54.667 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.185 * * * [progress]: [2/2] Setting up program. 0.230 * [progress]: [Phase 2 of 3] Improving. 0.230 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.230 * * [simplify]: Extracting # 0 : cost 0 0.230 * * [simplify]: Extracting # 1 : cost 0 0.230 * * [simplify]: Extracting # 2 : cost 0 0.230 * * [simplify]: Extracting # 3 : cost 0 0.231 * * [simplify]: Extracting # 4 : cost 0 0.231 * * [simplify]: Extracting # 5 : cost 0 0.231 * * [simplify]: Extracting # 6 : cost 0 0.231 * * [simplify]: Extracting # 7 : cost 0 0.231 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.235 * * [simplify]: Extracting # 0 : cost 0 0.235 * * [simplify]: Extracting # 1 : cost 0 0.235 * * [simplify]: Extracting # 2 : cost 0 0.235 * * [simplify]: Extracting # 3 : cost 0 0.235 * * [simplify]: Extracting # 4 : cost 0 0.235 * * [simplify]: Extracting # 5 : cost 0 0.235 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.243 * * [simplify]: Extracting # 0 : cost 0 0.243 * * [simplify]: Extracting # 1 : cost 0 0.243 * * [simplify]: Extracting # 2 : cost 0 0.243 * * [simplify]: Extracting # 3 : cost 0 0.243 * * [simplify]: Extracting # 4 : cost 0 0.243 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.256 * * [simplify]: Extracting # 0 : cost 0 0.256 * * [simplify]: Extracting # 1 : cost 0 0.256 * * [simplify]: Extracting # 2 : cost 0 0.256 * * [simplify]: Extracting # 3 : cost 0 0.256 * * [simplify]: Extracting # 4 : cost 0 0.257 * * [simplify]: iteration 3 : 119 enodes (cost 16 ) 0.311 * * [simplify]: Extracting # 0 : cost 0 0.312 * * [simplify]: Extracting # 1 : cost 0 0.313 * * [simplify]: Extracting # 2 : cost 0 0.313 * * [simplify]: Extracting # 3 : cost 0 0.314 * * [simplify]: Extracting # 4 : cost 0 0.314 * * [simplify]: iteration 4 : 313 enodes (cost 16 ) 0.575 * * [simplify]: Extracting # 0 : cost 0 0.577 * * [simplify]: Extracting # 1 : cost 0 0.579 * * [simplify]: Extracting # 2 : cost 0 0.580 * * [simplify]: Extracting # 3 : cost 0 0.581 * * [simplify]: Extracting # 4 : cost 0 0.583 * * [simplify]: iteration 5 : 853 enodes (cost 16 ) 2.178 * * [simplify]: Extracting # 0 : cost 0 2.184 * * [simplify]: Extracting # 1 : cost 0 2.190 * * [simplify]: Extracting # 2 : cost 0 2.195 * * [simplify]: Extracting # 3 : cost 0 2.200 * * [simplify]: Extracting # 4 : cost 0 2.210 * * [simplify]: iteration 6 : 3196 enodes (cost 16 ) 4.192 * * [simplify]: Extracting # 0 : cost 0 4.202 * * [simplify]: Extracting # 1 : cost 0 4.212 * * [simplify]: Extracting # 2 : cost 0 4.221 * * [simplify]: Extracting # 3 : cost 0 4.225 * * [simplify]: Extracting # 4 : cost 0 4.233 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 4.233 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 4.234 * * [progress]: iteration 1 / 4 4.234 * * * [progress]: picking best candidate 4.236 * * * * [pick]: Picked # 4.236 * * * [progress]: localizing error 4.258 * * * [progress]: generating rewritten candidates 4.258 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.284 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1) 4.291 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 4.321 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 4.389 * * * [progress]: generating series expansions 4.389 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.390 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.390 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.390 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.390 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.390 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.390 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.390 * [taylor]: Taking taylor expansion of 0.5 in k 4.390 * [backup-simplify]: Simplify 0.5 into 0.5 4.390 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.390 * [taylor]: Taking taylor expansion of 1.0 in k 4.390 * [backup-simplify]: Simplify 1.0 into 1.0 4.390 * [taylor]: Taking taylor expansion of k in k 4.390 * [backup-simplify]: Simplify 0 into 0 4.390 * [backup-simplify]: Simplify 1 into 1 4.390 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.390 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.390 * [taylor]: Taking taylor expansion of 2.0 in k 4.391 * [backup-simplify]: Simplify 2.0 into 2.0 4.391 * [taylor]: Taking taylor expansion of (* n PI) in k 4.391 * [taylor]: Taking taylor expansion of n in k 4.391 * [backup-simplify]: Simplify n into n 4.391 * [taylor]: Taking taylor expansion of PI in k 4.391 * [backup-simplify]: Simplify PI into PI 4.391 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.391 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.391 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.391 * [backup-simplify]: Simplify (- 0) into 0 4.391 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.392 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.392 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.392 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.392 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.392 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.392 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.392 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.392 * [taylor]: Taking taylor expansion of 0.5 in n 4.392 * [backup-simplify]: Simplify 0.5 into 0.5 4.392 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.392 * [taylor]: Taking taylor expansion of 1.0 in n 4.392 * [backup-simplify]: Simplify 1.0 into 1.0 4.392 * [taylor]: Taking taylor expansion of k in n 4.392 * [backup-simplify]: Simplify k into k 4.392 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.392 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.392 * [taylor]: Taking taylor expansion of 2.0 in n 4.392 * [backup-simplify]: Simplify 2.0 into 2.0 4.392 * [taylor]: Taking taylor expansion of (* n PI) in n 4.392 * [taylor]: Taking taylor expansion of n in n 4.392 * [backup-simplify]: Simplify 0 into 0 4.392 * [backup-simplify]: Simplify 1 into 1 4.392 * [taylor]: Taking taylor expansion of PI in n 4.392 * [backup-simplify]: Simplify PI into PI 4.392 * [backup-simplify]: Simplify (* 0 PI) into 0 4.393 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.394 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.395 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.395 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.395 * [backup-simplify]: Simplify (- k) into (- k) 4.395 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.395 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.396 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.397 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.398 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.398 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.398 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.398 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.398 * [taylor]: Taking taylor expansion of 0.5 in n 4.398 * [backup-simplify]: Simplify 0.5 into 0.5 4.398 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.398 * [taylor]: Taking taylor expansion of 1.0 in n 4.398 * [backup-simplify]: Simplify 1.0 into 1.0 4.398 * [taylor]: Taking taylor expansion of k in n 4.398 * [backup-simplify]: Simplify k into k 4.398 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.398 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.398 * [taylor]: Taking taylor expansion of 2.0 in n 4.398 * [backup-simplify]: Simplify 2.0 into 2.0 4.398 * [taylor]: Taking taylor expansion of (* n PI) in n 4.398 * [taylor]: Taking taylor expansion of n in n 4.398 * [backup-simplify]: Simplify 0 into 0 4.398 * [backup-simplify]: Simplify 1 into 1 4.398 * [taylor]: Taking taylor expansion of PI in n 4.398 * [backup-simplify]: Simplify PI into PI 4.398 * [backup-simplify]: Simplify (* 0 PI) into 0 4.399 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.400 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.401 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.401 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.401 * [backup-simplify]: Simplify (- k) into (- k) 4.401 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.401 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.402 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.403 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.404 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.404 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.404 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.404 * [taylor]: Taking taylor expansion of 0.5 in k 4.404 * [backup-simplify]: Simplify 0.5 into 0.5 4.404 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.404 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.404 * [taylor]: Taking taylor expansion of 1.0 in k 4.404 * [backup-simplify]: Simplify 1.0 into 1.0 4.404 * [taylor]: Taking taylor expansion of k in k 4.404 * [backup-simplify]: Simplify 0 into 0 4.404 * [backup-simplify]: Simplify 1 into 1 4.404 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.404 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.404 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.404 * [taylor]: Taking taylor expansion of 2.0 in k 4.404 * [backup-simplify]: Simplify 2.0 into 2.0 4.404 * [taylor]: Taking taylor expansion of PI in k 4.404 * [backup-simplify]: Simplify PI into PI 4.405 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.405 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.405 * [taylor]: Taking taylor expansion of (log n) in k 4.405 * [taylor]: Taking taylor expansion of n in k 4.405 * [backup-simplify]: Simplify n into n 4.405 * [backup-simplify]: Simplify (log n) into (log n) 4.406 * [backup-simplify]: Simplify (- 0) into 0 4.406 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.407 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.407 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.408 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.409 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.409 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.410 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.411 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.412 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.412 * [backup-simplify]: Simplify (- 0) into 0 4.412 * [backup-simplify]: Simplify (+ 0 0) into 0 4.412 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.413 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.418 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.420 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.421 * [taylor]: Taking taylor expansion of 0 in k 4.421 * [backup-simplify]: Simplify 0 into 0 4.421 * [backup-simplify]: Simplify 0 into 0 4.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.424 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.425 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.425 * [backup-simplify]: Simplify (+ 0 0) into 0 4.426 * [backup-simplify]: Simplify (- 1) into -1 4.426 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.428 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.430 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 4.433 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.435 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.435 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.436 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.438 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.438 * [backup-simplify]: Simplify (- 0) into 0 4.438 * [backup-simplify]: Simplify (+ 0 0) into 0 4.439 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.440 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.441 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.442 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.442 * [taylor]: Taking taylor expansion of 0 in k 4.442 * [backup-simplify]: Simplify 0 into 0 4.442 * [backup-simplify]: Simplify 0 into 0 4.442 * [backup-simplify]: Simplify 0 into 0 4.443 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.445 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.446 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.446 * [backup-simplify]: Simplify (+ 0 0) into 0 4.447 * [backup-simplify]: Simplify (- 0) into 0 4.447 * [backup-simplify]: Simplify (+ 0 0) into 0 4.448 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.450 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.452 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.456 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.462 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.462 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 4.462 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.462 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.462 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.463 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.463 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.463 * [taylor]: Taking taylor expansion of 0.5 in k 4.463 * [backup-simplify]: Simplify 0.5 into 0.5 4.463 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.463 * [taylor]: Taking taylor expansion of 1.0 in k 4.463 * [backup-simplify]: Simplify 1.0 into 1.0 4.463 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.463 * [taylor]: Taking taylor expansion of k in k 4.463 * [backup-simplify]: Simplify 0 into 0 4.463 * [backup-simplify]: Simplify 1 into 1 4.463 * [backup-simplify]: Simplify (/ 1 1) into 1 4.463 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.463 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.463 * [taylor]: Taking taylor expansion of 2.0 in k 4.463 * [backup-simplify]: Simplify 2.0 into 2.0 4.463 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.463 * [taylor]: Taking taylor expansion of PI in k 4.463 * [backup-simplify]: Simplify PI into PI 4.463 * [taylor]: Taking taylor expansion of n in k 4.463 * [backup-simplify]: Simplify n into n 4.463 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.463 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.463 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.463 * [backup-simplify]: Simplify (- 1) into -1 4.464 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.464 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.464 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.465 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.465 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.465 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.465 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.465 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.465 * [taylor]: Taking taylor expansion of 0.5 in n 4.465 * [backup-simplify]: Simplify 0.5 into 0.5 4.465 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.465 * [taylor]: Taking taylor expansion of 1.0 in n 4.465 * [backup-simplify]: Simplify 1.0 into 1.0 4.465 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.465 * [taylor]: Taking taylor expansion of k in n 4.465 * [backup-simplify]: Simplify k into k 4.465 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.465 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.465 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.465 * [taylor]: Taking taylor expansion of 2.0 in n 4.465 * [backup-simplify]: Simplify 2.0 into 2.0 4.465 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.465 * [taylor]: Taking taylor expansion of PI in n 4.465 * [backup-simplify]: Simplify PI into PI 4.465 * [taylor]: Taking taylor expansion of n in n 4.465 * [backup-simplify]: Simplify 0 into 0 4.465 * [backup-simplify]: Simplify 1 into 1 4.466 * [backup-simplify]: Simplify (/ PI 1) into PI 4.466 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.467 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.468 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.468 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.468 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.469 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.470 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.472 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.472 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.472 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.472 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.472 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.472 * [taylor]: Taking taylor expansion of 0.5 in n 4.472 * [backup-simplify]: Simplify 0.5 into 0.5 4.472 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.472 * [taylor]: Taking taylor expansion of 1.0 in n 4.472 * [backup-simplify]: Simplify 1.0 into 1.0 4.472 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.472 * [taylor]: Taking taylor expansion of k in n 4.472 * [backup-simplify]: Simplify k into k 4.472 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.472 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.472 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.472 * [taylor]: Taking taylor expansion of 2.0 in n 4.472 * [backup-simplify]: Simplify 2.0 into 2.0 4.472 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.472 * [taylor]: Taking taylor expansion of PI in n 4.472 * [backup-simplify]: Simplify PI into PI 4.472 * [taylor]: Taking taylor expansion of n in n 4.472 * [backup-simplify]: Simplify 0 into 0 4.472 * [backup-simplify]: Simplify 1 into 1 4.473 * [backup-simplify]: Simplify (/ PI 1) into PI 4.473 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.475 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.475 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.475 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.475 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.476 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.477 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.478 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.478 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.478 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.478 * [taylor]: Taking taylor expansion of 0.5 in k 4.478 * [backup-simplify]: Simplify 0.5 into 0.5 4.478 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.478 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.478 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.478 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.478 * [taylor]: Taking taylor expansion of 2.0 in k 4.478 * [backup-simplify]: Simplify 2.0 into 2.0 4.478 * [taylor]: Taking taylor expansion of PI in k 4.478 * [backup-simplify]: Simplify PI into PI 4.478 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.479 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.479 * [taylor]: Taking taylor expansion of (log n) in k 4.479 * [taylor]: Taking taylor expansion of n in k 4.479 * [backup-simplify]: Simplify n into n 4.479 * [backup-simplify]: Simplify (log n) into (log n) 4.479 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.479 * [taylor]: Taking taylor expansion of 1.0 in k 4.479 * [backup-simplify]: Simplify 1.0 into 1.0 4.479 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.479 * [taylor]: Taking taylor expansion of k in k 4.479 * [backup-simplify]: Simplify 0 into 0 4.479 * [backup-simplify]: Simplify 1 into 1 4.479 * [backup-simplify]: Simplify (/ 1 1) into 1 4.479 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.480 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.480 * [backup-simplify]: Simplify (- 1) into -1 4.481 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.481 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.482 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.483 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.484 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.485 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.486 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.486 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.486 * [backup-simplify]: Simplify (- 0) into 0 4.486 * [backup-simplify]: Simplify (+ 0 0) into 0 4.486 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.488 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.489 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.489 * [taylor]: Taking taylor expansion of 0 in k 4.489 * [backup-simplify]: Simplify 0 into 0 4.489 * [backup-simplify]: Simplify 0 into 0 4.489 * [backup-simplify]: Simplify 0 into 0 4.490 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.491 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.492 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.493 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.493 * [backup-simplify]: Simplify (- 0) into 0 4.493 * [backup-simplify]: Simplify (+ 0 0) into 0 4.494 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.495 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.497 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.497 * [taylor]: Taking taylor expansion of 0 in k 4.497 * [backup-simplify]: Simplify 0 into 0 4.497 * [backup-simplify]: Simplify 0 into 0 4.497 * [backup-simplify]: Simplify 0 into 0 4.497 * [backup-simplify]: Simplify 0 into 0 4.498 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.498 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.502 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.502 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.502 * [backup-simplify]: Simplify (- 0) into 0 4.502 * [backup-simplify]: Simplify (+ 0 0) into 0 4.503 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.505 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.507 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.507 * [taylor]: Taking taylor expansion of 0 in k 4.507 * [backup-simplify]: Simplify 0 into 0 4.507 * [backup-simplify]: Simplify 0 into 0 4.508 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.509 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 4.509 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.509 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.509 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.509 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.509 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.509 * [taylor]: Taking taylor expansion of 0.5 in k 4.509 * [backup-simplify]: Simplify 0.5 into 0.5 4.509 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.509 * [taylor]: Taking taylor expansion of k in k 4.509 * [backup-simplify]: Simplify 0 into 0 4.509 * [backup-simplify]: Simplify 1 into 1 4.510 * [backup-simplify]: Simplify (/ 1 1) into 1 4.510 * [taylor]: Taking taylor expansion of 1.0 in k 4.510 * [backup-simplify]: Simplify 1.0 into 1.0 4.510 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.510 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.510 * [taylor]: Taking taylor expansion of -2.0 in k 4.510 * [backup-simplify]: Simplify -2.0 into -2.0 4.510 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.510 * [taylor]: Taking taylor expansion of PI in k 4.510 * [backup-simplify]: Simplify PI into PI 4.510 * [taylor]: Taking taylor expansion of n in k 4.510 * [backup-simplify]: Simplify n into n 4.510 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.510 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.510 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.511 * [backup-simplify]: Simplify (+ 1 0) into 1 4.511 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.511 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.512 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.512 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.512 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.512 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.512 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.512 * [taylor]: Taking taylor expansion of 0.5 in n 4.512 * [backup-simplify]: Simplify 0.5 into 0.5 4.512 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.512 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.512 * [taylor]: Taking taylor expansion of k in n 4.512 * [backup-simplify]: Simplify k into k 4.512 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.512 * [taylor]: Taking taylor expansion of 1.0 in n 4.512 * [backup-simplify]: Simplify 1.0 into 1.0 4.512 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.512 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.512 * [taylor]: Taking taylor expansion of -2.0 in n 4.512 * [backup-simplify]: Simplify -2.0 into -2.0 4.512 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.512 * [taylor]: Taking taylor expansion of PI in n 4.512 * [backup-simplify]: Simplify PI into PI 4.512 * [taylor]: Taking taylor expansion of n in n 4.512 * [backup-simplify]: Simplify 0 into 0 4.512 * [backup-simplify]: Simplify 1 into 1 4.513 * [backup-simplify]: Simplify (/ PI 1) into PI 4.514 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.515 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.515 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.515 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.517 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.518 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.519 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.519 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.519 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.519 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.519 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.519 * [taylor]: Taking taylor expansion of 0.5 in n 4.519 * [backup-simplify]: Simplify 0.5 into 0.5 4.519 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.519 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.519 * [taylor]: Taking taylor expansion of k in n 4.519 * [backup-simplify]: Simplify k into k 4.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.520 * [taylor]: Taking taylor expansion of 1.0 in n 4.520 * [backup-simplify]: Simplify 1.0 into 1.0 4.520 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.520 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.520 * [taylor]: Taking taylor expansion of -2.0 in n 4.520 * [backup-simplify]: Simplify -2.0 into -2.0 4.520 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.520 * [taylor]: Taking taylor expansion of PI in n 4.520 * [backup-simplify]: Simplify PI into PI 4.520 * [taylor]: Taking taylor expansion of n in n 4.520 * [backup-simplify]: Simplify 0 into 0 4.520 * [backup-simplify]: Simplify 1 into 1 4.520 * [backup-simplify]: Simplify (/ PI 1) into PI 4.521 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.522 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.522 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.522 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.528 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.530 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.531 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.531 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.531 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.531 * [taylor]: Taking taylor expansion of 0.5 in k 4.531 * [backup-simplify]: Simplify 0.5 into 0.5 4.531 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.531 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.531 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.531 * [taylor]: Taking taylor expansion of k in k 4.531 * [backup-simplify]: Simplify 0 into 0 4.531 * [backup-simplify]: Simplify 1 into 1 4.532 * [backup-simplify]: Simplify (/ 1 1) into 1 4.532 * [taylor]: Taking taylor expansion of 1.0 in k 4.532 * [backup-simplify]: Simplify 1.0 into 1.0 4.532 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.532 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.532 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.532 * [taylor]: Taking taylor expansion of -2.0 in k 4.532 * [backup-simplify]: Simplify -2.0 into -2.0 4.532 * [taylor]: Taking taylor expansion of PI in k 4.532 * [backup-simplify]: Simplify PI into PI 4.533 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.534 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.534 * [taylor]: Taking taylor expansion of (log n) in k 4.534 * [taylor]: Taking taylor expansion of n in k 4.534 * [backup-simplify]: Simplify n into n 4.534 * [backup-simplify]: Simplify (log n) into (log n) 4.535 * [backup-simplify]: Simplify (+ 1 0) into 1 4.535 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.536 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.537 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.537 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.538 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.539 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.540 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.541 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.541 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.541 * [backup-simplify]: Simplify (+ 0 0) into 0 4.542 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.542 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.543 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.544 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.544 * [taylor]: Taking taylor expansion of 0 in k 4.544 * [backup-simplify]: Simplify 0 into 0 4.544 * [backup-simplify]: Simplify 0 into 0 4.544 * [backup-simplify]: Simplify 0 into 0 4.545 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.546 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.548 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.548 * [backup-simplify]: Simplify (+ 0 0) into 0 4.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.550 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.552 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.552 * [taylor]: Taking taylor expansion of 0 in k 4.552 * [backup-simplify]: Simplify 0 into 0 4.552 * [backup-simplify]: Simplify 0 into 0 4.552 * [backup-simplify]: Simplify 0 into 0 4.552 * [backup-simplify]: Simplify 0 into 0 4.