI) in n 214.509 * [taylor]: Taking taylor expansion of n in n 214.509 * [backup-simplify]: Simplify 0 into 0 214.509 * [backup-simplify]: Simplify 1 into 1 214.509 * [taylor]: Taking taylor expansion of PI in n 214.509 * [backup-simplify]: Simplify PI into PI 214.509 * [backup-simplify]: Simplify (* 0 PI) into 0 214.510 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 214.510 * [backup-simplify]: Simplify (sqrt 0) into 0 214.511 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.511 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))))) in n 214.511 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n)))) in n 214.511 * [taylor]: Taking taylor expansion of +nan.0 in n 214.511 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.511 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 n))) (sqrt (* PI n))) in n 214.511 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 n))) in n 214.511 * [taylor]: Taking taylor expansion of (sqrt 2) in n 214.511 * [taylor]: Taking taylor expansion of 2 in n 214.511 * [backup-simplify]: Simplify 2 into 2 214.512 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 214.512 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 214.512 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n 214.512 * [taylor]: Taking taylor expansion of (* 2 n) in n 214.512 * [taylor]: Taking taylor expansion of 2 in n 214.512 * [backup-simplify]: Simplify 2 into 2 214.512 * [taylor]: Taking taylor expansion of n in n 214.512 * [backup-simplify]: Simplify 0 into 0 214.512 * [backup-simplify]: Simplify 1 into 1 214.512 * [backup-simplify]: Simplify (* 2 0) into 0 214.513 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2 214.513 * [backup-simplify]: Simplify (log 2) into (log 2) 214.513 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 214.513 * [taylor]: Taking taylor expansion of (* PI n) in n 214.513 * [taylor]: Taking taylor expansion of PI in n 214.513 * [backup-simplify]: Simplify PI into PI 214.513 * [taylor]: Taking taylor expansion of n in n 214.513 * [backup-simplify]: Simplify 0 into 0 214.513 * [backup-simplify]: Simplify 1 into 1 214.513 * [backup-simplify]: Simplify (* PI 0) into 0 214.514 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 214.515 * [backup-simplify]: Simplify (sqrt 0) into 0 214.515 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 214.516 * [backup-simplify]: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 214.517 * [backup-simplify]: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 214.517 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.518 * [backup-simplify]: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 214.519 * [backup-simplify]: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 214.519 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 214.520 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.520 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.521 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.521 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) (+ (log 2) (log n))) into (pow (+ (log 2) (log n)) 2) 214.522 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log 2) (log n)) 2)) into (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 214.522 * [backup-simplify]: Simplify (* (* (pow (+ (log 2) (log n)) 2) (sqrt 2)) 0) into 0 214.522 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.523 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.523 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) (log PI)) into (* (+ (log 2) (log n)) (log PI)) 214.524 * [backup-simplify]: Simplify (* (sqrt 2) (* (+ (log 2) (log n)) (log PI))) into (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 214.525 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (* (sqrt 2) (log PI))) 0) into 0 214.525 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.526 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 214.526 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.526 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.527 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log 2) (log n))) into (* (+ (log 2) (log n)) (sqrt 2)) 214.527 * [backup-simplify]: Simplify (* (* (+ (log 2) (log n)) (sqrt 2)) 0) into 0 214.528 * [backup-simplify]: Simplify (* +nan.0 0) into 0 214.528 * [backup-simplify]: Simplify (- 0) into 0 214.528 * [backup-simplify]: Simplify (+ 0 0) into 0 214.528 * [backup-simplify]: Simplify (- 0) into 0 214.529 * [backup-simplify]: Simplify (+ 0 0) into 0 214.529 * [backup-simplify]: Simplify (- 0) into 0 214.529 * [backup-simplify]: Simplify (+ 0 0) into 0 214.529 * [backup-simplify]: Simplify (- 0) into 0 214.530 * [backup-simplify]: Simplify (+ 0 0) into 0 214.530 * [backup-simplify]: Simplify (- 0) into 0 214.530 * [backup-simplify]: Simplify (+ 0 0) into 0 214.530 * [backup-simplify]: Simplify (- 0) into 0 214.530 * [backup-simplify]: Simplify 0 into 0 214.531 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 214.532 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 214.534 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 214.538 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 214.540 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 214.547 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 214.548 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0 214.549 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.549 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n)) 214.550 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log 2) (log n)))) into 0 214.551 * [backup-simplify]: Simplify (+ (* (* (+ (log 2) (log n)) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 214.554 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 214.556 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))))) 214.561 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 214.566 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 214.573 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 214.583 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 214.593 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 214.594 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 214.596 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 214.597 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 214.599 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 214.604 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 214.606 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 214.608 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 214.626 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 214.627 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (/ (pow (* 2 (/ 1 n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k)))) into (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) 214.627 * [approximate]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (k n) around 0 214.627 * [taylor]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n 214.627 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 214.627 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 214.627 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 214.627 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 214.627 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.627 * [taylor]: Taking taylor expansion of 1/2 in n 214.627 * [backup-simplify]: Simplify 1/2 into 1/2 214.627 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.627 * [taylor]: Taking taylor expansion of 1/2 in n 214.627 * [backup-simplify]: Simplify 1/2 into 1/2 214.627 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.627 * [taylor]: Taking taylor expansion of k in n 214.627 * [backup-simplify]: Simplify k into k 214.627 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.627 * [taylor]: Taking taylor expansion of (log PI) in n 214.627 * [taylor]: Taking taylor expansion of PI in n 214.627 * [backup-simplify]: Simplify PI into PI 214.627 * [backup-simplify]: Simplify (log PI) into (log PI) 214.627 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.627 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.627 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.628 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 214.628 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.628 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.628 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.628 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.628 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.628 * [taylor]: Taking taylor expansion of 1/2 in n 214.628 * [backup-simplify]: Simplify 1/2 into 1/2 214.628 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.628 * [taylor]: Taking taylor expansion of 1/2 in n 214.628 * [backup-simplify]: Simplify 1/2 into 1/2 214.628 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.628 * [taylor]: Taking taylor expansion of k in n 214.628 * [backup-simplify]: Simplify k into k 214.628 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.628 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.628 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.628 * [taylor]: Taking taylor expansion of 2 in n 214.628 * [backup-simplify]: Simplify 2 into 2 214.628 * [taylor]: Taking taylor expansion of n in n 214.628 * [backup-simplify]: Simplify 0 into 0 214.628 * [backup-simplify]: Simplify 1 into 1 214.629 * [backup-simplify]: Simplify (/ 2 1) into 2 214.629 * [backup-simplify]: Simplify (log 2) into (log 2) 214.629 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.629 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.629 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.630 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.630 * [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)))) 214.630 * [taylor]: Taking taylor expansion of (sqrt k) in n 214.630 * [taylor]: Taking taylor expansion of k in n 214.630 * [backup-simplify]: Simplify k into k 214.630 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 214.630 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 214.630 * [taylor]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 214.630 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 214.630 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 214.630 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 214.630 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 214.630 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.630 * [taylor]: Taking taylor expansion of 1/2 in k 214.630 * [backup-simplify]: Simplify 1/2 into 1/2 214.630 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.630 * [taylor]: Taking taylor expansion of 1/2 in k 214.630 * [backup-simplify]: Simplify 1/2 into 1/2 214.630 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.630 * [taylor]: Taking taylor expansion of k in k 214.630 * [backup-simplify]: Simplify 0 into 0 214.630 * [backup-simplify]: Simplify 1 into 1 214.631 * [backup-simplify]: Simplify (/ 1 1) into 1 214.631 * [taylor]: Taking taylor expansion of (log PI) in k 214.631 * [taylor]: Taking taylor expansion of PI in k 214.631 * [backup-simplify]: Simplify PI into PI 214.631 * [backup-simplify]: Simplify (log PI) into (log PI) 214.631 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.632 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.632 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.632 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 214.633 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.633 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 214.633 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 214.633 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 214.633 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.633 * [taylor]: Taking taylor expansion of 1/2 in k 214.633 * [backup-simplify]: Simplify 1/2 into 1/2 214.633 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.633 * [taylor]: Taking taylor expansion of 1/2 in k 214.633 * [backup-simplify]: Simplify 1/2 into 1/2 214.633 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.633 * [taylor]: Taking taylor expansion of k in k 214.633 * [backup-simplify]: Simplify 0 into 0 214.633 * [backup-simplify]: Simplify 1 into 1 214.633 * [backup-simplify]: Simplify (/ 1 1) into 1 214.633 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 214.633 * [taylor]: Taking taylor expansion of (/ 2 n) in k 214.633 * [taylor]: Taking taylor expansion of 2 in k 214.633 * [backup-simplify]: Simplify 2 into 2 214.633 * [taylor]: Taking taylor expansion of n in k 214.633 * [backup-simplify]: Simplify n into n 214.633 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 214.633 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 214.634 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.634 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.634 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.634 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 214.634 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 214.634 * [taylor]: Taking taylor expansion of (sqrt k) in k 214.634 * [taylor]: Taking taylor expansion of k in k 214.634 * [backup-simplify]: Simplify 0 into 0 214.634 * [backup-simplify]: Simplify 1 into 1 214.635 * [backup-simplify]: Simplify (sqrt 0) into 0 214.635 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.635 * [taylor]: Taking taylor expansion of (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k 214.635 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 214.635 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 214.635 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 214.635 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 214.635 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.635 * [taylor]: Taking taylor expansion of 1/2 in k 214.635 * [backup-simplify]: Simplify 1/2 into 1/2 214.636 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.636 * [taylor]: Taking taylor expansion of 1/2 in k 214.636 * [backup-simplify]: Simplify 1/2 into 1/2 214.636 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.636 * [taylor]: Taking taylor expansion of k in k 214.636 * [backup-simplify]: Simplify 0 into 0 214.636 * [backup-simplify]: Simplify 1 into 1 214.636 * [backup-simplify]: Simplify (/ 1 1) into 1 214.636 * [taylor]: Taking taylor expansion of (log PI) in k 214.636 * [taylor]: Taking taylor expansion of PI in k 214.636 * [backup-simplify]: Simplify PI into PI 214.636 * [backup-simplify]: Simplify (log PI) into (log PI) 214.636 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.637 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.637 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.637 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 214.638 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.638 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 214.638 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in k 214.638 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in k 214.638 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 214.638 * [taylor]: Taking taylor expansion of 1/2 in k 214.638 * [backup-simplify]: Simplify 1/2 into 1/2 214.638 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.638 * [taylor]: Taking taylor expansion of 1/2 in k 214.638 * [backup-simplify]: Simplify 1/2 into 1/2 214.638 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.638 * [taylor]: Taking taylor expansion of k in k 214.638 * [backup-simplify]: Simplify 0 into 0 214.638 * [backup-simplify]: Simplify 1 into 1 214.638 * [backup-simplify]: Simplify (/ 1 1) into 1 214.638 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k 214.638 * [taylor]: Taking taylor expansion of (/ 2 n) in k 214.638 * [taylor]: Taking taylor expansion of 2 in k 214.638 * [backup-simplify]: Simplify 2 into 2 214.638 * [taylor]: Taking taylor expansion of n in k 214.638 * [backup-simplify]: Simplify n into n 214.639 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n) 214.639 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n)) 214.639 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.639 * [backup-simplify]: Simplify (- 1/2) into -1/2 214.639 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 214.639 * [backup-simplify]: Simplify (* -1/2 (log (/ 2 n))) into (* -1/2 (log (/ 2 n))) 214.639 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) into (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) 214.640 * [taylor]: Taking taylor expansion of (sqrt k) in k 214.640 * [taylor]: Taking taylor expansion of k in k 214.640 * [backup-simplify]: Simplify 0 into 0 214.640 * [backup-simplify]: Simplify 1 into 1 214.640 * [backup-simplify]: Simplify (sqrt 0) into 0 214.641 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 214.641 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 214.641 * [backup-simplify]: Simplify (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 214.641 * [taylor]: Taking taylor expansion of 0 in n 214.641 * [backup-simplify]: Simplify 0 into 0 214.641 * [backup-simplify]: Simplify 0 into 0 214.641 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 214.642 * [backup-simplify]: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 214.642 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 214.642 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 214.642 * [taylor]: Taking taylor expansion of +nan.0 in n 214.642 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.642 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 214.642 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 214.642 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 214.642 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 214.642 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.642 * [taylor]: Taking taylor expansion of 1/2 in n 214.642 * [backup-simplify]: Simplify 1/2 into 1/2 214.642 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.642 * [taylor]: Taking taylor expansion of 1/2 in n 214.642 * [backup-simplify]: Simplify 1/2 into 1/2 214.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.642 * [taylor]: Taking taylor expansion of k in n 214.642 * [backup-simplify]: Simplify k into k 214.642 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.642 * [taylor]: Taking taylor expansion of (log PI) in n 214.642 * [taylor]: Taking taylor expansion of PI in n 214.642 * [backup-simplify]: Simplify PI into PI 214.642 * [backup-simplify]: Simplify (log PI) into (log PI) 214.642 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.642 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.642 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.643 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 214.643 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.643 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.643 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.643 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.643 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.643 * [taylor]: Taking taylor expansion of 1/2 in n 214.643 * [backup-simplify]: Simplify 1/2 into 1/2 214.643 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.643 * [taylor]: Taking taylor expansion of 1/2 in n 214.643 * [backup-simplify]: Simplify 1/2 into 1/2 214.643 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.643 * [taylor]: Taking taylor expansion of k in n 214.643 * [backup-simplify]: Simplify k into k 214.643 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.643 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.643 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.643 * [taylor]: Taking taylor expansion of 2 in n 214.643 * [backup-simplify]: Simplify 2 into 2 214.643 * [taylor]: Taking taylor expansion of n in n 214.643 * [backup-simplify]: Simplify 0 into 0 214.643 * [backup-simplify]: Simplify 1 into 1 214.644 * [backup-simplify]: Simplify (/ 2 1) into 2 214.644 * [backup-simplify]: Simplify (log 2) into (log 2) 214.644 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.644 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.644 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.645 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.645 * [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)))) 214.646 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 214.646 * [backup-simplify]: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.646 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 214.647 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 214.647 * [backup-simplify]: Simplify 0 into 0 214.649 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 214.649 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 214.650 * [backup-simplify]: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 214.650 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 214.650 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 214.650 * [taylor]: Taking taylor expansion of +nan.0 in n 214.650 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.650 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 214.650 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 214.650 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 214.650 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 214.650 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.650 * [taylor]: Taking taylor expansion of 1/2 in n 214.650 * [backup-simplify]: Simplify 1/2 into 1/2 214.650 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.650 * [taylor]: Taking taylor expansion of 1/2 in n 214.650 * [backup-simplify]: Simplify 1/2 into 1/2 214.650 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.650 * [taylor]: Taking taylor expansion of k in n 214.650 * [backup-simplify]: Simplify k into k 214.650 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.650 * [taylor]: Taking taylor expansion of (log PI) in n 214.650 * [taylor]: Taking taylor expansion of PI in n 214.650 * [backup-simplify]: Simplify PI into PI 214.650 * [backup-simplify]: Simplify (log PI) into (log PI) 214.650 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.650 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.650 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.651 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 214.651 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.651 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.651 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.651 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.651 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.651 * [taylor]: Taking taylor expansion of 1/2 in n 214.651 * [backup-simplify]: Simplify 1/2 into 1/2 214.651 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.651 * [taylor]: Taking taylor expansion of 1/2 in n 214.651 * [backup-simplify]: Simplify 1/2 into 1/2 214.651 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.651 * [taylor]: Taking taylor expansion of k in n 214.651 * [backup-simplify]: Simplify k into k 214.651 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.651 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.651 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.651 * [taylor]: Taking taylor expansion of 2 in n 214.651 * [backup-simplify]: Simplify 2 into 2 214.651 * [taylor]: Taking taylor expansion of n in n 214.651 * [backup-simplify]: Simplify 0 into 0 214.651 * [backup-simplify]: Simplify 1 into 1 214.652 * [backup-simplify]: Simplify (/ 2 1) into 2 214.652 * [backup-simplify]: Simplify (log 2) into (log 2) 214.652 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.652 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.652 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.652 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.653 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.653 * [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)))) 214.653 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 214.654 * [backup-simplify]: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.654 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 214.655 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 214.655 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0 214.656 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 214.656 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.656 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.657 * [backup-simplify]: Simplify (- 0) into 0 214.657 * [backup-simplify]: Simplify (+ 0 0) into 0 214.657 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.658 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log 2) (log n)))) into 0 214.659 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.659 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 214.659 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.660 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.660 * [backup-simplify]: Simplify (- 0) into 0 214.660 * [backup-simplify]: Simplify (+ 0 0) into 0 214.661 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 214.661 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 214.662 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into 0 214.662 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into 0 214.663 * [backup-simplify]: Simplify (- 0) into 0 214.663 * [backup-simplify]: Simplify 0 into 0 214.663 * [backup-simplify]: Simplify 0 into 0 214.665 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 214.665 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 214.666 * [backup-simplify]: Simplify (+ (* (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) 214.666 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 214.666 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 214.666 * [taylor]: Taking taylor expansion of +nan.0 in n 214.666 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.666 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 214.666 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 214.666 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 214.666 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 214.666 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.666 * [taylor]: Taking taylor expansion of 1/2 in n 214.666 * [backup-simplify]: Simplify 1/2 into 1/2 214.666 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.666 * [taylor]: Taking taylor expansion of 1/2 in n 214.666 * [backup-simplify]: Simplify 1/2 into 1/2 214.666 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.666 * [taylor]: Taking taylor expansion of k in n 214.666 * [backup-simplify]: Simplify k into k 214.666 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.666 * [taylor]: Taking taylor expansion of (log PI) in n 214.666 * [taylor]: Taking taylor expansion of PI in n 214.666 * [backup-simplify]: Simplify PI into PI 214.667 * [backup-simplify]: Simplify (log PI) into (log PI) 214.667 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.667 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.667 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.667 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 214.668 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 214.668 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 214.668 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))) in n 214.668 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n))) in n 214.668 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 214.668 * [taylor]: Taking taylor expansion of 1/2 in n 214.668 * [backup-simplify]: Simplify 1/2 into 1/2 214.668 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.668 * [taylor]: Taking taylor expansion of 1/2 in n 214.668 * [backup-simplify]: Simplify 1/2 into 1/2 214.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.668 * [taylor]: Taking taylor expansion of k in n 214.668 * [backup-simplify]: Simplify k into k 214.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.668 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n 214.668 * [taylor]: Taking taylor expansion of (/ 2 n) in n 214.668 * [taylor]: Taking taylor expansion of 2 in n 214.668 * [backup-simplify]: Simplify 2 into 2 214.668 * [taylor]: Taking taylor expansion of n in n 214.668 * [backup-simplify]: Simplify 0 into 0 214.668 * [backup-simplify]: Simplify 1 into 1 214.668 * [backup-simplify]: Simplify (/ 2 1) into 2 214.668 * [backup-simplify]: Simplify (log 2) into (log 2) 214.668 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.668 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 214.669 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 214.669 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n)) 214.669 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) 214.670 * [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)))) 214.670 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) 214.670 * [backup-simplify]: Simplify (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) into (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))) 214.671 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 214.671 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) into (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))))) 214.673 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (pow PI (- 1/2 (* 1/2 k))) (exp (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow k 3)))))))) 214.673 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 (- k))))) (/ (pow (* 2 (/ 1 (- n))) (- 1/2 (* 1/2 (/ 1 (- k))))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 214.673 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (k n) around 0 214.673 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n 214.673 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 214.673 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.673 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.673 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.673 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.673 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.673 * [taylor]: Taking taylor expansion of 1/2 in n 214.673 * [backup-simplify]: Simplify 1/2 into 1/2 214.673 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.673 * [taylor]: Taking taylor expansion of k in n 214.673 * [backup-simplify]: Simplify k into k 214.674 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.674 * [taylor]: Taking taylor expansion of 1/2 in n 214.674 * [backup-simplify]: Simplify 1/2 into 1/2 214.674 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.674 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.674 * [taylor]: Taking taylor expansion of -2 in n 214.674 * [backup-simplify]: Simplify -2 into -2 214.674 * [taylor]: Taking taylor expansion of n in n 214.674 * [backup-simplify]: Simplify 0 into 0 214.674 * [backup-simplify]: Simplify 1 into 1 214.674 * [backup-simplify]: Simplify (/ -2 1) into -2 214.674 * [backup-simplify]: Simplify (log -2) into (log -2) 214.674 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.674 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.675 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.675 * [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)))) 214.675 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.675 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 214.676 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 214.676 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.676 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.676 * [taylor]: Taking taylor expansion of 1/2 in n 214.676 * [backup-simplify]: Simplify 1/2 into 1/2 214.676 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.676 * [taylor]: Taking taylor expansion of k in n 214.676 * [backup-simplify]: Simplify k into k 214.676 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.676 * [taylor]: Taking taylor expansion of 1/2 in n 214.676 * [backup-simplify]: Simplify 1/2 into 1/2 214.676 * [taylor]: Taking taylor expansion of (log PI) in n 214.676 * [taylor]: Taking taylor expansion of PI in n 214.676 * [backup-simplify]: Simplify PI into PI 214.676 * [backup-simplify]: Simplify (log PI) into (log PI) 214.676 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.676 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.676 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 214.677 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.677 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 214.677 * [taylor]: Taking taylor expansion of (/ -1 k) in n 214.677 * [taylor]: Taking taylor expansion of -1 in n 214.677 * [backup-simplify]: Simplify -1 into -1 214.677 * [taylor]: Taking taylor expansion of k in n 214.677 * [backup-simplify]: Simplify k into k 214.677 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 214.677 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 214.677 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 214.677 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 214.677 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 214.678 * [backup-simplify]: Simplify (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) into (/ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) 214.678 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 214.678 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 214.678 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.678 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 214.678 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 214.678 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.678 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.678 * [taylor]: Taking taylor expansion of 1/2 in k 214.678 * [backup-simplify]: Simplify 1/2 into 1/2 214.678 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.678 * [taylor]: Taking taylor expansion of k in k 214.678 * [backup-simplify]: Simplify 0 into 0 214.678 * [backup-simplify]: Simplify 1 into 1 214.678 * [backup-simplify]: Simplify (/ 1 1) into 1 214.678 * [taylor]: Taking taylor expansion of 1/2 in k 214.678 * [backup-simplify]: Simplify 1/2 into 1/2 214.678 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 214.678 * [taylor]: Taking taylor expansion of (/ -2 n) in k 214.678 * [taylor]: Taking taylor expansion of -2 in k 214.678 * [backup-simplify]: Simplify -2 into -2 214.678 * [taylor]: Taking taylor expansion of n in k 214.678 * [backup-simplify]: Simplify n into n 214.679 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 214.679 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 214.679 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.679 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.679 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 214.679 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 214.679 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.679 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 214.679 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 214.679 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.679 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.679 * [taylor]: Taking taylor expansion of 1/2 in k 214.679 * [backup-simplify]: Simplify 1/2 into 1/2 214.679 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.679 * [taylor]: Taking taylor expansion of k in k 214.679 * [backup-simplify]: Simplify 0 into 0 214.679 * [backup-simplify]: Simplify 1 into 1 214.680 * [backup-simplify]: Simplify (/ 1 1) into 1 214.680 * [taylor]: Taking taylor expansion of 1/2 in k 214.680 * [backup-simplify]: Simplify 1/2 into 1/2 214.680 * [taylor]: Taking taylor expansion of (log PI) in k 214.680 * [taylor]: Taking taylor expansion of PI in k 214.680 * [backup-simplify]: Simplify PI into PI 214.680 * [backup-simplify]: Simplify (log PI) into (log PI) 214.680 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.681 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.681 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.681 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.681 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 214.681 * [taylor]: Taking taylor expansion of (/ -1 k) in k 214.681 * [taylor]: Taking taylor expansion of -1 in k 214.681 * [backup-simplify]: Simplify -1 into -1 214.681 * [taylor]: Taking taylor expansion of k in k 214.681 * [backup-simplify]: Simplify 0 into 0 214.682 * [backup-simplify]: Simplify 1 into 1 214.682 * [backup-simplify]: Simplify (/ -1 1) into -1 214.682 * [backup-simplify]: Simplify (sqrt 0) into 0 214.683 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 214.683 * [backup-simplify]: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 214.683 * [backup-simplify]: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 214.683 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k 214.683 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 214.683 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.683 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in k 214.683 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in k 214.683 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.683 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.683 * [taylor]: Taking taylor expansion of 1/2 in k 214.683 * [backup-simplify]: Simplify 1/2 into 1/2 214.