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.554 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.557 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 4.557 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.557 * [backup-simplify]: Simplify (+ 0 0) into 0 4.558 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.560 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.562 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.562 * [taylor]: Taking taylor expansion of 0 in k 4.562 * [backup-simplify]: Simplify 0 into 0 4.562 * [backup-simplify]: Simplify 0 into 0 4.563 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.563 * * * * [progress]: [ 2 / 4 ] generating series at (2 1) 4.563 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.563 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.563 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.563 * [taylor]: Taking taylor expansion of 1.0 in k 4.563 * [backup-simplify]: Simplify 1.0 into 1.0 4.563 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.563 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.563 * [taylor]: Taking taylor expansion of k in k 4.563 * [backup-simplify]: Simplify 0 into 0 4.563 * [backup-simplify]: Simplify 1 into 1 4.563 * [backup-simplify]: Simplify (/ 1 1) into 1 4.564 * [backup-simplify]: Simplify (sqrt 0) into 0 4.565 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.565 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.565 * [taylor]: Taking taylor expansion of 1.0 in k 4.565 * [backup-simplify]: Simplify 1.0 into 1.0 4.565 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.565 * [taylor]: Taking taylor expansion of k in k 4.565 * [backup-simplify]: Simplify 0 into 0 4.565 * [backup-simplify]: Simplify 1 into 1 4.565 * [backup-simplify]: Simplify (/ 1 1) into 1 4.566 * [backup-simplify]: Simplify (sqrt 0) into 0 4.567 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.567 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.567 * [backup-simplify]: Simplify 0 into 0 4.569 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.569 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.570 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.572 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.574 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.574 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.575 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.578 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.581 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.581 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.583 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.583 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.583 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.583 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.583 * [taylor]: Taking taylor expansion of 1.0 in k 4.583 * [backup-simplify]: Simplify 1.0 into 1.0 4.583 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.583 * [taylor]: Taking taylor expansion of k in k 4.583 * [backup-simplify]: Simplify 0 into 0 4.583 * [backup-simplify]: Simplify 1 into 1 4.584 * [backup-simplify]: Simplify (sqrt 0) into 0 4.585 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.585 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.585 * [taylor]: Taking taylor expansion of 1.0 in k 4.585 * [backup-simplify]: Simplify 1.0 into 1.0 4.585 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.585 * [taylor]: Taking taylor expansion of k in k 4.585 * [backup-simplify]: Simplify 0 into 0 4.585 * [backup-simplify]: Simplify 1 into 1 4.585 * [backup-simplify]: Simplify (sqrt 0) into 0 4.586 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.586 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.586 * [backup-simplify]: Simplify 0 into 0 4.587 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.587 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.589 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.590 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.590 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.593 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.594 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.594 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.595 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.595 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.595 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.595 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.595 * [taylor]: Taking taylor expansion of 1.0 in k 4.595 * [backup-simplify]: Simplify 1.0 into 1.0 4.595 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.596 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.596 * [taylor]: Taking taylor expansion of -1 in k 4.596 * [backup-simplify]: Simplify -1 into -1 4.596 * [taylor]: Taking taylor expansion of k in k 4.596 * [backup-simplify]: Simplify 0 into 0 4.596 * [backup-simplify]: Simplify 1 into 1 4.596 * [backup-simplify]: Simplify (/ -1 1) into -1 4.596 * [backup-simplify]: Simplify (sqrt 0) into 0 4.597 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.597 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.597 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.597 * [taylor]: Taking taylor expansion of 1.0 in k 4.597 * [backup-simplify]: Simplify 1.0 into 1.0 4.597 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.597 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.597 * [taylor]: Taking taylor expansion of -1 in k 4.597 * [backup-simplify]: Simplify -1 into -1 4.597 * [taylor]: Taking taylor expansion of k in k 4.598 * [backup-simplify]: Simplify 0 into 0 4.598 * [backup-simplify]: Simplify 1 into 1 4.598 * [backup-simplify]: Simplify (/ -1 1) into -1 4.598 * [backup-simplify]: Simplify (sqrt 0) into 0 4.599 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.599 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.599 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.600 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.601 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.603 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.603 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.604 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.606 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.609 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.609 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.609 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.610 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 4.610 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.610 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.610 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.610 * [taylor]: Taking taylor expansion of 2.0 in n 4.610 * [backup-simplify]: Simplify 2.0 into 2.0 4.610 * [taylor]: Taking taylor expansion of (* n PI) in n 4.610 * [taylor]: Taking taylor expansion of n in n 4.610 * [backup-simplify]: Simplify 0 into 0 4.610 * [backup-simplify]: Simplify 1 into 1 4.610 * [taylor]: Taking taylor expansion of PI in n 4.610 * [backup-simplify]: Simplify PI into PI 4.610 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.610 * [taylor]: Taking taylor expansion of 2.0 in n 4.610 * [backup-simplify]: Simplify 2.0 into 2.0 4.610 * [taylor]: Taking taylor expansion of (* n PI) in n 4.610 * [taylor]: Taking taylor expansion of n in n 4.610 * [backup-simplify]: Simplify 0 into 0 4.610 * [backup-simplify]: Simplify 1 into 1 4.610 * [taylor]: Taking taylor expansion of PI in n 4.610 * [backup-simplify]: Simplify PI into PI 4.611 * [backup-simplify]: Simplify (* 0 PI) into 0 4.611 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.611 * [backup-simplify]: Simplify 0 into 0 4.612 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.613 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.613 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.614 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.614 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.614 * [backup-simplify]: Simplify 0 into 0 4.615 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.616 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.616 * [backup-simplify]: Simplify 0 into 0 4.617 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.618 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.618 * [backup-simplify]: Simplify 0 into 0 4.620 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.621 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.621 * [backup-simplify]: Simplify 0 into 0 4.623 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.625 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.625 * [backup-simplify]: Simplify 0 into 0 4.627 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.629 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.629 * [backup-simplify]: Simplify 0 into 0 4.630 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.635 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.635 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.635 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.635 * [taylor]: Taking taylor expansion of 2.0 in n 4.635 * [backup-simplify]: Simplify 2.0 into 2.0 4.635 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.635 * [taylor]: Taking taylor expansion of PI in n 4.635 * [backup-simplify]: Simplify PI into PI 4.635 * [taylor]: Taking taylor expansion of n in n 4.635 * [backup-simplify]: Simplify 0 into 0 4.635 * [backup-simplify]: Simplify 1 into 1 4.636 * [backup-simplify]: Simplify (/ PI 1) into PI 4.636 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.636 * [taylor]: Taking taylor expansion of 2.0 in n 4.636 * [backup-simplify]: Simplify 2.0 into 2.0 4.636 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.636 * [taylor]: Taking taylor expansion of PI in n 4.636 * [backup-simplify]: Simplify PI into PI 4.636 * [taylor]: Taking taylor expansion of n in n 4.636 * [backup-simplify]: Simplify 0 into 0 4.636 * [backup-simplify]: Simplify 1 into 1 4.637 * [backup-simplify]: Simplify (/ PI 1) into PI 4.637 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.638 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.639 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.640 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.640 * [backup-simplify]: Simplify 0 into 0 4.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.642 * [backup-simplify]: Simplify 0 into 0 4.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.644 * [backup-simplify]: Simplify 0 into 0 4.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.647 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.647 * [backup-simplify]: Simplify 0 into 0 4.648 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.650 * [backup-simplify]: Simplify 0 into 0 4.651 * [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 4.653 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.653 * [backup-simplify]: Simplify 0 into 0 4.654 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.654 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.654 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.654 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.654 * [taylor]: Taking taylor expansion of -2.0 in n 4.654 * [backup-simplify]: Simplify -2.0 into -2.0 4.654 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.654 * [taylor]: Taking taylor expansion of PI in n 4.654 * [backup-simplify]: Simplify PI into PI 4.654 * [taylor]: Taking taylor expansion of n in n 4.654 * [backup-simplify]: Simplify 0 into 0 4.654 * [backup-simplify]: Simplify 1 into 1 4.655 * [backup-simplify]: Simplify (/ PI 1) into PI 4.655 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.655 * [taylor]: Taking taylor expansion of -2.0 in n 4.655 * [backup-simplify]: Simplify -2.0 into -2.0 4.655 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.655 * [taylor]: Taking taylor expansion of PI in n 4.655 * [backup-simplify]: Simplify PI into PI 4.655 * [taylor]: Taking taylor expansion of n in n 4.655 * [backup-simplify]: Simplify 0 into 0 4.655 * [backup-simplify]: Simplify 1 into 1 4.656 * [backup-simplify]: Simplify (/ PI 1) into PI 4.656 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.657 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.659 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.659 * [backup-simplify]: Simplify 0 into 0 4.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.661 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.661 * [backup-simplify]: Simplify 0 into 0 4.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.663 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.663 * [backup-simplify]: Simplify 0 into 0 4.664 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.666 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.666 * [backup-simplify]: Simplify 0 into 0 4.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.669 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.669 * [backup-simplify]: Simplify 0 into 0 4.670 * [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 4.672 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.672 * [backup-simplify]: Simplify 0 into 0 4.673 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.673 * * * * [progress]: [ 4 / 4 ] generating series at (2) 4.674 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 4.674 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 4.674 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 4.674 * [taylor]: Taking taylor expansion of 1.0 in n 4.674 * [backup-simplify]: Simplify 1.0 into 1.0 4.674 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 4.674 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 4.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.674 * [taylor]: Taking taylor expansion of k in n 4.674 * [backup-simplify]: Simplify k into k 4.674 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.674 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 4.674 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.674 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 4.674 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.674 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.675 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.675 * [taylor]: Taking taylor expansion of 0.5 in n 4.675 * [backup-simplify]: Simplify 0.5 into 0.5 4.675 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.675 * [taylor]: Taking taylor expansion of 1.0 in n 4.675 * [backup-simplify]: Simplify 1.0 into 1.0 4.675 * [taylor]: Taking taylor expansion of k in n 4.675 * [backup-simplify]: Simplify k into k 4.675 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.675 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.675 * [taylor]: Taking taylor expansion of 2.0 in n 4.675 * [backup-simplify]: Simplify 2.0 into 2.0 4.675 * [taylor]: Taking taylor expansion of (* n PI) in n 4.675 * [taylor]: Taking taylor expansion of n in n 4.675 * [backup-simplify]: Simplify 0 into 0 4.675 * [backup-simplify]: Simplify 1 into 1 4.675 * [taylor]: Taking taylor expansion of PI in n 4.675 * [backup-simplify]: Simplify PI into PI 4.676 * [backup-simplify]: Simplify (* 0 PI) into 0 4.676 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.677 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.678 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.679 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.679 * [backup-simplify]: Simplify (- k) into (- k) 4.679 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.679 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.680 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.680 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.681 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.681 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.681 * [taylor]: Taking taylor expansion of 1.0 in k 4.681 * [backup-simplify]: Simplify 1.0 into 1.0 4.681 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.681 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.681 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.681 * [taylor]: Taking taylor expansion of k in k 4.681 * [backup-simplify]: Simplify 0 into 0 4.681 * [backup-simplify]: Simplify 1 into 1 4.681 * [backup-simplify]: Simplify (/ 1 1) into 1 4.682 * [backup-simplify]: Simplify (sqrt 0) into 0 4.683 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.683 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.683 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.683 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.683 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.683 * [taylor]: Taking taylor expansion of 0.5 in k 4.683 * [backup-simplify]: Simplify 0.5 into 0.5 4.683 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.683 * [taylor]: Taking taylor expansion of 1.0 in k 4.683 * [backup-simplify]: Simplify 1.0 into 1.0 4.683 * [taylor]: Taking taylor expansion of k in k 4.683 * [backup-simplify]: Simplify 0 into 0 4.683 * [backup-simplify]: Simplify 1 into 1 4.683 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.683 * [taylor]: Taking taylor expansion of 2.0 in k 4.683 * [backup-simplify]: Simplify 2.0 into 2.0 4.683 * [taylor]: Taking taylor expansion of (* n PI) in k 4.683 * [taylor]: Taking taylor expansion of n in k 4.683 * [backup-simplify]: Simplify n into n 4.683 * [taylor]: Taking taylor expansion of PI in k 4.683 * [backup-simplify]: Simplify PI into PI 4.683 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.683 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.683 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.683 * [backup-simplify]: Simplify (- 0) into 0 4.684 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.684 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.684 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.684 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.684 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 4.684 * [taylor]: Taking taylor expansion of 1.0 in k 4.684 * [backup-simplify]: Simplify 1.0 into 1.0 4.684 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 4.684 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.684 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.684 * [taylor]: Taking taylor expansion of k in k 4.684 * [backup-simplify]: Simplify 0 into 0 4.684 * [backup-simplify]: Simplify 1 into 1 4.685 * [backup-simplify]: Simplify (/ 1 1) into 1 4.685 * [backup-simplify]: Simplify (sqrt 0) into 0 4.686 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.686 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.686 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.686 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.686 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.686 * [taylor]: Taking taylor expansion of 0.5 in k 4.686 * [backup-simplify]: Simplify 0.5 into 0.5 4.686 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.686 * [taylor]: Taking taylor expansion of 1.0 in k 4.686 * [backup-simplify]: Simplify 1.0 into 1.0 4.686 * [taylor]: Taking taylor expansion of k in k 4.686 * [backup-simplify]: Simplify 0 into 0 4.686 * [backup-simplify]: Simplify 1 into 1 4.686 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.686 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.686 * [taylor]: Taking taylor expansion of 2.0 in k 4.686 * [backup-simplify]: Simplify 2.0 into 2.0 4.686 * [taylor]: Taking taylor expansion of (* n PI) in k 4.686 * [taylor]: Taking taylor expansion of n in k 4.686 * [backup-simplify]: Simplify n into n 4.686 * [taylor]: Taking taylor expansion of PI in k 4.686 * [backup-simplify]: Simplify PI into PI 4.686 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.686 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.686 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.686 * [backup-simplify]: Simplify (- 0) into 0 4.687 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.687 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.687 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.687 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.687 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 4.688 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.688 * [taylor]: Taking taylor expansion of 0 in n 4.688 * [backup-simplify]: Simplify 0 into 0 4.688 * [backup-simplify]: Simplify 0 into 0 4.688 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 4.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 4.689 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 4.689 * [backup-simplify]: Simplify (- 1) into -1 4.689 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.690 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 4.691 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 4.691 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.692 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.694 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.694 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 4.694 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.694 * [taylor]: Taking taylor expansion of +nan.0 in n 4.694 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.694 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.694 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.694 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.694 * [taylor]: Taking taylor expansion of 0.5 in n 4.694 * [backup-simplify]: Simplify 0.5 into 0.5 4.694 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.694 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.694 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.694 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.694 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.694 * [taylor]: Taking taylor expansion of 1.0 in n 4.694 * [backup-simplify]: Simplify 1.0 into 1.0 4.694 * [taylor]: Taking taylor expansion of (log PI) in n 4.694 * [taylor]: Taking taylor expansion of PI in n 4.694 * [backup-simplify]: Simplify PI into PI 4.694 * [backup-simplify]: Simplify (log PI) into (log PI) 4.695 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.696 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.696 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.696 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.696 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.696 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.696 * [taylor]: Taking taylor expansion of 1.0 in n 4.696 * [backup-simplify]: Simplify 1.0 into 1.0 4.696 * [taylor]: Taking taylor expansion of (log n) in n 4.696 * [taylor]: Taking taylor expansion of n in n 4.696 * [backup-simplify]: Simplify 0 into 0 4.696 * [backup-simplify]: Simplify 1 into 1 4.696 * [backup-simplify]: Simplify (log 1) into 0 4.697 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.697 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.697 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.697 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.697 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.697 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.697 * [taylor]: Taking taylor expansion of 1.0 in n 4.697 * [backup-simplify]: Simplify 1.0 into 1.0 4.697 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.697 * [taylor]: Taking taylor expansion of 2.0 in n 4.697 * [backup-simplify]: Simplify 2.0 into 2.0 4.697 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.698 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.699 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.699 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.700 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.701 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.702 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.703 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.704 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.705 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 4.706 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.706 * [backup-simplify]: Simplify 0 into 0 4.707 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 4.708 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 4.710 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 4.710 * [backup-simplify]: Simplify (- 0) into 0 4.711 * [backup-simplify]: Simplify (+ 0 0) into 0 4.712 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 4.713 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 4.714 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.715 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.718 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.722 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.727 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 4.727 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 4.727 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 4.727 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 4.727 * [taylor]: Taking taylor expansion of +nan.0 in n 4.727 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.727 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 4.727 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 4.727 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 4.727 * [taylor]: Taking taylor expansion of 0.5 in n 4.727 * [backup-simplify]: Simplify 0.5 into 0.5 4.727 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 4.727 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 4.728 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.728 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.728 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.728 * [taylor]: Taking taylor expansion of 1.0 in n 4.728 * [backup-simplify]: Simplify 1.0 into 1.0 4.728 * [taylor]: Taking taylor expansion of (log PI) in n 4.728 * [taylor]: Taking taylor expansion of PI in n 4.728 * [backup-simplify]: Simplify PI into PI 4.728 * [backup-simplify]: Simplify (log PI) into (log PI) 4.729 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.731 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.731 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 4.731 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.731 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.731 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.731 * [taylor]: Taking taylor expansion of 1.0 in n 4.731 * [backup-simplify]: Simplify 1.0 into 1.0 4.731 * [taylor]: Taking taylor expansion of (log n) in n 4.731 * [taylor]: Taking taylor expansion of n in n 4.731 * [backup-simplify]: Simplify 0 into 0 4.731 * [backup-simplify]: Simplify 1 into 1 4.732 * [backup-simplify]: Simplify (log 1) into 0 4.732 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.732 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.732 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.732 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.732 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.732 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.732 * [taylor]: Taking taylor expansion of 1.0 in n 4.732 * [backup-simplify]: Simplify 1.0 into 1.0 4.732 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.732 * [taylor]: Taking taylor expansion of 2.0 in n 4.733 * [backup-simplify]: Simplify 2.0 into 2.0 4.733 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.734 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.735 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.736 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 4.737 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 4.738 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 4.740 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 4.741 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.741 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 4.741 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 4.741 * [taylor]: Taking taylor expansion of +nan.0 in n 4.741 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.741 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 4.741 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.741 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.742 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.742 * [taylor]: Taking taylor expansion of 0.5 in n 4.742 * [backup-simplify]: Simplify 0.5 into 0.5 4.742 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.742 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.742 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.742 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.742 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.742 * [taylor]: Taking taylor expansion of 1.0 in n 4.742 * [backup-simplify]: Simplify 1.0 into 1.0 4.742 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.742 * [taylor]: Taking taylor expansion of 2.0 in n 4.742 * [backup-simplify]: Simplify 2.0 into 2.0 4.742 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.743 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.745 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.745 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.745 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.745 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.745 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.745 * [taylor]: Taking taylor expansion of 1.0 in n 4.745 * [backup-simplify]: Simplify 1.0 into 1.0 4.745 * [taylor]: Taking taylor expansion of (log PI) in n 4.745 * [taylor]: Taking taylor expansion of PI in n 4.745 * [backup-simplify]: Simplify PI into PI 4.746 * [backup-simplify]: Simplify (log PI) into (log PI) 4.747 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.748 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.748 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.748 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.748 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.748 * [taylor]: Taking taylor expansion of 1.0 in n 4.748 * [backup-simplify]: Simplify 1.0 into 1.0 4.748 * [taylor]: Taking taylor expansion of (log n) in n 4.748 * [taylor]: Taking taylor expansion of n in n 4.748 * [backup-simplify]: Simplify 0 into 0 4.748 * [backup-simplify]: Simplify 1 into 1 4.749 * [backup-simplify]: Simplify (log 1) into 0 4.749 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.749 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.749 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.750 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.751 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.753 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.754 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.756 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.756 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.756 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.756 * [taylor]: Taking taylor expansion of 2.0 in n 4.756 * [backup-simplify]: Simplify 2.0 into 2.0 4.756 * [taylor]: Taking taylor expansion of (* n PI) in n 4.756 * [taylor]: Taking taylor expansion of n in n 4.756 * [backup-simplify]: Simplify 0 into 0 4.756 * [backup-simplify]: Simplify 1 into 1 4.756 * [taylor]: Taking taylor expansion of PI in n 4.756 * [backup-simplify]: Simplify PI into PI 4.757 * [backup-simplify]: Simplify (* 0 PI) into 0 4.757 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.759 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.760 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.761 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.763 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 4.764 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.767 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.769 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.772 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 4.782 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.787 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.791 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.792 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 4.792 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 4.793 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 4.794 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 4.795 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.795 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 4.795 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 4.796 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 4.797 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 4.797 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 4.798 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 4.799 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 4.800 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 4.802 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 4.803 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.804 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 4.804 * [backup-simplify]: Simplify (- 0) into 0 4.804 * [backup-simplify]: Simplify 0 into 0 4.804 * [backup-simplify]: Simplify 0 into 0 4.805 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.806 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 4.808 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 4.808 * [backup-simplify]: Simplify (- 0) into 0 4.808 * [backup-simplify]: Simplify (+ 0 0) into 0 4.809 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 4.810 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 4.811 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.811 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.814 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.818 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 4.830 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 4.830 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 4.830 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 4.830 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 4.830 * [taylor]: Taking taylor expansion of +nan.0 in n 4.830 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.830 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 4.830 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 4.830 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 4.830 * [taylor]: Taking taylor expansion of 0.5 in n 4.830 * [backup-simplify]: Simplify 0.5 into 0.5 4.830 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 4.830 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 4.830 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.830 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.830 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.830 * [taylor]: Taking taylor expansion of 1.0 in n 4.830 * [backup-simplify]: Simplify 1.0 into 1.0 4.830 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.830 * [taylor]: Taking taylor expansion of 2.0 in n 4.830 * [backup-simplify]: Simplify 2.0 into 2.0 4.831 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.832 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.834 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.834 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 4.834 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.834 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.834 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.834 * [taylor]: Taking taylor expansion of 1.0 in n 4.834 * [backup-simplify]: Simplify 1.0 into 1.0 4.834 * [taylor]: Taking taylor expansion of (log n) in n 4.834 * [taylor]: Taking taylor expansion of n in n 4.834 * [backup-simplify]: Simplify 0 into 0 4.834 * [backup-simplify]: Simplify 1 into 1 4.835 * [backup-simplify]: Simplify (log 1) into 0 4.835 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.835 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.835 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.835 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.835 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.835 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.835 * [taylor]: Taking taylor expansion of 1.0 in n 4.835 * [backup-simplify]: Simplify 1.0 into 1.0 4.835 * [taylor]: Taking taylor expansion of (log PI) in n 4.835 * [taylor]: Taking taylor expansion of PI in n 4.835 * [backup-simplify]: Simplify PI into PI 4.836 * [backup-simplify]: Simplify (log PI) into (log PI) 4.837 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.839 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.839 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.841 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.842 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.844 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.846 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.846 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 4.846 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 4.846 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 4.846 * [taylor]: Taking taylor expansion of +nan.0 in n 4.846 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.846 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 4.846 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.846 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.846 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.846 * [taylor]: Taking taylor expansion of 0.5 in n 4.846 * [backup-simplify]: Simplify 0.5 into 0.5 4.846 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.846 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.846 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.846 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.846 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.846 * [taylor]: Taking taylor expansion of 1.0 in n 4.846 * [backup-simplify]: Simplify 1.0 into 1.0 4.846 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.846 * [taylor]: Taking taylor expansion of 2.0 in n 4.846 * [backup-simplify]: Simplify 2.0 into 2.0 4.847 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.848 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.849 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.849 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.849 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.849 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.849 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.850 * [taylor]: Taking taylor expansion of 1.0 in n 4.850 * [backup-simplify]: Simplify 1.0 into 1.0 4.850 * [taylor]: Taking taylor expansion of (log PI) in n 4.850 * [taylor]: Taking taylor expansion of PI in n 4.850 * [backup-simplify]: Simplify PI into PI 4.850 * [backup-simplify]: Simplify (log PI) into (log PI) 4.851 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.853 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.853 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.853 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.853 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.853 * [taylor]: Taking taylor expansion of 1.0 in n 4.853 * [backup-simplify]: Simplify 1.0 into 1.0 4.853 * [taylor]: Taking taylor expansion of (log n) in n 4.853 * [taylor]: Taking taylor expansion of n in n 4.853 * [backup-simplify]: Simplify 0 into 0 4.853 * [backup-simplify]: Simplify 1 into 1 4.853 * [backup-simplify]: Simplify (log 1) into 0 4.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.854 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.854 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.855 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.856 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.857 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.859 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.860 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.860 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.860 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.860 * [taylor]: Taking taylor expansion of 2.0 in n 4.860 * [backup-simplify]: Simplify 2.0 into 2.0 4.860 * [taylor]: Taking taylor expansion of (* n PI) in n 4.860 * [taylor]: Taking taylor expansion of n in n 4.860 * [backup-simplify]: Simplify 0 into 0 4.861 * [backup-simplify]: Simplify 1 into 1 4.861 * [taylor]: Taking taylor expansion of PI in n 4.861 * [backup-simplify]: Simplify PI into PI 4.861 * [backup-simplify]: Simplify (* 0 PI) into 0 4.861 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.863 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.865 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.866 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.866 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 4.866 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 4.866 * [taylor]: Taking taylor expansion of +nan.0 in n 4.866 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.866 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 4.866 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 4.866 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 4.866 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 4.866 * [taylor]: Taking taylor expansion of 0.5 in n 4.866 * [backup-simplify]: Simplify 0.5 into 0.5 4.866 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 4.866 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 4.866 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 4.867 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 4.867 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 4.867 * [taylor]: Taking taylor expansion of 1.0 in n 4.867 * [backup-simplify]: Simplify 1.0 into 1.0 4.867 * [taylor]: Taking taylor expansion of (log 2.0) in n 4.867 * [taylor]: Taking taylor expansion of 2.0 in n 4.867 * [backup-simplify]: Simplify 2.0 into 2.0 4.867 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 4.868 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 4.870 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 4.870 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 4.870 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 4.870 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 4.870 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 4.870 * [taylor]: Taking taylor expansion of 1.0 in n 4.870 * [backup-simplify]: Simplify 1.0 into 1.0 4.870 * [taylor]: Taking taylor expansion of (log PI) in n 4.870 * [taylor]: Taking taylor expansion of PI in n 4.870 * [backup-simplify]: Simplify PI into PI 4.870 * [backup-simplify]: Simplify (log PI) into (log PI) 4.871 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 4.873 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 4.873 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 4.873 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 4.873 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 4.873 * [taylor]: Taking taylor expansion of 1.0 in n 4.873 * [backup-simplify]: Simplify 1.0 into 1.0 4.873 * [taylor]: Taking taylor expansion of (log n) in n 4.873 * [taylor]: Taking taylor expansion of n in n 4.873 * [backup-simplify]: Simplify 0 into 0 4.873 * [backup-simplify]: Simplify 1 into 1 4.874 * [backup-simplify]: Simplify (log 1) into 0 4.874 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 4.874 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 4.874 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 4.875 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 4.876 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 4.877 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 4.879 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 4.880 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 4.880 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 4.880 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.881 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.881 * [taylor]: Taking taylor expansion of 2.0 in n 4.881 * [backup-simplify]: Simplify 2.0 into 2.0 4.881 * [taylor]: Taking taylor expansion of (* n PI) in n 4.881 * [taylor]: Taking taylor expansion of n in n 4.881 * [backup-simplify]: Simplify 0 into 0 4.881 * [backup-simplify]: Simplify 1 into 1 4.881 * [taylor]: Taking taylor expansion of PI in n 4.881 * [backup-simplify]: Simplify PI into PI 4.881 * [backup-simplify]: Simplify (* 0 PI) into 0 4.882 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.883 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.885 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.886 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.887 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.889 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.890 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.893 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.896 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.897 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.898 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.899 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 4.901 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 4.903 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 4.905 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 4.916 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 4.927 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 4.943 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.958 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.968 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 4.983 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 4.984 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 4.984 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 4.984 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 4.984 * [taylor]: Taking taylor expansion of 1.0 in n 4.984 * [backup-simplify]: Simplify 1.0 into 1.0 4.984 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 4.984 * [taylor]: Taking taylor expansion of (sqrt k) in n 4.984 * [taylor]: Taking taylor expansion of k in n 4.984 * [backup-simplify]: Simplify k into k 4.984 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 4.984 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 4.984 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.985 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.985 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.985 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.985 * [taylor]: Taking taylor expansion of 0.5 in n 4.985 * [backup-simplify]: Simplify 0.5 into 0.5 4.985 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.985 * [taylor]: Taking taylor expansion of 1.0 in n 4.985 * [backup-simplify]: Simplify 1.0 into 1.0 4.985 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.985 * [taylor]: Taking taylor expansion of k in n 4.985 * [backup-simplify]: Simplify k into k 4.985 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.985 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.985 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.985 * [taylor]: Taking taylor expansion of 2.0 in n 4.985 * [backup-simplify]: Simplify 2.0 into 2.0 4.985 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.985 * [taylor]: Taking taylor expansion of PI in n 4.985 * [backup-simplify]: Simplify PI into PI 4.985 * [taylor]: Taking taylor expansion of n in n 4.985 * [backup-simplify]: Simplify 0 into 0 4.985 * [backup-simplify]: Simplify 1 into 1 4.985 * [backup-simplify]: Simplify (/ PI 1) into PI 4.986 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.986 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.986 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.986 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.986 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.987 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.988 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.989 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.989 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.989 * [taylor]: Taking taylor expansion of 1.0 in k 4.989 * [backup-simplify]: Simplify 1.0 into 1.0 4.989 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.989 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.989 * [taylor]: Taking taylor expansion of k in k 4.989 * [backup-simplify]: Simplify 0 into 0 4.989 * [backup-simplify]: Simplify 1 into 1 4.989 * [backup-simplify]: Simplify (sqrt 0) into 0 4.990 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.990 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.990 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.990 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.990 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.990 * [taylor]: Taking taylor expansion of 0.5 in k 4.990 * [backup-simplify]: Simplify 0.5 into 0.5 4.990 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.990 * [taylor]: Taking taylor expansion of 1.0 in k 4.990 * [backup-simplify]: Simplify 1.0 into 1.0 4.990 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.990 * [taylor]: Taking taylor expansion of k in k 4.990 * [backup-simplify]: Simplify 0 into 0 4.990 * [backup-simplify]: Simplify 1 into 1 4.991 * [backup-simplify]: Simplify (/ 1 1) into 1 4.991 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.991 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.991 * [taylor]: Taking taylor expansion of 2.0 in k 4.991 * [backup-simplify]: Simplify 2.0 into 2.0 4.991 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.991 * [taylor]: Taking taylor expansion of PI in k 4.991 * [backup-simplify]: Simplify PI into PI 4.991 * [taylor]: Taking taylor expansion of n in k 4.991 * [backup-simplify]: Simplify n into n 4.991 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.991 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.991 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.991 * [backup-simplify]: Simplify (- 1) into -1 4.991 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.992 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.992 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.992 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.992 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 4.992 * [taylor]: Taking taylor expansion of 1.0 in k 4.992 * [backup-simplify]: Simplify 1.0 into 1.0 4.992 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 4.992 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.992 * [taylor]: Taking taylor expansion of k in k 4.992 * [backup-simplify]: Simplify 0 into 0 4.992 * [backup-simplify]: Simplify 1 into 1 4.992 * [backup-simplify]: Simplify (sqrt 0) into 0 4.993 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.993 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.993 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.993 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.993 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.993 * [taylor]: Taking taylor expansion of 0.5 in k 4.993 * [backup-simplify]: Simplify 0.5 into 0.5 4.993 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.993 * [taylor]: Taking taylor expansion of 1.0 in k 4.993 * [backup-simplify]: Simplify 1.0 into 1.0 4.993 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.993 * [taylor]: Taking taylor expansion of k in k 4.993 * [backup-simplify]: Simplify 0 into 0 4.993 * [backup-simplify]: Simplify 1 into 1 4.994 * [backup-simplify]: Simplify (/ 1 1) into 1 4.994 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.994 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.994 * [taylor]: Taking taylor expansion of 2.0 in k 4.994 * [backup-simplify]: Simplify 2.0 into 2.0 4.994 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.994 * [taylor]: Taking taylor expansion of PI in k 4.994 * [backup-simplify]: Simplify PI into PI 4.994 * [taylor]: Taking taylor expansion of n in k 4.994 * [backup-simplify]: Simplify n into n 4.994 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.994 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.994 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.994 * [backup-simplify]: Simplify (- 1) into -1 4.994 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.995 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.995 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.995 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.995 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 4.996 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.996 * [taylor]: Taking taylor expansion of 0 in n 4.996 * [backup-simplify]: Simplify 0 into 0 4.996 * [backup-simplify]: Simplify 0 into 0 4.996 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.996 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 4.997 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 4.997 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 4.997 * [taylor]: Taking taylor expansion of +nan.0 in n 4.997 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.997 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 4.997 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 4.997 * [taylor]: Taking taylor expansion of 0.5 in n 4.997 * [backup-simplify]: Simplify 0.5 into 0.5 4.997 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 4.997 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.997 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.997 * [taylor]: Taking taylor expansion of 2.0 in n 4.997 * [backup-simplify]: Simplify 2.0 into 2.0 4.997 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.997 * [taylor]: Taking taylor expansion of PI in n 4.997 * [backup-simplify]: Simplify PI into PI 4.997 * [taylor]: Taking taylor expansion of n in n 4.997 * [backup-simplify]: Simplify 0 into 0 4.997 * [backup-simplify]: Simplify 1 into 1 4.997 * [backup-simplify]: Simplify (/ PI 1) into PI 4.997 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.998 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.998 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.998 * [taylor]: Taking taylor expansion of 1.0 in n 4.998 * [backup-simplify]: Simplify 1.0 into 1.0 4.998 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.998 * [taylor]: Taking taylor expansion of k in n 4.998 * [backup-simplify]: Simplify k into k 4.998 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.999 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.999 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.000 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.001 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.001 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.002 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.003 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.004 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.004 * [backup-simplify]: Simplify 0 into 0 5.006 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.006 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.007 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.007 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 5.007 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 5.007 * [taylor]: Taking taylor expansion of +nan.0 in n 5.007 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.007 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 5.007 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 5.007 * [taylor]: Taking taylor expansion of 0.5 in n 5.007 * [backup-simplify]: Simplify 0.5 into 0.5 5.007 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 5.007 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.007 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.007 * [taylor]: Taking taylor expansion of 2.0 in n 5.007 * [backup-simplify]: Simplify 2.0 into 2.0 5.007 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.007 * [taylor]: Taking taylor expansion of PI in n 5.007 * [backup-simplify]: Simplify PI into PI 5.007 * [taylor]: Taking taylor expansion of n in n 5.007 * [backup-simplify]: Simplify 0 into 0 5.007 * [backup-simplify]: Simplify 1 into 1 5.008 * [backup-simplify]: Simplify (/ PI 1) into PI 5.008 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.009 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.009 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.009 * [taylor]: Taking taylor expansion of 1.0 in n 5.009 * [backup-simplify]: Simplify 1.0 into 1.0 5.009 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.009 * [taylor]: Taking taylor expansion of k in n 5.009 * [backup-simplify]: Simplify k into k 5.009 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.010 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.010 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.010 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.010 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.016 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.018 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.019 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.020 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.022 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.024 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.025 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.025 * [backup-simplify]: Simplify (- 0) into 0 5.025 * [backup-simplify]: Simplify (+ 0 0) into 0 5.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.027 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.029 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.031 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 5.032 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 5.034 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.036 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 5.036 * [backup-simplify]: Simplify (- 0) into 0 5.036 * [backup-simplify]: Simplify 0 into 0 5.036 * [backup-simplify]: Simplify 0 into 0 5.041 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.042 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.044 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 5.044 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 5.044 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 5.044 * [taylor]: Taking taylor expansion of +nan.0 in n 5.044 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.044 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 5.044 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 5.044 * [taylor]: Taking taylor expansion of 0.5 in n 5.044 * [backup-simplify]: Simplify 0.5 into 0.5 5.044 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 5.044 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.044 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.044 * [taylor]: Taking taylor expansion of 2.0 in n 5.044 * [backup-simplify]: Simplify 2.0 into 2.0 5.044 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.045 * [taylor]: Taking taylor expansion of PI in n 5.045 * [backup-simplify]: Simplify PI into PI 5.045 * [taylor]: Taking taylor expansion of n in n 5.045 * [backup-simplify]: Simplify 0 into 0 5.045 * [backup-simplify]: Simplify 1 into 1 5.045 * [backup-simplify]: Simplify (/ PI 1) into PI 5.046 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.047 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.047 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.047 * [taylor]: Taking taylor expansion of 1.0 in n 5.047 * [backup-simplify]: Simplify 1.0 into 1.0 5.