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.683 * [taylor]: Taking taylor expansion of k in k 214.683 * [backup-simplify]: Simplify 0 into 0 214.683 * [backup-simplify]: Simplify 1 into 1 214.684 * [backup-simplify]: Simplify (/ 1 1) into 1 214.684 * [taylor]: Taking taylor expansion of 1/2 in k 214.684 * [backup-simplify]: Simplify 1/2 into 1/2 214.684 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k 214.684 * [taylor]: Taking taylor expansion of (/ -2 n) in k 214.684 * [taylor]: Taking taylor expansion of -2 in k 214.684 * [backup-simplify]: Simplify -2 into -2 214.684 * [taylor]: Taking taylor expansion of n in k 214.684 * [backup-simplify]: Simplify n into n 214.684 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n) 214.684 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n)) 214.684 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.684 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.684 * [backup-simplify]: Simplify (* 1/2 (log (/ -2 n))) into (* 1/2 (log (/ -2 n))) 214.684 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) into (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 214.685 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 214.685 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 214.685 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 214.685 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 214.685 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 214.685 * [taylor]: Taking taylor expansion of 1/2 in k 214.685 * [backup-simplify]: Simplify 1/2 into 1/2 214.685 * [taylor]: Taking taylor expansion of (/ 1 k) in k 214.685 * [taylor]: Taking taylor expansion of k in k 214.685 * [backup-simplify]: Simplify 0 into 0 214.685 * [backup-simplify]: Simplify 1 into 1 214.685 * [backup-simplify]: Simplify (/ 1 1) into 1 214.685 * [taylor]: Taking taylor expansion of 1/2 in k 214.685 * [backup-simplify]: Simplify 1/2 into 1/2 214.685 * [taylor]: Taking taylor expansion of (log PI) in k 214.685 * [taylor]: Taking taylor expansion of PI in k 214.685 * [backup-simplify]: Simplify PI into PI 214.685 * [backup-simplify]: Simplify (log PI) into (log PI) 214.686 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 214.686 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 214.686 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 214.687 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.687 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 214.687 * [taylor]: Taking taylor expansion of (/ -1 k) in k 214.687 * [taylor]: Taking taylor expansion of -1 in k 214.687 * [backup-simplify]: Simplify -1 into -1 214.687 * [taylor]: Taking taylor expansion of k in k 214.687 * [backup-simplify]: Simplify 0 into 0 214.687 * [backup-simplify]: Simplify 1 into 1 214.687 * [backup-simplify]: Simplify (/ -1 1) into -1 214.687 * [backup-simplify]: Simplify (sqrt 0) into 0 214.688 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 214.688 * [backup-simplify]: Simplify (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 214.689 * [backup-simplify]: Simplify (/ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 214.689 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 214.689 * [taylor]: Taking taylor expansion of +nan.0 in n 214.689 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.689 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 214.689 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.689 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.689 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.689 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.689 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.689 * [taylor]: Taking taylor expansion of 1/2 in n 214.689 * [backup-simplify]: Simplify 1/2 into 1/2 214.689 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.689 * [taylor]: Taking taylor expansion of k in n 214.689 * [backup-simplify]: Simplify k into k 214.689 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.689 * [taylor]: Taking taylor expansion of 1/2 in n 214.689 * [backup-simplify]: Simplify 1/2 into 1/2 214.689 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.689 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.689 * [taylor]: Taking taylor expansion of -2 in n 214.689 * [backup-simplify]: Simplify -2 into -2 214.689 * [taylor]: Taking taylor expansion of n in n 214.689 * [backup-simplify]: Simplify 0 into 0 214.689 * [backup-simplify]: Simplify 1 into 1 214.689 * [backup-simplify]: Simplify (/ -2 1) into -2 214.690 * [backup-simplify]: Simplify (log -2) into (log -2) 214.690 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.690 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.690 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.690 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.691 * [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)))) 214.691 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.691 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 214.691 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 214.691 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.691 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.691 * [taylor]: Taking taylor expansion of 1/2 in n 214.691 * [backup-simplify]: Simplify 1/2 into 1/2 214.691 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.691 * [taylor]: Taking taylor expansion of k in n 214.691 * [backup-simplify]: Simplify k into k 214.691 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.691 * [taylor]: Taking taylor expansion of 1/2 in n 214.691 * [backup-simplify]: Simplify 1/2 into 1/2 214.691 * [taylor]: Taking taylor expansion of (log PI) in n 214.691 * [taylor]: Taking taylor expansion of PI in n 214.691 * [backup-simplify]: Simplify PI into PI 214.691 * [backup-simplify]: Simplify (log PI) into (log PI) 214.691 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.691 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.692 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 214.692 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.692 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 214.693 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 214.693 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 214.693 * [backup-simplify]: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 214.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 214.696 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 214.696 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 214.696 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 214.696 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 214.696 * [taylor]: Taking taylor expansion of +nan.0 in n 214.696 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.696 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 214.696 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.696 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.697 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.697 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.697 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.697 * [taylor]: Taking taylor expansion of 1/2 in n 214.697 * [backup-simplify]: Simplify 1/2 into 1/2 214.697 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.697 * [taylor]: Taking taylor expansion of k in n 214.697 * [backup-simplify]: Simplify k into k 214.697 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.697 * [taylor]: Taking taylor expansion of 1/2 in n 214.697 * [backup-simplify]: Simplify 1/2 into 1/2 214.697 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.697 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.697 * [taylor]: Taking taylor expansion of -2 in n 214.697 * [backup-simplify]: Simplify -2 into -2 214.697 * [taylor]: Taking taylor expansion of n in n 214.697 * [backup-simplify]: Simplify 0 into 0 214.697 * [backup-simplify]: Simplify 1 into 1 214.697 * [backup-simplify]: Simplify (/ -2 1) into -2 214.697 * [backup-simplify]: Simplify (log -2) into (log -2) 214.697 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.697 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.698 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.699 * [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)))) 214.699 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.699 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 214.699 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 214.699 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.699 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.699 * [taylor]: Taking taylor expansion of 1/2 in n 214.699 * [backup-simplify]: Simplify 1/2 into 1/2 214.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.699 * [taylor]: Taking taylor expansion of k in n 214.699 * [backup-simplify]: Simplify k into k 214.699 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.699 * [taylor]: Taking taylor expansion of 1/2 in n 214.699 * [backup-simplify]: Simplify 1/2 into 1/2 214.699 * [taylor]: Taking taylor expansion of (log PI) in n 214.699 * [taylor]: Taking taylor expansion of PI in n 214.699 * [backup-simplify]: Simplify PI into PI 214.699 * [backup-simplify]: Simplify (log PI) into (log PI) 214.699 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.699 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.699 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 214.700 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.700 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 214.701 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 214.701 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 214.701 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 214.702 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 214.702 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.703 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.703 * [backup-simplify]: Simplify (+ 0 0) into 0 214.703 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 214.704 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 214.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0 214.705 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0 214.705 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 214.706 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 214.706 * [backup-simplify]: Simplify (+ 0 0) into 0 214.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.707 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -2) (log n)))) into 0 214.708 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 214.708 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 214.709 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 214.709 * [backup-simplify]: Simplify 0 into 0 214.709 * [backup-simplify]: Simplify (+ (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 214.710 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 214.716 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 214.717 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 214.717 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 214.717 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 214.717 * [taylor]: Taking taylor expansion of +nan.0 in n 214.717 * [backup-simplify]: Simplify +nan.0 into +nan.0 214.717 * [taylor]: Taking taylor expansion of (* (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 214.717 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.717 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))) in n 214.717 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n))) in n 214.717 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.717 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.717 * [taylor]: Taking taylor expansion of 1/2 in n 214.717 * [backup-simplify]: Simplify 1/2 into 1/2 214.717 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.717 * [taylor]: Taking taylor expansion of k in n 214.717 * [backup-simplify]: Simplify k into k 214.717 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.717 * [taylor]: Taking taylor expansion of 1/2 in n 214.717 * [backup-simplify]: Simplify 1/2 into 1/2 214.717 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n 214.717 * [taylor]: Taking taylor expansion of (/ -2 n) in n 214.717 * [taylor]: Taking taylor expansion of -2 in n 214.717 * [backup-simplify]: Simplify -2 into -2 214.717 * [taylor]: Taking taylor expansion of n in n 214.717 * [backup-simplify]: Simplify 0 into 0 214.717 * [backup-simplify]: Simplify 1 into 1 214.718 * [backup-simplify]: Simplify (/ -2 1) into -2 214.718 * [backup-simplify]: Simplify (log -2) into (log -2) 214.718 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.718 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n)) 214.719 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) 214.719 * [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)))) 214.719 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 214.719 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 214.719 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 214.719 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 214.719 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 214.719 * [taylor]: Taking taylor expansion of 1/2 in n 214.719 * [backup-simplify]: Simplify 1/2 into 1/2 214.719 * [taylor]: Taking taylor expansion of (/ 1 k) in n 214.719 * [taylor]: Taking taylor expansion of k in n 214.719 * [backup-simplify]: Simplify k into k 214.719 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 214.719 * [taylor]: Taking taylor expansion of 1/2 in n 214.719 * [backup-simplify]: Simplify 1/2 into 1/2 214.719 * [taylor]: Taking taylor expansion of (log PI) in n 214.719 * [taylor]: Taking taylor expansion of PI in n 214.719 * [backup-simplify]: Simplify PI into PI 214.720 * [backup-simplify]: Simplify (log PI) into (log PI) 214.720 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 214.720 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 214.720 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 214.720 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 214.721 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 214.721 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 214.722 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 214.722 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 214.724 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) k)) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (pow PI (- 1/2 (* 1/2 k)))) (pow k 2)))))))) 214.724 * * * [progress]: simplifying candidates 214.724 * * * * [progress]: [ 1 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 2 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 3 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 4 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 5 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 6 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 7 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 8 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 9 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 10 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 11 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 12 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 13 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 14 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 15 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 16 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 17 / 281 ] simplifiying candidate # 214.724 * * * * [progress]: [ 18 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 19 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 20 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 21 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 22 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 23 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 24 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 25 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 26 / 281 ] simplifiying candidate #real (real->posit16 (pow (* 2 n) (- 1/2 (* 1/2 k))))) (sqrt k))))> 214.725 * * * * [progress]: [ 27 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 28 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 29 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 30 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 31 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 32 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 33 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 34 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 35 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 36 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 37 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 38 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 39 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 40 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 41 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 42 / 281 ] simplifiying candidate # 214.725 * * * * [progress]: [ 43 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 44 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 45 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 46 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 47 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 48 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 49 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 50 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 51 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 52 / 281 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (* 1/2 k))))) (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))))> 214.726 * * * * [progress]: [ 53 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 54 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 55 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 56 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 57 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 58 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 59 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 60 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 61 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 62 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 63 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 64 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 65 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 66 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 67 / 281 ] simplifiying candidate # 214.726 * * * * [progress]: [ 68 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 69 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 70 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 71 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 72 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 73 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 74 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 75 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 76 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 77 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 78 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 79 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 80 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 81 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 82 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 83 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 84 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 85 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 86 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 87 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 88 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 89 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 90 / 281 ] simplifiying candidate # 214.727 * * * * [progress]: [ 91 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 92 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 93 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 94 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 95 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 96 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 97 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 98 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 99 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 100 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 101 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 102 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 103 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 104 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 105 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 106 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 107 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 108 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 109 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 110 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 111 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 112 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 113 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 114 / 281 ] simplifiying candidate # 214.728 * * * * [progress]: [ 115 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 116 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 117 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 118 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 119 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 120 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 121 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 122 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 123 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 124 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 125 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 126 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 127 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 128 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 129 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 130 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 131 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 132 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 133 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 134 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 135 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 136 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 137 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 138 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 139 / 281 ] simplifiying candidate # 214.729 * * * * [progress]: [ 140 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 141 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 142 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 143 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 144 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 145 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 146 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 147 / 281 ] simplifiying candidate #real (real->posit16 (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))))))> 214.730 * * * * [progress]: [ 148 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 149 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 150 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 151 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 152 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 153 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 154 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 155 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 156 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 157 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 158 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 159 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 160 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 161 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 162 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 163 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 164 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 165 / 281 ] simplifiying candidate # 214.730 * * * * [progress]: [ 166 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 167 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 168 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 169 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 170 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 171 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 172 / 281 ] simplifiying candidate # 214.731 * * * * [progress]: [ 173 / 281 ] simplifiying candidate # 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* * [progress]: [ 263 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 264 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 265 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 266 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 267 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 268 / 281 ] simplifiying candidate #real (real->posit16 (* (pow PI (- 1/2 (* 1/2 k))) (/ (pow (* 2 n) (- 1/2 (* 1/2 k))) (sqrt k))))))> 214.735 * * * * [progress]: [ 269 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 270 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 271 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 272 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 273 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 274 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 275 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 276 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 277 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 278 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 279 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 280 / 281 ] simplifiying candidate # 214.735 * * * * [progress]: [ 281 / 281 ] simplifiying candidate # 214.738 * [simplify]: Simplifying: (expm1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (log1p (pow (* 2 n) (- 1/2 (* 1/2 k)))) (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) (* (log (* 2 n)) (- 1/2 (* 1/2 k))) (* (log (* 2 n)) (- 1/2 (* 1/2 k))) (* 1 (- 1/2 (* 1/2 k))) (* 1 (- 1/2 (* 1/2 k))) (pow (* 2 n) 1/2) (pow (* 2 n) (* 1/2 k)) (pow (* 2 n) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow (* 2 n) (sqrt (- 1/2 (* 1/2 k)))) (pow (* 2 n) 1) (pow (* 2 n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* k 1/2)))) (pow (* 2 n) (fma (- k) 1/2 (* k 1/2))) (pow (* 2 n) (fma (sqrt 1/2) (sqrt 1/2) (- (* k 1/2)))) (pow (* 2 n) (fma (- k) 1/2 (* 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Extracting #6: cost 131 inf + 654351 215.741 * * [simplify]: Extracting #7: cost 60 inf + 706087 215.841 * * [simplify]: Extracting #8: cost 13 inf + 743861 215.944 * * [simplify]: Extracting #9: cost 0 inf + 747647 216.047 * * [simplify]: Extracting #10: cost 0 inf + 742437 216.150 * * [simplify]: Extracting #11: cost 0 inf + 741027 216.252 * * [simplify]: Extracting #12: cost 0 inf + 740947 216.356 * [simplify]: Simplified to: (expm1 (pow (* 2 n) (- 1/2 (* 1/2 k)))) (log1p (pow (* 2 n) (- 1/2 (* 1/2 k)))) (* (log (* 2 n)) (- 1/2 (* 1/2 k))) (* (log (* 2 n)) (- 1/2 (* 1/2 k))) (* (log (* 2 n)) (- 1/2 (* 1/2 k))) (- 1/2 (* 1/2 k)) (- 1/2 (* 1/2 k)) (sqrt (* 2 n)) (pow (* 2 n) (* 1/2 k)) (pow (* 2 n) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow (* 2 n) (sqrt (- 1/2 (* 1/2 k)))) (* 2 n) (pow (* 2 n) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (* -1/2 k))) (pow (* 2 n) (fma -1/2 k (* 1/2 k))) (pow (* 2 n) (- 1/2 (* 1/2 k))) (pow (* 2 n) (fma -1/2 k (* 1/2 k))) (pow (* 2 n) (- 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(* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (fabs (cbrt k))) (/ (* (pow PI (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (sqrt k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (/ (* (pow PI (- 1/2 (* 1/2 k))) (pow 2 (- 1/2 (* 1/2 k)))) (sqrt (sqrt k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (* (* (pow PI (- 1/2 (* 1/2 k))) (/ (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k)))) (/ (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k)))) (/ (* (* (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k))))) (pow PI (- 1/2 (* 1/2 k)))) (fabs (cbrt k))) (* (pow PI (- 1/2 (* 1/2 k))) (/ (* (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))) (* (pow PI (- 1/2 (* 1/2 k))) (* (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))))) (* (pow PI (- 1/2 (* 1/2 k))) (/ (* (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))) (* (pow PI (- 1/2 (* 1/2 k))) (* (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (pow (* 2 n) (- 1/2 (* 1/2 k)))))) (* (/ (pow PI (- 1/2 (* 1/2 k))) (cbrt (sqrt k))) (/ (sqrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k)))) (/ (* (sqrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (fabs (cbrt k))) (* (/ (sqrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k))) (pow PI (- 1/2 (* 1/2 k)))) (* (sqrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (* (/ (sqrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k))) (pow PI (- 1/2 (* 1/2 k)))) (* (sqrt (pow (* 2 n) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) (/ (pow PI (- 1/2 (* 1/2 k))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (* 1/2 k))) (fabs (cbrt k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k))) (pow PI (- 1/2 (* 1/2 k))) (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k))) (pow PI (- 1/2 (* 1/2 k))) (/ (* (pow PI (- 1/2 (* 1/2 k))) (pow (* 2 n) (/ (- 1/2 (* 1/2 k)) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (* 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2)))))) (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (+ (sqrt PI) (* (sqrt PI) (- (* 1/8 (* (* k (log PI)) (* k (log PI)))) (* (* 1/2 (log PI)) k)))) (pow PI (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))) (- (- (* (* (exp (* (log (* 2 n)) 1/2)) (* k +nan.0)) (log n)) (- (* (* (log 2) (* (log 2) (* (exp (* (log (* 2 n)) 1/2)) (* k k)))) +nan.0) (+ (- (* (log 2) (* (* +nan.0 (* (log n) (exp (* (log (* 2 n)) 1/2)))) (* k k))) (* (exp (* (log (* 2 n)) 1/2)) (* k +nan.0))) (+ (- (* (* +nan.0 (* (exp (* (log (* 2 n)) 1/2)) (* k k))) (* (log n) (log n))) (* (* +nan.0 (* (log n) (exp (* (log (* 2 n)) 1/2)))) (* k k))) (+ (- (* (* +nan.0 (* (exp (* (log (* 2 n)) 1/2)) (* k k))) (log 2)) (* (exp (* (log (* 2 n)) 1/2)) +nan.0)) (- (* (log 2) (* (exp (* (log (* 2 n)) 1/2)) (* k +nan.0))) (* +nan.0 (* (exp (* (log (* 2 n)) 1/2)) (* k k)))))))))) (+ (- (* (/ +nan.0 (* k k)) (/ (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k)))) k))) (* +nan.0 (- (/ (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k)))) k) (/ (/ (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k)))) k) k)))) (+ (* (- +nan.0) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (* k k))) (* +nan.0 (- (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) k)))) (- (+ (- (* +nan.0 (* (* n PI) (* k (sqrt 2)))) (* (* +nan.0 (sqrt 2)) (* n PI))) (+ (- (* (* (log 2) (* (* n PI) (* k (sqrt 2)))) +nan.0) (* (* +nan.0 (sqrt 2)) (* (* (log n) k) (* PI n)))) (* (* +nan.0 (sqrt 2)) (- (* (* (* n PI) k) (log PI)) (* (* PI n) (* PI n))))))) (+ (/ (- (* +nan.0 (* (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (* k k)) (* +nan.0 (- (/ (* (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))) k) (/ (pow PI (- 1/2 (* 1/2 k))) (/ (* (* k k) k) (exp (* (log (* 2 n)) (- 1/2 (* 1/2 k))))))))) (- (* (* (- +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (pow PI (- 1/2 (* 1/2 k)))) (+ (/ (* (* (- +nan.0) (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (pow PI (- 1/2 (* 1/2 k)))) k) (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))) (/ (* k k) (pow PI (- 1/2 (* 1/2 k)))))))) 216.381 * * * [progress]: adding candidates to table 218.793 * * [progress]: iteration 4 / 4 218.793 * * * [progress]: picking best candidate 218.819 * * * * [pick]: Picked # 218.819 * * * [progress]: localizing error 218.846 * * * [progress]: generating rewritten candidates 218.846 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 218.850 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 218.853 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 218.890 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 218.903 * * * [progress]: generating series expansions 218.903 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 218.903 * [backup-simplify]: Simplify (pow n (- 1/2 (* 1/2 k))) into (pow n (- 1/2 (* 1/2 k))) 218.903 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0 218.903 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 218.903 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 218.904 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 218.904 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 218.904 * [taylor]: Taking taylor expansion of 1/2 in k 218.904 * [backup-simplify]: Simplify 1/2 into 1/2 218.904 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 218.904 * [taylor]: Taking taylor expansion of 1/2 in k 218.904 * [backup-simplify]: Simplify 1/2 into 1/2 218.904 * [taylor]: Taking taylor expansion of k in k 218.904 * [backup-simplify]: Simplify 0 into 0 218.904 * [backup-simplify]: Simplify 1 into 1 218.904 * [taylor]: Taking taylor expansion of (log n) in k 218.904 * [taylor]: Taking taylor expansion of n in k 218.904 * [backup-simplify]: Simplify n into n 218.904 * [backup-simplify]: Simplify (log n) into (log n) 218.904 * [backup-simplify]: Simplify (* 1/2 0) into 0 218.905 * [backup-simplify]: Simplify (- 0) into 0 218.905 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 218.905 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 218.905 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 218.905 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 218.905 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 218.905 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 218.905 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 218.905 * [taylor]: Taking taylor expansion of 1/2 in n 218.905 * [backup-simplify]: Simplify 1/2 into 1/2 218.905 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 218.905 * [taylor]: Taking taylor expansion of 1/2 in n 218.905 * [backup-simplify]: Simplify 1/2 into 1/2 218.905 * [taylor]: Taking taylor expansion of k in n 218.905 * [backup-simplify]: Simplify k into k 218.905 * [taylor]: Taking taylor expansion of (log n) in n 218.905 * [taylor]: Taking taylor expansion of n in n 218.905 * [backup-simplify]: Simplify 0 into 0 218.905 * [backup-simplify]: Simplify 1 into 1 218.905 * [backup-simplify]: Simplify (log 1) into 0 218.905 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 218.905 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 218.905 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 218.906 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 218.906 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 218.906 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 218.906 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 218.906 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 218.906 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 218.906 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 218.906 * [taylor]: Taking taylor expansion of 1/2 in n 218.906 * [backup-simplify]: Simplify 1/2 into 1/2 218.906 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 218.906 * [taylor]: Taking taylor expansion of 1/2 in n 218.906 * [backup-simplify]: Simplify 1/2 into 1/2 218.906 * [taylor]: Taking taylor expansion of k in n 218.906 * [backup-simplify]: Simplify k into k 218.906 * [taylor]: Taking taylor expansion of (log n) in n 218.906 * [taylor]: Taking taylor expansion of n in n 218.906 * [backup-simplify]: Simplify 0 into 0 218.906 * [backup-simplify]: Simplify 1 into 1 218.906 * [backup-simplify]: Simplify (log 1) into 0 218.906 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 218.907 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 218.907 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 218.907 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 218.907 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 218.907 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 218.907 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 218.907 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 218.907 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 218.907 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 218.907 * [taylor]: Taking taylor expansion of 1/2 in k 218.907 * [backup-simplify]: Simplify 1/2 into 1/2 218.907 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 218.907 * [taylor]: Taking taylor expansion of 1/2 in k 218.907 * [backup-simplify]: Simplify 1/2 into 1/2 218.907 * [taylor]: Taking taylor expansion of k in k 218.907 * [backup-simplify]: Simplify 0 into 0 218.907 * [backup-simplify]: Simplify 1 into 1 218.907 * [taylor]: Taking taylor expansion of (log n) in k 218.907 * [taylor]: Taking taylor expansion of n in k 218.907 * [backup-simplify]: Simplify n into n 218.907 * [backup-simplify]: Simplify (log n) into (log n) 218.908 * [backup-simplify]: Simplify (* 1/2 0) into 0 218.908 * [backup-simplify]: Simplify (- 0) into 0 218.908 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 218.908 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 218.908 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 218.908 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2) 218.909 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 218.909 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 218.909 * [backup-simplify]: Simplify (- 0) into 0 218.910 * [backup-simplify]: Simplify (+ 0 0) into 0 218.910 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 218.910 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 218.911 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 218.911 * [taylor]: Taking taylor expansion of 0 in k 218.911 * [backup-simplify]: Simplify 0 into 0 218.911 * [backup-simplify]: Simplify 0 into 0 218.911 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 218.912 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 218.912 * [backup-simplify]: Simplify (- 1/2) into -1/2 218.912 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 218.912 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 218.912 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 218.913 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n))) 218.914 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 218.915 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 218.915 * [backup-simplify]: Simplify (- 0) into 0 218.915 * [backup-simplify]: Simplify (+ 0 0) into 0 218.915 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 218.916 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 218.916 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 218.916 * [taylor]: Taking taylor expansion of 0 in k 218.916 * [backup-simplify]: Simplify 0 into 0 218.916 * [backup-simplify]: Simplify 0 into 0 218.916 * [backup-simplify]: Simplify 0 into 0 218.917 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 218.918 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 218.918 * [backup-simplify]: Simplify (- 0) into 0 218.918 * [backup-simplify]: Simplify (+ 0 0) into 0 218.919 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 218.919 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 218.920 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 218.920 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) 218.920 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 218.920 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 218.920 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 218.920 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 218.920 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 218.920 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 218.920 * [taylor]: Taking taylor expansion of 1/2 in k 218.920 * [backup-simplify]: Simplify 1/2 into 1/2 218.920 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 218.920 * [taylor]: Taking taylor expansion of 1/2 in k 218.920 * [backup-simplify]: Simplify 1/2 into 1/2 218.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k 218.920 * [taylor]: Taking taylor expansion of k in k 218.920 * [backup-simplify]: Simplify 0 into 0 218.920 * [backup-simplify]: Simplify 1 into 1 218.921 * [backup-simplify]: Simplify (/ 1 1) into 1 218.921 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 218.921 * [taylor]: Taking taylor expansion of (/ 1 n) in k 218.921 * [taylor]: Taking taylor expansion of n in k 218.921 * [backup-simplify]: Simplify n into n 218.921 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 218.921 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 218.921 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 218.921 * [backup-simplify]: Simplify (- 1/2) into -1/2 218.921 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 218.921 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 218.922 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 218.922 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 218.922 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 218.922 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 218.922 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 218.922 * [taylor]: Taking taylor expansion of 1/2 in n 218.922 * [backup-simplify]: Simplify 1/2 into 1/2 218.922 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 218.922 * [taylor]: Taking taylor expansion of 1/2 in n 218.922 * [backup-simplify]: Simplify 1/2 into 1/2 218.922 * [taylor]: Taking taylor expansion of (/ 1 k) in n 218.922 * [taylor]: Taking taylor expansion of k in n 218.922 * [backup-simplify]: Simplify k into k 218.922 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 218.922 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 218.922 * [taylor]: Taking taylor expansion of (/ 1 n) in n 218.922 * [taylor]: Taking taylor expansion of n in n 218.922 * [backup-simplify]: Simplify 0 into 0 218.922 * [backup-simplify]: Simplify 1 into 1 218.925 * [backup-simplify]: Simplify (/ 1 1) into 1 218.925 * [backup-simplify]: Simplify (log 1) into 0 218.925 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 218.925 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 218.925 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 218.926 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 218.926 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 218.926 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 218.926 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 218.926 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 218.926 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 218.926 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 218.926 * [taylor]: Taking taylor expansion of 1/2 in n 218.926 * [backup-simplify]: Simplify 1/2 into 1/2 218.926 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 218.926 * [taylor]: Taking taylor expansion of 1/2 in n 218.926 * [backup-simplify]: Simplify 1/2 into 1/2 218.926 * [taylor]: Taking taylor expansion of (/ 1 k) in n 218.926 * [taylor]: Taking taylor expansion of k in n 218.926 * [backup-simplify]: Simplify k into k 218.926 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 218.926 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 218.926 * [taylor]: Taking taylor expansion of (/ 1 n) in n 218.926 * [taylor]: Taking taylor expansion of n in n 218.926 * [backup-simplify]: Simplify 0 into 0 218.926 * [backup-simplify]: Simplify 1 into 1 218.927 * [backup-simplify]: Simplify (/ 1 1) into 1 218.927 * [backup-simplify]: Simplify (log 1) into 0 218.927 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 218.927 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 218.927 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 218.927 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 218.927 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 218.927 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 218.928 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 218.928 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 218.928 * [taylor]: Taking taylor expansion of -1 in k 218.928 * [backup-simplify]: Simplify -1 into -1 218.928 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 218.928 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 218.928 * [taylor]: Taking taylor expansion of 1/2 in k 218.928 * [backup-simplify]: Simplify 1/2 into 1/2 218.928 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 218.928 * [taylor]: Taking taylor expansion of 1/2 in k 218.928 * [backup-simplify]: Simplify 1/2 into 1/2 218.928 * [taylor]: Taking taylor expansion of (/ 1 k) in k 218.928 * [taylor]: Taking taylor expansion of k in k 218.928 * [backup-simplify]: Simplify 0 into 0 218.928 * [backup-simplify]: Simplify 1 into 1 218.928 * [backup-simplify]: Simplify (/ 1 1) into 1 218.928 * [taylor]: Taking taylor expansion of (log n) in k 218.928 * [taylor]: Taking taylor expansion of n in k 218.928 * [backup-simplify]: Simplify n into n 218.928 * [backup-simplify]: Simplify (log n) into (log n) 218.928 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 218.929 * [backup-simplify]: Simplify (- 1/2) into -1/2 218.929 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 218.929 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 218.929 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 218.929 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 218.929 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 218.930 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 218.930 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 218.930 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 218.931 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 218.931 * [backup-simplify]: Simplify (- 0) into 0 218.931 * [backup-simplify]: Simplify (+ 0 0) into 0 218.931 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 218.932 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 218.932 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 218.932 * [taylor]: Taking taylor expansion of 0 in k 218.932 * [backup-simplify]: Simplify 0 into 0 218.932 * [backup-simplify]: Simplify 0 into 0 218.932 * [backup-simplify]: Simplify 0 into 0 218.933 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 218.934 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 218.934 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 218.935 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 218.935 * [backup-simplify]: Simplify (- 0) into 0 218.935 * [backup-simplify]: Simplify (+ 0 0) into 0 218.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 218.936 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 218.937 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 218.937 * [taylor]: Taking taylor expansion of 0 in k 218.937 * [backup-simplify]: Simplify 0 into 0 218.937 * [backup-simplify]: Simplify 0 into 0 218.937 * [backup-simplify]: Simplify 0 into 0 218.937 * [backup-simplify]: Simplify 0 into 0 218.937 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 218.940 * [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 0 218.940 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 218.941 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 218.941 * [backup-simplify]: Simplify (- 0) into 0 218.941 * [backup-simplify]: Simplify (+ 0 0) into 0 218.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 218.942 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 218.943 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 218.943 * [taylor]: Taking taylor expansion of 0 in k 218.943 * [backup-simplify]: Simplify 0 into 0 218.943 * [backup-simplify]: Simplify 0 into 0 218.943 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) into (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) 218.943 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (* 1/2 (/ 1 (- k))))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 218.943 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 218.943 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 218.943 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 218.943 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 218.943 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 218.943 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 218.943 * [taylor]: Taking taylor expansion of 1/2 in k 218.943 * [backup-simplify]: Simplify 1/2 into 1/2 218.943 * [taylor]: Taking taylor expansion of (/ 1 k) in k 218.943 * [taylor]: Taking taylor expansion of k in k 218.943 * [backup-simplify]: Simplify 0 into 0 218.943 * [backup-simplify]: Simplify 1 into 1 218.944 * [backup-simplify]: Simplify (/ 1 1) into 1 218.944 * [taylor]: Taking taylor expansion of 1/2 in k 218.944 * [backup-simplify]: Simplify 1/2 into 1/2 218.944 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 218.944 * [taylor]: Taking taylor expansion of (/ -1 n) in k 218.944 * [taylor]: Taking taylor expansion of -1 in k 218.944 * [backup-simplify]: Simplify -1 into -1 218.944 * [taylor]: Taking taylor expansion of n in k 218.944 * [backup-simplify]: Simplify n into n 218.944 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 218.944 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 218.944 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 218.944 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 218.944 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 218.945 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 218.945 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 218.945 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 218.945 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 218.945 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 218.945 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 218.945 * [taylor]: Taking taylor expansion of 1/2 in n 218.945 * [backup-simplify]: Simplify 1/2 into 1/2 218.945 * [taylor]: Taking taylor expansion of (/ 1 k) in n 218.945 * [taylor]: Taking taylor expansion of k in n 218.945 * [backup-simplify]: Simplify k into k 218.945 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 218.945 * [taylor]: Taking taylor expansion of 1/2 in n 218.945 * [backup-simplify]: Simplify 1/2 into 1/2 218.945 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 218.945 * [taylor]: Taking taylor expansion of (/ -1 n) in n 218.945 * [taylor]: Taking taylor expansion of -1 in n 218.945 * [backup-simplify]: Simplify -1 into -1 218.945 * [taylor]: Taking taylor expansion of n in n 218.945 * [backup-simplify]: Simplify 0 into 0 218.945 * [backup-simplify]: Simplify 1 into 1 218.945 * [backup-simplify]: Simplify (/ -1 1) into -1 218.945 * [backup-simplify]: Simplify (log -1) into (log -1) 218.946 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 218.946 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 218.946 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 218.946 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 218.947 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 218.947 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 218.947 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 218.947 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 218.947 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 218.947 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 218.947 * [taylor]: Taking taylor expansion of 1/2 in n 218.947 * [backup-simplify]: Simplify 1/2 into 1/2 218.947 * [taylor]: Taking taylor expansion of (/ 1 k) in n 218.947 * [taylor]: Taking taylor expansion of k in n 218.947 * [backup-simplify]: Simplify k into k 218.947 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 218.947 * [taylor]: Taking taylor expansion of 1/2 in n 218.947 * [backup-simplify]: Simplify 1/2 into 1/2 218.947 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 218.947 * [taylor]: Taking taylor expansion of (/ -1 n) in n 218.947 * [taylor]: Taking taylor expansion of -1 in n 218.947 * [backup-simplify]: Simplify -1 into -1 218.947 * [taylor]: Taking taylor expansion of n in n 218.947 * [backup-simplify]: Simplify 0 into 0 218.947 * [backup-simplify]: Simplify 1 into 1 218.947 * [backup-simplify]: Simplify (/ -1 1) into -1 218.948 * [backup-simplify]: Simplify (log -1) into (log -1) 218.948 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 218.948 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 218.948 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 218.948 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 218.949 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 218.949 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 218.949 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 218.949 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 218.949 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 218.949 * [taylor]: Taking taylor expansion of 1/2 in k 218.949 * [backup-simplify]: Simplify 1/2 into 1/2 218.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k 218.949 * [taylor]: Taking taylor expansion of k in k 218.949 * [backup-simplify]: Simplify 0 into 0 218.949 * [backup-simplify]: Simplify 1 into 1 218.949 * [backup-simplify]: Simplify (/ 1 1) into 1 218.949 * [taylor]: Taking taylor expansion of 1/2 in k 218.949 * [backup-simplify]: Simplify 1/2 into 1/2 218.949 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 218.949 * [taylor]: Taking taylor expansion of (log -1) in k 218.949 * [taylor]: Taking taylor expansion of -1 in k 218.949 * [backup-simplify]: Simplify -1 into -1 218.950 * [backup-simplify]: Simplify (log -1) into (log -1) 218.950 * [taylor]: Taking taylor expansion of (log n) in k 218.950 * [taylor]: Taking taylor expansion of n in k 218.950 * [backup-simplify]: Simplify n into n 218.950 * [backup-simplify]: Simplify (log n) into (log n) 218.950 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 218.950 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 218.950 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 218.951 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 218.951 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 218.951 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 218.951 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 218.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 218.953 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 218.953 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 218.953 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 218.953 * [backup-simplify]: Simplify (+ 0 0) into 0 218.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 218.954 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 218.955 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 218.955 * [taylor]: Taking taylor expansion of 0 in k 218.955 * [backup-simplify]: Simplify 0 into 0 218.955 * [backup-simplify]: Simplify 0 into 0 218.955 * [backup-simplify]: Simplify 0 into 0 218.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 218.957 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 218.957 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 218.958 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 218.958 * [backup-simplify]: Simplify (+ 0 0) into 0 218.958 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 218.959 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 218.960 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 218.960 * [taylor]: Taking taylor expansion of 0 in k 218.960 * [backup-simplify]: Simplify 0 into 0 218.960 * [backup-simplify]: Simplify 0 into 0 218.960 * [backup-simplify]: Simplify 0 into 0 218.960 * [backup-simplify]: Simplify 0 into 0 218.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 218.963 * [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 0 218.964 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 218.964 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 218.965 * [backup-simplify]: Simplify (+ 0 0) into 0 218.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 218.966 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 218.967 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 218.967 * [taylor]: Taking taylor expansion of 0 in k 218.967 * [backup-simplify]: Simplify 0 into 0 218.967 * [backup-simplify]: Simplify 0 into 0 218.967 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) 218.967 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 218.968 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 k))) into (pow PI (- 1/2 (* 1/2 k))) 218.968 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in (k) around 0 218.968 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 218.968 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 218.968 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 218.968 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 218.968 * [taylor]: Taking taylor expansion of 1/2 in k 218.968 * [backup-simplify]: Simplify 1/2 into 1/2 218.968 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 218.968 * [taylor]: Taking taylor expansion of 1/2 in k 218.968 * [backup-simplify]: Simplify 1/2 into 1/2 218.968 * [taylor]: Taking taylor expansion of k in k 218.968 * [backup-simplify]: Simplify 0 into 0 218.968 * [backup-simplify]: Simplify 1 into 1 218.968 * [taylor]: Taking taylor expansion of (log PI) in k 218.968 * [taylor]: Taking taylor expansion of PI in k 218.968 * [backup-simplify]: Simplify PI into PI 218.968 * [backup-simplify]: Simplify (log PI) into (log PI) 218.968 * [backup-simplify]: Simplify (* 1/2 0) into 0 218.969 * [backup-simplify]: Simplify (- 0) into 0 218.969 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 218.969 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 218.970 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 218.970 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 218.970 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 218.970 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 218.970 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 218.970 * [taylor]: Taking taylor expansion of 1/2 in k 218.970 * [backup-simplify]: Simplify 1/2 into 1/2 218.970 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 218.970 * [taylor]: Taking taylor expansion of 1/2 in k 218.970 * [backup-simplify]: Simplify 1/2 into 1/2 218.970 * [taylor]: Taking taylor expansion of k in k 218.970 * [backup-simplify]: Simplify 0 into 0 218.970 * [backup-simplify]: Simplify 1 into 1 218.970 * [taylor]: Taking taylor expansion of (log PI) in k 218.970 * [taylor]: Taking taylor expansion of PI in k 218.970 * [backup-simplify]: Simplify PI into PI 218.971 * [backup-simplify]: Simplify (log PI) into (log PI) 218.971 * [backup-simplify]: Simplify (* 1/2 0) into 0 218.971 * [backup-simplify]: Simplify (- 0) into 0 218.971 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 218.972 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 218.973 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 218.973 * [backup-simplify]: Simplify (pow PI 1/2) into (pow PI 1/2) 218.974 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 218.974 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 218.975 * [backup-simplify]: Simplify (- 1/2) into -1/2 218.975 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 218.976 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 218.981 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 218.982 * [backup-simplify]: Simplify (* -1/2 (* (log PI) (sqrt PI))) into (* -1/2 (* (log PI) (sqrt PI))) 218.984 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 218.985 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 218.985 * [backup-simplify]: Simplify (- 0) into 0 218.985 * [backup-simplify]: Simplify (+ 0 0) into 0 218.986 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 218.992 * [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))) 218.994 * [backup-simplify]: Simplify (* 1/8 (* (pow (log PI) 2) (sqrt PI))) into (* 1/8 (* (pow (log PI) 2) (sqrt PI))) 218.997 * [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)))) 218.997 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 218.997 * [approximate]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0 218.997 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 218.997 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 218.997 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 218.997 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 218.997 * [taylor]: Taking taylor expansion of 1/2 in k 218.997 * [backup-simplify]: Simplify 1/2 into 1/2 218.997 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 218.997 * [taylor]: Taking taylor expansion of 1/2 in k 218.997 * [backup-simplify]: Simplify 1/2 into 1/2 218.997 * [taylor]: Taking taylor expansion of (/ 1 k) in k 218.997 * [taylor]: Taking taylor expansion of k in k 218.997 * [backup-simplify]: Simplify 0 into 0 218.997 * [backup-simplify]: Simplify 1 into 1 218.997 * [backup-simplify]: Simplify (/ 1 1) into 1 218.998 * [taylor]: Taking taylor expansion of (log PI) in k 218.998 * [taylor]: Taking taylor expansion of PI in k 218.998 * [backup-simplify]: Simplify PI into PI 218.998 * [backup-simplify]: Simplify (log PI) into (log PI) 218.998 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 218.998 * [backup-simplify]: Simplify (- 1/2) into -1/2 218.999 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 218.999 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 218.999 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 218.999 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 218.999 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 218.999 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 218.999 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.000 * [taylor]: Taking taylor expansion of 1/2 in k 219.000 * [backup-simplify]: Simplify 1/2 into 1/2 219.000 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.000 * [taylor]: Taking taylor expansion of 1/2 in k 219.000 * [backup-simplify]: Simplify 1/2 into 1/2 219.000 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.000 * [taylor]: Taking taylor expansion of k in k 219.000 * [backup-simplify]: Simplify 0 into 0 219.000 * [backup-simplify]: Simplify 1 into 1 219.000 * [backup-simplify]: Simplify (/ 1 1) into 1 219.000 * [taylor]: Taking taylor expansion of (log PI) in k 219.000 * [taylor]: Taking taylor expansion of PI in k 219.000 * [backup-simplify]: Simplify PI into PI 219.000 * [backup-simplify]: Simplify (log PI) into (log PI) 219.000 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.001 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.001 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.001 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 219.002 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.002 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 k)))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow PI (- 1/2 (* 1/2 k))) 219.002 * [backup-simplify]: Simplify (pow PI (- 1/2 (* 1/2 (/ 1 (- k))))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.002 * [approximate]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0 219.002 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.002 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 219.002 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 219.002 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.002 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.002 * [taylor]: Taking taylor expansion of 1/2 in k 219.002 * [backup-simplify]: Simplify 1/2 into 1/2 219.002 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.002 * [taylor]: Taking taylor expansion of k in k 219.002 * [backup-simplify]: Simplify 0 into 0 219.002 * [backup-simplify]: Simplify 1 into 1 219.003 * [backup-simplify]: Simplify (/ 1 1) into 1 219.003 * [taylor]: Taking taylor expansion of 1/2 in k 219.003 * [backup-simplify]: Simplify 1/2 into 1/2 219.003 * [taylor]: Taking taylor expansion of (log PI) in k 219.003 * [taylor]: Taking taylor expansion of PI in k 219.003 * [backup-simplify]: Simplify PI into PI 219.003 * [backup-simplify]: Simplify (log PI) into (log PI) 219.003 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.004 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.004 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 219.004 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.004 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.004 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 219.004 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 219.004 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.004 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.004 * [taylor]: Taking taylor expansion of 1/2 in k 219.005 * [backup-simplify]: Simplify 1/2 into 1/2 219.005 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.005 * [taylor]: Taking taylor expansion of k in k 219.005 * [backup-simplify]: Simplify 0 into 0 219.005 * [backup-simplify]: Simplify 1 into 1 219.007 * [backup-simplify]: Simplify (/ 1 1) into 1 219.007 * [taylor]: Taking taylor expansion of 1/2 in k 219.007 * [backup-simplify]: Simplify 1/2 into 1/2 219.007 * [taylor]: Taking taylor expansion of (log PI) in k 219.007 * [taylor]: Taking taylor expansion of PI in k 219.007 * [backup-simplify]: Simplify PI into PI 219.008 * [backup-simplify]: Simplify (log PI) into (log PI) 219.008 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.008 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.009 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 219.009 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.009 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.009 * [backup-simplify]: Simplify 0 into 0 219.009 * [backup-simplify]: Simplify 0 into 0 219.009 * [backup-simplify]: Simplify 0 into 0 219.009 * [backup-simplify]: Simplify 0 into 0 219.009 * [backup-simplify]: Simplify 0 into 0 219.009 * [backup-simplify]: Simplify 0 into 0 219.010 * [backup-simplify]: Simplify (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow PI (- 1/2 (* 1/2 k))) 219.010 * * * * [progress]: [ 3 / 4 ] generating series at (2) 219.010 * [backup-simplify]: Simplify (* (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))) into (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) 219.010 * [approximate]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in (k n) around 0 219.010 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in n 219.010 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in n 219.010 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 219.010 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 219.010 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 219.010 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 219.010 * [taylor]: Taking taylor expansion of 1/2 in n 219.010 * [backup-simplify]: Simplify 1/2 into 1/2 219.010 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 219.010 * [taylor]: Taking taylor expansion of 1/2 in n 219.010 * [backup-simplify]: Simplify 1/2 into 1/2 219.010 * [taylor]: Taking taylor expansion of k in n 219.010 * [backup-simplify]: Simplify k into k 219.010 * [taylor]: Taking taylor expansion of (log n) in n 219.010 * [taylor]: Taking taylor expansion of n in n 219.010 * [backup-simplify]: Simplify 0 into 0 219.010 * [backup-simplify]: Simplify 1 into 1 219.010 * [backup-simplify]: Simplify (log 1) into 0 219.010 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 219.010 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 219.010 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 219.