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.047 * [taylor]: Taking taylor expansion of k in n 5.047 * [backup-simplify]: Simplify k into k 5.047 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.049 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.049 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.049 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.050 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 5.051 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.053 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.054 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 5.055 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.056 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 5.061 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 5.063 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 5.063 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 5.063 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 5.063 * [taylor]: Taking taylor expansion of 1.0 in n 5.063 * [backup-simplify]: Simplify 1.0 into 1.0 5.063 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 5.063 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.063 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.063 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.063 * [taylor]: Taking taylor expansion of 0.5 in n 5.063 * [backup-simplify]: Simplify 0.5 into 0.5 5.063 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.063 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.063 * [taylor]: Taking taylor expansion of k in n 5.063 * [backup-simplify]: Simplify k into k 5.063 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.063 * [taylor]: Taking taylor expansion of 1.0 in n 5.063 * [backup-simplify]: Simplify 1.0 into 1.0 5.063 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.063 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.063 * [taylor]: Taking taylor expansion of -2.0 in n 5.063 * [backup-simplify]: Simplify -2.0 into -2.0 5.063 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.063 * [taylor]: Taking taylor expansion of PI in n 5.063 * [backup-simplify]: Simplify PI into PI 5.063 * [taylor]: Taking taylor expansion of n in n 5.064 * [backup-simplify]: Simplify 0 into 0 5.064 * [backup-simplify]: Simplify 1 into 1 5.064 * [backup-simplify]: Simplify (/ PI 1) into PI 5.065 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.066 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.066 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.066 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.067 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.069 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.070 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.070 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 5.070 * [taylor]: Taking taylor expansion of (/ -1 k) in n 5.070 * [taylor]: Taking taylor expansion of -1 in n 5.070 * [backup-simplify]: Simplify -1 into -1 5.070 * [taylor]: Taking taylor expansion of k in n 5.070 * [backup-simplify]: Simplify k into k 5.070 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 5.070 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 5.070 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 5.071 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 5.072 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 5.072 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 5.073 * [taylor]: Taking taylor expansion of 1.0 in k 5.073 * [backup-simplify]: Simplify 1.0 into 1.0 5.073 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 5.073 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.073 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.073 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.073 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.073 * [taylor]: Taking taylor expansion of 0.5 in k 5.073 * [backup-simplify]: Simplify 0.5 into 0.5 5.073 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.073 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.073 * [taylor]: Taking taylor expansion of k in k 5.073 * [backup-simplify]: Simplify 0 into 0 5.073 * [backup-simplify]: Simplify 1 into 1 5.074 * [backup-simplify]: Simplify (/ 1 1) into 1 5.074 * [taylor]: Taking taylor expansion of 1.0 in k 5.074 * [backup-simplify]: Simplify 1.0 into 1.0 5.074 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.074 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.074 * [taylor]: Taking taylor expansion of -2.0 in k 5.074 * [backup-simplify]: Simplify -2.0 into -2.0 5.074 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.074 * [taylor]: Taking taylor expansion of PI in k 5.074 * [backup-simplify]: Simplify PI into PI 5.074 * [taylor]: Taking taylor expansion of n in k 5.074 * [backup-simplify]: Simplify n into n 5.074 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.074 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.074 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.075 * [backup-simplify]: Simplify (+ 1 0) into 1 5.075 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.075 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.076 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.076 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.076 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.076 * [taylor]: Taking taylor expansion of -1 in k 5.076 * [backup-simplify]: Simplify -1 into -1 5.076 * [taylor]: Taking taylor expansion of k in k 5.076 * [backup-simplify]: Simplify 0 into 0 5.076 * [backup-simplify]: Simplify 1 into 1 5.076 * [backup-simplify]: Simplify (/ -1 1) into -1 5.077 * [backup-simplify]: Simplify (sqrt 0) into 0 5.078 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.079 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.079 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 5.079 * [taylor]: Taking taylor expansion of 1.0 in k 5.079 * [backup-simplify]: Simplify 1.0 into 1.0 5.079 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 5.079 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.079 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.079 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.079 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.079 * [taylor]: Taking taylor expansion of 0.5 in k 5.079 * [backup-simplify]: Simplify 0.5 into 0.5 5.079 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.079 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.079 * [taylor]: Taking taylor expansion of k in k 5.079 * [backup-simplify]: Simplify 0 into 0 5.079 * [backup-simplify]: Simplify 1 into 1 5.079 * [backup-simplify]: Simplify (/ 1 1) into 1 5.079 * [taylor]: Taking taylor expansion of 1.0 in k 5.079 * [backup-simplify]: Simplify 1.0 into 1.0 5.080 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.080 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.080 * [taylor]: Taking taylor expansion of -2.0 in k 5.080 * [backup-simplify]: Simplify -2.0 into -2.0 5.080 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.080 * [taylor]: Taking taylor expansion of PI in k 5.080 * [backup-simplify]: Simplify PI into PI 5.080 * [taylor]: Taking taylor expansion of n in k 5.080 * [backup-simplify]: Simplify n into n 5.080 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.080 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.080 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.080 * [backup-simplify]: Simplify (+ 1 0) into 1 5.081 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.081 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.081 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.081 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 5.081 * [taylor]: Taking taylor expansion of (/ -1 k) in k 5.081 * [taylor]: Taking taylor expansion of -1 in k 5.081 * [backup-simplify]: Simplify -1 into -1 5.081 * [taylor]: Taking taylor expansion of k in k 5.081 * [backup-simplify]: Simplify 0 into 0 5.081 * [backup-simplify]: Simplify 1 into 1 5.082 * [backup-simplify]: Simplify (/ -1 1) into -1 5.082 * [backup-simplify]: Simplify (sqrt 0) into 0 5.083 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 5.084 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.084 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 5.084 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.084 * [taylor]: Taking taylor expansion of +nan.0 in n 5.084 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.084 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.084 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.084 * [taylor]: Taking taylor expansion of 0.5 in n 5.084 * [backup-simplify]: Simplify 0.5 into 0.5 5.085 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.085 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.085 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.085 * [taylor]: Taking taylor expansion of k in n 5.085 * [backup-simplify]: Simplify k into k 5.085 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.085 * [taylor]: Taking taylor expansion of 1.0 in n 5.085 * [backup-simplify]: Simplify 1.0 into 1.0 5.085 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.085 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.085 * [taylor]: Taking taylor expansion of -2.0 in n 5.085 * [backup-simplify]: Simplify -2.0 into -2.0 5.085 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.085 * [taylor]: Taking taylor expansion of PI in n 5.085 * [backup-simplify]: Simplify PI into PI 5.085 * [taylor]: Taking taylor expansion of n in n 5.085 * [backup-simplify]: Simplify 0 into 0 5.085 * [backup-simplify]: Simplify 1 into 1 5.086 * [backup-simplify]: Simplify (/ PI 1) into PI 5.086 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.087 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.087 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.090 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.091 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.092 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.094 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.095 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 5.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 5.101 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.101 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.101 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 5.101 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.101 * [taylor]: Taking taylor expansion of +nan.0 in n 5.101 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.101 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.101 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.101 * [taylor]: Taking taylor expansion of 0.5 in n 5.102 * [backup-simplify]: Simplify 0.5 into 0.5 5.102 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.102 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.102 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.102 * [taylor]: Taking taylor expansion of k in n 5.102 * [backup-simplify]: Simplify k into k 5.102 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.102 * [taylor]: Taking taylor expansion of 1.0 in n 5.102 * [backup-simplify]: Simplify 1.0 into 1.0 5.102 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.102 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.102 * [taylor]: Taking taylor expansion of -2.0 in n 5.102 * [backup-simplify]: Simplify -2.0 into -2.0 5.102 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.102 * [taylor]: Taking taylor expansion of PI in n 5.102 * [backup-simplify]: Simplify PI into PI 5.102 * [taylor]: Taking taylor expansion of n in n 5.102 * [backup-simplify]: Simplify 0 into 0 5.102 * [backup-simplify]: Simplify 1 into 1 5.103 * [backup-simplify]: Simplify (/ PI 1) into PI 5.103 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.104 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.104 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.106 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.107 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.108 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.109 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.111 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.113 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.114 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.115 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.116 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.118 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 5.118 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.119 * [backup-simplify]: Simplify (+ 0 0) into 0 5.120 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.121 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 5.123 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 5.124 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.126 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 5.126 * [backup-simplify]: Simplify 0 into 0 5.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.128 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 5.130 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.130 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 5.130 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 5.130 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 5.130 * [taylor]: Taking taylor expansion of +nan.0 in n 5.130 * [backup-simplify]: Simplify +nan.0 into +nan.0 5.130 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 5.130 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 5.130 * [taylor]: Taking taylor expansion of 0.5 in n 5.130 * [backup-simplify]: Simplify 0.5 into 0.5 5.130 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 5.130 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.130 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.130 * [taylor]: Taking taylor expansion of k in n 5.130 * [backup-simplify]: Simplify k into k 5.130 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.130 * [taylor]: Taking taylor expansion of 1.0 in n 5.130 * [backup-simplify]: Simplify 1.0 into 1.0 5.130 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.130 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.130 * [taylor]: Taking taylor expansion of -2.0 in n 5.130 * [backup-simplify]: Simplify -2.0 into -2.0 5.131 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.131 * [taylor]: Taking taylor expansion of PI in n 5.131 * [backup-simplify]: Simplify PI into PI 5.131 * [taylor]: Taking taylor expansion of n in n 5.131 * [backup-simplify]: Simplify 0 into 0 5.131 * [backup-simplify]: Simplify 1 into 1 5.131 * [backup-simplify]: Simplify (/ PI 1) into PI 5.131 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.132 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.132 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.133 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.134 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 5.134 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.135 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.136 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 5.137 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.137 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 5.140 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.141 * * * [progress]: simplifying candidates 5.144 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.149 * * [simplify]: Extracting # 0 : cost 0 5.149 * * [simplify]: Extracting # 1 : cost 0 5.149 * * [simplify]: Extracting # 2 : cost 0 5.150 * * [simplify]: Extracting # 3 : cost 0 5.150 * * [simplify]: Extracting # 4 : cost 0 5.150 * * [simplify]: Extracting # 5 : cost 0 5.151 * * [simplify]: Extracting # 6 : cost 0 5.151 * * [simplify]: Extracting # 7 : cost 0 5.152 * * [simplify]: Extracting # 8 : cost 0 5.152 * * [simplify]: Extracting # 9 : cost 0 5.157 * * [simplify]: Extracting # 10 : cost 0 5.158 * * [simplify]: Extracting # 11 : cost 0 5.158 * * [simplify]: Extracting # 12 : cost 0 5.159 * * [simplify]: Extracting # 13 : cost 0 5.159 * * [simplify]: Extracting # 14 : cost 0 5.160 * * [simplify]: Extracting # 15 : cost 0 5.160 * * [simplify]: Extracting # 16 : cost 0 5.161 * * [simplify]: Extracting # 17 : cost 0 5.161 * * [simplify]: Extracting # 18 : cost 0 5.162 * * [simplify]: Extracting # 19 : cost 0 5.162 * * [simplify]: Extracting # 20 : cost 0 5.163 * * [simplify]: Extracting # 21 : cost 0 5.163 * * [simplify]: Extracting # 22 : cost 0 5.164 * * [simplify]: Extracting # 23 : cost 0 5.164 * * [simplify]: Extracting # 24 : cost 0 5.165 * * [simplify]: Extracting # 25 : cost 0 5.165 * * [simplify]: Extracting # 26 : cost 0 5.166 * * [simplify]: Extracting # 27 : cost 0 5.166 * * [simplify]: Extracting # 28 : cost 0 5.167 * * [simplify]: Extracting # 29 : cost 0 5.167 * * [simplify]: Extracting # 30 : cost 0 5.168 * * [simplify]: Extracting # 31 : cost 0 5.168 * * [simplify]: Extracting # 32 : cost 0 5.169 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 5.346 * * [simplify]: Extracting # 0 : cost 0 5.349 * * [simplify]: Extracting # 1 : cost 0 5.352 * * [simplify]: Extracting # 2 : cost 0 5.355 * * [simplify]: Extracting # 3 : cost 0 5.358 * * [simplify]: Extracting # 4 : cost 0 5.360 * * [simplify]: Extracting # 5 : cost 0 5.363 * * [simplify]: Extracting # 6 : cost 0 5.366 * * [simplify]: iteration 1 : 961 enodes (cost 2712 ) 5.964 * * [simplify]: Extracting # 0 : cost 0 5.967 * * [simplify]: Extracting # 1 : cost 0 5.971 * * [simplify]: Extracting # 2 : cost 0 5.975 * * [simplify]: Extracting # 3 : cost 0 5.979 * * [simplify]: Extracting # 4 : cost 0 5.983 * * [simplify]: Extracting # 5 : cost 0 5.990 * * [simplify]: iteration 2 : 3131 enodes (cost 2550 ) 7.654 * * [simplify]: Extracting # 0 : cost 0 7.666 * * [simplify]: Extracting # 1 : cost 0 7.675 * * [simplify]: Extracting # 2 : cost 0 7.688 * * [simplify]: Extracting # 3 : cost 0 7.695 * * [simplify]: Extracting # 4 : cost 0 7.702 * * [simplify]: iteration done: 5000 enodes (cost 2540 ) 7.705 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (/ (fabs (cbrt k)) (cbrt 1.0))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* n PI)) 3) (pow (* 2.0 (* n PI)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* n PI)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (/ (/ (pow 1.0 3) k) (sqrt k))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (fma (- 0.5) (* k (fma (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5) (* (log n) (pow (* 2.0 (* n PI)) 0.5)))) (fma (* 0.125 (pow k 2)) (fma (pow (log (* 2.0 PI)) 2) (pow (* 2.0 (* n PI)) 0.5) (* (pow (* 2.0 (* n PI)) 0.5) (pow (log n) 2))) (fma 0.25 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* 2.0 (* n PI)) 0.5)) (pow (* 2.0 (* n PI)) 0.5)))) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (pow (exp (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) 0.5) (- (- (fma k +nan.0 +nan.0) (* (* +nan.0 k) k))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (fma (* +nan.0 (* (pow k 2) (pow (log (* 2.0 PI)) 2))) (- (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (fma (* (pow k 2) (log (* 2.0 PI))) (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) +nan.0) (fma (- (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (log n))))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (fma (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) +nan.0 (fma +nan.0 (- (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (fma +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) +nan.0 (- (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* (* +nan.0 (* k (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) (fma +nan.0 (- (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) k) (/ (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)) (pow k 2))) (- (/ +nan.0 (/ (pow k 3) (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k)))))) (fma (- +nan.0) (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 7.707 * * * [progress]: adding candidates to table 8.521 * * [progress]: iteration 2 / 4 8.521 * * * [progress]: picking best candidate 8.571 * * * * [pick]: Picked # 8.571 * * * [progress]: localizing error 8.592 * * * [progress]: generating rewritten candidates 8.592 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 8.630 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 8.656 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 8.662 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 8.726 * * * [progress]: generating series expansions 8.726 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 8.727 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.727 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.727 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.727 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.727 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.727 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.727 * [taylor]: Taking taylor expansion of 0.25 in k 8.727 * [backup-simplify]: Simplify 0.25 into 0.25 8.727 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.727 * [taylor]: Taking taylor expansion of 1.0 in k 8.727 * [backup-simplify]: Simplify 1.0 into 1.0 8.727 * [taylor]: Taking taylor expansion of k in k 8.727 * [backup-simplify]: Simplify 0 into 0 8.727 * [backup-simplify]: Simplify 1 into 1 8.727 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.727 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.727 * [taylor]: Taking taylor expansion of 2.0 in k 8.727 * [backup-simplify]: Simplify 2.0 into 2.0 8.727 * [taylor]: Taking taylor expansion of (* n PI) in k 8.727 * [taylor]: Taking taylor expansion of n in k 8.727 * [backup-simplify]: Simplify n into n 8.727 * [taylor]: Taking taylor expansion of PI in k 8.727 * [backup-simplify]: Simplify PI into PI 8.727 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.728 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.728 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.728 * [backup-simplify]: Simplify (- 0) into 0 8.729 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.729 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.729 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.729 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.729 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.729 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.729 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.729 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.729 * [taylor]: Taking taylor expansion of 0.25 in n 8.729 * [backup-simplify]: Simplify 0.25 into 0.25 8.729 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.730 * [taylor]: Taking taylor expansion of 1.0 in n 8.730 * [backup-simplify]: Simplify 1.0 into 1.0 8.730 * [taylor]: Taking taylor expansion of k in n 8.730 * [backup-simplify]: Simplify k into k 8.730 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.730 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.730 * [taylor]: Taking taylor expansion of 2.0 in n 8.730 * [backup-simplify]: Simplify 2.0 into 2.0 8.730 * [taylor]: Taking taylor expansion of (* n PI) in n 8.730 * [taylor]: Taking taylor expansion of n in n 8.730 * [backup-simplify]: Simplify 0 into 0 8.730 * [backup-simplify]: Simplify 1 into 1 8.730 * [taylor]: Taking taylor expansion of PI in n 8.730 * [backup-simplify]: Simplify PI into PI 8.730 * [backup-simplify]: Simplify (* 0 PI) into 0 8.731 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.732 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.734 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.735 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.735 * [backup-simplify]: Simplify (- k) into (- k) 8.735 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.735 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.737 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.738 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.739 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.739 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.739 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.739 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.739 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.739 * [taylor]: Taking taylor expansion of 0.25 in n 8.739 * [backup-simplify]: Simplify 0.25 into 0.25 8.739 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.739 * [taylor]: Taking taylor expansion of 1.0 in n 8.739 * [backup-simplify]: Simplify 1.0 into 1.0 8.739 * [taylor]: Taking taylor expansion of k in n 8.739 * [backup-simplify]: Simplify k into k 8.739 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.739 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.739 * [taylor]: Taking taylor expansion of 2.0 in n 8.739 * [backup-simplify]: Simplify 2.0 into 2.0 8.740 * [taylor]: Taking taylor expansion of (* n PI) in n 8.740 * [taylor]: Taking taylor expansion of n in n 8.740 * [backup-simplify]: Simplify 0 into 0 8.740 * [backup-simplify]: Simplify 1 into 1 8.740 * [taylor]: Taking taylor expansion of PI in n 8.740 * [backup-simplify]: Simplify PI into PI 8.740 * [backup-simplify]: Simplify (* 0 PI) into 0 8.740 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.742 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.743 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.745 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.745 * [backup-simplify]: Simplify (- k) into (- k) 8.745 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.745 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.746 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.747 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.748 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.749 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.749 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.749 * [taylor]: Taking taylor expansion of 0.25 in k 8.749 * [backup-simplify]: Simplify 0.25 into 0.25 8.749 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.749 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.749 * [taylor]: Taking taylor expansion of 1.0 in k 8.749 * [backup-simplify]: Simplify 1.0 into 1.0 8.749 * [taylor]: Taking taylor expansion of k in k 8.749 * [backup-simplify]: Simplify 0 into 0 8.749 * [backup-simplify]: Simplify 1 into 1 8.749 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.749 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.749 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.749 * [taylor]: Taking taylor expansion of 2.0 in k 8.749 * [backup-simplify]: Simplify 2.0 into 2.0 8.749 * [taylor]: Taking taylor expansion of PI in k 8.749 * [backup-simplify]: Simplify PI into PI 8.750 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.750 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.751 * [taylor]: Taking taylor expansion of (log n) in k 8.751 * [taylor]: Taking taylor expansion of n in k 8.751 * [backup-simplify]: Simplify n into n 8.751 * [backup-simplify]: Simplify (log n) into (log n) 8.751 * [backup-simplify]: Simplify (- 0) into 0 8.751 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.752 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.754 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.755 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.756 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.757 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.758 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.759 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.761 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.761 * [backup-simplify]: Simplify (- 0) into 0 8.762 * [backup-simplify]: Simplify (+ 0 0) into 0 8.762 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.763 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.765 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.766 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.766 * [taylor]: Taking taylor expansion of 0 in k 8.766 * [backup-simplify]: Simplify 0 into 0 8.766 * [backup-simplify]: Simplify 0 into 0 8.767 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.769 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.770 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.771 * [backup-simplify]: Simplify (+ 0 0) into 0 8.771 * [backup-simplify]: Simplify (- 1) into -1 8.772 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.773 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.775 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 8.779 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.782 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 8.783 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 8.785 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 8.789 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.789 * [backup-simplify]: Simplify (- 0) into 0 8.790 * [backup-simplify]: Simplify (+ 0 0) into 0 8.790 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 8.792 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.794 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.796 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.797 * [taylor]: Taking taylor expansion of 0 in k 8.797 * [backup-simplify]: Simplify 0 into 0 8.797 * [backup-simplify]: Simplify 0 into 0 8.797 * [backup-simplify]: Simplify 0 into 0 8.798 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.802 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.804 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 8.804 * [backup-simplify]: Simplify (+ 0 0) into 0 8.804 * [backup-simplify]: Simplify (- 0) into 0 8.805 * [backup-simplify]: Simplify (+ 0 0) into 0 8.807 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 8.809 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 8.813 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.819 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 8.830 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 8.831 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 8.831 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 8.831 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 8.831 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 8.831 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 8.831 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 8.831 * [taylor]: Taking taylor expansion of 0.25 in k 8.831 * [backup-simplify]: Simplify 0.25 into 0.25 8.831 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.831 * [taylor]: Taking taylor expansion of 1.0 in k 8.831 * [backup-simplify]: Simplify 1.0 into 1.0 8.831 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.831 * [taylor]: Taking taylor expansion of k in k 8.831 * [backup-simplify]: Simplify 0 into 0 8.831 * [backup-simplify]: Simplify 1 into 1 8.831 * [backup-simplify]: Simplify (/ 1 1) into 1 8.832 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 8.832 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 8.832 * [taylor]: Taking taylor expansion of 2.0 in k 8.832 * [backup-simplify]: Simplify 2.0 