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.011 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 219.011 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 219.011 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in n 219.011 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in n 219.011 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in n 219.011 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in n 219.011 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 219.011 * [taylor]: Taking taylor expansion of 1/2 in n 219.011 * [backup-simplify]: Simplify 1/2 into 1/2 219.011 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 219.011 * [taylor]: Taking taylor expansion of 1/2 in n 219.011 * [backup-simplify]: Simplify 1/2 into 1/2 219.011 * [taylor]: Taking taylor expansion of k in n 219.011 * [backup-simplify]: Simplify k into k 219.011 * [taylor]: Taking taylor expansion of (log 2) in n 219.011 * [taylor]: Taking taylor expansion of 2 in n 219.011 * [backup-simplify]: Simplify 2 into 2 219.011 * [backup-simplify]: Simplify (log 2) into (log 2) 219.011 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 219.012 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 219.012 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 219.012 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log 2)) into (* (log 2) (- 1/2 (* 1/2 k))) 219.012 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 k)))) into (exp (* (log 2) (- 1/2 (* 1/2 k)))) 219.012 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in n 219.012 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in n 219.012 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in n 219.012 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 219.012 * [taylor]: Taking taylor expansion of 1/2 in n 219.012 * [backup-simplify]: Simplify 1/2 into 1/2 219.012 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 219.012 * [taylor]: Taking taylor expansion of 1/2 in n 219.012 * [backup-simplify]: Simplify 1/2 into 1/2 219.012 * [taylor]: Taking taylor expansion of k in n 219.012 * [backup-simplify]: Simplify k into k 219.012 * [taylor]: Taking taylor expansion of (log PI) in n 219.012 * [taylor]: Taking taylor expansion of PI in n 219.012 * [backup-simplify]: Simplify PI into PI 219.013 * [backup-simplify]: Simplify (log PI) into (log PI) 219.013 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 219.013 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 219.013 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 219.013 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log PI)) into (* (- 1/2 (* 1/2 k)) (log PI)) 219.013 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log PI))) into (pow PI (- 1/2 (* 1/2 k))) 219.013 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 219.013 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.013 * [taylor]: Taking taylor expansion of k in n 219.013 * [backup-simplify]: Simplify k into k 219.013 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.013 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 219.014 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.014 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 219.014 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in k 219.014 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 219.014 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 219.014 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 219.014 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 219.014 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.014 * [taylor]: Taking taylor expansion of 1/2 in k 219.014 * [backup-simplify]: Simplify 1/2 into 1/2 219.014 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.014 * [taylor]: Taking taylor expansion of 1/2 in k 219.014 * [backup-simplify]: Simplify 1/2 into 1/2 219.014 * [taylor]: Taking taylor expansion of k in k 219.014 * [backup-simplify]: Simplify 0 into 0 219.014 * [backup-simplify]: Simplify 1 into 1 219.014 * [taylor]: Taking taylor expansion of (log n) in k 219.014 * [taylor]: Taking taylor expansion of n in k 219.014 * [backup-simplify]: Simplify n into n 219.014 * [backup-simplify]: Simplify (log n) into (log n) 219.014 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.014 * [backup-simplify]: Simplify (- 0) into 0 219.015 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.015 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 219.015 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 219.015 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 219.015 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 219.015 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 219.015 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 219.015 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.015 * [taylor]: Taking taylor expansion of 1/2 in k 219.015 * [backup-simplify]: Simplify 1/2 into 1/2 219.015 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.015 * [taylor]: Taking taylor expansion of 1/2 in k 219.015 * [backup-simplify]: Simplify 1/2 into 1/2 219.015 * [taylor]: Taking taylor expansion of k in k 219.015 * [backup-simplify]: Simplify 0 into 0 219.015 * [backup-simplify]: Simplify 1 into 1 219.015 * [taylor]: Taking taylor expansion of (log 2) in k 219.015 * [taylor]: Taking taylor expansion of 2 in k 219.015 * [backup-simplify]: Simplify 2 into 2 219.015 * [backup-simplify]: Simplify (log 2) into (log 2) 219.016 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.016 * [backup-simplify]: Simplify (- 0) into 0 219.016 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.017 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 219.017 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 219.018 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 219.018 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 219.018 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 219.018 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.018 * [taylor]: Taking taylor expansion of 1/2 in k 219.018 * [backup-simplify]: Simplify 1/2 into 1/2 219.018 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.018 * [taylor]: Taking taylor expansion of 1/2 in k 219.018 * [backup-simplify]: Simplify 1/2 into 1/2 219.018 * [taylor]: Taking taylor expansion of k in k 219.018 * [backup-simplify]: Simplify 0 into 0 219.018 * [backup-simplify]: Simplify 1 into 1 219.018 * [taylor]: Taking taylor expansion of (log PI) in k 219.018 * [taylor]: Taking taylor expansion of PI in k 219.018 * [backup-simplify]: Simplify PI into PI 219.018 * [backup-simplify]: Simplify (log PI) into (log PI) 219.018 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.018 * [backup-simplify]: Simplify (- 0) into 0 219.019 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.019 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 219.020 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 219.020 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 219.020 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.020 * [taylor]: Taking taylor expansion of k in k 219.020 * [backup-simplify]: Simplify 0 into 0 219.020 * [backup-simplify]: Simplify 1 into 1 219.020 * [backup-simplify]: Simplify (/ 1 1) into 1 219.021 * [backup-simplify]: Simplify (sqrt 0) into 0 219.022 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.022 * [taylor]: Taking taylor expansion of (* (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) (sqrt (/ 1 k))) in k 219.022 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k))))) in k 219.022 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 219.022 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 219.022 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 219.022 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.022 * [taylor]: Taking taylor expansion of 1/2 in k 219.022 * [backup-simplify]: Simplify 1/2 into 1/2 219.022 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.022 * [taylor]: Taking taylor expansion of 1/2 in k 219.022 * [backup-simplify]: Simplify 1/2 into 1/2 219.022 * [taylor]: Taking taylor expansion of k in k 219.022 * [backup-simplify]: Simplify 0 into 0 219.022 * [backup-simplify]: Simplify 1 into 1 219.022 * [taylor]: Taking taylor expansion of (log n) in k 219.022 * [taylor]: Taking taylor expansion of n in k 219.022 * [backup-simplify]: Simplify n into n 219.022 * [backup-simplify]: Simplify (log n) into (log n) 219.022 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.022 * [backup-simplify]: Simplify (- 0) into 0 219.023 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.023 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 219.023 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 219.023 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) in k 219.023 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 k))) in k 219.023 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log 2))) in k 219.023 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log 2)) in k 219.023 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.023 * [taylor]: Taking taylor expansion of 1/2 in k 219.023 * [backup-simplify]: Simplify 1/2 into 1/2 219.023 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.023 * [taylor]: Taking taylor expansion of 1/2 in k 219.023 * [backup-simplify]: Simplify 1/2 into 1/2 219.023 * [taylor]: Taking taylor expansion of k in k 219.023 * [backup-simplify]: Simplify 0 into 0 219.023 * [backup-simplify]: Simplify 1 into 1 219.023 * [taylor]: Taking taylor expansion of (log 2) in k 219.023 * [taylor]: Taking taylor expansion of 2 in k 219.023 * [backup-simplify]: Simplify 2 into 2 219.023 * [backup-simplify]: Simplify (log 2) into (log 2) 219.024 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.024 * [backup-simplify]: Simplify (- 0) into 0 219.024 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.025 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 219.025 * [backup-simplify]: Simplify (exp (* 1/2 (log 2))) into (pow 2 1/2) 219.025 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 k))) in k 219.025 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log PI))) in k 219.026 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log PI)) in k 219.026 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.026 * [taylor]: Taking taylor expansion of 1/2 in k 219.026 * [backup-simplify]: Simplify 1/2 into 1/2 219.026 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.026 * [taylor]: Taking taylor expansion of 1/2 in k 219.026 * [backup-simplify]: Simplify 1/2 into 1/2 219.026 * [taylor]: Taking taylor expansion of k in k 219.026 * [backup-simplify]: Simplify 0 into 0 219.026 * [backup-simplify]: Simplify 1 into 1 219.026 * [taylor]: Taking taylor expansion of (log PI) in k 219.026 * [taylor]: Taking taylor expansion of PI in k 219.026 * [backup-simplify]: Simplify PI into PI 219.026 * [backup-simplify]: Simplify (log PI) into (log PI) 219.026 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.026 * [backup-simplify]: Simplify (- 0) into 0 219.027 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.027 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 219.028 * [backup-simplify]: Simplify (exp (* 1/2 (log PI))) into (pow PI 1/2) 219.028 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 219.028 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.028 * [taylor]: Taking taylor expansion of k in k 219.028 * [backup-simplify]: Simplify 0 into 0 219.028 * [backup-simplify]: Simplify 1 into 1 219.029 * [backup-simplify]: Simplify (/ 1 1) into 1 219.029 * [backup-simplify]: Simplify (sqrt 0) into 0 219.030 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.031 * [backup-simplify]: Simplify (* (pow 2 1/2) (pow PI 1/2)) into (sqrt (* PI 2)) 219.031 * [backup-simplify]: Simplify (* (pow n 1/2) (sqrt (* PI 2))) into (* (sqrt 2) (sqrt (* n PI))) 219.032 * [backup-simplify]: Simplify (* (* (sqrt 2) (sqrt (* n PI))) 0) into 0 219.032 * [taylor]: Taking taylor expansion of 0 in n 219.032 * [backup-simplify]: Simplify 0 into 0 219.032 * [backup-simplify]: Simplify 0 into 0 219.032 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 219.033 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 219.033 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.033 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.035 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log PI))) into (- (* 1/2 (log PI))) 219.039 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 1) 1)))) into (* -1/2 (* (log PI) (sqrt PI))) 219.040 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 219.041 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 219.041 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.041 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.042 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log 2))) into (- (* 1/2 (log 2))) 219.047 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 1) 1)))) into (* -1/2 (* (log 2) (sqrt 2))) 219.053 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/2 (* (log 2) (sqrt 2))) (pow PI 1/2))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI))))) 219.053 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 219.054 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 219.054 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.054 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 219.054 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 219.062 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/2 (* (sqrt n) (log n))) (sqrt (* PI 2)))) into (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 219.064 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) 219.064 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 219.064 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 219.064 * [taylor]: Taking taylor expansion of +nan.0 in n 219.064 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.064 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 219.064 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.064 * [taylor]: Taking taylor expansion of 2 in n 219.064 * [backup-simplify]: Simplify 2 into 2 219.064 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.065 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.065 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.065 * [taylor]: Taking taylor expansion of (* n PI) in n 219.065 * [taylor]: Taking taylor expansion of n in n 219.065 * [backup-simplify]: Simplify 0 into 0 219.065 * [backup-simplify]: Simplify 1 into 1 219.065 * [taylor]: Taking taylor expansion of PI in n 219.065 * [backup-simplify]: Simplify PI into PI 219.065 * [backup-simplify]: Simplify (* 0 PI) into 0 219.066 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.066 * [backup-simplify]: Simplify (sqrt 0) into 0 219.067 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.067 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 219.068 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.068 * [backup-simplify]: Simplify (- 0) into 0 219.068 * [backup-simplify]: Simplify 0 into 0 219.068 * [backup-simplify]: Simplify 0 into 0 219.068 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 219.070 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 219.072 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 219.072 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 219.073 * [backup-simplify]: Simplify (- 0) into 0 219.073 * [backup-simplify]: Simplify (+ 0 0) into 0 219.073 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log PI)))) into 0 219.080 * [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))) 219.081 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0 219.082 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 219.082 * [backup-simplify]: Simplify (- 0) into 0 219.082 * [backup-simplify]: Simplify (+ 0 0) into 0 219.083 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log 2)))) into 0 219.091 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (pow (log 2) 2) (sqrt 2))) 219.104 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (pow PI 1/2)))) into (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI))))) 219.105 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 219.106 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 219.106 * [backup-simplify]: Simplify (- 0) into 0 219.106 * [backup-simplify]: Simplify (+ 0 0) into 0 219.106 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 219.107 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 219.126 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (sqrt (* PI 2))))) into (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 219.135 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) 0))) into (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) 219.135 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))))) in n 219.135 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))))) in n 219.135 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 219.135 * [taylor]: Taking taylor expansion of +nan.0 in n 219.135 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.135 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 219.135 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 219.135 * [taylor]: Taking taylor expansion of (log 2) in n 219.135 * [taylor]: Taking taylor expansion of 2 in n 219.135 * [backup-simplify]: Simplify 2 into 2 219.135 * [backup-simplify]: Simplify (log 2) into (log 2) 219.136 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.136 * [taylor]: Taking taylor expansion of 2 in n 219.136 * [backup-simplify]: Simplify 2 into 2 219.136 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.136 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.136 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.136 * [taylor]: Taking taylor expansion of (* n PI) in n 219.136 * [taylor]: Taking taylor expansion of n in n 219.136 * [backup-simplify]: Simplify 0 into 0 219.136 * [backup-simplify]: Simplify 1 into 1 219.136 * [taylor]: Taking taylor expansion of PI in n 219.136 * [backup-simplify]: Simplify PI into PI 219.137 * [backup-simplify]: Simplify (* 0 PI) into 0 219.137 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.138 * [backup-simplify]: Simplify (sqrt 0) into 0 219.139 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.139 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))))) in n 219.139 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))))) in n 219.139 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 219.139 * [taylor]: Taking taylor expansion of +nan.0 in n 219.139 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.139 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 219.139 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 219.139 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.139 * [taylor]: Taking taylor expansion of 2 in n 219.139 * [backup-simplify]: Simplify 2 into 2 219.139 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.139 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.139 * [taylor]: Taking taylor expansion of (log PI) in n 219.139 * [taylor]: Taking taylor expansion of PI in n 219.139 * [backup-simplify]: Simplify PI into PI 219.140 * [backup-simplify]: Simplify (log PI) into (log PI) 219.140 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 219.140 * [taylor]: Taking taylor expansion of (* PI n) in n 219.140 * [taylor]: Taking taylor expansion of PI in n 219.140 * [backup-simplify]: Simplify PI into PI 219.140 * [taylor]: Taking taylor expansion of n in n 219.140 * [backup-simplify]: Simplify 0 into 0 219.140 * [backup-simplify]: Simplify 1 into 1 219.140 * [backup-simplify]: Simplify (* PI 0) into 0 219.141 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 219.141 * [backup-simplify]: Simplify (sqrt 0) into 0 219.142 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.142 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) in n 219.142 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))))) in n 219.142 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 219.142 * [taylor]: Taking taylor expansion of +nan.0 in n 219.142 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.142 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 219.142 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.142 * [taylor]: Taking taylor expansion of 2 in n 219.142 * [backup-simplify]: Simplify 2 into 2 219.142 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.143 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.143 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.143 * [taylor]: Taking taylor expansion of (* n PI) in n 219.143 * [taylor]: Taking taylor expansion of n in n 219.143 * [backup-simplify]: Simplify 0 into 0 219.143 * [backup-simplify]: Simplify 1 into 1 219.143 * [taylor]: Taking taylor expansion of PI in n 219.143 * [backup-simplify]: Simplify PI into PI 219.143 * [backup-simplify]: Simplify (* 0 PI) into 0 219.144 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.144 * [backup-simplify]: Simplify (sqrt 0) into 0 219.145 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.145 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))) in n 219.145 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n 219.145 * [taylor]: Taking taylor expansion of +nan.0 in n 219.145 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.145 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n 219.145 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log n)) in n 219.145 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.145 * [taylor]: Taking taylor expansion of 2 in n 219.145 * [backup-simplify]: Simplify 2 into 2 219.145 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.146 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.146 * [taylor]: Taking taylor expansion of (log n) in n 219.146 * [taylor]: Taking taylor expansion of n in n 219.146 * [backup-simplify]: Simplify 0 into 0 219.146 * [backup-simplify]: Simplify 1 into 1 219.146 * [backup-simplify]: Simplify (log 1) into 0 219.146 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.146 * [taylor]: Taking taylor expansion of (* n PI) in n 219.146 * [taylor]: Taking taylor expansion of n in n 219.146 * [backup-simplify]: Simplify 0 into 0 219.146 * [backup-simplify]: Simplify 1 into 1 219.146 * [taylor]: Taking taylor expansion of PI in n 219.146 * [backup-simplify]: Simplify PI into PI 219.146 * [backup-simplify]: Simplify (* 0 PI) into 0 219.147 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.148 * [backup-simplify]: Simplify (sqrt 0) into 0 219.148 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.149 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 219.149 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 219.150 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.151 * [backup-simplify]: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 219.151 * [backup-simplify]: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 219.151 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.152 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 219.152 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.152 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.152 * [backup-simplify]: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 219.153 * [backup-simplify]: Simplify (* (* (sqrt 2) (log n)) 0) into 0 219.153 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.153 * [backup-simplify]: Simplify (- 0) into 0 219.153 * [backup-simplify]: Simplify (+ 0 0) into 0 219.154 * [backup-simplify]: Simplify (- 0) into 0 219.154 * [backup-simplify]: Simplify (+ 0 0) into 0 219.154 * [backup-simplify]: Simplify (- 0) into 0 219.154 * [backup-simplify]: Simplify (+ 0 0) into 0 219.155 * [backup-simplify]: Simplify (- 0) into 0 219.155 * [backup-simplify]: Simplify 0 into 0 219.156 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 219.159 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 219.161 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 219.162 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 219.162 * [backup-simplify]: Simplify 0 into 0 219.166 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.168 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 219.171 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow PI 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow PI 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow PI 1)))) 6) into 0 219.172 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 219.172 * [backup-simplify]: Simplify (- 0) into 0 219.172 * [backup-simplify]: Simplify (+ 0 0) into 0 219.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log PI))))) into 0 219.181 * [backup-simplify]: Simplify (* (exp (* 1/2 (log PI))) (+ (* (/ (pow (- (* 1/2 (log PI))) 3) 6)) (* (/ (pow (- (* 1/2 (log PI))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log PI) 3) (sqrt PI))) 219.183 * [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 0 219.184 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 219.184 * [backup-simplify]: Simplify (- 0) into 0 219.185 * [backup-simplify]: Simplify (+ 0 0) into 0 219.185 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log 2))))) into 0 219.193 * [backup-simplify]: Simplify (* (exp (* 1/2 (log 2))) (+ (* (/ (pow (- (* 1/2 (log 2))) 3) 6)) (* (/ (pow (- (* 1/2 (log 2))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (pow (log 2) 3) (sqrt 2))) 219.215 * [backup-simplify]: Simplify (+ (* (pow 2 1/2) (* -1/48 (* (pow (log PI) 3) (sqrt PI)))) (+ (* (* -1/2 (* (log 2) (sqrt 2))) (* 1/8 (* (pow (log PI) 2) (sqrt PI)))) (+ (* (* 1/8 (* (pow (log 2) 2) (sqrt 2))) (* -1/2 (* (log PI) (sqrt PI)))) (* (* -1/48 (* (pow (log 2) 3) (sqrt 2))) (pow PI 1/2))))) into (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI))))))) 219.217 * [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 0 219.218 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 219.218 * [backup-simplify]: Simplify (- 0) into 0 219.218 * [backup-simplify]: Simplify (+ 0 0) into 0 219.219 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 219.220 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 219.266 * [backup-simplify]: Simplify (+ (* (pow n 1/2) (- (+ (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt PI))) (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt PI))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt PI))) (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt PI)))))))) (+ (* (* -1/2 (* (sqrt n) (log n))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt PI))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt PI))) (* 1/8 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt PI)))))) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt PI))) (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt PI)))))) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) (sqrt (* PI 2)))))) into (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 219.289 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (sqrt (* n PI))) +nan.0) (+ (* (- (+ (* 1/2 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/2 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (* 1/2 (* (* (sqrt 2) (log n)) (sqrt (* n PI))))))) +nan.0) (+ (* (+ (* 1/8 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/8 (* (sqrt (* PI n)) (* (sqrt 2) (pow (log PI) 2)))) (+ (* 1/4 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (* 1/4 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))))))))) +nan.0) (* (- (+ (* 1/48 (* (* (pow (log 2) 3) (sqrt 2)) (sqrt (* n PI)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log n) 2))) (sqrt (* n PI)))) (+ (* 1/16 (* (* (sqrt 2) (* (log PI) (pow (log n) 2))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (log 2) (* (sqrt 2) (pow (log PI) 2))) (sqrt (* PI n)))) (+ (* 1/48 (* (* (sqrt 2) (pow (log n) 3)) (sqrt (* n PI)))) (+ (* 1/8 (* (* (log 2) (* (sqrt 2) (* (log PI) (log n)))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (pow (log 2) 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (+ (* 1/16 (* (* (sqrt 2) (* (pow (log PI) 2) (log n))) (sqrt (* PI n)))) (* 1/48 (* (* (sqrt 2) (pow (log PI) 3)) (sqrt (* PI n)))))))))))))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) 219.289 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))))) in n 219.289 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))))) in n 219.289 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI)))) in n 219.289 * [taylor]: Taking taylor expansion of +nan.0 in n 219.289 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.289 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log n) 2)) (sqrt (* n PI))) in n 219.289 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log n) 2)) in n 219.289 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.289 * [taylor]: Taking taylor expansion of 2 in n 219.289 * [backup-simplify]: Simplify 2 into 2 219.290 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.290 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.290 * [taylor]: Taking taylor expansion of (pow (log n) 2) in n 219.290 * [taylor]: Taking taylor expansion of (log n) in n 219.290 * [taylor]: Taking taylor expansion of n in n 219.290 * [backup-simplify]: Simplify 0 into 0 219.290 * [backup-simplify]: Simplify 1 into 1 219.290 * [backup-simplify]: Simplify (log 1) into 0 219.291 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.291 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.291 * [taylor]: Taking taylor expansion of (* n PI) in n 219.291 * [taylor]: Taking taylor expansion of n in n 219.291 * [backup-simplify]: Simplify 0 into 0 219.291 * [backup-simplify]: Simplify 1 into 1 219.291 * [taylor]: Taking taylor expansion of PI in n 219.291 * [backup-simplify]: Simplify PI into PI 219.291 * [backup-simplify]: Simplify (* 0 PI) into 0 219.292 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.292 * [backup-simplify]: Simplify (sqrt 0) into 0 219.293 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.293 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))))) in n 219.293 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))))) in n 219.293 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n)))) in n 219.293 * [taylor]: Taking taylor expansion of +nan.0 in n 219.293 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.293 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log PI) 2)) (sqrt (* PI n))) in n 219.293 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log PI) 2)) in n 219.293 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.293 * [taylor]: Taking taylor expansion of 2 in n 219.293 * [backup-simplify]: Simplify 2 