into 2.0 8.832 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.832 * [taylor]: Taking taylor expansion of PI in k 8.832 * [backup-simplify]: Simplify PI into PI 8.832 * [taylor]: Taking taylor expansion of n in k 8.832 * [backup-simplify]: Simplify n into n 8.832 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.832 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 8.832 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 8.832 * [backup-simplify]: Simplify (- 1) into -1 8.833 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.833 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 8.833 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 8.834 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 8.834 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.834 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.834 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.834 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.834 * [taylor]: Taking taylor expansion of 0.25 in n 8.834 * [backup-simplify]: Simplify 0.25 into 0.25 8.834 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.834 * [taylor]: Taking taylor expansion of 1.0 in n 8.834 * [backup-simplify]: Simplify 1.0 into 1.0 8.834 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.834 * [taylor]: Taking taylor expansion of k in n 8.834 * [backup-simplify]: Simplify k into k 8.834 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.834 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.834 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.834 * [taylor]: Taking taylor expansion of 2.0 in n 8.834 * [backup-simplify]: Simplify 2.0 into 2.0 8.834 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.834 * [taylor]: Taking taylor expansion of PI in n 8.834 * [backup-simplify]: Simplify PI into PI 8.834 * [taylor]: Taking taylor expansion of n in n 8.834 * [backup-simplify]: Simplify 0 into 0 8.834 * [backup-simplify]: Simplify 1 into 1 8.835 * [backup-simplify]: Simplify (/ PI 1) into PI 8.835 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.837 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.837 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.837 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.837 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.840 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.841 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.841 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 8.841 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 8.841 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 8.841 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 8.841 * [taylor]: Taking taylor expansion of 0.25 in n 8.841 * [backup-simplify]: Simplify 0.25 into 0.25 8.841 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 8.841 * [taylor]: Taking taylor expansion of 1.0 in n 8.841 * [backup-simplify]: Simplify 1.0 into 1.0 8.841 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.841 * [taylor]: Taking taylor expansion of k in n 8.841 * [backup-simplify]: Simplify k into k 8.842 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.842 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 8.842 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 8.842 * [taylor]: Taking taylor expansion of 2.0 in n 8.842 * [backup-simplify]: Simplify 2.0 into 2.0 8.842 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.842 * [taylor]: Taking taylor expansion of PI in n 8.842 * [backup-simplify]: Simplify PI into PI 8.842 * [taylor]: Taking taylor expansion of n in n 8.842 * [backup-simplify]: Simplify 0 into 0 8.842 * [backup-simplify]: Simplify 1 into 1 8.849 * [backup-simplify]: Simplify (/ PI 1) into PI 8.849 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.850 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.851 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 8.851 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 8.851 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 8.852 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.853 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 8.855 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.855 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 8.855 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 8.855 * [taylor]: Taking taylor expansion of 0.25 in k 8.855 * [backup-simplify]: Simplify 0.25 into 0.25 8.855 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 8.855 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 8.855 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.855 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.855 * [taylor]: Taking taylor expansion of 2.0 in k 8.855 * [backup-simplify]: Simplify 2.0 into 2.0 8.855 * [taylor]: Taking taylor expansion of PI in k 8.855 * [backup-simplify]: Simplify PI into PI 8.855 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.857 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.857 * [taylor]: Taking taylor expansion of (log n) in k 8.857 * [taylor]: Taking taylor expansion of n in k 8.857 * [backup-simplify]: Simplify n into n 8.857 * [backup-simplify]: Simplify (log n) into (log n) 8.857 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 8.857 * [taylor]: Taking taylor expansion of 1.0 in k 8.857 * [backup-simplify]: Simplify 1.0 into 1.0 8.857 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.857 * [taylor]: Taking taylor expansion of k in k 8.857 * [backup-simplify]: Simplify 0 into 0 8.857 * [backup-simplify]: Simplify 1 into 1 8.857 * [backup-simplify]: Simplify (/ 1 1) into 1 8.857 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.858 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 8.859 * [backup-simplify]: Simplify (- 1) into -1 8.859 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.860 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 8.861 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 8.863 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.864 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 8.865 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.865 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.867 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.868 * [backup-simplify]: Simplify (- 0) into 0 8.868 * [backup-simplify]: Simplify (+ 0 0) into 0 8.868 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 8.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.871 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 8.873 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.873 * [taylor]: Taking taylor expansion of 0 in k 8.873 * [backup-simplify]: Simplify 0 into 0 8.874 * [backup-simplify]: Simplify 0 into 0 8.874 * [backup-simplify]: Simplify 0 into 0 8.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.876 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.880 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 8.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.880 * [backup-simplify]: Simplify (- 0) into 0 8.881 * [backup-simplify]: Simplify (+ 0 0) into 0 8.882 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 8.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.885 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 8.888 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.888 * [taylor]: Taking taylor expansion of 0 in k 8.888 * [backup-simplify]: Simplify 0 into 0 8.888 * [backup-simplify]: Simplify 0 into 0 8.888 * [backup-simplify]: Simplify 0 into 0 8.888 * [backup-simplify]: Simplify 0 into 0 8.889 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.890 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.893 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 8.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.894 * [backup-simplify]: Simplify (- 0) into 0 8.894 * [backup-simplify]: Simplify (+ 0 0) into 0 8.895 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 8.896 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 8.897 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 8.899 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.899 * [taylor]: Taking taylor expansion of 0 in k 8.899 * [backup-simplify]: Simplify 0 into 0 8.899 * [backup-simplify]: Simplify 0 into 0 8.900 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 8.900 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 8.900 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 8.900 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 8.900 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 8.900 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 8.900 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 8.900 * [taylor]: Taking taylor expansion of 0.25 in k 8.900 * [backup-simplify]: Simplify 0.25 into 0.25 8.901 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.901 * [taylor]: Taking taylor expansion of k in k 8.901 * [backup-simplify]: Simplify 0 into 0 8.901 * [backup-simplify]: Simplify 1 into 1 8.901 * [backup-simplify]: Simplify (/ 1 1) into 1 8.901 * [taylor]: Taking taylor expansion of 1.0 in k 8.901 * [backup-simplify]: Simplify 1.0 into 1.0 8.901 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 8.901 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 8.901 * [taylor]: Taking taylor expansion of -2.0 in k 8.901 * [backup-simplify]: Simplify -2.0 into -2.0 8.901 * [taylor]: Taking taylor expansion of (/ PI n) in k 8.901 * [taylor]: Taking taylor expansion of PI in k 8.901 * [backup-simplify]: Simplify PI into PI 8.901 * [taylor]: Taking taylor expansion of n in k 8.901 * [backup-simplify]: Simplify n into n 8.901 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 8.901 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 8.901 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 8.901 * [backup-simplify]: Simplify (+ 1 0) into 1 8.902 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 8.902 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 8.902 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 8.902 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.902 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.902 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.902 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.902 * [taylor]: Taking taylor expansion of 0.25 in n 8.902 * [backup-simplify]: Simplify 0.25 into 0.25 8.902 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.902 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.902 * [taylor]: Taking taylor expansion of k in n 8.902 * [backup-simplify]: Simplify k into k 8.902 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.902 * [taylor]: Taking taylor expansion of 1.0 in n 8.902 * [backup-simplify]: Simplify 1.0 into 1.0 8.902 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.902 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.902 * [taylor]: Taking taylor expansion of -2.0 in n 8.902 * [backup-simplify]: Simplify -2.0 into -2.0 8.902 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.902 * [taylor]: Taking taylor expansion of PI in n 8.902 * [backup-simplify]: Simplify PI into PI 8.902 * [taylor]: Taking taylor expansion of n in n 8.902 * [backup-simplify]: Simplify 0 into 0 8.902 * [backup-simplify]: Simplify 1 into 1 8.903 * [backup-simplify]: Simplify (/ PI 1) into PI 8.903 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.904 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.904 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.904 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.906 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.906 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.906 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 8.906 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 8.906 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 8.906 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 8.906 * [taylor]: Taking taylor expansion of 0.25 in n 8.906 * [backup-simplify]: Simplify 0.25 into 0.25 8.906 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 8.907 * [taylor]: Taking taylor expansion of (/ 1 k) in n 8.907 * [taylor]: Taking taylor expansion of k in n 8.907 * [backup-simplify]: Simplify k into k 8.907 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 8.907 * [taylor]: Taking taylor expansion of 1.0 in n 8.907 * [backup-simplify]: Simplify 1.0 into 1.0 8.907 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 8.907 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 8.907 * [taylor]: Taking taylor expansion of -2.0 in n 8.907 * [backup-simplify]: Simplify -2.0 into -2.0 8.907 * [taylor]: Taking taylor expansion of (/ PI n) in n 8.907 * [taylor]: Taking taylor expansion of PI in n 8.907 * [backup-simplify]: Simplify PI into PI 8.907 * [taylor]: Taking taylor expansion of n in n 8.907 * [backup-simplify]: Simplify 0 into 0 8.907 * [backup-simplify]: Simplify 1 into 1 8.907 * [backup-simplify]: Simplify (/ PI 1) into PI 8.907 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.908 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.908 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 8.908 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 8.909 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.910 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 8.911 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.911 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 8.911 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 8.911 * [taylor]: Taking taylor expansion of 0.25 in k 8.911 * [backup-simplify]: Simplify 0.25 into 0.25 8.911 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 8.911 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 8.911 * [taylor]: Taking taylor expansion of (/ 1 k) in k 8.911 * [taylor]: Taking taylor expansion of k in k 8.911 * [backup-simplify]: Simplify 0 into 0 8.911 * [backup-simplify]: Simplify 1 into 1 8.911 * [backup-simplify]: Simplify (/ 1 1) into 1 8.911 * [taylor]: Taking taylor expansion of 1.0 in k 8.911 * [backup-simplify]: Simplify 1.0 into 1.0 8.911 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 8.911 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 8.911 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 8.911 * [taylor]: Taking taylor expansion of -2.0 in k 8.911 * [backup-simplify]: Simplify -2.0 into -2.0 8.911 * [taylor]: Taking taylor expansion of PI in k 8.911 * [backup-simplify]: Simplify PI into PI 8.912 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 8.912 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 8.912 * [taylor]: Taking taylor expansion of (log n) in k 8.912 * [taylor]: Taking taylor expansion of n in k 8.912 * [backup-simplify]: Simplify n into n 8.912 * [backup-simplify]: Simplify (log n) into (log n) 8.913 * [backup-simplify]: Simplify (+ 1 0) into 1 8.913 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 8.913 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 8.914 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 8.915 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 8.915 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.916 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 8.917 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 8.918 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 8.920 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 8.920 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 8.921 * [backup-simplify]: Simplify (+ 0 0) into 0 8.921 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 8.923 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.924 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 8.926 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.926 * [taylor]: Taking taylor expansion of 0 in k 8.926 * [backup-simplify]: Simplify 0 into 0 8.926 * [backup-simplify]: Simplify 0 into 0 8.926 * [backup-simplify]: Simplify 0 into 0 8.927 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.928 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 8.932 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 8.932 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.932 * [backup-simplify]: Simplify (+ 0 0) into 0 8.933 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 8.935 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.937 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 8.939 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 8.939 * [taylor]: Taking taylor expansion of 0 in k 8.939 * [backup-simplify]: Simplify 0 into 0 8.939 * [backup-simplify]: Simplify 0 into 0 8.939 * [backup-simplify]: Simplify 0 into 0 8.939 * [backup-simplify]: Simplify 0 into 0 8.941 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 8.942 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 8.948 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 8.948 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 8.949 * [backup-simplify]: Simplify (+ 0 0) into 0 8.949 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 8.950 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 8.952 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 8.953 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 8.953 * [taylor]: Taking taylor expansion of 0 in k 8.953 * [backup-simplify]: Simplify 0 into 0 8.953 * [backup-simplify]: Simplify 0 into 0 8.954 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 8.954 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 8.955 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 8.955 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 8.955 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 8.955 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 8.955 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 8.955 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 8.955 * [taylor]: Taking taylor expansion of 0.25 in k 8.955 * [backup-simplify]: Simplify 0.25 into 0.25 8.955 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.955 * [taylor]: Taking taylor expansion of 1.0 in k 8.955 * [backup-simplify]: Simplify 1.0 into 1.0 8.955 * [taylor]: Taking taylor expansion of k in k 8.955 * [backup-simplify]: Simplify 0 into 0 8.955 * [backup-simplify]: Simplify 1 into 1 8.955 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 8.955 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 8.955 * [taylor]: Taking taylor expansion of 2.0 in k 8.955 * [backup-simplify]: Simplify 2.0 into 2.0 8.955 * [taylor]: Taking taylor expansion of (* n PI) in k 8.955 * [taylor]: Taking taylor expansion of n in k 8.955 * [backup-simplify]: Simplify n into n 8.955 * [taylor]: Taking taylor expansion of PI in k 8.955 * [backup-simplify]: Simplify PI into PI 8.955 * [backup-simplify]: Simplify (* n PI) into (* n PI) 8.955 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 8.955 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 8.955 * [backup-simplify]: Simplify (- 0) into 0 8.956 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.956 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 8.956 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 8.956 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 8.956 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.956 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.956 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.956 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.956 * [taylor]: Taking taylor expansion of 0.25 in n 8.956 * [backup-simplify]: Simplify 0.25 into 0.25 8.956 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.956 * [taylor]: Taking taylor expansion of 1.0 in n 8.956 * [backup-simplify]: Simplify 1.0 into 1.0 8.956 * [taylor]: Taking taylor expansion of k in n 8.956 * [backup-simplify]: Simplify k into k 8.956 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.956 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.956 * [taylor]: Taking taylor expansion of 2.0 in n 8.956 * [backup-simplify]: Simplify 2.0 into 2.0 8.956 * [taylor]: Taking taylor expansion of (* n PI) in n 8.956 * [taylor]: Taking taylor expansion of n in n 8.956 * [backup-simplify]: Simplify 0 into 0 8.956 * [backup-simplify]: Simplify 1 into 1 8.957 * [taylor]: Taking taylor expansion of PI in n 8.957 * [backup-simplify]: Simplify PI into PI 8.957 * [backup-simplify]: Simplify (* 0 PI) into 0 8.957 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.958 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.959 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.960 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.960 * [backup-simplify]: Simplify (- k) into (- k) 8.960 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.960 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.961 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.961 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.962 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.962 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 8.962 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 8.962 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 8.962 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 8.962 * [taylor]: Taking taylor expansion of 0.25 in n 8.962 * [backup-simplify]: Simplify 0.25 into 0.25 8.962 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 8.962 * [taylor]: Taking taylor expansion of 1.0 in n 8.962 * [backup-simplify]: Simplify 1.0 into 1.0 8.962 * [taylor]: Taking taylor expansion of k in n 8.962 * [backup-simplify]: Simplify k into k 8.962 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 8.962 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 8.962 * [taylor]: Taking taylor expansion of 2.0 in n 8.962 * [backup-simplify]: Simplify 2.0 into 2.0 8.962 * [taylor]: Taking taylor expansion of (* n PI) in n 8.962 * [taylor]: Taking taylor expansion of n in n 8.962 * [backup-simplify]: Simplify 0 into 0 8.962 * [backup-simplify]: Simplify 1 into 1 8.962 * [taylor]: Taking taylor expansion of PI in n 8.963 * [backup-simplify]: Simplify PI into PI 8.963 * [backup-simplify]: Simplify (* 0 PI) into 0 8.963 * [backup-simplify]: Simplify (* 2.0 0) into 0 8.964 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 8.965 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 8.966 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.966 * [backup-simplify]: Simplify (- k) into (- k) 8.966 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 8.966 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 8.967 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.967 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 8.971 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 8.971 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 8.971 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 8.971 * [taylor]: Taking taylor expansion of 0.25 in k 8.971 * [backup-simplify]: Simplify 0.25 into 0.25 8.971 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 8.971 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 8.971 * [taylor]: Taking taylor expansion of 1.0 in k 8.971 * [backup-simplify]: Simplify 1.0 into 1.0 8.971 * [taylor]: Taking taylor expansion of k in k 8.971 * [backup-simplify]: Simplify 0 into 0 8.971 * [backup-simplify]: Simplify 1 into 1 8.971 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 8.971 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 8.971 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 8.971 * [taylor]: Taking taylor expansion of 2.0 in k 8.971 * [backup-simplify]: Simplify 2.0 into 2.0 8.971 * [taylor]: Taking taylor expansion of PI in k 8.971 * [backup-simplify]: Simplify PI into PI 8.972 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 8.973 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 8.973 * [taylor]: Taking taylor expansion of (log n) in k 8.973 * [taylor]: Taking taylor expansion of n in k 8.973 * [backup-simplify]: Simplify n into n 8.973 * [backup-simplify]: Simplify (log n) into (log n) 8.973 * [backup-simplify]: Simplify (- 0) into 0 8.973 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 8.974 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 8.974 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 8.975 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 8.976 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.977 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 8.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 8.979 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 8.981 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.982 * [backup-simplify]: Simplify (- 0) into 0 8.982 * [backup-simplify]: Simplify (+ 0 0) into 0 8.983 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 8.984 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 8.985 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 8.988 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 8.988 * [taylor]: Taking taylor expansion of 0 in k 8.988 * [backup-simplify]: Simplify 0 into 0 8.988 * [backup-simplify]: Simplify 0 into 0 8.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 8.991 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 8.992 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 8.992 * [backup-simplify]: Simplify (+ 0 0) into 0 8.992 * [backup-simplify]: Simplify (- 1) into -1 8.993 * [backup-simplify]: Simplify (+ 0 -1) into -1 8.994 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 8.997 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 9.001 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.004 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.006 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.008 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.008 * [backup-simplify]: Simplify (- 0) into 0 9.009 * [backup-simplify]: Simplify (+ 0 0) into 0 9.009 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.010 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.011 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.013 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.013 * [taylor]: Taking taylor expansion of 0 in k 9.013 * [backup-simplify]: Simplify 0 into 0 9.013 * [backup-simplify]: Simplify 0 into 0 9.013 * [backup-simplify]: Simplify 0 into 0 9.014 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.015 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.017 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.017 * [backup-simplify]: Simplify (+ 0 0) into 0 9.017 * [backup-simplify]: Simplify (- 0) into 0 9.017 * [backup-simplify]: Simplify (+ 0 0) into 0 9.019 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.020 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.023 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.026 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.032 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 9.033 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 9.033 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.033 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.033 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.033 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.033 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.033 * [taylor]: Taking taylor expansion of 0.25 in k 9.033 * [backup-simplify]: Simplify 0.25 into 0.25 9.033 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.033 * [taylor]: Taking taylor expansion of 1.0 in k 9.033 * [backup-simplify]: Simplify 1.0 into 1.0 9.033 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.033 * [taylor]: Taking taylor expansion of k in k 9.033 * [backup-simplify]: Simplify 0 into 0 9.033 * [backup-simplify]: Simplify 1 into 1 9.033 * [backup-simplify]: Simplify (/ 1 1) into 1 9.033 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.034 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.034 * [taylor]: Taking taylor expansion of 2.0 in k 9.034 * [backup-simplify]: Simplify 2.0 into 2.0 9.034 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.034 * [taylor]: Taking taylor expansion of PI in k 9.034 * [backup-simplify]: Simplify PI into PI 9.034 * [taylor]: Taking taylor expansion of n in k 9.034 * [backup-simplify]: Simplify n into n 9.034 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.034 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.034 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.034 * [backup-simplify]: Simplify (- 1) into -1 9.034 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.035 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.035 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.035 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 9.035 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.035 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.035 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.035 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.035 * [taylor]: Taking taylor expansion of 0.25 in n 9.035 * [backup-simplify]: Simplify 0.25 into 0.25 9.035 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.035 * [taylor]: Taking taylor expansion of 1.0 in n 9.035 * [backup-simplify]: Simplify 1.0 into 1.0 9.035 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.035 * [taylor]: Taking taylor expansion of k in n 9.035 * [backup-simplify]: Simplify k into k 9.035 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.035 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.035 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.035 * [taylor]: Taking taylor expansion of 2.0 in n 9.035 * [backup-simplify]: Simplify 2.0 into 2.0 9.035 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.035 * [taylor]: Taking taylor expansion of PI in n 9.035 * [backup-simplify]: Simplify PI into PI 9.035 * [taylor]: Taking taylor expansion of n in n 9.035 * [backup-simplify]: Simplify 0 into 0 9.035 * [backup-simplify]: Simplify 1 into 1 9.036 * [backup-simplify]: Simplify (/ PI 1) into PI 9.036 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.037 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.037 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.037 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.037 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.039 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.040 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.041 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.041 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.041 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.041 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.041 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.041 * [taylor]: Taking taylor expansion of 0.25 in n 9.041 * [backup-simplify]: Simplify 0.25 into 0.25 9.041 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.041 * [taylor]: Taking taylor expansion of 1.0 in n 9.041 * [backup-simplify]: Simplify 1.0 into 1.0 9.042 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.042 * [taylor]: Taking taylor expansion of k in n 9.042 * [backup-simplify]: Simplify k into k 9.042 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.042 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.042 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.042 * [taylor]: Taking taylor expansion of 2.0 in n 9.042 * [backup-simplify]: Simplify 2.0 into 2.0 9.042 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.042 * [taylor]: Taking taylor expansion of PI in n 9.042 * [backup-simplify]: Simplify PI into PI 9.042 * [taylor]: Taking taylor expansion of n in n 9.042 * [backup-simplify]: Simplify 0 into 0 9.042 * [backup-simplify]: Simplify 1 into 1 9.042 * [backup-simplify]: Simplify (/ PI 1) into PI 9.043 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.044 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.044 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.044 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.044 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.046 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.047 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.048 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.048 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.049 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.049 * [taylor]: Taking taylor expansion of 0.25 in k 9.049 * [backup-simplify]: Simplify 0.25 into 0.25 9.049 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.049 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.049 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.049 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.049 * [taylor]: Taking taylor expansion of 2.0 in k 9.049 * [backup-simplify]: Simplify 2.0 into 2.0 9.049 * [taylor]: Taking taylor expansion of PI in k 9.049 * [backup-simplify]: Simplify PI into PI 9.049 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.050 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.050 * [taylor]: Taking taylor expansion of (log n) in k 9.050 * [taylor]: Taking taylor expansion of n in k 9.050 * [backup-simplify]: Simplify n into n 9.051 * [backup-simplify]: Simplify (log n) into (log n) 9.051 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.051 * [taylor]: Taking taylor expansion of 1.0 in k 9.051 * [backup-simplify]: Simplify 1.0 into 1.0 9.051 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.051 * [taylor]: Taking taylor expansion of k in k 9.051 * [backup-simplify]: Simplify 0 into 0 9.051 * [backup-simplify]: Simplify 1 into 1 9.051 * [backup-simplify]: Simplify (/ 1 1) into 1 9.051 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.052 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.053 * [backup-simplify]: Simplify (- 1) into -1 9.053 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.054 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.055 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.057 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.058 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.060 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.062 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.062 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.063 * [backup-simplify]: Simplify (- 0) into 0 9.063 * [backup-simplify]: Simplify (+ 0 0) into 0 9.063 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.066 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.068 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.068 * [taylor]: Taking taylor expansion of 0 in k 9.068 * [backup-simplify]: Simplify 0 into 0 9.068 * [backup-simplify]: Simplify 0 into 0 9.068 * [backup-simplify]: Simplify 0 into 0 9.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.070 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.074 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.075 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.075 * [backup-simplify]: Simplify (- 0) into 0 9.075 * [backup-simplify]: Simplify (+ 0 0) into 0 9.076 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.078 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.080 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.082 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.082 * [taylor]: Taking taylor expansion of 0 in k 9.082 * [backup-simplify]: Simplify 0 into 0 9.082 * [backup-simplify]: Simplify 0 into 0 9.082 * [backup-simplify]: Simplify 0 into 0 9.082 * [backup-simplify]: Simplify 0 into 0 9.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.085 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.091 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 9.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.092 * [backup-simplify]: Simplify (- 0) into 0 9.093 * [backup-simplify]: Simplify (+ 0 0) into 0 9.094 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.096 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.098 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.106 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.106 * [taylor]: Taking taylor expansion of 0 in k 9.106 * [backup-simplify]: Simplify 0 into 0 9.107 * [backup-simplify]: Simplify 0 into 0 9.108 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 9.109 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 9.109 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.109 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.109 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.109 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.109 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.109 * [taylor]: Taking taylor expansion of 0.25 in k 9.109 * [backup-simplify]: Simplify 0.25 into 0.25 9.109 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.109 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.109 * [taylor]: Taking taylor expansion of k in k 9.109 * [backup-simplify]: Simplify 0 into 0 9.109 * [backup-simplify]: Simplify 1 into 1 9.110 * [backup-simplify]: Simplify (/ 1 1) into 1 9.110 * [taylor]: Taking taylor expansion of 1.0 in k 9.110 * [backup-simplify]: Simplify 1.0 into 1.0 9.110 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.110 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.110 * [taylor]: Taking taylor expansion of -2.0 in k 9.110 * [backup-simplify]: Simplify -2.0 into -2.0 9.110 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.110 * [taylor]: Taking taylor expansion of PI in k 9.110 * [backup-simplify]: Simplify PI into PI 9.110 * [taylor]: Taking taylor expansion of n in k 9.110 * [backup-simplify]: Simplify n into n 9.110 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.110 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.110 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.111 * [backup-simplify]: Simplify (+ 1 0) into 1 9.112 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.112 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.112 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 9.112 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.112 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.112 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.112 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.112 * [taylor]: Taking taylor expansion of 0.25 in n 9.112 * [backup-simplify]: Simplify 0.25 into 0.25 9.112 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.112 * [taylor]: Taking taylor expansion of k in n 9.112 * [backup-simplify]: Simplify k into k 9.113 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.113 * [taylor]: Taking taylor expansion of 1.0 in n 9.113 * [backup-simplify]: Simplify 1.0 into 1.0 9.113 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.113 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.113 * [taylor]: Taking taylor expansion of -2.0 in n 9.113 * [backup-simplify]: Simplify -2.0 into -2.0 9.113 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.113 * [taylor]: Taking taylor expansion of PI in n 9.113 * [backup-simplify]: Simplify PI into PI 9.113 * [taylor]: Taking taylor expansion of n in n 9.113 * [backup-simplify]: Simplify 0 into 0 9.113 * [backup-simplify]: Simplify 1 into 1 9.113 * [backup-simplify]: Simplify (/ PI 1) into PI 9.114 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.115 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.115 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.115 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.117 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.119 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.120 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.120 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.120 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.120 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.120 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.120 * [taylor]: Taking taylor expansion of 0.25 in n 9.120 * [backup-simplify]: Simplify 0.25 into 0.25 9.120 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.120 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.120 * [taylor]: Taking taylor expansion of k in n 9.120 * [backup-simplify]: Simplify k into k 9.120 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.120 * [taylor]: Taking taylor expansion of 1.0 in n 9.120 * [backup-simplify]: Simplify 1.0 into 1.0 9.120 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.120 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.120 * [taylor]: Taking taylor expansion of -2.0 in n 9.120 * [backup-simplify]: Simplify -2.0 into -2.0 9.120 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.120 * [taylor]: Taking taylor expansion of PI in n 9.120 * [backup-simplify]: Simplify PI into PI 9.120 * [taylor]: Taking taylor expansion of n in n 9.120 * [backup-simplify]: Simplify 0 into 0 9.120 * [backup-simplify]: Simplify 1 into 1 9.121 * [backup-simplify]: Simplify (/ PI 1) into PI 9.121 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.122 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.122 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.122 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.123 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.124 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.124 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.124 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.124 * [taylor]: Taking taylor expansion of 0.25 in k 9.124 * [backup-simplify]: Simplify 0.25 into 0.25 9.124 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.124 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.124 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.124 * [taylor]: Taking taylor expansion of k in k 9.124 * [backup-simplify]: Simplify 0 into 0 9.124 * [backup-simplify]: Simplify 1 into 1 9.125 * [backup-simplify]: Simplify (/ 1 1) into 1 9.125 * [taylor]: Taking taylor expansion of 1.0 in k 9.125 * [backup-simplify]: Simplify 1.0 into 1.0 9.125 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.125 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.125 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.125 * [taylor]: Taking taylor expansion of -2.0 in k 9.125 * [backup-simplify]: Simplify -2.0 into -2.0 9.125 * [taylor]: Taking taylor expansion of PI in k 9.125 * [backup-simplify]: Simplify PI into PI 9.125 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.126 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.126 * [taylor]: Taking taylor expansion of (log n) in k 9.126 * [taylor]: Taking taylor expansion of n in k 9.126 * [backup-simplify]: Simplify n into n 9.126 * [backup-simplify]: Simplify (log n) into (log n) 9.126 * [backup-simplify]: Simplify (+ 1 0) into 1 9.126 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.127 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.127 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.128 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.129 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.130 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.131 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.132 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.132 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.132 * [backup-simplify]: Simplify (+ 0 0) into 0 9.133 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.134 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.134 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.136 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.136 * [taylor]: Taking taylor expansion of 0 in k 9.136 * [backup-simplify]: Simplify 0 into 0 9.136 * [backup-simplify]: Simplify 0 into 0 9.136 * [backup-simplify]: Simplify 0 into 0 9.136 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.137 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.139 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 9.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.139 * [backup-simplify]: Simplify (+ 0 0) into 0 9.140 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.141 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.142 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.143 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.143 * [taylor]: Taking taylor expansion of 0 in k 9.143 * [backup-simplify]: Simplify 0 into 0 9.143 * [backup-simplify]: Simplify 0 into 0 9.143 * [backup-simplify]: Simplify 0 into 0 9.143 * [backup-simplify]: Simplify 0 into 0 9.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.145 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.148 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 9.148 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.148 * [backup-simplify]: Simplify (+ 0 0) into 0 9.149 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.151 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.153 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.153 * [taylor]: Taking taylor expansion of 0 in k 9.153 * [backup-simplify]: Simplify 0 into 0 9.153 * [backup-simplify]: Simplify 0 into 0 9.154 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 9.154 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 9.154 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 9.154 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 9.154 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.154 * [taylor]: Taking taylor expansion of 1.0 in k 9.155 * [backup-simplify]: Simplify 1.0 into 1.0 9.155 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.155 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.155 * [taylor]: Taking taylor expansion of k in k 9.155 * [backup-simplify]: Simplify 0 into 0 9.155 * [backup-simplify]: Simplify 1 into 1 9.155 * [backup-simplify]: Simplify (/ 1 1) into 1 9.155 * [backup-simplify]: Simplify (sqrt 0) into 0 9.156 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.156 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.156 * [taylor]: Taking taylor expansion of 1.0 in k 9.156 * [backup-simplify]: Simplify 1.0 into 1.0 9.156 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.156 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.156 * [taylor]: Taking taylor expansion of k in k 9.156 * [backup-simplify]: Simplify 0 into 0 9.156 * [backup-simplify]: Simplify 1 into 1 9.156 * [backup-simplify]: Simplify (/ 1 1) into 1 9.157 * [backup-simplify]: Simplify (sqrt 0) into 0 9.157 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.158 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.158 * [backup-simplify]: Simplify 0 into 0 9.159 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.159 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.159 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.161 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.162 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.163 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.163 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.165 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.167 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.167 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.168 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 9.168 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.168 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.168 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.168 * [taylor]: Taking taylor expansion of 1.0 in k 9.168 * [backup-simplify]: Simplify 1.0 into 1.0 9.168 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.168 * [taylor]: Taking taylor expansion of k in k 9.168 * [backup-simplify]: Simplify 0 into 0 9.168 * [backup-simplify]: Simplify 1 into 1 9.168 * [backup-simplify]: Simplify (sqrt 0) into 0 9.169 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.169 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.169 * [taylor]: Taking taylor expansion of 1.0 in k 9.169 * [backup-simplify]: Simplify 1.0 into 1.0 9.169 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.169 * [taylor]: Taking taylor expansion of k in k 9.169 * [backup-simplify]: Simplify 0 into 0 9.169 * [backup-simplify]: Simplify 1 into 1 9.170 * [backup-simplify]: Simplify (sqrt 0) into 0 9.170 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.171 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.171 * [backup-simplify]: Simplify 0 into 0 9.172 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.172 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.175 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.176 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.177 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.179 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.180 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.181 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.182 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 9.182 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.182 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.182 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.182 * [taylor]: Taking taylor expansion of 1.0 in k 9.182 * [backup-simplify]: Simplify 1.0 into 1.0 9.182 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.182 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.182 * [taylor]: Taking taylor expansion of -1 in k 9.182 * [backup-simplify]: Simplify -1 into -1 9.182 * [taylor]: Taking taylor expansion of k in k 9.182 * [backup-simplify]: Simplify 0 into 0 9.182 * [backup-simplify]: Simplify 1 into 1 9.182 * [backup-simplify]: Simplify (/ -1 1) into -1 9.183 * [backup-simplify]: Simplify (sqrt 0) into 0 9.183 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.184 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.184 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.184 * [taylor]: Taking taylor expansion of 1.0 in k 9.184 * [backup-simplify]: Simplify 1.0 into 1.0 9.184 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.184 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.184 * [taylor]: Taking taylor expansion of -1 in k 9.184 * [backup-simplify]: Simplify -1 into -1 9.184 * [taylor]: Taking taylor expansion of k in k 9.184 * [backup-simplify]: Simplify 0 into 0 9.184 * [backup-simplify]: Simplify 1 into 1 9.184 * [backup-simplify]: Simplify (/ -1 1) into -1 9.184 * [backup-simplify]: Simplify (sqrt 0) into 0 9.185 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.186 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.186 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.186 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.188 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.189 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.190 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.190 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.193 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.195 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.195 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.196 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 9.196 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 9.196 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.196 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.196 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.196 * [taylor]: Taking taylor expansion of 2.0 in n 9.196 * [backup-simplify]: Simplify 2.0 into 2.0 9.196 * [taylor]: Taking taylor expansion of (* n PI) in n 9.196 * [taylor]: Taking taylor expansion of n in n 9.197 * [backup-simplify]: Simplify 0 into 0 9.197 * [backup-simplify]: Simplify 1 into 1 9.197 * [taylor]: Taking taylor expansion of PI in n 9.197 * [backup-simplify]: Simplify PI into PI 9.197 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.197 * [taylor]: Taking taylor expansion of 2.0 in n 9.197 * [backup-simplify]: Simplify 2.0 into 2.0 9.197 * [taylor]: Taking taylor expansion of (* n PI) in n 9.197 * [taylor]: Taking taylor expansion of n in n 9.197 * [backup-simplify]: Simplify 0 into 0 9.197 * [backup-simplify]: Simplify 1 into 1 9.197 * [taylor]: Taking taylor expansion of PI in n 9.197 * [backup-simplify]: Simplify PI into PI 9.197 * [backup-simplify]: Simplify (* 0 PI) into 0 9.197 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.197 * [backup-simplify]: Simplify 0 into 0 9.198 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.199 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.199 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.200 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.204 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.204 * [backup-simplify]: Simplify 0 into 0 9.205 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.206 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.206 * [backup-simplify]: Simplify 0 into 0 9.207 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.207 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.207 * [backup-simplify]: Simplify 0 into 0 9.209 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.210 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.210 * [backup-simplify]: Simplify 0 into 0 9.212 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.214 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.214 * [backup-simplify]: Simplify 0 into 0 9.216 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.218 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.218 * [backup-simplify]: Simplify 0 into 0 9.219 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.219 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.219 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.219 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.219 * [taylor]: Taking taylor expansion of 2.0 in n 9.219 * [backup-simplify]: Simplify 2.0 into 2.0 9.219 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.219 * [taylor]: Taking taylor expansion of PI in n 9.219 * [backup-simplify]: Simplify PI into PI 9.219 * [taylor]: Taking taylor expansion of n in n 9.220 * [backup-simplify]: Simplify 0 into 0 9.220 * [backup-simplify]: Simplify 1 into 1 9.220 * [backup-simplify]: Simplify (/ PI 1) into PI 9.220 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.220 * [taylor]: Taking taylor expansion of 2.0 in n 9.220 * [backup-simplify]: Simplify 2.0 into 2.0 9.220 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.220 * [taylor]: Taking taylor expansion of PI in n 9.220 * [backup-simplify]: Simplify PI into PI 9.220 * [taylor]: Taking taylor expansion of n in n 9.220 * [backup-simplify]: Simplify 0 into 0 9.220 * [backup-simplify]: Simplify 1 into 1 9.221 * [backup-simplify]: Simplify (/ PI 1) into PI 9.221 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.222 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.223 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.224 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.224 * [backup-simplify]: Simplify 0 into 0 9.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.226 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.226 * [backup-simplify]: Simplify 0 into 0 9.227 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.229 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.229 * [backup-simplify]: Simplify 0 into 0 9.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.232 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.232 * [backup-simplify]: Simplify 0 into 0 9.233 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.235 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.235 * [backup-simplify]: Simplify 0 into 0 9.236 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.238 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.238 * [backup-simplify]: Simplify 0 into 0 9.238 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.239 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.239 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.239 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.239 * [taylor]: Taking taylor expansion of -2.0 in n 9.239 * [backup-simplify]: Simplify -2.0 into -2.0 9.239 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.239 * [taylor]: Taking taylor expansion of PI in n 9.239 * [backup-simplify]: Simplify PI into PI 9.239 * [taylor]: Taking taylor expansion of n in n 9.239 * [backup-simplify]: Simplify 0 into 0 9.239 * [backup-simplify]: Simplify 1 into 1 9.240 * [backup-simplify]: Simplify (/ PI 1) into PI 9.240 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.240 * [taylor]: Taking taylor expansion of -2.0 in n 9.240 * [backup-simplify]: Simplify -2.0 into -2.0 9.240 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.240 * [taylor]: Taking taylor expansion of PI in n 9.240 * [backup-simplify]: Simplify PI into PI 9.240 * [taylor]: Taking taylor expansion of n in n 9.240 * [backup-simplify]: Simplify 0 into 0 9.240 * [backup-simplify]: Simplify 1 into 1 9.241 * [backup-simplify]: Simplify (/ PI 1) into PI 9.241 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.242 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.243 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.243 * [backup-simplify]: Simplify 0 into 0 9.244 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.246 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.246 * [backup-simplify]: Simplify 0 into 0 9.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.248 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.248 * [backup-simplify]: Simplify 0 into 0 9.249 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.250 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.251 * [backup-simplify]: Simplify 0 into 0 9.252 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.253 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.253 * [backup-simplify]: Simplify 0 into 0 9.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.256 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.256 * [backup-simplify]: Simplify 0 into 0 9.257 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.257 * * * [progress]: simplifying candidates 9.260 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* 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k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 9.265 * * [simplify]: Extracting # 0 : cost 0 9.266 * * [simplify]: Extracting # 1 : cost 0 9.266 * * [simplify]: Extracting # 2 : cost 0 9.266 * * [simplify]: Extracting # 3 : cost 0 9.267 * * [simplify]: Extracting # 4 : cost 0 9.267 * * [simplify]: Extracting # 5 : cost 0 9.267 * * [simplify]: Extracting # 6 : cost 0 9.268 * * [simplify]: Extracting # 7 : cost 0 9.268 * * [simplify]: Extracting # 8 : cost 0 9.269 * * [simplify]: Extracting # 9 : cost 0 9.269 * * [simplify]: Extracting # 10 : cost 0 9.270 * * [simplify]: Extracting # 11 : cost 0 9.270 * * [simplify]: Extracting # 12 : cost 0 9.271 * * [simplify]: Extracting # 13 : cost 0 9.271 * * [simplify]: Extracting # 14 : cost 0 9.272 * * [simplify]: iteration 0 : 332 enodes (cost 3588 ) 9.431 * * [simplify]: Extracting # 0 : cost 0 9.432 * * [simplify]: Extracting # 1 : cost 0 9.433 * * [simplify]: Extracting # 2 : cost 0 9.434 * * [simplify]: Extracting # 3 : cost 0 9.435 * * [simplify]: Extracting # 4 : cost 0 9.437 * * [simplify]: Extracting # 5 : cost 0 9.438 * * [simplify]: Extracting # 6 : cost 0 9.439 * * [simplify]: Extracting # 7 : cost 0 9.440 * * [simplify]: iteration 1 : 854 enodes (cost 3308 ) 10.037 * * [simplify]: Extracting # 0 : cost 0 10.043 * * [simplify]: Extracting # 1 : cost 0 10.050 * * [simplify]: Extracting # 2 : cost 0 10.056 * * [simplify]: Extracting # 3 : cost 0 10.062 * * [simplify]: Extracting # 4 : cost 0 10.069 * * [simplify]: iteration 2 : 2490 enodes (cost 3202 ) 10.928 * * [simplify]: Extracting # 0 : cost 0 10.939 * * [simplify]: Extracting # 1 : cost 0 10.952 * * [simplify]: Extracting # 2 : cost 0 10.978 * * [simplify]: Extracting # 3 : cost 0 10.987 * * [simplify]: Extracting # 4 : cost 0 10.994 * * [simplify]: iteration done: 5002 enodes (cost 3197 ) 10.996 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* PI n) 2.0) (- 1.0 k)) (* (* PI n) 2.