into 2 219.293 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.294 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.294 * [taylor]: Taking taylor expansion of (pow (log PI) 2) in n 219.294 * [taylor]: Taking taylor expansion of (log PI) in n 219.294 * [taylor]: Taking taylor expansion of PI in n 219.294 * [backup-simplify]: Simplify PI into PI 219.294 * [backup-simplify]: Simplify (log PI) into (log PI) 219.294 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 219.294 * [taylor]: Taking taylor expansion of (* PI n) in n 219.294 * [taylor]: Taking taylor expansion of PI in n 219.294 * [backup-simplify]: Simplify PI into PI 219.294 * [taylor]: Taking taylor expansion of n in n 219.294 * [backup-simplify]: Simplify 0 into 0 219.294 * [backup-simplify]: Simplify 1 into 1 219.295 * [backup-simplify]: Simplify (* PI 0) into 0 219.295 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 219.296 * [backup-simplify]: Simplify (sqrt 0) into 0 219.296 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.296 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))))) in n 219.296 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))))) in n 219.296 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI)))) in n 219.297 * [taylor]: Taking taylor expansion of +nan.0 in n 219.297 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.297 * [taylor]: Taking taylor expansion of (* (* (pow (log 2) 2) (sqrt 2)) (sqrt (* n PI))) in n 219.297 * [taylor]: Taking taylor expansion of (* (pow (log 2) 2) (sqrt 2)) in n 219.297 * [taylor]: Taking taylor expansion of (pow (log 2) 2) in n 219.297 * [taylor]: Taking taylor expansion of (log 2) in n 219.297 * [taylor]: Taking taylor expansion of 2 in n 219.297 * [backup-simplify]: Simplify 2 into 2 219.297 * [backup-simplify]: Simplify (log 2) into (log 2) 219.297 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.297 * [taylor]: Taking taylor expansion of 2 in n 219.297 * [backup-simplify]: Simplify 2 into 2 219.297 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.298 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.298 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.298 * [taylor]: Taking taylor expansion of (* n PI) in n 219.298 * [taylor]: Taking taylor expansion of n in n 219.298 * [backup-simplify]: Simplify 0 into 0 219.298 * [backup-simplify]: Simplify 1 into 1 219.298 * [taylor]: Taking taylor expansion of PI in n 219.298 * [backup-simplify]: Simplify PI into PI 219.298 * [backup-simplify]: Simplify (* 0 PI) into 0 219.299 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.299 * [backup-simplify]: Simplify (sqrt 0) into 0 219.300 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.300 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))))) in n 219.300 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))))) in n 219.300 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 219.300 * [taylor]: Taking taylor expansion of +nan.0 in n 219.300 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.300 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 219.300 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.300 * [taylor]: Taking taylor expansion of 2 in n 219.300 * [backup-simplify]: Simplify 2 into 2 219.300 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.301 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.301 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.301 * [taylor]: Taking taylor expansion of (* n PI) in n 219.301 * [taylor]: Taking taylor expansion of n in n 219.301 * [backup-simplify]: Simplify 0 into 0 219.301 * [backup-simplify]: Simplify 1 into 1 219.301 * [taylor]: Taking taylor expansion of PI in n 219.301 * [backup-simplify]: Simplify PI into PI 219.301 * [backup-simplify]: Simplify (* 0 PI) into 0 219.302 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.302 * [backup-simplify]: Simplify (sqrt 0) into 0 219.303 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.303 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))))) in n 219.303 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))))) in n 219.303 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log n)) (sqrt (* n PI)))) in n 219.303 * [taylor]: Taking taylor expansion of +nan.0 in n 219.303 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.303 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log n)) (sqrt (* n PI))) in n 219.303 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log n)) in n 219.303 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.303 * [taylor]: Taking taylor expansion of 2 in n 219.303 * [backup-simplify]: Simplify 2 into 2 219.303 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.304 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.304 * [taylor]: Taking taylor expansion of (log n) in n 219.304 * [taylor]: Taking taylor expansion of n in n 219.304 * [backup-simplify]: Simplify 0 into 0 219.304 * [backup-simplify]: Simplify 1 into 1 219.304 * [backup-simplify]: Simplify (log 1) into 0 219.304 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.304 * [taylor]: Taking taylor expansion of (* n PI) in n 219.304 * [taylor]: Taking taylor expansion of n in n 219.304 * [backup-simplify]: Simplify 0 into 0 219.304 * [backup-simplify]: Simplify 1 into 1 219.304 * [taylor]: Taking taylor expansion of PI in n 219.304 * [backup-simplify]: Simplify PI into PI 219.304 * [backup-simplify]: Simplify (* 0 PI) into 0 219.305 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.305 * [backup-simplify]: Simplify (sqrt 0) into 0 219.306 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.306 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))))) in n 219.306 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))))) in n 219.306 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log PI)) (sqrt (* PI n)))) in n 219.306 * [taylor]: Taking taylor expansion of +nan.0 in n 219.306 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.306 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log PI)) (sqrt (* PI n))) in n 219.306 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 219.306 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.306 * [taylor]: Taking taylor expansion of 2 in n 219.306 * [backup-simplify]: Simplify 2 into 2 219.307 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.307 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.307 * [taylor]: Taking taylor expansion of (log PI) in n 219.307 * [taylor]: Taking taylor expansion of PI in n 219.307 * [backup-simplify]: Simplify PI into PI 219.307 * [backup-simplify]: Simplify (log PI) into (log PI) 219.307 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 219.307 * [taylor]: Taking taylor expansion of (* PI n) in n 219.307 * [taylor]: Taking taylor expansion of PI in n 219.307 * [backup-simplify]: Simplify PI into PI 219.307 * [taylor]: Taking taylor expansion of n in n 219.307 * [backup-simplify]: Simplify 0 into 0 219.307 * [backup-simplify]: Simplify 1 into 1 219.308 * [backup-simplify]: Simplify (* PI 0) into 0 219.309 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 219.309 * [backup-simplify]: Simplify (sqrt 0) into 0 219.310 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.310 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))))) in n 219.310 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))))) in n 219.310 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n)))) in n 219.310 * [taylor]: Taking taylor expansion of +nan.0 in n 219.310 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.310 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log PI) (log n))) (sqrt (* PI n))) in n 219.310 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log PI) (log n))) in n 219.310 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.310 * [taylor]: Taking taylor expansion of 2 in n 219.310 * [backup-simplify]: Simplify 2 into 2 219.310 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.310 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.310 * [taylor]: Taking taylor expansion of (* (log PI) (log n)) in n 219.310 * [taylor]: Taking taylor expansion of (log PI) in n 219.310 * [taylor]: Taking taylor expansion of PI in n 219.310 * [backup-simplify]: Simplify PI into PI 219.311 * [backup-simplify]: Simplify (log PI) into (log PI) 219.311 * [taylor]: Taking taylor expansion of (log n) in n 219.311 * [taylor]: Taking taylor expansion of n in n 219.311 * [backup-simplify]: Simplify 0 into 0 219.311 * [backup-simplify]: Simplify 1 into 1 219.311 * [backup-simplify]: Simplify (log 1) into 0 219.311 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 219.311 * [taylor]: Taking taylor expansion of (* PI n) in n 219.311 * [taylor]: Taking taylor expansion of PI in n 219.311 * [backup-simplify]: Simplify PI into PI 219.311 * [taylor]: Taking taylor expansion of n in n 219.311 * [backup-simplify]: Simplify 0 into 0 219.311 * [backup-simplify]: Simplify 1 into 1 219.311 * [backup-simplify]: Simplify (* PI 0) into 0 219.312 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 219.312 * [backup-simplify]: Simplify (sqrt 0) into 0 219.313 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.313 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))))) in n 219.313 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))))) in n 219.313 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI)))) in n 219.313 * [taylor]: Taking taylor expansion of +nan.0 in n 219.313 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.313 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log n))) (sqrt (* n PI))) in n 219.313 * [taylor]: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log n))) in n 219.313 * [taylor]: Taking taylor expansion of (log 2) in n 219.313 * [taylor]: Taking taylor expansion of 2 in n 219.313 * [backup-simplify]: Simplify 2 into 2 219.314 * [backup-simplify]: Simplify (log 2) into (log 2) 219.314 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log n)) in n 219.314 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.314 * [taylor]: Taking taylor expansion of 2 in n 219.314 * [backup-simplify]: Simplify 2 into 2 219.314 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.314 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.314 * [taylor]: Taking taylor expansion of (log n) in n 219.314 * [taylor]: Taking taylor expansion of n in n 219.314 * [backup-simplify]: Simplify 0 into 0 219.314 * [backup-simplify]: Simplify 1 into 1 219.315 * [backup-simplify]: Simplify (log 1) into 0 219.315 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.315 * [taylor]: Taking taylor expansion of (* n PI) in n 219.315 * [taylor]: Taking taylor expansion of n in n 219.315 * [backup-simplify]: Simplify 0 into 0 219.315 * [backup-simplify]: Simplify 1 into 1 219.315 * [taylor]: Taking taylor expansion of PI in n 219.315 * [backup-simplify]: Simplify PI into PI 219.315 * [backup-simplify]: Simplify (* 0 PI) into 0 219.316 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.316 * [backup-simplify]: Simplify (sqrt 0) into 0 219.317 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.317 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))))) in n 219.317 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))))) in n 219.317 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n)))) in n 219.317 * [taylor]: Taking taylor expansion of +nan.0 in n 219.317 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.317 * [taylor]: Taking taylor expansion of (* (* (log 2) (* (sqrt 2) (log PI))) (sqrt (* PI n))) in n 219.317 * [taylor]: Taking taylor expansion of (* (log 2) (* (sqrt 2) (log PI))) in n 219.317 * [taylor]: Taking taylor expansion of (log 2) in n 219.317 * [taylor]: Taking taylor expansion of 2 in n 219.317 * [backup-simplify]: Simplify 2 into 2 219.320 * [backup-simplify]: Simplify (log 2) into (log 2) 219.320 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log PI)) in n 219.320 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.320 * [taylor]: Taking taylor expansion of 2 in n 219.320 * [backup-simplify]: Simplify 2 into 2 219.320 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.321 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.321 * [taylor]: Taking taylor expansion of (log PI) in n 219.321 * [taylor]: Taking taylor expansion of PI in n 219.321 * [backup-simplify]: Simplify PI into PI 219.321 * [backup-simplify]: Simplify (log PI) into (log PI) 219.321 * [taylor]: Taking taylor expansion of (sqrt (* PI n)) in n 219.321 * [taylor]: Taking taylor expansion of (* PI n) in n 219.321 * [taylor]: Taking taylor expansion of PI in n 219.321 * [backup-simplify]: Simplify PI into PI 219.321 * [taylor]: Taking taylor expansion of n in n 219.321 * [backup-simplify]: Simplify 0 into 0 219.321 * [backup-simplify]: Simplify 1 into 1 219.321 * [backup-simplify]: Simplify (* PI 0) into 0 219.322 * [backup-simplify]: Simplify (+ (* PI 1) (* 0 0)) into PI 219.322 * [backup-simplify]: Simplify (sqrt 0) into 0 219.323 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.323 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI))))) in n 219.323 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log 2) (sqrt 2)) (sqrt (* n PI)))) in n 219.323 * [taylor]: Taking taylor expansion of +nan.0 in n 219.323 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.323 * [taylor]: Taking taylor expansion of (* (* (log 2) (sqrt 2)) (sqrt (* n PI))) in n 219.323 * [taylor]: Taking taylor expansion of (* (log 2) (sqrt 2)) in n 219.323 * [taylor]: Taking taylor expansion of (log 2) in n 219.323 * [taylor]: Taking taylor expansion of 2 in n 219.323 * [backup-simplify]: Simplify 2 into 2 219.324 * [backup-simplify]: Simplify (log 2) into (log 2) 219.324 * [taylor]: Taking taylor expansion of (sqrt 2) in n 219.324 * [taylor]: Taking taylor expansion of 2 in n 219.324 * [backup-simplify]: Simplify 2 into 2 219.324 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 219.324 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 219.324 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 219.324 * [taylor]: Taking taylor expansion of (* n PI) in n 219.324 * [taylor]: Taking taylor expansion of n in n 219.324 * [backup-simplify]: Simplify 0 into 0 219.324 * [backup-simplify]: Simplify 1 into 1 219.324 * [taylor]: Taking taylor expansion of PI in n 219.324 * [backup-simplify]: Simplify PI into PI 219.325 * [backup-simplify]: Simplify (* 0 PI) into 0 219.326 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 219.326 * [backup-simplify]: Simplify (sqrt 0) into 0 219.327 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 219.327 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.327 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.327 * [backup-simplify]: Simplify (* (log n) (log n)) into (pow (log n) 2) 219.327 * [backup-simplify]: Simplify (* (sqrt 2) (pow (log n) 2)) into (* (sqrt 2) (pow (log n) 2)) 219.328 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (log n) 2)) 0) into 0 219.328 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.329 * [backup-simplify]: Simplify (* (log PI) (log PI)) into (pow (log PI) 2) 219.330 * [backup-simplify]: Simplify (* (sqrt 2) (pow (log PI) 2)) into (* (sqrt 2) (pow (log PI) 2)) 219.331 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (log PI) 2)) 0) into 0 219.331 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.332 * [backup-simplify]: Simplify (* (log 2) (log 2)) into (pow (log 2) 2) 219.333 * [backup-simplify]: Simplify (* (pow (log 2) 2) (sqrt 2)) into (* (pow (log 2) 2) (sqrt 2)) 219.333 * [backup-simplify]: Simplify (* (* (pow (log 2) 2) (sqrt 2)) 0) into 0 219.334 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.334 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 219.334 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.334 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.335 * [backup-simplify]: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 219.335 * [backup-simplify]: Simplify (* (* (sqrt 2) (log n)) 0) into 0 219.335 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.336 * [backup-simplify]: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 219.336 * [backup-simplify]: Simplify (* (* (sqrt 2) (log PI)) 0) into 0 219.337 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.337 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.337 * [backup-simplify]: Simplify (* (log PI) (log n)) into (* (log PI) (log n)) 219.338 * [backup-simplify]: Simplify (* (sqrt 2) (* (log PI) (log n))) into (* (sqrt 2) (* (log PI) (log n))) 219.338 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (log PI) (log n))) 0) into 0 219.339 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.339 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.339 * [backup-simplify]: Simplify (* (sqrt 2) (log n)) into (* (sqrt 2) (log n)) 219.340 * [backup-simplify]: Simplify (* (log 2) (* (sqrt 2) (log n))) into (* (log 2) (* (sqrt 2) (log n))) 219.340 * [backup-simplify]: Simplify (* (* (log 2) (* (sqrt 2) (log n))) 0) into 0 219.340 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.341 * [backup-simplify]: Simplify (* (sqrt 2) (log PI)) into (* (sqrt 2) (log PI)) 219.343 * [backup-simplify]: Simplify (* (log 2) (* (sqrt 2) (log PI))) into (* (log 2) (* (sqrt 2) (log PI))) 219.343 * [backup-simplify]: Simplify (* (* (log 2) (* (sqrt 2) (log PI))) 0) into 0 219.344 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.344 * [backup-simplify]: Simplify (* (log 2) (sqrt 2)) into (* (log 2) (sqrt 2)) 219.345 * [backup-simplify]: Simplify (* (* (log 2) (sqrt 2)) 0) into 0 219.345 * [backup-simplify]: Simplify (* +nan.0 0) into 0 219.345 * [backup-simplify]: Simplify (- 0) into 0 219.345 * [backup-simplify]: Simplify (+ 0 0) into 0 219.346 * [backup-simplify]: Simplify (- 0) into 0 219.346 * [backup-simplify]: Simplify (+ 0 0) into 0 219.346 * [backup-simplify]: Simplify (- 0) into 0 219.346 * [backup-simplify]: Simplify (+ 0 0) into 0 219.347 * [backup-simplify]: Simplify (- 0) into 0 219.347 * [backup-simplify]: Simplify (+ 0 0) into 0 219.347 * [backup-simplify]: Simplify (- 0) into 0 219.347 * [backup-simplify]: Simplify (+ 0 0) into 0 219.348 * [backup-simplify]: Simplify (- 0) into 0 219.348 * [backup-simplify]: Simplify (+ 0 0) into 0 219.348 * [backup-simplify]: Simplify (- 0) into 0 219.348 * [backup-simplify]: Simplify (+ 0 0) into 0 219.348 * [backup-simplify]: Simplify (- 0) into 0 219.349 * [backup-simplify]: Simplify (+ 0 0) into 0 219.349 * [backup-simplify]: Simplify (- 0) into 0 219.349 * [backup-simplify]: Simplify (+ 0 0) into 0 219.349 * [backup-simplify]: Simplify (- 0) into 0 219.349 * [backup-simplify]: Simplify 0 into 0 219.350 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 219.351 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (sqrt 2))) into 0 219.353 * [backup-simplify]: Simplify (+ (* (* (log 2) (sqrt 2)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 219.357 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (log 2) (* (sqrt 2) PI))))) (* 0 0)) into (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) 219.358 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 219.359 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (log PI))) into 0 219.361 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (log PI)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 219.365 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* (log PI) PI))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) 219.367 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 219.370 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 219.370 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 219.371 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.371 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (log n))) into 0 219.372 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (log n)) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 219.372 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 219.373 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (* +nan.0 (* (sqrt 2) (* PI (log n))))) 219.374 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) (* PI (log n)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) 219.376 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))) 219.380 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (sqrt 2) (* (log PI) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 219.386 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))) 219.393 * [backup-simplify]: Simplify (+ (- (* +nan.0 (* (log 2) (* (sqrt 2) PI)))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 219.406 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI)))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 219.416 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) 219.417 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 219.419 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 219.420 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 219.422 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 219.427 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 219.429 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 219.431 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 219.445 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (+ (* +nan.0 (* (sqrt 2) (* (log PI) PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) PI))) (- (* +nan.0 (* (sqrt 2) PI))))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log 2) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log PI) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))) 219.445 * [backup-simplify]: Simplify (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) (/ (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k)))) into (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) 219.445 * [approximate]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in (k n) around 0 219.445 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in n 219.445 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 219.445 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in n 219.445 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in n 219.445 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in n 219.445 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.445 * [taylor]: Taking taylor expansion of 1/2 in n 219.445 * [backup-simplify]: Simplify 1/2 into 1/2 219.445 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.445 * [taylor]: Taking taylor expansion of 1/2 in n 219.445 * [backup-simplify]: Simplify 1/2 into 1/2 219.445 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.445 * [taylor]: Taking taylor expansion of k in n 219.445 * [backup-simplify]: Simplify k into k 219.445 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.445 * [taylor]: Taking taylor expansion of (log 2) in n 219.445 * [taylor]: Taking taylor expansion of 2 in n 219.445 * [backup-simplify]: Simplify 2 into 2 219.445 * [backup-simplify]: Simplify (log 2) into (log 2) 219.446 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.446 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.446 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.446 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 219.446 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 219.446 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.446 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 219.446 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 219.446 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 219.446 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.446 * [taylor]: Taking taylor expansion of 1/2 in n 219.446 * [backup-simplify]: Simplify 1/2 into 1/2 219.446 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.446 * [taylor]: Taking taylor expansion of 1/2 in n 219.446 * [backup-simplify]: Simplify 1/2 into 1/2 219.446 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.446 * [taylor]: Taking taylor expansion of k in n 219.447 * [backup-simplify]: Simplify k into k 219.447 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.447 * [taylor]: Taking taylor expansion of (log PI) in n 219.447 * [taylor]: Taking taylor expansion of PI in n 219.447 * [backup-simplify]: Simplify PI into PI 219.447 * [backup-simplify]: Simplify (log PI) into (log PI) 219.447 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.447 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.447 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.447 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 219.448 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.448 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.448 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 219.448 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 219.448 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.448 * [taylor]: Taking taylor expansion of 1/2 in n 219.448 * [backup-simplify]: Simplify 1/2 into 1/2 219.448 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.448 * [taylor]: Taking taylor expansion of 1/2 in n 219.448 * [backup-simplify]: Simplify 1/2 into 1/2 219.448 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.448 * [taylor]: Taking taylor expansion of k in n 219.448 * [backup-simplify]: Simplify k into k 219.448 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.448 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 219.448 * [taylor]: Taking taylor expansion of (/ 1 n) in n 219.448 * [taylor]: Taking taylor expansion of n in n 219.448 * [backup-simplify]: Simplify 0 into 0 219.448 * [backup-simplify]: Simplify 1 into 1 219.448 * [backup-simplify]: Simplify (/ 1 1) into 1 219.448 * [backup-simplify]: Simplify (log 1) into 0 219.448 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.448 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.449 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.449 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 219.449 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.449 * [taylor]: Taking taylor expansion of (sqrt k) in n 219.449 * [taylor]: Taking taylor expansion of k in n 219.449 * [backup-simplify]: Simplify k into k 219.449 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 219.449 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 219.449 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in k 219.449 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 219.449 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 219.449 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 219.449 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 219.449 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.449 * [taylor]: Taking taylor expansion of 1/2 in k 219.449 * [backup-simplify]: Simplify 1/2 into 1/2 219.449 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.449 * [taylor]: Taking taylor expansion of 1/2 in k 219.449 * [backup-simplify]: Simplify 1/2 into 1/2 219.449 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.449 * [taylor]: Taking taylor expansion of k in k 219.449 * [backup-simplify]: Simplify 0 into 0 219.449 * [backup-simplify]: Simplify 1 into 1 219.450 * [backup-simplify]: Simplify (/ 1 1) into 1 219.450 * [taylor]: Taking taylor expansion of (log 2) in k 219.450 * [taylor]: Taking taylor expansion of 2 in k 219.450 * [backup-simplify]: Simplify 2 into 2 219.450 * [backup-simplify]: Simplify (log 2) into (log 2) 219.450 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.450 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.451 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.451 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 219.452 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 219.452 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 219.452 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 219.452 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 219.452 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 219.452 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.452 * [taylor]: Taking taylor expansion of 1/2 in k 219.452 * [backup-simplify]: Simplify 1/2 into 1/2 219.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.452 * [taylor]: Taking taylor expansion of 1/2 in k 219.452 * [backup-simplify]: Simplify 1/2 into 1/2 219.452 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.452 * [taylor]: Taking taylor expansion of k in k 219.452 * [backup-simplify]: Simplify 0 into 0 219.452 * [backup-simplify]: Simplify 1 into 1 219.452 * [backup-simplify]: Simplify (/ 1 1) into 1 219.452 * [taylor]: Taking taylor expansion of (log PI) in k 219.452 * [taylor]: Taking taylor expansion of PI in k 219.452 * [backup-simplify]: Simplify PI into PI 219.452 * [backup-simplify]: Simplify (log PI) into (log PI) 219.453 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.453 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.453 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.454 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 219.454 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.454 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 219.454 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 219.454 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 219.454 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.454 * [taylor]: Taking taylor expansion of 1/2 in k 219.454 * [backup-simplify]: Simplify 1/2 into 1/2 219.454 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.454 * [taylor]: Taking taylor expansion of 1/2 in k 219.454 * [backup-simplify]: Simplify 1/2 into 1/2 219.454 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.454 * [taylor]: Taking taylor expansion of k in k 219.454 * [backup-simplify]: Simplify 0 into 0 219.454 * [backup-simplify]: Simplify 1 into 1 219.454 * [backup-simplify]: Simplify (/ 1 1) into 1 219.454 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 219.454 * [taylor]: Taking taylor expansion of (/ 1 n) in k 219.454 * [taylor]: Taking taylor expansion of n in k 219.454 * [backup-simplify]: Simplify n into n 219.455 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 219.455 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 219.455 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.455 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.455 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.455 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 219.455 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 219.456 * [taylor]: Taking taylor expansion of (sqrt k) in k 219.456 * [taylor]: Taking taylor expansion of k in k 219.456 * [backup-simplify]: Simplify 0 into 0 219.456 * [backup-simplify]: Simplify 1 into 1 219.456 * [backup-simplify]: Simplify (sqrt 0) into 0 219.457 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.457 * [taylor]: Taking taylor expansion of (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) (sqrt k)) in k 219.457 * [taylor]: Taking taylor expansion of (* (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in k 219.457 * [taylor]: Taking taylor expansion of (pow 2 (- 1/2 (* 1/2 (/ 1 k)))) in k 219.457 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) in k 219.457 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log 2)) in k 219.457 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.457 * [taylor]: Taking taylor expansion of 1/2 in k 219.457 * [backup-simplify]: Simplify 1/2 into 1/2 219.457 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.457 * [taylor]: Taking taylor expansion of 1/2 in k 219.457 * [backup-simplify]: Simplify 1/2 into 1/2 219.457 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.457 * [taylor]: Taking taylor expansion of k in k 219.457 * [backup-simplify]: Simplify 0 into 0 219.457 * [backup-simplify]: Simplify 1 into 1 219.457 * [backup-simplify]: Simplify (/ 1 1) into 1 219.457 * [taylor]: Taking taylor expansion of (log 2) in k 219.457 * [taylor]: Taking taylor expansion of 2 in k 219.457 * [backup-simplify]: Simplify 2 into 2 219.457 * [backup-simplify]: Simplify (log 2) into (log 2) 219.458 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.458 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.458 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.459 * [backup-simplify]: Simplify (* -1/2 (log 2)) into (* -1/2 (log 2)) 219.459 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log 2))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 219.459 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in k 219.459 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in k 219.459 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in k 219.459 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in k 219.459 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.459 * [taylor]: Taking taylor expansion of 1/2 in k 219.459 * [backup-simplify]: Simplify 1/2 into 1/2 219.459 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.459 * [taylor]: Taking taylor expansion of 1/2 in k 219.459 * [backup-simplify]: Simplify 1/2 into 1/2 219.459 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.459 * [taylor]: Taking taylor expansion of k in k 219.459 * [backup-simplify]: Simplify 0 into 0 219.459 * [backup-simplify]: Simplify 1 into 1 219.460 * [backup-simplify]: Simplify (/ 1 1) into 1 219.460 * [taylor]: Taking taylor expansion of (log PI) in k 219.460 * [taylor]: Taking taylor expansion of PI in k 219.460 * [backup-simplify]: Simplify PI into PI 219.460 * [backup-simplify]: Simplify (log PI) into (log PI) 219.460 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.460 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.461 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.461 * [backup-simplify]: Simplify (* -1/2 (log PI)) into (* -1/2 (log PI)) 219.461 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.461 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 219.462 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 219.462 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 219.462 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.462 * [taylor]: Taking taylor expansion of 1/2 in k 219.462 * [backup-simplify]: Simplify 1/2 into 1/2 219.462 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.462 * [taylor]: Taking taylor expansion of 1/2 in k 219.462 * [backup-simplify]: Simplify 1/2 into 1/2 219.462 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.462 * [taylor]: Taking taylor expansion of k in k 219.462 * [backup-simplify]: Simplify 0 into 0 219.462 * [backup-simplify]: Simplify 1 into 1 219.462 * [backup-simplify]: Simplify (/ 1 1) into 1 219.462 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 219.462 * [taylor]: Taking taylor expansion of (/ 1 n) in k 219.462 * [taylor]: Taking taylor expansion of n in k 219.462 * [backup-simplify]: Simplify n into n 219.462 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 219.462 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 219.462 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.463 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.463 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.463 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 219.463 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 219.463 * [taylor]: Taking taylor expansion of (sqrt k) in k 219.463 * [taylor]: Taking taylor expansion of k in k 219.463 * [backup-simplify]: Simplify 0 into 0 219.463 * [backup-simplify]: Simplify 1 into 1 219.463 * [backup-simplify]: Simplify (sqrt 0) into 0 219.464 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.464 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) into (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) 219.465 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 219.465 * [backup-simplify]: Simplify (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) 0) into 0 219.465 * [taylor]: Taking taylor expansion of 0 in n 219.465 * [backup-simplify]: Simplify 0 into 0 219.465 * [backup-simplify]: Simplify 0 into 0 219.465 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) into 0 219.466 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 219.466 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 219.467 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 219.467 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 219.467 * [taylor]: Taking taylor expansion of +nan.0 in n 219.467 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.467 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 219.467 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.467 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.467 * [taylor]: Taking taylor expansion of (log 2) in n 219.467 * [taylor]: Taking taylor expansion of 2 in n 219.467 * [backup-simplify]: Simplify 2 into 2 219.467 * [backup-simplify]: Simplify (log 2) into (log 2) 219.467 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.467 * [taylor]: Taking taylor expansion of 1/2 in n 219.467 * [backup-simplify]: Simplify 1/2 into 1/2 219.467 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.467 * [taylor]: Taking taylor expansion of 1/2 in n 219.467 * [backup-simplify]: Simplify 1/2 into 1/2 219.467 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.467 * [taylor]: Taking taylor expansion of k in n 219.467 * [backup-simplify]: Simplify k into k 219.