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (* (/ (- 1.0 k) 2.0) 1/2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* 2.0 (* PI n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* 2.0 (* PI n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* 2.0 (* PI n)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* 2.0 (* PI n)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* PI n) 2.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* PI n) 2.0) (- 1.0 k)) (* (* PI n) 2.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* 2.0 (* PI n)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* k (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* PI n) 2.0) (* (* PI n) 2.0) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (log (* (* PI n) 2.0)) (exp (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (pow (* 2.0 (* PI n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* 2.0 (* PI n)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (fma (- 0.25) (* k (fma (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n)))) (fma (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2)) (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (fma (* 0.0625 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* 2.0 (* PI n)) 0.25) (log n)) (pow (* 2.0 (* PI n)) 0.25))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- 0.25) (* k (fma (pow (* 2.0 (* PI n)) 0.25) (log (* 2.0 PI)) (* (pow (* 2.0 (* PI n)) 0.25) (log n)))) (fma (* 0.03125 (pow k 2)) (* (pow (* 2.0 (* PI n)) 0.25) (pow (log (* 2.0 PI)) 2)) (fma (* 0.03125 (pow k 2)) (* (pow (log n) 2) (pow (* 2.0 (* PI n)) 0.25)) (fma (* 0.0625 (* (pow k 2) (log (* 2.0 PI)))) (* (pow (* 2.0 (* PI n)) 0.25) (log n)) (pow (* 2.0 (* PI n)) 0.25))))) (pow (pow (* 2.0 (* PI n)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (fma +nan.0 (pow k 2) (- +nan.0))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3)))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) +nan.0)) (* (* PI n) 2.0) (* (* PI n) 2.0) (* (* PI n) 2.0) 10.997 * * * [progress]: adding candidates to table 12.317 * * [progress]: iteration 3 / 4 12.317 * * * [progress]: picking best candidate 12.375 * * * * [pick]: Picked # 12.375 * * * [progress]: localizing error 12.432 * * * [progress]: generating rewritten candidates 12.432 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1) 12.452 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 12.494 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 12.508 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 2) 12.540 * * * [progress]: generating series expansions 12.540 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1) 12.540 * [backup-simplify]: Simplify (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.540 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.540 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.540 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.540 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.540 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.540 * [taylor]: Taking taylor expansion of 0.5 in k 12.541 * [backup-simplify]: Simplify 0.5 into 0.5 12.541 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.541 * [taylor]: Taking taylor expansion of 1.0 in k 12.541 * [backup-simplify]: Simplify 1.0 into 1.0 12.541 * [taylor]: Taking taylor expansion of k in k 12.541 * [backup-simplify]: Simplify 0 into 0 12.541 * [backup-simplify]: Simplify 1 into 1 12.541 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.541 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.541 * [taylor]: Taking taylor expansion of 2.0 in k 12.541 * [backup-simplify]: Simplify 2.0 into 2.0 12.541 * [taylor]: Taking taylor expansion of (* n PI) in k 12.541 * [taylor]: Taking taylor expansion of n in k 12.541 * [backup-simplify]: Simplify n into n 12.541 * [taylor]: Taking taylor expansion of PI in k 12.541 * [backup-simplify]: Simplify PI into PI 12.541 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.541 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.541 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.541 * [backup-simplify]: Simplify (- 0) into 0 12.542 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.542 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.542 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.542 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.542 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.542 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.542 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.542 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.542 * [taylor]: Taking taylor expansion of 0.5 in n 12.542 * [backup-simplify]: Simplify 0.5 into 0.5 12.542 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.542 * [taylor]: Taking taylor expansion of 1.0 in n 12.542 * [backup-simplify]: Simplify 1.0 into 1.0 12.542 * [taylor]: Taking taylor expansion of k in n 12.543 * [backup-simplify]: Simplify k into k 12.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.543 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.543 * [taylor]: Taking taylor expansion of 2.0 in n 12.543 * [backup-simplify]: Simplify 2.0 into 2.0 12.543 * [taylor]: Taking taylor expansion of (* n PI) in n 12.543 * [taylor]: Taking taylor expansion of n in n 12.543 * [backup-simplify]: Simplify 0 into 0 12.543 * [backup-simplify]: Simplify 1 into 1 12.543 * [taylor]: Taking taylor expansion of PI in n 12.543 * [backup-simplify]: Simplify PI into PI 12.543 * [backup-simplify]: Simplify (* 0 PI) into 0 12.543 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.544 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.545 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.546 * [backup-simplify]: Simplify (- k) into (- k) 12.546 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.546 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.547 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.548 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.549 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.549 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.549 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.549 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.549 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.549 * [taylor]: Taking taylor expansion of 0.5 in n 12.549 * [backup-simplify]: Simplify 0.5 into 0.5 12.549 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.549 * [taylor]: Taking taylor expansion of 1.0 in n 12.549 * [backup-simplify]: Simplify 1.0 into 1.0 12.549 * [taylor]: Taking taylor expansion of k in n 12.549 * [backup-simplify]: Simplify k into k 12.549 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.549 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.549 * [taylor]: Taking taylor expansion of 2.0 in n 12.549 * [backup-simplify]: Simplify 2.0 into 2.0 12.549 * [taylor]: Taking taylor expansion of (* n PI) in n 12.549 * [taylor]: Taking taylor expansion of n in n 12.549 * [backup-simplify]: Simplify 0 into 0 12.549 * [backup-simplify]: Simplify 1 into 1 12.549 * [taylor]: Taking taylor expansion of PI in n 12.549 * [backup-simplify]: Simplify PI into PI 12.549 * [backup-simplify]: Simplify (* 0 PI) into 0 12.550 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.550 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.551 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.552 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.552 * [backup-simplify]: Simplify (- k) into (- k) 12.552 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.552 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.553 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.554 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.555 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.555 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.555 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.555 * [taylor]: Taking taylor expansion of 0.5 in k 12.555 * [backup-simplify]: Simplify 0.5 into 0.5 12.555 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.555 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.555 * [taylor]: Taking taylor expansion of 1.0 in k 12.555 * [backup-simplify]: Simplify 1.0 into 1.0 12.555 * [taylor]: Taking taylor expansion of k in k 12.555 * [backup-simplify]: Simplify 0 into 0 12.555 * [backup-simplify]: Simplify 1 into 1 12.555 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.555 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.555 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.555 * [taylor]: Taking taylor expansion of 2.0 in k 12.555 * [backup-simplify]: Simplify 2.0 into 2.0 12.555 * [taylor]: Taking taylor expansion of PI in k 12.555 * [backup-simplify]: Simplify PI into PI 12.555 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.556 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.556 * [taylor]: Taking taylor expansion of (log n) in k 12.556 * [taylor]: Taking taylor expansion of n in k 12.556 * [backup-simplify]: Simplify n into n 12.556 * [backup-simplify]: Simplify (log n) into (log n) 12.556 * [backup-simplify]: Simplify (- 0) into 0 12.557 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.557 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.558 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.559 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.559 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.560 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.561 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.561 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.562 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.563 * [backup-simplify]: Simplify (- 0) into 0 12.563 * [backup-simplify]: Simplify (+ 0 0) into 0 12.563 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.564 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.565 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.566 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.566 * [taylor]: Taking taylor expansion of 0 in k 12.566 * [backup-simplify]: Simplify 0 into 0 12.566 * [backup-simplify]: Simplify 0 into 0 12.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.568 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.569 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.569 * [backup-simplify]: Simplify (+ 0 0) into 0 12.570 * [backup-simplify]: Simplify (- 1) into -1 12.570 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.571 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.574 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 12.577 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.581 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.582 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.584 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.587 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.588 * [backup-simplify]: Simplify (- 0) into 0 12.588 * [backup-simplify]: Simplify (+ 0 0) into 0 12.589 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.590 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.591 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.592 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.592 * [taylor]: Taking taylor expansion of 0 in k 12.592 * [backup-simplify]: Simplify 0 into 0 12.592 * [backup-simplify]: Simplify 0 into 0 12.592 * [backup-simplify]: Simplify 0 into 0 12.593 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.595 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.596 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.596 * [backup-simplify]: Simplify (+ 0 0) into 0 12.596 * [backup-simplify]: Simplify (- 0) into 0 12.597 * [backup-simplify]: Simplify (+ 0 0) into 0 12.598 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.599 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.602 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.606 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.613 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.613 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 n) PI)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.613 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.613 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.613 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.613 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.613 * [taylor]: Taking taylor expansion of 0.5 in k 12.613 * [backup-simplify]: Simplify 0.5 into 0.5 12.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.613 * [taylor]: Taking taylor expansion of 1.0 in k 12.613 * [backup-simplify]: Simplify 1.0 into 1.0 12.613 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.613 * [taylor]: Taking taylor expansion of k in k 12.613 * [backup-simplify]: Simplify 0 into 0 12.613 * [backup-simplify]: Simplify 1 into 1 12.613 * [backup-simplify]: Simplify (/ 1 1) into 1 12.613 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.613 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.613 * [taylor]: Taking taylor expansion of 2.0 in k 12.613 * [backup-simplify]: Simplify 2.0 into 2.0 12.613 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.613 * [taylor]: Taking taylor expansion of PI in k 12.613 * [backup-simplify]: Simplify PI into PI 12.614 * [taylor]: Taking taylor expansion of n in k 12.614 * [backup-simplify]: Simplify n into n 12.614 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.614 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.614 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.614 * [backup-simplify]: Simplify (- 1) into -1 12.614 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.614 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.615 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.615 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.615 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.615 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.615 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.615 * [taylor]: Taking taylor expansion of 0.5 in n 12.615 * [backup-simplify]: Simplify 0.5 into 0.5 12.615 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.615 * [taylor]: Taking taylor expansion of 1.0 in n 12.615 * [backup-simplify]: Simplify 1.0 into 1.0 12.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.615 * [taylor]: Taking taylor expansion of k in n 12.615 * [backup-simplify]: Simplify k into k 12.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.615 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.615 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.615 * [taylor]: Taking taylor expansion of 2.0 in n 12.615 * [backup-simplify]: Simplify 2.0 into 2.0 12.615 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.615 * [taylor]: Taking taylor expansion of PI in n 12.615 * [backup-simplify]: Simplify PI into PI 12.615 * [taylor]: Taking taylor expansion of n in n 12.615 * [backup-simplify]: Simplify 0 into 0 12.615 * [backup-simplify]: Simplify 1 into 1 12.616 * [backup-simplify]: Simplify (/ PI 1) into PI 12.616 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.617 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.617 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.617 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.617 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.618 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.619 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.619 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.619 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.619 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.619 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.619 * [taylor]: Taking taylor expansion of 0.5 in n 12.619 * [backup-simplify]: Simplify 0.5 into 0.5 12.619 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.619 * [taylor]: Taking taylor expansion of 1.0 in n 12.619 * [backup-simplify]: Simplify 1.0 into 1.0 12.619 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.619 * [taylor]: Taking taylor expansion of k in n 12.619 * [backup-simplify]: Simplify k into k 12.619 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.619 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.619 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.619 * [taylor]: Taking taylor expansion of 2.0 in n 12.619 * [backup-simplify]: Simplify 2.0 into 2.0 12.620 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.620 * [taylor]: Taking taylor expansion of PI in n 12.620 * [backup-simplify]: Simplify PI into PI 12.620 * [taylor]: Taking taylor expansion of n in n 12.620 * [backup-simplify]: Simplify 0 into 0 12.620 * [backup-simplify]: Simplify 1 into 1 12.620 * [backup-simplify]: Simplify (/ PI 1) into PI 12.620 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.621 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.622 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.622 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.622 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.624 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.626 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.626 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.626 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.626 * [taylor]: Taking taylor expansion of 0.5 in k 12.626 * [backup-simplify]: Simplify 0.5 into 0.5 12.626 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.626 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.626 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.626 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.626 * [taylor]: Taking taylor expansion of 2.0 in k 12.626 * [backup-simplify]: Simplify 2.0 into 2.0 12.626 * [taylor]: Taking taylor expansion of PI in k 12.626 * [backup-simplify]: Simplify PI into PI 12.636 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.637 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.637 * [taylor]: Taking taylor expansion of (log n) in k 12.637 * [taylor]: Taking taylor expansion of n in k 12.637 * [backup-simplify]: Simplify n into n 12.637 * [backup-simplify]: Simplify (log n) into (log n) 12.637 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.637 * [taylor]: Taking taylor expansion of 1.0 in k 12.637 * [backup-simplify]: Simplify 1.0 into 1.0 12.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.637 * [taylor]: Taking taylor expansion of k in k 12.637 * [backup-simplify]: Simplify 0 into 0 12.637 * [backup-simplify]: Simplify 1 into 1 12.638 * [backup-simplify]: Simplify (/ 1 1) into 1 12.638 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.639 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.639 * [backup-simplify]: Simplify (- 1) into -1 12.640 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.641 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.642 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.643 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.644 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.645 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.648 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.648 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.649 * [backup-simplify]: Simplify (- 0) into 0 12.649 * [backup-simplify]: Simplify (+ 0 0) into 0 12.650 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.651 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.652 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.655 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.655 * [taylor]: Taking taylor expansion of 0 in k 12.655 * [backup-simplify]: Simplify 0 into 0 12.655 * [backup-simplify]: Simplify 0 into 0 12.655 * [backup-simplify]: Simplify 0 into 0 12.656 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.657 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.661 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.661 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.661 * [backup-simplify]: Simplify (- 0) into 0 12.662 * [backup-simplify]: Simplify (+ 0 0) into 0 12.663 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.666 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.668 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.668 * [taylor]: Taking taylor expansion of 0 in k 12.668 * [backup-simplify]: Simplify 0 into 0 12.668 * [backup-simplify]: Simplify 0 into 0 12.668 * [backup-simplify]: Simplify 0 into 0 12.668 * [backup-simplify]: Simplify 0 into 0 12.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.671 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.677 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.677 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.678 * [backup-simplify]: Simplify (- 0) into 0 12.678 * [backup-simplify]: Simplify (+ 0 0) into 0 12.680 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.681 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.683 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.686 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.686 * [taylor]: Taking taylor expansion of 0 in k 12.686 * [backup-simplify]: Simplify 0 into 0 12.686 * [backup-simplify]: Simplify 0 into 0 12.688 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.688 * [backup-simplify]: Simplify (pow (* 2.0 (* (/ 1 (- n)) PI)) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.688 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.688 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.688 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.688 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.688 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.689 * [taylor]: Taking taylor expansion of 0.5 in k 12.689 * [backup-simplify]: Simplify 0.5 into 0.5 12.689 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.689 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.689 * [taylor]: Taking taylor expansion of k in k 12.689 * [backup-simplify]: Simplify 0 into 0 12.689 * [backup-simplify]: Simplify 1 into 1 12.689 * [backup-simplify]: Simplify (/ 1 1) into 1 12.689 * [taylor]: Taking taylor expansion of 1.0 in k 12.689 * [backup-simplify]: Simplify 1.0 into 1.0 12.689 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.689 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.689 * [taylor]: Taking taylor expansion of -2.0 in k 12.689 * [backup-simplify]: Simplify -2.0 into -2.0 12.689 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.689 * [taylor]: Taking taylor expansion of PI in k 12.689 * [backup-simplify]: Simplify PI into PI 12.690 * [taylor]: Taking taylor expansion of n in k 12.690 * [backup-simplify]: Simplify n into n 12.690 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.690 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.690 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.691 * [backup-simplify]: Simplify (+ 1 0) into 1 12.691 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.691 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.691 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.692 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.692 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.692 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.692 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.692 * [taylor]: Taking taylor expansion of 0.5 in n 12.692 * [backup-simplify]: Simplify 0.5 into 0.5 12.692 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.692 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.692 * [taylor]: Taking taylor expansion of k in n 12.692 * [backup-simplify]: Simplify k into k 12.692 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.692 * [taylor]: Taking taylor expansion of 1.0 in n 12.692 * [backup-simplify]: Simplify 1.0 into 1.0 12.692 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.692 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.692 * [taylor]: Taking taylor expansion of -2.0 in n 12.692 * [backup-simplify]: Simplify -2.0 into -2.0 12.692 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.692 * [taylor]: Taking taylor expansion of PI in n 12.692 * [backup-simplify]: Simplify PI into PI 12.692 * [taylor]: Taking taylor expansion of n in n 12.692 * [backup-simplify]: Simplify 0 into 0 12.692 * [backup-simplify]: Simplify 1 into 1 12.693 * [backup-simplify]: Simplify (/ PI 1) into PI 12.693 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.695 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.695 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.695 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.698 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.699 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.699 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.699 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.699 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.699 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.699 * [taylor]: Taking taylor expansion of 0.5 in n 12.699 * [backup-simplify]: Simplify 0.5 into 0.5 12.699 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.699 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.699 * [taylor]: Taking taylor expansion of k in n 12.699 * [backup-simplify]: Simplify k into k 12.699 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.699 * [taylor]: Taking taylor expansion of 1.0 in n 12.699 * [backup-simplify]: Simplify 1.0 into 1.0 12.700 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.700 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.700 * [taylor]: Taking taylor expansion of -2.0 in n 12.700 * [backup-simplify]: Simplify -2.0 into -2.0 12.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.700 * [taylor]: Taking taylor expansion of PI in n 12.700 * [backup-simplify]: Simplify PI into PI 12.700 * [taylor]: Taking taylor expansion of n in n 12.700 * [backup-simplify]: Simplify 0 into 0 12.700 * [backup-simplify]: Simplify 1 into 1 12.700 * [backup-simplify]: Simplify (/ PI 1) into PI 12.701 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.702 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.702 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.702 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.704 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.705 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.706 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.706 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.706 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.707 * [taylor]: Taking taylor expansion of 0.5 in k 12.707 * [backup-simplify]: Simplify 0.5 into 0.5 12.707 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.707 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.707 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.707 * [taylor]: Taking taylor expansion of k in k 12.707 * [backup-simplify]: Simplify 0 into 0 12.707 * [backup-simplify]: Simplify 1 into 1 12.707 * [backup-simplify]: Simplify (/ 1 1) into 1 12.707 * [taylor]: Taking taylor expansion of 1.0 in k 12.707 * [backup-simplify]: Simplify 1.0 into 1.0 12.707 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.707 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.707 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.707 * [taylor]: Taking taylor expansion of -2.0 in k 12.707 * [backup-simplify]: Simplify -2.0 into -2.0 12.707 * [taylor]: Taking taylor expansion of PI in k 12.707 * [backup-simplify]: Simplify PI into PI 12.708 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.709 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.709 * [taylor]: Taking taylor expansion of (log n) in k 12.709 * [taylor]: Taking taylor expansion of n in k 12.709 * [backup-simplify]: Simplify n into n 12.709 * [backup-simplify]: Simplify (log n) into (log n) 12.709 * [backup-simplify]: Simplify (+ 1 0) into 1 12.709 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.711 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.712 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.713 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.714 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.716 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.718 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.720 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.720 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.721 * [backup-simplify]: Simplify (+ 0 0) into 0 12.721 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.723 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.725 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.727 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.727 * [taylor]: Taking taylor expansion of 0 in k 12.727 * [backup-simplify]: Simplify 0 into 0 12.727 * [backup-simplify]: Simplify 0 into 0 12.727 * [backup-simplify]: Simplify 0 into 0 12.728 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.729 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.733 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.734 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.734 * [backup-simplify]: Simplify (+ 0 0) into 0 12.735 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.737 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.739 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.742 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.742 * [taylor]: Taking taylor expansion of 0 in k 12.742 * [backup-simplify]: Simplify 0 into 0 12.742 * [backup-simplify]: Simplify 0 into 0 12.742 * [backup-simplify]: Simplify 0 into 0 12.742 * [backup-simplify]: Simplify 0 into 0 12.