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.467 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.467 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.467 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.468 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 219.468 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 219.468 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.468 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 219.468 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 219.468 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 219.468 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.468 * [taylor]: Taking taylor expansion of 1/2 in n 219.468 * [backup-simplify]: Simplify 1/2 into 1/2 219.468 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.468 * [taylor]: Taking taylor expansion of 1/2 in n 219.468 * [backup-simplify]: Simplify 1/2 into 1/2 219.468 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.468 * [taylor]: Taking taylor expansion of k in n 219.468 * [backup-simplify]: Simplify k into k 219.468 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.468 * [taylor]: Taking taylor expansion of (log PI) in n 219.468 * [taylor]: Taking taylor expansion of PI in n 219.468 * [backup-simplify]: Simplify PI into PI 219.468 * [backup-simplify]: Simplify (log PI) into (log PI) 219.469 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.469 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.469 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.469 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 219.469 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.469 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.469 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 219.469 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 219.469 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.469 * [taylor]: Taking taylor expansion of 1/2 in n 219.469 * [backup-simplify]: Simplify 1/2 into 1/2 219.469 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.469 * [taylor]: Taking taylor expansion of 1/2 in n 219.469 * [backup-simplify]: Simplify 1/2 into 1/2 219.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.469 * [taylor]: Taking taylor expansion of k in n 219.469 * [backup-simplify]: Simplify k into k 219.469 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.470 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 219.470 * [taylor]: Taking taylor expansion of (/ 1 n) in n 219.470 * [taylor]: Taking taylor expansion of n in n 219.470 * [backup-simplify]: Simplify 0 into 0 219.470 * [backup-simplify]: Simplify 1 into 1 219.470 * [backup-simplify]: Simplify (/ 1 1) into 1 219.470 * [backup-simplify]: Simplify (log 1) into 0 219.470 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.470 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.470 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.470 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.471 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 219.471 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.471 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 219.471 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 219.472 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 219.472 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 219.473 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 219.473 * [backup-simplify]: Simplify 0 into 0 219.474 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 219.475 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) into 0 219.476 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 219.476 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 219.476 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 219.476 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 219.476 * [taylor]: Taking taylor expansion of +nan.0 in n 219.477 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.477 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 219.477 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.477 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.477 * [taylor]: Taking taylor expansion of (log 2) in n 219.477 * [taylor]: Taking taylor expansion of 2 in n 219.477 * [backup-simplify]: Simplify 2 into 2 219.477 * [backup-simplify]: Simplify (log 2) into (log 2) 219.477 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.477 * [taylor]: Taking taylor expansion of 1/2 in n 219.477 * [backup-simplify]: Simplify 1/2 into 1/2 219.477 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.477 * [taylor]: Taking taylor expansion of 1/2 in n 219.477 * [backup-simplify]: Simplify 1/2 into 1/2 219.477 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.477 * [taylor]: Taking taylor expansion of k in n 219.477 * [backup-simplify]: Simplify k into k 219.477 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.477 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.477 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.477 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.477 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 219.478 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 219.478 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.478 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 219.478 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 219.478 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 219.478 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.478 * [taylor]: Taking taylor expansion of 1/2 in n 219.478 * [backup-simplify]: Simplify 1/2 into 1/2 219.478 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.478 * [taylor]: Taking taylor expansion of 1/2 in n 219.478 * [backup-simplify]: Simplify 1/2 into 1/2 219.478 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.478 * [taylor]: Taking taylor expansion of k in n 219.478 * [backup-simplify]: Simplify k into k 219.478 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.478 * [taylor]: Taking taylor expansion of (log PI) in n 219.478 * [taylor]: Taking taylor expansion of PI in n 219.478 * [backup-simplify]: Simplify PI into PI 219.478 * [backup-simplify]: Simplify (log PI) into (log PI) 219.478 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.478 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.479 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.479 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 219.482 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.482 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.482 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 219.482 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 219.482 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.482 * [taylor]: Taking taylor expansion of 1/2 in n 219.482 * [backup-simplify]: Simplify 1/2 into 1/2 219.482 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.482 * [taylor]: Taking taylor expansion of 1/2 in n 219.482 * [backup-simplify]: Simplify 1/2 into 1/2 219.482 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.482 * [taylor]: Taking taylor expansion of k in n 219.482 * [backup-simplify]: Simplify k into k 219.482 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.483 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 219.483 * [taylor]: Taking taylor expansion of (/ 1 n) in n 219.483 * [taylor]: Taking taylor expansion of n in n 219.483 * [backup-simplify]: Simplify 0 into 0 219.483 * [backup-simplify]: Simplify 1 into 1 219.483 * [backup-simplify]: Simplify (/ 1 1) into 1 219.483 * [backup-simplify]: Simplify (log 1) into 0 219.483 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.483 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.483 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.484 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.484 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 219.484 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.484 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 219.484 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 219.485 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 219.485 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 219.486 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 219.486 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 219.487 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 219.487 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.487 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.488 * [backup-simplify]: Simplify (- 0) into 0 219.488 * [backup-simplify]: Simplify (+ 0 0) into 0 219.488 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.488 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 219.489 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 219.490 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 219.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.490 * [backup-simplify]: Simplify (- 0) into 0 219.490 * [backup-simplify]: Simplify (+ 0 0) into 0 219.491 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (log PI))) into 0 219.492 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 219.492 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into 0 219.492 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.492 * [backup-simplify]: Simplify (- 0) into 0 219.493 * [backup-simplify]: Simplify (+ 0 0) into 0 219.493 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 219.494 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0 219.494 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 219.495 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into 0 219.496 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 219.496 * [backup-simplify]: Simplify (- 0) into 0 219.496 * [backup-simplify]: Simplify 0 into 0 219.496 * [backup-simplify]: Simplify 0 into 0 219.498 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 219.499 * [backup-simplify]: Simplify (+ (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) into 0 219.500 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))))) into 0 219.501 * [backup-simplify]: Simplify (+ (* (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) 219.501 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))))) in n 219.501 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))))) in n 219.501 * [taylor]: Taking taylor expansion of +nan.0 in n 219.501 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.501 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))))) in n 219.501 * [taylor]: Taking taylor expansion of (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.501 * [taylor]: Taking taylor expansion of (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.501 * [taylor]: Taking taylor expansion of (log 2) in n 219.501 * [taylor]: Taking taylor expansion of 2 in n 219.501 * [backup-simplify]: Simplify 2 into 2 219.501 * [backup-simplify]: Simplify (log 2) into (log 2) 219.501 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.501 * [taylor]: Taking taylor expansion of 1/2 in n 219.501 * [backup-simplify]: Simplify 1/2 into 1/2 219.501 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.501 * [taylor]: Taking taylor expansion of 1/2 in n 219.501 * [backup-simplify]: Simplify 1/2 into 1/2 219.501 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.501 * [taylor]: Taking taylor expansion of k in n 219.501 * [backup-simplify]: Simplify k into k 219.501 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.501 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.501 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.501 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.502 * [backup-simplify]: Simplify (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) into (* (log 2) (- 1/2 (* 1/2 (/ 1 k)))) 219.502 * [backup-simplify]: Simplify (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) into (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) 219.502 * [taylor]: Taking taylor expansion of (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))) in n 219.502 * [taylor]: Taking taylor expansion of (pow PI (- 1/2 (* 1/2 (/ 1 k)))) in n 219.502 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) in n 219.502 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) in n 219.502 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.502 * [taylor]: Taking taylor expansion of 1/2 in n 219.502 * [backup-simplify]: Simplify 1/2 into 1/2 219.502 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.502 * [taylor]: Taking taylor expansion of 1/2 in n 219.502 * [backup-simplify]: Simplify 1/2 into 1/2 219.502 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.502 * [taylor]: Taking taylor expansion of k in n 219.502 * [backup-simplify]: Simplify k into k 219.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.502 * [taylor]: Taking taylor expansion of (log PI) in n 219.502 * [taylor]: Taking taylor expansion of PI in n 219.502 * [backup-simplify]: Simplify PI into PI 219.503 * [backup-simplify]: Simplify (log PI) into (log PI) 219.503 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.503 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.503 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.503 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) into (* (- 1/2 (* 1/2 (/ 1 k))) (log PI)) 219.503 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log PI))) into (pow PI (- 1/2 (* 1/2 (/ 1 k)))) 219.503 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.503 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 219.503 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 219.503 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.503 * [taylor]: Taking taylor expansion of 1/2 in n 219.503 * [backup-simplify]: Simplify 1/2 into 1/2 219.503 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.503 * [taylor]: Taking taylor expansion of 1/2 in n 219.503 * [backup-simplify]: Simplify 1/2 into 1/2 219.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.504 * [taylor]: Taking taylor expansion of k in n 219.504 * [backup-simplify]: Simplify k into k 219.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.504 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 219.504 * [taylor]: Taking taylor expansion of (/ 1 n) in n 219.504 * [taylor]: Taking taylor expansion of n in n 219.504 * [backup-simplify]: Simplify 0 into 0 219.504 * [backup-simplify]: Simplify 1 into 1 219.504 * [backup-simplify]: Simplify (/ 1 1) into 1 219.504 * [backup-simplify]: Simplify (log 1) into 0 219.504 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.504 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.504 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.505 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.505 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 219.505 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.505 * [backup-simplify]: Simplify (* (pow PI (- 1/2 (* 1/2 (/ 1 k)))) (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))) 219.505 * [backup-simplify]: Simplify (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))) 219.506 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) into (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k))))))) 219.506 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 219.507 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) into (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 k))))) (pow PI (- 1/2 (* 1/2 (/ 1 k)))))))) 219.509 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 (/ 1 (/ 1 k)))))) (pow PI (- 1/2 (* 1/2 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k)) (- (* +nan.0 (/ (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2)))))))) 219.509 * [backup-simplify]: Simplify (* (* (pow 2 (- 1/2 (* 1/2 (/ 1 (- k))))) (pow PI (- 1/2 (* 1/2 (/ 1 (- k)))))) (/ (pow (/ 1 (- n)) (- 1/2 (* 1/2 (/ 1 (- k))))) (sqrt (/ 1 (- k))))) into (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) 219.509 * [approximate]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in (k n) around 0 219.509 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in n 219.509 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 219.509 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.509 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.509 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.509 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.509 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.509 * [taylor]: Taking taylor expansion of 1/2 in n 219.509 * [backup-simplify]: Simplify 1/2 into 1/2 219.509 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.509 * [taylor]: Taking taylor expansion of k in n 219.509 * [backup-simplify]: Simplify k into k 219.509 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.509 * [taylor]: Taking taylor expansion of 1/2 in n 219.509 * [backup-simplify]: Simplify 1/2 into 1/2 219.509 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.509 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.510 * [taylor]: Taking taylor expansion of -1 in n 219.510 * [backup-simplify]: Simplify -1 into -1 219.510 * [taylor]: Taking taylor expansion of n in n 219.510 * [backup-simplify]: Simplify 0 into 0 219.510 * [backup-simplify]: Simplify 1 into 1 219.510 * [backup-simplify]: Simplify (/ -1 1) into -1 219.510 * [backup-simplify]: Simplify (log -1) into (log -1) 219.510 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.510 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.511 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.511 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.511 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.511 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.511 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in n 219.511 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in n 219.511 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.511 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.511 * [taylor]: Taking taylor expansion of 1/2 in n 219.511 * [backup-simplify]: Simplify 1/2 into 1/2 219.512 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.512 * [taylor]: Taking taylor expansion of k in n 219.512 * [backup-simplify]: Simplify k into k 219.512 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.512 * [taylor]: Taking taylor expansion of 1/2 in n 219.512 * [backup-simplify]: Simplify 1/2 into 1/2 219.512 * [taylor]: Taking taylor expansion of (log 2) in n 219.512 * [taylor]: Taking taylor expansion of 2 in n 219.512 * [backup-simplify]: Simplify 2 into 2 219.512 * [backup-simplify]: Simplify (log 2) into (log 2) 219.512 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.512 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.512 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 219.513 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.513 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.513 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 219.513 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 219.513 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.513 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.513 * [taylor]: Taking taylor expansion of 1/2 in n 219.513 * [backup-simplify]: Simplify 1/2 into 1/2 219.513 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.513 * [taylor]: Taking taylor expansion of k in n 219.513 * [backup-simplify]: Simplify k into k 219.513 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.513 * [taylor]: Taking taylor expansion of 1/2 in n 219.513 * [backup-simplify]: Simplify 1/2 into 1/2 219.513 * [taylor]: Taking taylor expansion of (log PI) in n 219.513 * [taylor]: Taking taylor expansion of PI in n 219.513 * [backup-simplify]: Simplify PI into PI 219.513 * [backup-simplify]: Simplify (log PI) into (log PI) 219.513 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.513 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.514 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 219.514 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.514 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 219.514 * [taylor]: Taking taylor expansion of (/ -1 k) in n 219.514 * [taylor]: Taking taylor expansion of -1 in n 219.514 * [backup-simplify]: Simplify -1 into -1 219.514 * [taylor]: Taking taylor expansion of k in n 219.514 * [backup-simplify]: Simplify k into k 219.514 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 219.514 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 219.514 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 219.514 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 219.515 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.515 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.516 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) into (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) 219.516 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in k 219.516 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 219.516 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.516 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 219.516 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 219.516 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.516 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.516 * [taylor]: Taking taylor expansion of 1/2 in k 219.516 * [backup-simplify]: Simplify 1/2 into 1/2 219.516 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.516 * [taylor]: Taking taylor expansion of k in k 219.516 * [backup-simplify]: Simplify 0 into 0 219.516 * [backup-simplify]: Simplify 1 into 1 219.516 * [backup-simplify]: Simplify (/ 1 1) into 1 219.516 * [taylor]: Taking taylor expansion of 1/2 in k 219.516 * [backup-simplify]: Simplify 1/2 into 1/2 219.516 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 219.516 * [taylor]: Taking taylor expansion of (/ -1 n) in k 219.516 * [taylor]: Taking taylor expansion of -1 in k 219.517 * [backup-simplify]: Simplify -1 into -1 219.517 * [taylor]: Taking taylor expansion of n in k 219.517 * [backup-simplify]: Simplify n into n 219.517 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 219.517 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 219.517 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.517 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.517 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 219.517 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 219.517 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 219.517 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.517 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 219.517 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 219.517 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.517 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.517 * [taylor]: Taking taylor expansion of 1/2 in k 219.517 * [backup-simplify]: Simplify 1/2 into 1/2 219.517 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.517 * [taylor]: Taking taylor expansion of k in k 219.518 * [backup-simplify]: Simplify 0 into 0 219.518 * [backup-simplify]: Simplify 1 into 1 219.518 * [backup-simplify]: Simplify (/ 1 1) into 1 219.518 * [taylor]: Taking taylor expansion of 1/2 in k 219.518 * [backup-simplify]: Simplify 1/2 into 1/2 219.518 * [taylor]: Taking taylor expansion of (log 2) in k 219.518 * [taylor]: Taking taylor expansion of 2 in k 219.518 * [backup-simplify]: Simplify 2 into 2 219.518 * [backup-simplify]: Simplify (log 2) into (log 2) 219.518 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.519 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.519 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 219.519 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.519 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.520 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 219.520 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 219.520 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.520 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.520 * [taylor]: Taking taylor expansion of 1/2 in k 219.520 * [backup-simplify]: Simplify 1/2 into 1/2 219.520 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.520 * [taylor]: Taking taylor expansion of k in k 219.520 * [backup-simplify]: Simplify 0 into 0 219.520 * [backup-simplify]: Simplify 1 into 1 219.520 * [backup-simplify]: Simplify (/ 1 1) into 1 219.520 * [taylor]: Taking taylor expansion of 1/2 in k 219.520 * [backup-simplify]: Simplify 1/2 into 1/2 219.520 * [taylor]: Taking taylor expansion of (log PI) in k 219.520 * [taylor]: Taking taylor expansion of PI in k 219.520 * [backup-simplify]: Simplify PI into PI 219.520 * [backup-simplify]: Simplify (log PI) into (log PI) 219.520 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.521 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.521 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 219.522 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.522 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 219.522 * [taylor]: Taking taylor expansion of (/ -1 k) in k 219.522 * [taylor]: Taking taylor expansion of -1 in k 219.522 * [backup-simplify]: Simplify -1 into -1 219.522 * [taylor]: Taking taylor expansion of k in k 219.522 * [backup-simplify]: Simplify 0 into 0 219.522 * [backup-simplify]: Simplify 1 into 1 219.522 * [backup-simplify]: Simplify (/ -1 1) into -1 219.522 * [backup-simplify]: Simplify (sqrt 0) into 0 219.523 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 219.523 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.524 * [backup-simplify]: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.524 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.524 * [taylor]: Taking taylor expansion of (/ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) (sqrt (/ -1 k))) in k 219.524 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in k 219.524 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.524 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 219.524 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 219.524 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.524 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.524 * [taylor]: Taking taylor expansion of 1/2 in k 219.524 * [backup-simplify]: Simplify 1/2 into 1/2 219.524 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.524 * [taylor]: Taking taylor expansion of k in k 219.525 * [backup-simplify]: Simplify 0 into 0 219.525 * [backup-simplify]: Simplify 1 into 1 219.525 * [backup-simplify]: Simplify (/ 1 1) into 1 219.525 * [taylor]: Taking taylor expansion of 1/2 in k 219.525 * [backup-simplify]: Simplify 1/2 into 1/2 219.525 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 219.525 * [taylor]: Taking taylor expansion of (/ -1 n) in k 219.525 * [taylor]: Taking taylor expansion of -1 in k 219.525 * [backup-simplify]: Simplify -1 into -1 219.525 * [taylor]: Taking taylor expansion of n in k 219.525 * [backup-simplify]: Simplify n into n 219.525 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 219.525 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 219.525 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.526 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.526 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 219.526 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 219.526 * [taylor]: Taking taylor expansion of (* (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in k 219.526 * [taylor]: Taking taylor expansion of (pow 2 (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.526 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) in k 219.526 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2)) in k 219.526 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.526 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.526 * [taylor]: Taking taylor expansion of 1/2 in k 219.526 * [backup-simplify]: Simplify 1/2 into 1/2 219.526 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.526 * [taylor]: Taking taylor expansion of k in k 219.526 * [backup-simplify]: Simplify 0 into 0 219.526 * [backup-simplify]: Simplify 1 into 1 219.526 * [backup-simplify]: Simplify (/ 1 1) into 1 219.526 * [taylor]: Taking taylor expansion of 1/2 in k 219.526 * [backup-simplify]: Simplify 1/2 into 1/2 219.526 * [taylor]: Taking taylor expansion of (log 2) in k 219.526 * [taylor]: Taking taylor expansion of 2 in k 219.526 * [backup-simplify]: Simplify 2 into 2 219.526 * [backup-simplify]: Simplify (log 2) into (log 2) 219.527 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.527 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.528 * [backup-simplify]: Simplify (* 1/2 (log 2)) into (* 1/2 (log 2)) 219.528 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log 2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.528 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.528 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in k 219.528 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in k 219.528 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.528 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.528 * [taylor]: Taking taylor expansion of 1/2 in k 219.528 * [backup-simplify]: Simplify 1/2 into 1/2 219.528 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.528 * [taylor]: Taking taylor expansion of k in k 219.528 * [backup-simplify]: Simplify 0 into 0 219.528 * [backup-simplify]: Simplify 1 into 1 219.528 * [backup-simplify]: Simplify (/ 1 1) into 1 219.528 * [taylor]: Taking taylor expansion of 1/2 in k 219.528 * [backup-simplify]: Simplify 1/2 into 1/2 219.528 * [taylor]: Taking taylor expansion of (log PI) in k 219.528 * [taylor]: Taking taylor expansion of PI in k 219.528 * [backup-simplify]: Simplify PI into PI 219.529 * [backup-simplify]: Simplify (log PI) into (log PI) 219.529 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.529 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.530 * [backup-simplify]: Simplify (* 1/2 (log PI)) into (* 1/2 (log PI)) 219.530 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.530 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 219.530 * [taylor]: Taking taylor expansion of (/ -1 k) in k 219.530 * [taylor]: Taking taylor expansion of -1 in k 219.530 * [backup-simplify]: Simplify -1 into -1 219.530 * [taylor]: Taking taylor expansion of k in k 219.530 * [backup-simplify]: Simplify 0 into 0 219.530 * [backup-simplify]: Simplify 1 into 1 219.530 * [backup-simplify]: Simplify (/ -1 1) into -1 219.531 * [backup-simplify]: Simplify (sqrt 0) into 0 219.531 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 219.532 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.532 * [backup-simplify]: Simplify (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.533 * [backup-simplify]: Simplify (/ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.533 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 219.533 * [taylor]: Taking taylor expansion of +nan.0 in n 219.533 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.533 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 219.533 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.533 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.533 * [taylor]: Taking taylor expansion of (log 2) in n 219.533 * [taylor]: Taking taylor expansion of 2 in n 219.533 * [backup-simplify]: Simplify 2 into 2 219.533 * [backup-simplify]: Simplify (log 2) into (log 2) 219.533 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.533 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.533 * [taylor]: Taking taylor expansion of 1/2 in n 219.533 * [backup-simplify]: Simplify 1/2 into 1/2 219.533 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.533 * [taylor]: Taking taylor expansion of k in n 219.533 * [backup-simplify]: Simplify k into k 219.533 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.533 * [taylor]: Taking taylor expansion of 1/2 in n 219.533 * [backup-simplify]: Simplify 1/2 into 1/2 219.533 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.533 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.534 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 219.534 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.534 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.534 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.534 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.534 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.534 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.534 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.534 * [taylor]: Taking taylor expansion of 1/2 in n 219.534 * [backup-simplify]: Simplify 1/2 into 1/2 219.534 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.534 * [taylor]: Taking taylor expansion of k in n 219.534 * [backup-simplify]: Simplify k into k 219.534 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.534 * [taylor]: Taking taylor expansion of 1/2 in n 219.534 * [backup-simplify]: Simplify 1/2 into 1/2 219.534 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.534 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.534 * [taylor]: Taking taylor expansion of -1 in n 219.534 * [backup-simplify]: Simplify -1 into -1 219.534 * [taylor]: Taking taylor expansion of n in n 219.534 * [backup-simplify]: Simplify 0 into 0 219.534 * [backup-simplify]: Simplify 1 into 1 219.535 * [backup-simplify]: Simplify (/ -1 1) into -1 219.535 * [backup-simplify]: Simplify (log -1) into (log -1) 219.535 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.535 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.535 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.536 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.536 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.536 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.536 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 219.536 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 219.536 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.536 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.536 * [taylor]: Taking taylor expansion of 1/2 in n 219.536 * [backup-simplify]: Simplify 1/2 into 1/2 219.536 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.536 * [taylor]: Taking taylor expansion of k in n 219.536 * [backup-simplify]: Simplify k into k 219.536 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.536 * [taylor]: Taking taylor expansion of 1/2 in n 219.536 * [backup-simplify]: Simplify 1/2 into 1/2 219.536 * [taylor]: Taking taylor expansion of (log PI) in n 219.536 * [taylor]: Taking taylor expansion of PI in n 219.536 * [backup-simplify]: Simplify PI into PI 219.537 * [backup-simplify]: Simplify (log PI) into (log PI) 219.537 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.537 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.537 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 219.537 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.538 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.538 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.539 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.540 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.540 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 219.541 * [backup-simplify]: Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 219.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 219.543 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 219.544 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.544 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 219.544 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 219.544 * [taylor]: Taking taylor expansion of +nan.0 in n 219.544 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.544 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 219.544 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.544 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.544 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.544 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.544 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.544 * [taylor]: Taking taylor expansion of 1/2 in n 219.544 * [backup-simplify]: Simplify 1/2 into 1/2 219.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.544 * [taylor]: Taking taylor expansion of k in n 219.544 * [backup-simplify]: Simplify k into k 219.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.544 * [taylor]: Taking taylor expansion of 1/2 in n 219.544 * [backup-simplify]: Simplify 1/2 into 1/2 219.544 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.544 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.544 * [taylor]: Taking taylor expansion of -1 in n 219.544 * [backup-simplify]: Simplify -1 into -1 219.544 * [taylor]: Taking taylor expansion of n in n 219.544 * [backup-simplify]: Simplify 0 into 0 219.545 * [backup-simplify]: Simplify 1 into 1 219.545 * [backup-simplify]: Simplify (/ -1 1) into -1 219.545 * [backup-simplify]: Simplify (log -1) into (log -1) 219.545 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.545 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.546 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.546 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.546 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.546 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.546 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.546 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.546 * [taylor]: Taking taylor expansion of (log 2) in n 219.546 * [taylor]: Taking taylor expansion of 2 in n 219.546 * [backup-simplify]: Simplify 2 into 2 219.547 * [backup-simplify]: Simplify (log 2) into (log 2) 219.547 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.547 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.547 * [taylor]: Taking taylor expansion of 1/2 in n 219.547 * [backup-simplify]: Simplify 1/2 into 1/2 219.547 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.547 * [taylor]: Taking taylor expansion of k in n 219.547 * [backup-simplify]: Simplify k into k 219.547 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.547 * [taylor]: Taking taylor expansion of 1/2 in n 219.547 * [backup-simplify]: Simplify 1/2 into 1/2 219.547 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.547 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.547 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 219.547 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.548 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.548 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 219.548 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 219.548 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.548 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.548 * [taylor]: Taking taylor expansion of 1/2 in n 219.548 * [backup-simplify]: Simplify 1/2 into 1/2 219.548 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.548 * [taylor]: Taking taylor expansion of k in n 219.548 * [backup-simplify]: Simplify k into k 219.548 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.548 * [taylor]: Taking taylor expansion of 1/2 in n 219.548 * [backup-simplify]: Simplify 1/2 into 1/2 219.548 * [taylor]: Taking taylor expansion of (log PI) in n 219.548 * [taylor]: Taking taylor expansion of PI in n 219.548 * [backup-simplify]: Simplify PI into PI 219.548 * [backup-simplify]: Simplify (log PI) into (log PI) 219.548 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.548 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.548 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 219.549 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.549 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.550 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.550 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.551 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.552 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.553 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 219.553 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.553 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.553 * [backup-simplify]: Simplify (+ 0 0) into 0 219.554 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (log PI))) into 0 219.555 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 219.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 219.556 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 219.556 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.556 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.556 * [backup-simplify]: Simplify (+ 0 0) into 0 219.557 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.557 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 219.558 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 219.558 * [backup-simplify]: Simplify (+ (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 219.558 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.559 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.559 * [backup-simplify]: Simplify (+ 0 0) into 0 219.560 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0 219.560 * [backup-simplify]: Simplify (+ (* (log 2) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 219.561 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (+ (* (/ (pow 0 1) 1)))) into 0 219.562 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (* 0 (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 219.563 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 219.563 * [backup-simplify]: Simplify 0 into 0 219.563 * [backup-simplify]: Simplify (+ (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 0) (+ (* 0 0) (* 0 (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into 0 219.564 * [backup-simplify]: Simplify (+ (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into 0 219.564 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.569 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 219.571 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) (/ +nan.0 +nan.0)))) into (- (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) 219.571 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))))) in n 219.571 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) in n 219.571 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 219.571 * [taylor]: Taking taylor expansion of +nan.0 in n 219.571 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.571 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 219.571 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.571 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.571 * [taylor]: Taking taylor expansion of (log 2) in n 219.571 * [taylor]: Taking taylor expansion of 2 in n 219.571 * [backup-simplify]: Simplify 2 into 2 219.572 * [backup-simplify]: Simplify (log 2) into (log 2) 219.572 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.572 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.572 * [taylor]: Taking taylor expansion of 1/2 in n 219.572 * [backup-simplify]: Simplify 1/2 into 1/2 219.572 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.572 * [taylor]: Taking taylor expansion of k in n 219.572 * [backup-simplify]: Simplify k into k 219.572 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.572 * [taylor]: Taking taylor expansion of 1/2 in n 219.572 * [backup-simplify]: Simplify 1/2 into 1/2 219.572 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.572 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.572 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 219.573 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.573 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.573 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.573 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.573 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.573 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.573 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.573 * [taylor]: Taking taylor expansion of 1/2 in n 219.573 * [backup-simplify]: Simplify 1/2 into 1/2 219.573 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.573 * [taylor]: Taking taylor expansion of k in n 219.573 * [backup-simplify]: Simplify k into k 219.573 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.573 * [taylor]: Taking taylor expansion of 1/2 in n 219.573 * [backup-simplify]: Simplify 1/2 into 1/2 219.573 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.573 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.573 * [taylor]: Taking taylor expansion of -1 in n 219.573 * [backup-simplify]: Simplify -1 into -1 219.573 * [taylor]: Taking taylor expansion of n in n 219.573 * [backup-simplify]: Simplify 0 into 0 219.573 * [backup-simplify]: Simplify 1 into 1 219.573 * [backup-simplify]: Simplify (/ -1 1) into -1 219.573 * [backup-simplify]: Simplify (log -1) into (log -1) 219.574 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.574 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.574 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.574 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.575 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.575 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.575 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 219.575 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 219.575 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.575 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.575 * [taylor]: Taking taylor expansion of 1/2 in n 219.575 * [backup-simplify]: Simplify 1/2 into 1/2 219.575 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.575 * [taylor]: Taking taylor expansion of k in n 219.575 * [backup-simplify]: Simplify k into k 219.575 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.575 * [taylor]: Taking taylor expansion of 1/2 in n 219.575 * [backup-simplify]: Simplify 1/2 into 1/2 219.575 * [taylor]: Taking taylor expansion of (log PI) in n 219.575 * [taylor]: Taking taylor expansion of PI in n 219.575 * [backup-simplify]: Simplify PI into PI 219.575 * [backup-simplify]: Simplify (log PI) into (log PI) 219.575 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.575 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.576 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 219.576 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.576 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 219.576 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) in n 219.576 * [taylor]: Taking taylor expansion of +nan.0 in n 219.576 * [backup-simplify]: Simplify +nan.0 into +nan.0 219.576 * [taylor]: Taking taylor expansion of (* (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) in n 219.576 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.576 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.576 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.576 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.576 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.576 * [taylor]: Taking taylor expansion of 1/2 in n 219.576 * [backup-simplify]: Simplify 1/2 into 1/2 219.576 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.576 * [taylor]: Taking taylor expansion of k in n 219.576 * [backup-simplify]: Simplify k into k 219.576 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.576 * [taylor]: Taking taylor expansion of 1/2 in n 219.576 * [backup-simplify]: Simplify 1/2 into 1/2 219.576 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.576 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.576 * [taylor]: Taking taylor expansion of -1 in n 219.576 * [backup-simplify]: Simplify -1 into -1 219.576 * [taylor]: Taking taylor expansion of n in n 219.576 * [backup-simplify]: Simplify 0 into 0 219.576 * [backup-simplify]: Simplify 1 into 1 219.577 * [backup-simplify]: Simplify (/ -1 1) into -1 219.577 * [backup-simplify]: Simplify (log -1) into (log -1) 219.577 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.577 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.578 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.578 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.578 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.578 * [taylor]: Taking taylor expansion of (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.578 * [taylor]: Taking taylor expansion of (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) in n 219.578 * [taylor]: Taking taylor expansion of (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.578 * [taylor]: Taking taylor expansion of (log 2) in n 219.578 * [taylor]: Taking taylor expansion of 2 in n 219.578 * [backup-simplify]: Simplify 2 into 2 219.579 * [backup-simplify]: Simplify (log 2) into (log 2) 219.579 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.579 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.579 * [taylor]: Taking taylor expansion of 1/2 in n 219.579 * [backup-simplify]: Simplify 1/2 into 1/2 219.579 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.579 * [taylor]: Taking taylor expansion of k in n 219.579 * [backup-simplify]: Simplify k into k 219.579 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.579 * [taylor]: Taking taylor expansion of 1/2 in n 219.579 * [backup-simplify]: Simplify 1/2 into 1/2 219.579 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.579 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.579 * [backup-simplify]: Simplify (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) into (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2)) 219.579 * [backup-simplify]: Simplify (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) into (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) 219.579 * [taylor]: Taking taylor expansion of (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.579 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) in n 219.579 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) in n 219.580 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.580 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.580 * [taylor]: Taking taylor expansion of 1/2 in n 219.580 * [backup-simplify]: Simplify 1/2 into 1/2 219.580 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.580 * [taylor]: Taking taylor expansion of k in n 219.580 * [backup-simplify]: Simplify k into k 219.580 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.580 * [taylor]: Taking taylor expansion of 1/2 in n 219.580 * [backup-simplify]: Simplify 1/2 into 1/2 219.580 * [taylor]: Taking taylor expansion of (log PI) in n 219.580 * [taylor]: Taking taylor expansion of PI in n 219.580 * [backup-simplify]: Simplify PI into PI 219.580 * [backup-simplify]: Simplify (log PI) into (log PI) 219.580 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.580 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.580 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) into (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI)) 219.581 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log PI))) into (pow PI (+ (* 1/2 (/ 1 k)) 1/2)) 219.581 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.582 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.582 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.583 * [backup-simplify]: Simplify (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))) 219.583 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) into (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))) 219.584 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) into (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) 219.585 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.586 * [backup-simplify]: Simplify (+ (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))) (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.587 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2))))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.588 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) into (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 k)) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (pow PI (+ (* 1/2 (/ 1 k)) 1/2)))))) 219.591 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* (log 2) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))) (* (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) (pow PI (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2))))))) into (- (+ (* +nan.0 (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k)))))) (- (+ (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) (pow k 2))) (- (* +nan.0 (/ (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (* (exp (* (log 2) (- 1/2 (* 1/2 k)))) (pow PI (- 1/2 (* 1/2 k))))) k))))))) 219.591 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 219.591 * [backup-simplify]: Simplify (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k)) into (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 219.591 * [approximate]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 219.591 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 219.591 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 219.591 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 219.591 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 219.591 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.591 * [taylor]: Taking taylor expansion of 1/2 in k 219.591 * [backup-simplify]: Simplify 1/2 into 1/2 219.591 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.591 * [taylor]: Taking taylor expansion of 1/2 in k 219.591 * [backup-simplify]: Simplify 1/2 into 1/2 219.591 * [taylor]: Taking taylor expansion of k in k 219.591 * [backup-simplify]: Simplify 0 into 0 219.591 * [backup-simplify]: Simplify 1 into 1 219.591 * [taylor]: Taking taylor expansion of (log n) in k 219.591 * [taylor]: Taking taylor expansion of n in k 219.591 * [backup-simplify]: Simplify n into n 219.591 * [backup-simplify]: Simplify (log n) into (log n) 219.592 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.592 * [backup-simplify]: Simplify (- 0) into 0 219.592 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.592 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 219.592 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 219.592 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 219.592 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.592 * [taylor]: Taking taylor expansion of k in k 219.592 * [backup-simplify]: Simplify 0 into 0 219.592 * [backup-simplify]: Simplify 1 into 1 219.592 * [backup-simplify]: Simplify (/ 1 1) into 1 219.593 * [backup-simplify]: Simplify (sqrt 0) into 0 219.593 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.594 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 219.594 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 219.594 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 219.594 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 219.594 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 219.594 * [taylor]: Taking taylor expansion of 1/2 in n 219.594 * [backup-simplify]: Simplify 1/2 into 1/2 219.594 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 219.594 * [taylor]: Taking taylor expansion of 1/2 in n 219.594 * [backup-simplify]: Simplify 1/2 into 1/2 219.594 * [taylor]: Taking taylor expansion of k in n 219.594 * [backup-simplify]: Simplify k into k 219.594 * [taylor]: Taking taylor expansion of (log n) in n 219.594 * [taylor]: Taking taylor expansion of n in n 219.594 * [backup-simplify]: Simplify 0 into 0 219.594 * [backup-simplify]: Simplify 1 into 1 219.594 * [backup-simplify]: Simplify (log 1) into 0 219.594 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 219.594 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 219.594 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 219.594 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.594 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 219.595 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 219.595 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 219.595 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.595 * [taylor]: Taking taylor expansion of k in n 219.595 * [backup-simplify]: Simplify k into k 219.595 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.595 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 219.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.595 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 219.595 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 219.595 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n 219.595 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n 219.595 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n 219.595 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 219.595 * [taylor]: Taking taylor expansion of 1/2 in n 219.595 * [backup-simplify]: Simplify 1/2 into 1/2 219.595 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 219.595 * [taylor]: Taking taylor expansion of 1/2 in n 219.595 * [backup-simplify]: Simplify 1/2 into 1/2 219.595 * [taylor]: Taking taylor expansion of k in n 219.595 * [backup-simplify]: Simplify k into k 219.595 * [taylor]: Taking taylor expansion of (log n) in n 219.595 * [taylor]: Taking taylor expansion of n in n 219.595 * [backup-simplify]: Simplify 0 into 0 219.595 * [backup-simplify]: Simplify 1 into 1 219.595 * [backup-simplify]: Simplify (log 1) into 0 219.595 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 219.595 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 219.595 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 219.596 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.596 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n)) 219.596 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k))) 219.596 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 219.596 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.596 * [taylor]: Taking taylor expansion of k in n 219.596 * [backup-simplify]: Simplify k into k 219.596 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.596 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 219.596 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.596 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 219.596 * [backup-simplify]: Simplify (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) into (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 219.596 * [taylor]: Taking taylor expansion of (* (pow n (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 219.596 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k 219.596 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k 219.596 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k 219.596 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 219.596 * [taylor]: Taking taylor expansion of 1/2 in k 219.596 * [backup-simplify]: Simplify 1/2 into 1/2 219.596 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 219.596 * [taylor]: Taking taylor expansion of 1/2 in k 219.596 * [backup-simplify]: Simplify 1/2 into 1/2 219.596 * [taylor]: Taking taylor expansion of k in k 219.596 * [backup-simplify]: Simplify 0 into 0 219.596 * [backup-simplify]: Simplify 1 into 1 219.597 * [taylor]: Taking taylor expansion of (log n) in k 219.597 * [taylor]: Taking taylor expansion of n in k 219.597 * [backup-simplify]: Simplify n into n 219.597 * [backup-simplify]: Simplify (log n) into (log n) 219.597 * [backup-simplify]: Simplify (* 1/2 0) into 0 219.597 * [backup-simplify]: Simplify (- 0) into 0 219.597 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.597 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n)) 219.597 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2) 219.597 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 219.597 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.597 * [taylor]: Taking taylor expansion of k in k 219.598 * [backup-simplify]: Simplify 0 into 0 219.598 * [backup-simplify]: Simplify 1 into 1 219.598 * [backup-simplify]: Simplify (/ 1 1) into 1 219.598 * [backup-simplify]: Simplify (sqrt 0) into 0 219.599 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.599 * [backup-simplify]: Simplify (* (pow n 1/2) 0) into 0 219.599 * [backup-simplify]: Simplify 0 into 0 219.600 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 219.600 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 219.600 * [backup-simplify]: Simplify (- 0) into 0 219.600 * [backup-simplify]: Simplify (+ 0 0) into 0 219.601 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.601 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0 219.601 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 219.601 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (* 0 (sqrt (/ 1 k)))) into 0 219.601 * [taylor]: Taking taylor expansion of 0 in k 219.601 * [backup-simplify]: Simplify 0 into 0 219.602 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 219.602 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 219.602 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.603 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.603 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n))) 219.603 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n))) 219.603 * [backup-simplify]: Simplify (+ (* (pow n 1/2) +nan.0) (* (* -1/2 (* (sqrt n) (log n))) 0)) into (- (* +nan.0 (sqrt n))) 219.603 * [backup-simplify]: Simplify (- (* +nan.0 (sqrt n))) into (- (* +nan.0 (sqrt n))) 219.603 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 219.604 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 219.605 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 219.606 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 219.606 * [backup-simplify]: Simplify (- 0) into 0 219.606 * [backup-simplify]: Simplify (+ 0 0) into 0 219.607 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.607 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 219.608 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 219.608 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 219.608 * [taylor]: Taking taylor expansion of 0 in k 219.608 * [backup-simplify]: Simplify 0 into 0 219.608 * [backup-simplify]: Simplify 0 into 0 219.608 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 219.610 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 219.611 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 219.612 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 219.612 * [backup-simplify]: Simplify (- 0) into 0 219.612 * [backup-simplify]: Simplify (+ 0 0) into 0 219.613 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0 219.613 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2))) 219.613 * [backup-simplify]: Simplify (+ (* (pow n 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt n) (log n))) +nan.0) (* (* 1/8 (* (sqrt n) (pow (log n) 2))) 0))) into (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (* +nan.0 (sqrt n))))) 219.614 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (* +nan.0 (sqrt n))))) into (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (* +nan.0 (sqrt n))))) 219.614 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 219.614 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 219.617 * [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 0 219.618 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 219.618 * [backup-simplify]: Simplify (- 0) into 0 219.618 * [backup-simplify]: Simplify (+ 0 0) into 0 219.618 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 219.619 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 219.620 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 219.620 * [backup-simplify]: Simplify (+ (* (pow n (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 219.620 * [taylor]: Taking taylor expansion of 0 in k 219.620 * [backup-simplify]: Simplify 0 into 0 219.620 * [backup-simplify]: Simplify 0 into 0 219.620 * [backup-simplify]: Simplify 0 into 0 219.621 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.623 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 219.625 * [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 0 219.625 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 219.625 * [backup-simplify]: Simplify (- 0) into 0 219.626 * [backup-simplify]: Simplify (+ 0 0) into 0 219.626 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log n))))) into 0 219.627 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 3) 6)) (* (/ (pow (- (* 1/2 (log n))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt n) (pow (log n) 3))) 219.628 * [backup-simplify]: Simplify (+ (* (pow n 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt n) (log n))) +nan.0) (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) +nan.0) (* (* -1/48 (* (sqrt n) (pow (log n) 3))) 0)))) into (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (+ (* +nan.0 (* (sqrt n) (pow (log n) 2))) (- (* +nan.0 (sqrt n))))))) 219.628 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (+ (* +nan.0 (* (sqrt n) (pow (log n) 2))) (- (* +nan.0 (sqrt n))))))) into (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (+ (* +nan.0 (* (sqrt n) (pow (log n) 2))) (- (* +nan.0 (sqrt n))))))) 219.629 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (+ (* +nan.0 (* (sqrt n) (pow (log n) 2))) (- (* +nan.0 (sqrt n))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt n) (log n))) (- (* +nan.0 (sqrt n))))) (* k 1)) (- (* +nan.0 (sqrt n))))) into (- (+ (* +nan.0 (* (sqrt n) k)) (- (+ (* +nan.0 (* (sqrt n) (* (log n) k))) (- (+ (* +nan.0 (* (sqrt n) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (sqrt n) (pow k 2))) (- (+ (* +nan.0 (sqrt n)) (- (* +nan.0 (* (sqrt n) (* (log n) (pow k 2))))))))))))))) 219.629 * [backup-simplify]: Simplify (/ (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt (/ 1 k))) into (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 219.629 * [approximate]: Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (n k) around 0 219.629 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 219.629 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k 219.629 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k 219.629 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k 219.629 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.629 * [taylor]: Taking taylor expansion of 1/2 in k 219.629 * [backup-simplify]: Simplify 1/2 into 1/2 219.629 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.629 * [taylor]: Taking taylor expansion of 1/2 in k 219.629 * [backup-simplify]: Simplify 1/2 into 1/2 219.629 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.629 * [taylor]: Taking taylor expansion of k in k 219.629 * [backup-simplify]: Simplify 0 into 0 219.629 * [backup-simplify]: Simplify 1 into 1 219.629 * [backup-simplify]: Simplify (/ 1 1) into 1 219.630 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 219.630 * [taylor]: Taking taylor expansion of (/ 1 n) in k 219.630 * [taylor]: Taking taylor expansion of n in k 219.630 * [backup-simplify]: Simplify n into n 219.630 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 219.630 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 219.630 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.630 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.630 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.630 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n))) 219.631 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) 219.631 * [taylor]: Taking taylor expansion of (sqrt k) in k 219.631 * [taylor]: Taking taylor expansion of k in k 219.631 * [backup-simplify]: Simplify 0 into 0 219.631 * [backup-simplify]: Simplify 1 into 1 219.631 * [backup-simplify]: Simplify (sqrt 0) into 0 219.632 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.632 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 219.632 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.632 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 219.632 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 219.632 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.632 * [taylor]: Taking taylor expansion of 1/2 in n 219.632 * [backup-simplify]: Simplify 1/2 into 1/2 219.632 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.632 * [taylor]: Taking taylor expansion of 1/2 in n 219.632 * [backup-simplify]: Simplify 1/2 into 1/2 219.632 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.632 * [taylor]: Taking taylor expansion of k in n 219.632 * [backup-simplify]: Simplify k into k 219.632 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.632 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 219.632 * [taylor]: Taking taylor expansion of (/ 1 n) in n 219.632 * [taylor]: Taking taylor expansion of n in n 219.632 * [backup-simplify]: Simplify 0 into 0 219.632 * [backup-simplify]: Simplify 1 into 1 219.632 * [backup-simplify]: Simplify (/ 1 1) into 1 219.632 * [backup-simplify]: Simplify (log 1) into 0 219.632 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.633 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.633 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.633 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.633 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 219.633 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.633 * [taylor]: Taking taylor expansion of (sqrt k) in n 219.633 * [taylor]: Taking taylor expansion of k in n 219.633 * [backup-simplify]: Simplify k into k 219.633 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 219.633 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 219.633 * [taylor]: Taking taylor expansion of (* (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 219.633 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n 219.633 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n 219.633 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n 219.633 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 219.633 * [taylor]: Taking taylor expansion of 1/2 in n 219.633 * [backup-simplify]: Simplify 1/2 into 1/2 219.633 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.633 * [taylor]: Taking taylor expansion of 1/2 in n 219.633 * [backup-simplify]: Simplify 1/2 into 1/2 219.633 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.633 * [taylor]: Taking taylor expansion of k in n 219.633 * [backup-simplify]: Simplify k into k 219.633 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.633 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 219.633 * [taylor]: Taking taylor expansion of (/ 1 n) in n 219.634 * [taylor]: Taking taylor expansion of n in n 219.634 * [backup-simplify]: Simplify 0 into 0 219.634 * [backup-simplify]: Simplify 1 into 1 219.634 * [backup-simplify]: Simplify (/ 1 1) into 1 219.634 * [backup-simplify]: Simplify (log 1) into 0 219.634 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.634 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 219.634 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 219.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.635 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) 219.635 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.635 * [taylor]: Taking taylor expansion of (sqrt k) in n 219.635 * [taylor]: Taking taylor expansion of k in n 219.635 * [backup-simplify]: Simplify k into k 219.635 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 219.635 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 219.635 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (sqrt k)) into (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (sqrt k)) 219.635 * [taylor]: Taking taylor expansion of (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (sqrt k)) in k 219.635 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k 219.635 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k 219.635 * [taylor]: Taking taylor expansion of -1 in k 219.635 * [backup-simplify]: Simplify -1 into -1 219.635 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k 219.635 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 219.635 * [taylor]: Taking taylor expansion of 1/2 in k 219.635 * [backup-simplify]: Simplify 1/2 into 1/2 219.635 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.635 * [taylor]: Taking taylor expansion of 1/2 in k 219.635 * [backup-simplify]: Simplify 1/2 into 1/2 219.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.635 * [taylor]: Taking taylor expansion of k in k 219.635 * [backup-simplify]: Simplify 0 into 0 219.635 * [backup-simplify]: Simplify 1 into 1 219.635 * [backup-simplify]: Simplify (/ 1 1) into 1 219.635 * [taylor]: Taking taylor expansion of (log n) in k 219.635 * [taylor]: Taking taylor expansion of n in k 219.636 * [backup-simplify]: Simplify n into n 219.636 * [backup-simplify]: Simplify (log n) into (log n) 219.636 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.636 * [backup-simplify]: Simplify (- 1/2) into -1/2 219.636 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 219.636 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n)) 219.636 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n)) 219.636 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 219.637 * [taylor]: Taking taylor expansion of (sqrt k) in k 219.637 * [taylor]: Taking taylor expansion of k in k 219.637 * [backup-simplify]: Simplify 0 into 0 219.637 * [backup-simplify]: Simplify 1 into 1 219.637 * [backup-simplify]: Simplify (sqrt 0) into 0 219.638 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 219.638 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) into 0 219.638 * [backup-simplify]: Simplify 0 into 0 219.638 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 219.639 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 219.639 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.639 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.640 * [backup-simplify]: Simplify (- 0) into 0 219.640 * [backup-simplify]: Simplify (+ 0 0) into 0 219.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.640 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 219.641 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 219.641 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (* 0 (sqrt k))) into 0 219.641 * [taylor]: Taking taylor expansion of 0 in k 219.641 * [backup-simplify]: Simplify 0 into 0 219.641 * [backup-simplify]: Simplify 0 into 0 219.641 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) 219.641 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) 219.642 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 219.642 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.644 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 219.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 219.645 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 219.645 * [backup-simplify]: Simplify (- 0) into 0 219.645 * [backup-simplify]: Simplify (+ 0 0) into 0 219.645 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.646 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 219.646 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 219.647 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0 219.647 * [taylor]: Taking taylor expansion of 0 in k 219.647 * [backup-simplify]: Simplify 0 into 0 219.647 * [backup-simplify]: Simplify 0 into 0 219.647 * [backup-simplify]: Simplify 0 into 0 219.651 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 219.652 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) 219.652 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) 219.653 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 219.653 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.656 * [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 0 219.656 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 219.657 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 219.657 * [backup-simplify]: Simplify (- 0) into 0 219.657 * [backup-simplify]: Simplify (+ 0 0) into 0 219.657 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 219.658 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 219.659 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 219.659 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0 219.659 * [taylor]: Taking taylor expansion of 0 in k 219.659 * [backup-simplify]: Simplify 0 into 0 219.659 * [backup-simplify]: Simplify 0 into 0 219.659 * [backup-simplify]: Simplify 0 into 0 219.660 * [backup-simplify]: Simplify 0 into 0 219.662 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 219.662 * [backup-simplify]: Simplify (+ (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) 219.662 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) into (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))))) 219.663 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow k 3)))))))) 219.663 * [backup-simplify]: Simplify (/ (pow (/ 1 (- n)) (- 1/2 (* 1/2 (/ 1 (- k))))) (sqrt (/ 1 (- k)))) into (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 219.663 * [approximate]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 219.663 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 219.663 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k 219.663 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k 219.663 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k 219.663 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.663 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.663 * [taylor]: Taking taylor expansion of 1/2 in k 219.663 * [backup-simplify]: Simplify 1/2 into 1/2 219.663 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.663 * [taylor]: Taking taylor expansion of k in k 219.663 * [backup-simplify]: Simplify 0 into 0 219.663 * [backup-simplify]: Simplify 1 into 1 219.664 * [backup-simplify]: Simplify (/ 1 1) into 1 219.664 * [taylor]: Taking taylor expansion of 1/2 in k 219.664 * [backup-simplify]: Simplify 1/2 into 1/2 219.664 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 219.664 * [taylor]: Taking taylor expansion of (/ -1 n) in k 219.664 * [taylor]: Taking taylor expansion of -1 in k 219.664 * [backup-simplify]: Simplify -1 into -1 219.664 * [taylor]: Taking taylor expansion of n in k 219.664 * [backup-simplify]: Simplify n into n 219.664 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 219.664 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 219.664 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.664 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.665 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n))) 219.665 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) 219.665 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 219.665 * [taylor]: Taking taylor expansion of (/ -1 k) in k 219.665 * [taylor]: Taking taylor expansion of -1 in k 219.665 * [backup-simplify]: Simplify -1 into -1 219.665 * [taylor]: Taking taylor expansion of k in k 219.665 * [backup-simplify]: Simplify 0 into 0 219.665 * [backup-simplify]: Simplify 1 into 1 219.665 * [backup-simplify]: Simplify (/ -1 1) into -1 219.665 * [backup-simplify]: Simplify (sqrt 0) into 0 219.666 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 219.666 * [backup-simplify]: Simplify (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) +nan.0) into (* +nan.0 (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))) 219.666 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 219.666 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.666 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.666 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.666 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.666 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.666 * [taylor]: Taking taylor expansion of 1/2 in n 219.666 * [backup-simplify]: Simplify 1/2 into 1/2 219.666 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.666 * [taylor]: Taking taylor expansion of k in n 219.666 * [backup-simplify]: Simplify k into k 219.666 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.666 * [taylor]: Taking taylor expansion of 1/2 in n 219.666 * [backup-simplify]: Simplify 1/2 into 1/2 219.666 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.666 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.666 * [taylor]: Taking taylor expansion of -1 in n 219.666 * [backup-simplify]: Simplify -1 into -1 219.666 * [taylor]: Taking taylor expansion of n in n 219.666 * [backup-simplify]: Simplify 0 into 0 219.667 * [backup-simplify]: Simplify 1 into 1 219.667 * [backup-simplify]: Simplify (/ -1 1) into -1 219.667 * [backup-simplify]: Simplify (log -1) into (log -1) 219.667 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.667 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.668 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.668 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.668 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.668 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 219.668 * [taylor]: Taking taylor expansion of (/ -1 k) in n 219.668 * [taylor]: Taking taylor expansion of -1 in n 219.668 * [backup-simplify]: Simplify -1 into -1 219.668 * [taylor]: Taking taylor expansion of k in n 219.668 * [backup-simplify]: Simplify k into k 219.668 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 219.668 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 219.669 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 219.669 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 219.669 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 219.669 * [taylor]: Taking taylor expansion of (/ (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 219.669 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n 219.669 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n 219.669 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n 219.669 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 219.669 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 219.669 * [taylor]: Taking taylor expansion of 1/2 in n 219.669 * [backup-simplify]: Simplify 1/2 into 1/2 219.669 * [taylor]: Taking taylor expansion of (/ 1 k) in n 219.669 * [taylor]: Taking taylor expansion of k in n 219.669 * [backup-simplify]: Simplify k into k 219.669 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 219.669 * [taylor]: Taking taylor expansion of 1/2 in n 219.669 * [backup-simplify]: Simplify 1/2 into 1/2 219.669 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 219.669 * [taylor]: Taking taylor expansion of (/ -1 n) in n 219.669 * [taylor]: Taking taylor expansion of -1 in n 219.669 * [backup-simplify]: Simplify -1 into -1 219.669 * [taylor]: Taking taylor expansion of n in n 219.669 * [backup-simplify]: Simplify 0 into 0 219.669 * [backup-simplify]: Simplify 1 into 1 219.670 * [backup-simplify]: Simplify (/ -1 1) into -1 219.670 * [backup-simplify]: Simplify (log -1) into (log -1) 219.670 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 219.670 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 219.670 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.671 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) 219.671 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.671 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 219.671 * [taylor]: Taking taylor expansion of (/ -1 k) in n 219.671 * [taylor]: Taking taylor expansion of -1 in n 219.671 * [backup-simplify]: Simplify -1 into -1 219.671 * [taylor]: Taking taylor expansion of k in n 219.671 * [backup-simplify]: Simplify k into k 219.671 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 219.671 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 219.671 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 219.671 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 219.672 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) 219.672 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) in k 219.672 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k 219.672 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k 219.672 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 219.672 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 219.672 * [taylor]: Taking taylor expansion of 1/2 in k 219.672 * [backup-simplify]: Simplify 1/2 into 1/2 219.672 * [taylor]: Taking taylor expansion of (/ 1 k) in k 219.672 * [taylor]: Taking taylor expansion of k in k 219.672 * [backup-simplify]: Simplify 0 into 0 219.672 * [backup-simplify]: Simplify 1 into 1 219.672 * [backup-simplify]: Simplify (/ 1 1) into 1 219.672 * [taylor]: Taking taylor expansion of 1/2 in k 219.672 * [backup-simplify]: Simplify 1/2 into 1/2 219.672 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 219.672 * [taylor]: Taking taylor expansion of (log -1) in k 219.672 * [taylor]: Taking taylor expansion of -1 in k 219.672 * [backup-simplify]: Simplify -1 into -1 219.673 * [backup-simplify]: Simplify (log -1) into (log -1) 219.673 * [taylor]: Taking taylor expansion of (log n) in k 219.673 * [taylor]: Taking taylor expansion of n in k 219.673 * [backup-simplify]: Simplify n into n 219.673 * [backup-simplify]: Simplify (log n) into (log n) 219.673 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 219.673 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 219.673 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 219.673 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 219.674 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n))) 219.674 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) 219.674 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 219.674 * [taylor]: Taking taylor expansion of (/ -1 k) in k 219.674 * [taylor]: Taking taylor expansion of -1 in k 219.674 * [backup-simplify]: Simplify -1 into -1 219.674 * [taylor]: Taking taylor expansion of k in k 219.674 * [backup-simplify]: Simplify 0 into 0 219.674 * [backup-simplify]: Simplify 1 into 1 219.674 * [backup-simplify]: Simplify (/ -1 1) into -1 219.675 * [backup-simplify]: Simplify (sqrt 0) into 0 219.675 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 219.676 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 219.676 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) 219.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 219.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 219.678 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 219.678 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 219.678 * [backup-simplify]: Simplify (+ 0 0) into 0 219.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.679 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0 219.680 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 219.680 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 219.680 * [taylor]: Taking taylor expansion of 0 in k 219.680 * [backup-simplify]: Simplify 0 into 0 219.680 * [backup-simplify]: Simplify 0 into 0 219.681 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 219.682 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 219.683 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 219.684 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 219.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.686 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 219.686 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 219.686 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 219.686 * [backup-simplify]: Simplify (+ 0 0) into 0 219.687 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 219.687 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 219.688 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 219.689 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 219.689 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 219.689 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 219.690 * [taylor]: Taking taylor expansion of 0 in k 219.690 * [backup-simplify]: Simplify 0 into 0 219.690 * [backup-simplify]: Simplify 0 into 0 219.690 * [backup-simplify]: Simplify 0 into 0 219.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 219.693 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 219.694 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 219.694 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))))) 219.696 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))))))))) 219.696 * * * [progress]: simplifying candidates 219.696 * * * * [progress]: [ 1 / 312 ] simplifiying candidate # 219.696 * * * * [progress]: [ 2 / 312 ] simplifiying candidate # 219.696 * * * * [progress]: [ 3 / 312 ] simplifiying candidate # 219.696 * * * * [progress]: [ 4 / 312 ] simplifiying candidate # 219.696 * * * * [progress]: [ 5 / 312 ] simplifiying candidate # 219.696 * * * * [progress]: [ 6 / 312 ] simplifiying candidate # 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* [progress]: [ 22 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 23 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 24 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 25 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 26 / 312 ] simplifiying candidate #real (real->posit16 (pow n (- 1/2 (* 1/2 k))))) (sqrt k))))> 219.697 * * * * [progress]: [ 27 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 28 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 29 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 30 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 31 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 32 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 33 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 34 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 35 / 312 ] simplifiying candidate # 219.697 * * * * [progress]: [ 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simplifiying candidate # 219.698 * * * * [progress]: [ 52 / 312 ] simplifiying candidate #real (real->posit16 (pow PI (- 1/2 (* 1/2 k)))))) (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))))> 219.698 * * * * [progress]: [ 53 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 54 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 55 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 56 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 57 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 58 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 59 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 60 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 61 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 62 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 63 / 312 ] simplifiying candidate # 219.698 * * * * [progress]: [ 64 / 312 ] simplifiying candidate # 219.698 * * * * 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candidate # 219.703 * * * * [progress]: [ 170 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 171 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 172 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 173 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 174 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 175 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 176 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 177 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 178 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 179 / 312 ] simplifiying candidate # 219.703 * * * * [progress]: [ 180 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 181 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 182 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 183 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 184 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 185 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 186 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 187 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 188 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 189 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 190 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 191 / 312 ] simplifiying candidate #real (real->posit16 (* (* (pow 2 (- 1/2 (* 1/2 k))) (pow PI (- 1/2 (* 1/2 k)))) (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))))))> 219.704 * * * * [progress]: [ 192 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 193 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 194 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 195 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 196 / 312 ] simplifiying candidate # 219.704 * * * * [progress]: [ 197 / 312 ] 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* * * * [progress]: [ 272 / 312 ] simplifiying candidate # 219.707 * * * * [progress]: [ 273 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 274 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 275 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 276 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 277 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 278 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 279 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 280 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 281 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 282 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 283 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 284 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 285 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 286 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 287 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 288 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 289 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 290 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 291 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 292 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 293 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 294 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 295 / 312 ] simplifiying candidate # 219.708 * * * * [progress]: [ 296 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 297 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 298 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 299 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 300 / 312 ] simplifiying candidate #real (real->posit16 (/ (pow n (- 1/2 (* 1/2 k))) (sqrt k))))))> 219.709 * * * * [progress]: [ 301 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 302 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 303 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 304 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 305 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 306 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 307 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 308 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 309 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 310 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 311 / 312 ] simplifiying candidate # 219.709 * * * * [progress]: [ 312 / 312 ] simplifiying candidate # 219.712 * [simplify]: Simplifying: (expm1 (pow n (- 1/2 (* 1/2 k)))) (log1p (pow n (- 1/2 (* 1/2 k)))) (* (log n) (- 1/2 (* 1/2 k))) (* (log n) (- 1/2 (* 1/2 k))) (* 1 (- 1/2 (* 1/2 k))) (pow n 1/2) (pow n (* 1/2 k)) (pow n (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k))))) (pow n (sqrt (- 1/2 (* 1/2 k)))) (pow n 1) (pow n (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* k 1/2)))) (pow n (fma (- k) 1/2 (* k 1/2))) (pow n (fma (sqrt 1/2) (sqrt 1/2) (- (* k 1/2)))) (pow n (fma (- k) 1/2 (* k 1/2))) (pow n (fma 1 1/2 (- (* k 1/2)))) (pow n (fma (- k) 1/2 (* k 1/2))) (pow n 1/2) (pow n (- (* 1/2 k))) (pow n 1/2) (pow n (- (* 1/2 k))) (pow (* (cbrt n) (cbrt n)) (- 1/2 (* 1/2 k))) (pow (cbrt n) (- 1/2 (* 1/2 k))) (pow (sqrt n) (- 1/2 (* 1/2 k))) (pow (sqrt n) (- 1/2 (* 1/2 k))) (pow 1 (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k))) (log (pow n (- 1/2 (* 1/2 k)))) (exp (pow n (- 1/2 (* 1/2 k)))) (* (cbrt (pow n (- 1/2 (* 1/2 k)))) (cbrt (pow n (- 1/2 (* 1/2 k))))) (cbrt (pow n (- 1/2 (* 1/2 k)))) (* (* (pow n (- 1/2 (* 1/2 k))) (pow n (- 1/2 (* 1/2 k)))) (pow n (- 1/2 (* 1/2 k)))) (sqrt (pow n (- 1/2 (* 1/2 k)))) (sqrt (pow n (- 1/2 (* 1/2 k)))) (pow n (/ (- 1/2 (* 1/2 k)) 2)) (pow 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(* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))))))))) 219.718 * * [simplify]: iteration 1: (466 enodes) 219.888 * * [simplify]: iteration 2: (1395 enodes) 220.477 * * [simplify]: Extracting #0: cost 197 inf + 0 220.479 * * [simplify]: Extracting #1: cost 853 inf + 44 220.485 * * [simplify]: Extracting #2: cost 1362 inf + 2836 220.494 * * [simplify]: Extracting #3: cost 1440 inf + 66395 220.533 * * [simplify]: Extracting #4: cost 763 inf + 447879 220.617 * * [simplify]: Extracting #5: cost 223 inf + 766503 220.717 * * [simplify]: Extracting #6: cost 75 inf + 830192 220.827 * * [simplify]: Extracting #7: cost 15 inf + 878821 220.940 * * [simplify]: Extracting #8: cost 0 inf + 884361 221.054 * * [simplify]: Extracting #9: cost 0 inf + 880461 221.168 * * [simplify]: Extracting #10: cost 0 inf + 880421 221.284 * [simplify]: Simplified to: (expm1 (pow n (- 1/2 (* k 1/2)))) (log1p (pow n (- 1/2 (* k 1/2)))) (* (- 1/2 (* k 1/2)) (log n)) (* (- 1/2 (* k 1/2)) (log n)) (- 1/2 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(* (exp (+ (* (- 1/2 (* k 1/2)) (- (log -1) (log (/ -1 n)))) (* (- 1/2 (* k 1/2)) (log 2)))) (pow PI (- 1/2 (* k 1/2)))) k)))) (- (fma (* +nan.0 (sqrt n)) k (- (fma (* +nan.0 (sqrt n)) (* k (log n)) (+ (* (- (* +nan.0 (sqrt n))) (* (* k (log n)) (* k (log n)))) (fma (* +nan.0 (sqrt n)) (* k k) (- (- (* +nan.0 (sqrt n))) (* (- (* +nan.0 (sqrt n))) (* (log n) (* k k)))))))))) (+ (- (/ (/ (* (exp (- (- (* (log n) (- 1/2 (* k 1/2)))))) +nan.0) k) k)) (- (/ (* (exp (- (- (* (log n) (- 1/2 (* k 1/2)))))) +nan.0) k) (/ (/ (* (exp (- (- (* (log n) (- 1/2 (* k 1/2)))))) +nan.0) k) (* k k)))) (+ (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log -1) (log (/ -1 n))))) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (- (log -1) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* k 1/2)) (- (log -1) (log (/ -1 n)))))))) 221.313 * * * [progress]: adding candidates to table 223.963 * [progress]: [Phase 3 of 3] Extracting. 223.963 * * [regime]: Finding splitpoints for: (# # # # # # # #) 223.965 * * * [regime-changes]: Trying 2 branch expressions: (n k) 223.965 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 224.008 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 224.050 * * * [regime]: Found split indices: #