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.746 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.753 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.753 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.753 * [backup-simplify]: Simplify (+ 0 0) into 0 12.755 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.759 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.762 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.762 * [taylor]: Taking taylor expansion of 0 in k 12.762 * [backup-simplify]: Simplify 0 into 0 12.762 * [backup-simplify]: Simplify 0 into 0 12.763 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.763 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 12.764 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 12.764 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.764 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.764 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.764 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.764 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.764 * [taylor]: Taking taylor expansion of 0.25 in k 12.764 * [backup-simplify]: Simplify 0.25 into 0.25 12.764 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.764 * [taylor]: Taking taylor expansion of 1.0 in k 12.765 * [backup-simplify]: Simplify 1.0 into 1.0 12.765 * [taylor]: Taking taylor expansion of k in k 12.765 * [backup-simplify]: Simplify 0 into 0 12.765 * [backup-simplify]: Simplify 1 into 1 12.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.765 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.765 * [taylor]: Taking taylor expansion of 2.0 in k 12.765 * [backup-simplify]: Simplify 2.0 into 2.0 12.765 * [taylor]: Taking taylor expansion of (* n PI) in k 12.765 * [taylor]: Taking taylor expansion of n in k 12.765 * [backup-simplify]: Simplify n into n 12.765 * [taylor]: Taking taylor expansion of PI in k 12.765 * [backup-simplify]: Simplify PI into PI 12.765 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.765 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.765 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.766 * [backup-simplify]: Simplify (- 0) into 0 12.766 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.766 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.767 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.767 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.767 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.767 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.767 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.767 * [taylor]: Taking taylor expansion of 0.25 in n 12.767 * [backup-simplify]: Simplify 0.25 into 0.25 12.767 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.767 * [taylor]: Taking taylor expansion of 1.0 in n 12.767 * [backup-simplify]: Simplify 1.0 into 1.0 12.767 * [taylor]: Taking taylor expansion of k in n 12.767 * [backup-simplify]: Simplify k into k 12.767 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.767 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.767 * [taylor]: Taking taylor expansion of 2.0 in n 12.767 * [backup-simplify]: Simplify 2.0 into 2.0 12.767 * [taylor]: Taking taylor expansion of (* n PI) in n 12.767 * [taylor]: Taking taylor expansion of n in n 12.767 * [backup-simplify]: Simplify 0 into 0 12.767 * [backup-simplify]: Simplify 1 into 1 12.767 * [taylor]: Taking taylor expansion of PI in n 12.767 * [backup-simplify]: Simplify PI into PI 12.768 * [backup-simplify]: Simplify (* 0 PI) into 0 12.768 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.770 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.772 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.773 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.773 * [backup-simplify]: Simplify (- k) into (- k) 12.773 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.773 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.775 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.776 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.777 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.777 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.777 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.777 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.777 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.777 * [taylor]: Taking taylor expansion of 0.25 in n 12.777 * [backup-simplify]: Simplify 0.25 into 0.25 12.777 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.777 * [taylor]: Taking taylor expansion of 1.0 in n 12.777 * [backup-simplify]: Simplify 1.0 into 1.0 12.777 * [taylor]: Taking taylor expansion of k in n 12.777 * [backup-simplify]: Simplify k into k 12.777 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.777 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.778 * [taylor]: Taking taylor expansion of 2.0 in n 12.778 * [backup-simplify]: Simplify 2.0 into 2.0 12.778 * [taylor]: Taking taylor expansion of (* n PI) in n 12.778 * [taylor]: Taking taylor expansion of n in n 12.778 * [backup-simplify]: Simplify 0 into 0 12.778 * [backup-simplify]: Simplify 1 into 1 12.778 * [taylor]: Taking taylor expansion of PI in n 12.778 * [backup-simplify]: Simplify PI into PI 12.778 * [backup-simplify]: Simplify (* 0 PI) into 0 12.779 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.780 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.782 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.783 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.783 * [backup-simplify]: Simplify (- k) into (- k) 12.783 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.783 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.785 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.786 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.787 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.787 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.787 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.787 * [taylor]: Taking taylor expansion of 0.25 in k 12.787 * [backup-simplify]: Simplify 0.25 into 0.25 12.787 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.788 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.788 * [taylor]: Taking taylor expansion of 1.0 in k 12.788 * [backup-simplify]: Simplify 1.0 into 1.0 12.788 * [taylor]: Taking taylor expansion of k in k 12.788 * [backup-simplify]: Simplify 0 into 0 12.788 * [backup-simplify]: Simplify 1 into 1 12.788 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.788 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.788 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.788 * [taylor]: Taking taylor expansion of 2.0 in k 12.788 * [backup-simplify]: Simplify 2.0 into 2.0 12.788 * [taylor]: Taking taylor expansion of PI in k 12.788 * [backup-simplify]: Simplify PI into PI 12.788 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.789 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.790 * [taylor]: Taking taylor expansion of (log n) in k 12.790 * [taylor]: Taking taylor expansion of n in k 12.790 * [backup-simplify]: Simplify n into n 12.790 * [backup-simplify]: Simplify (log n) into (log n) 12.790 * [backup-simplify]: Simplify (- 0) into 0 12.791 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.792 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.793 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.794 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.804 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.806 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.807 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.808 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.811 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.811 * [backup-simplify]: Simplify (- 0) into 0 12.812 * [backup-simplify]: Simplify (+ 0 0) into 0 12.812 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.814 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.815 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.818 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.818 * [taylor]: Taking taylor expansion of 0 in k 12.818 * [backup-simplify]: Simplify 0 into 0 12.818 * [backup-simplify]: Simplify 0 into 0 12.819 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.821 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.822 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.823 * [backup-simplify]: Simplify (+ 0 0) into 0 12.823 * [backup-simplify]: Simplify (- 1) into -1 12.824 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.825 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.828 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 12.830 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.831 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.832 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.833 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.835 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.835 * [backup-simplify]: Simplify (- 0) into 0 12.835 * [backup-simplify]: Simplify (+ 0 0) into 0 12.836 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.837 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.838 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.839 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.839 * [taylor]: Taking taylor expansion of 0 in k 12.839 * [backup-simplify]: Simplify 0 into 0 12.839 * [backup-simplify]: Simplify 0 into 0 12.839 * [backup-simplify]: Simplify 0 into 0 12.840 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.842 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.843 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.844 * [backup-simplify]: Simplify (+ 0 0) into 0 12.844 * [backup-simplify]: Simplify (- 0) into 0 12.844 * [backup-simplify]: Simplify (+ 0 0) into 0 12.845 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.847 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.849 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 12.852 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 12.859 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.860 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 12.860 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.860 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.860 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.860 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.860 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.860 * [taylor]: Taking taylor expansion of 0.25 in k 12.860 * [backup-simplify]: Simplify 0.25 into 0.25 12.860 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.860 * [taylor]: Taking taylor expansion of 1.0 in k 12.860 * [backup-simplify]: Simplify 1.0 into 1.0 12.860 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.860 * [taylor]: Taking taylor expansion of k in k 12.860 * [backup-simplify]: Simplify 0 into 0 12.860 * [backup-simplify]: Simplify 1 into 1 12.860 * [backup-simplify]: Simplify (/ 1 1) into 1 12.860 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.860 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.860 * [taylor]: Taking taylor expansion of 2.0 in k 12.860 * [backup-simplify]: Simplify 2.0 into 2.0 12.861 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.861 * [taylor]: Taking taylor expansion of PI in k 12.861 * [backup-simplify]: Simplify PI into PI 12.861 * [taylor]: Taking taylor expansion of n in k 12.861 * [backup-simplify]: Simplify n into n 12.861 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.861 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.861 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.861 * [backup-simplify]: Simplify (- 1) into -1 12.862 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.862 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.862 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.862 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.862 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.862 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.862 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.862 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.862 * [taylor]: Taking taylor expansion of 0.25 in n 12.862 * [backup-simplify]: Simplify 0.25 into 0.25 12.862 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.862 * [taylor]: Taking taylor expansion of 1.0 in n 12.862 * [backup-simplify]: Simplify 1.0 into 1.0 12.862 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.862 * [taylor]: Taking taylor expansion of k in n 12.863 * [backup-simplify]: Simplify k into k 12.863 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.863 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.863 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.863 * [taylor]: Taking taylor expansion of 2.0 in n 12.863 * [backup-simplify]: Simplify 2.0 into 2.0 12.863 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.863 * [taylor]: Taking taylor expansion of PI in n 12.863 * [backup-simplify]: Simplify PI into PI 12.863 * [taylor]: Taking taylor expansion of n in n 12.863 * [backup-simplify]: Simplify 0 into 0 12.863 * [backup-simplify]: Simplify 1 into 1 12.863 * [backup-simplify]: Simplify (/ PI 1) into PI 12.863 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.864 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.864 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.864 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.864 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.865 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.866 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.867 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.867 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.867 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.867 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.867 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.867 * [taylor]: Taking taylor expansion of 0.25 in n 12.867 * [backup-simplify]: Simplify 0.25 into 0.25 12.867 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.867 * [taylor]: Taking taylor expansion of 1.0 in n 12.867 * [backup-simplify]: Simplify 1.0 into 1.0 12.867 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.867 * [taylor]: Taking taylor expansion of k in n 12.867 * [backup-simplify]: Simplify k into k 12.867 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.867 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.867 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.867 * [taylor]: Taking taylor expansion of 2.0 in n 12.867 * [backup-simplify]: Simplify 2.0 into 2.0 12.867 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.867 * [taylor]: Taking taylor expansion of PI in n 12.867 * [backup-simplify]: Simplify PI into PI 12.867 * [taylor]: Taking taylor expansion of n in n 12.867 * [backup-simplify]: Simplify 0 into 0 12.867 * [backup-simplify]: Simplify 1 into 1 12.867 * [backup-simplify]: Simplify (/ PI 1) into PI 12.868 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.868 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.868 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.868 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.869 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.869 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.870 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.871 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.871 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.871 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.871 * [taylor]: Taking taylor expansion of 0.25 in k 12.871 * [backup-simplify]: Simplify 0.25 into 0.25 12.871 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.871 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.871 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.871 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.871 * [taylor]: Taking taylor expansion of 2.0 in k 12.871 * [backup-simplify]: Simplify 2.0 into 2.0 12.871 * [taylor]: Taking taylor expansion of PI in k 12.871 * [backup-simplify]: Simplify PI into PI 12.872 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.872 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.872 * [taylor]: Taking taylor expansion of (log n) in k 12.872 * [taylor]: Taking taylor expansion of n in k 12.872 * [backup-simplify]: Simplify n into n 12.872 * [backup-simplify]: Simplify (log n) into (log n) 12.872 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.872 * [taylor]: Taking taylor expansion of 1.0 in k 12.872 * [backup-simplify]: Simplify 1.0 into 1.0 12.872 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.872 * [taylor]: Taking taylor expansion of k in k 12.872 * [backup-simplify]: Simplify 0 into 0 12.872 * [backup-simplify]: Simplify 1 into 1 12.873 * [backup-simplify]: Simplify (/ 1 1) into 1 12.873 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.873 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.874 * [backup-simplify]: Simplify (- 1) into -1 12.874 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.875 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.875 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.876 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.877 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.877 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.878 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.879 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.879 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.879 * [backup-simplify]: Simplify (- 0) into 0 12.879 * [backup-simplify]: Simplify (+ 0 0) into 0 12.880 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.881 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.882 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.883 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.883 * [taylor]: Taking taylor expansion of 0 in k 12.883 * [backup-simplify]: Simplify 0 into 0 12.883 * [backup-simplify]: Simplify 0 into 0 12.883 * [backup-simplify]: Simplify 0 into 0 12.884 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.884 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.886 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.887 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.887 * [backup-simplify]: Simplify (- 0) into 0 12.887 * [backup-simplify]: Simplify (+ 0 0) into 0 12.888 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.889 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.891 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.891 * [taylor]: Taking taylor expansion of 0 in k 12.891 * [backup-simplify]: Simplify 0 into 0 12.891 * [backup-simplify]: Simplify 0 into 0 12.891 * [backup-simplify]: Simplify 0 into 0 12.891 * [backup-simplify]: Simplify 0 into 0 12.892 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.893 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.899 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.899 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.900 * [backup-simplify]: Simplify (- 0) into 0 12.900 * [backup-simplify]: Simplify (+ 0 0) into 0 12.901 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.903 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.905 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.908 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.908 * [taylor]: Taking taylor expansion of 0 in k 12.908 * [backup-simplify]: Simplify 0 into 0 12.908 * [backup-simplify]: Simplify 0 into 0 12.909 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.910 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 12.910 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.910 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.910 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.910 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.910 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.910 * [taylor]: Taking taylor expansion of 0.25 in k 12.910 * [backup-simplify]: Simplify 0.25 into 0.25 12.910 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.910 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.911 * [taylor]: Taking taylor expansion of k in k 12.911 * [backup-simplify]: Simplify 0 into 0 12.911 * [backup-simplify]: Simplify 1 into 1 12.911 * [backup-simplify]: Simplify (/ 1 1) into 1 12.911 * [taylor]: Taking taylor expansion of 1.0 in k 12.911 * [backup-simplify]: Simplify 1.0 into 1.0 12.911 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.911 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.911 * [taylor]: Taking taylor expansion of -2.0 in k 12.911 * [backup-simplify]: Simplify -2.0 into -2.0 12.911 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.911 * [taylor]: Taking taylor expansion of PI in k 12.911 * [backup-simplify]: Simplify PI into PI 12.911 * [taylor]: Taking taylor expansion of n in k 12.911 * [backup-simplify]: Simplify n into n 12.911 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.912 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.912 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.912 * [backup-simplify]: Simplify (+ 1 0) into 1 12.913 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.913 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.913 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.913 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.913 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.913 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.913 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.913 * [taylor]: Taking taylor expansion of 0.25 in n 12.913 * [backup-simplify]: Simplify 0.25 into 0.25 12.913 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.913 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.913 * [taylor]: Taking taylor expansion of k in n 12.913 * [backup-simplify]: Simplify k into k 12.914 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.914 * [taylor]: Taking taylor expansion of 1.0 in n 12.914 * [backup-simplify]: Simplify 1.0 into 1.0 12.914 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.914 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.914 * [taylor]: Taking taylor expansion of -2.0 in n 12.914 * [backup-simplify]: Simplify -2.0 into -2.0 12.914 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.914 * [taylor]: Taking taylor expansion of PI in n 12.914 * [backup-simplify]: Simplify PI into PI 12.914 * [taylor]: Taking taylor expansion of n in n 12.914 * [backup-simplify]: Simplify 0 into 0 12.914 * [backup-simplify]: Simplify 1 into 1 12.922 * [backup-simplify]: Simplify (/ PI 1) into PI 12.923 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.924 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.925 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.925 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.926 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.928 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.929 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.929 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.929 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.929 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.929 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.929 * [taylor]: Taking taylor expansion of 0.25 in n 12.929 * [backup-simplify]: Simplify 0.25 into 0.25 12.929 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.929 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.929 * [taylor]: Taking taylor expansion of k in n 12.929 * [backup-simplify]: Simplify k into k 12.930 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.930 * [taylor]: Taking taylor expansion of 1.0 in n 12.930 * [backup-simplify]: Simplify 1.0 into 1.0 12.930 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.930 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.930 * [taylor]: Taking taylor expansion of -2.0 in n 12.930 * [backup-simplify]: Simplify -2.0 into -2.0 12.930 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.930 * [taylor]: Taking taylor expansion of PI in n 12.930 * [backup-simplify]: Simplify PI into PI 12.930 * [taylor]: Taking taylor expansion of n in n 12.930 * [backup-simplify]: Simplify 0 into 0 12.930 * [backup-simplify]: Simplify 1 into 1 12.930 * [backup-simplify]: Simplify (/ PI 1) into PI 12.931 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.932 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.932 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.932 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.935 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.937 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.937 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.937 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.937 * [taylor]: Taking taylor expansion of 0.25 in k 12.937 * [backup-simplify]: Simplify 0.25 into 0.25 12.937 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.937 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.937 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.937 * [taylor]: Taking taylor expansion of k in k 12.937 * [backup-simplify]: Simplify 0 into 0 12.937 * [backup-simplify]: Simplify 1 into 1 12.938 * [backup-simplify]: Simplify (/ 1 1) into 1 12.938 * [taylor]: Taking taylor expansion of 1.0 in k 12.938 * [backup-simplify]: Simplify 1.0 into 1.0 12.938 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.938 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.938 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.938 * [taylor]: Taking taylor expansion of -2.0 in k 12.938 * [backup-simplify]: Simplify -2.0 into -2.0 12.938 * [taylor]: Taking taylor expansion of PI in k 12.938 * [backup-simplify]: Simplify PI into PI 12.938 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.939 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.940 * [taylor]: Taking taylor expansion of (log n) in k 12.940 * [taylor]: Taking taylor expansion of n in k 12.940 * [backup-simplify]: Simplify n into n 12.940 * [backup-simplify]: Simplify (log n) into (log n) 12.940 * [backup-simplify]: Simplify (+ 1 0) into 1 12.940 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.942 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.943 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.944 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.946 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.947 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.948 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.950 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.951 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.952 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.952 * [backup-simplify]: Simplify (+ 0 0) into 0 12.953 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.956 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.958 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.958 * [taylor]: Taking taylor expansion of 0 in k 12.958 * [backup-simplify]: Simplify 0 into 0 12.958 * [backup-simplify]: Simplify 0 into 0 12.958 * [backup-simplify]: Simplify 0 into 0 12.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.960 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.962 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.962 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.962 * [backup-simplify]: Simplify (+ 0 0) into 0 12.963 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.965 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.967 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.967 * [taylor]: Taking taylor expansion of 0 in k 12.967 * [backup-simplify]: Simplify 0 into 0 12.967 * [backup-simplify]: Simplify 0 into 0 12.967 * [backup-simplify]: Simplify 0 into 0 12.967 * [backup-simplify]: Simplify 0 into 0 12.967 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.968 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.971 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.972 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.972 * [backup-simplify]: Simplify (+ 0 0) into 0 12.973 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.975 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.977 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.977 * [taylor]: Taking taylor expansion of 0 in k 12.977 * [backup-simplify]: Simplify 0 into 0 12.977 * [backup-simplify]: Simplify 0 into 0 12.978 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.978 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 12.978 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 12.978 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 12.978 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.978 * [taylor]: Taking taylor expansion of 1.0 in k 12.978 * [backup-simplify]: Simplify 1.0 into 1.0 12.978 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.978 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.978 * [taylor]: Taking taylor expansion of k in k 12.978 * [backup-simplify]: Simplify 0 into 0 12.978 * [backup-simplify]: Simplify 1 into 1 12.978 * [backup-simplify]: Simplify (/ 1 1) into 1 12.979 * [backup-simplify]: Simplify (sqrt 0) into 0 12.979 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.979 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 12.979 * [taylor]: Taking taylor expansion of 1.0 in k 12.980 * [backup-simplify]: Simplify 1.0 into 1.0 12.980 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.980 * [taylor]: Taking taylor expansion of k in k 12.980 * [backup-simplify]: Simplify 0 into 0 12.980 * [backup-simplify]: Simplify 1 into 1 12.980 * [backup-simplify]: Simplify (/ 1 1) into 1 12.980 * [backup-simplify]: Simplify (sqrt 0) into 0 12.981 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.981 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.981 * [backup-simplify]: Simplify 0 into 0 12.982 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.982 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.983 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.985 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.986 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 12.986 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.987 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.990 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.992 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 12.992 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 12.993 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 12.994 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 12.994 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 12.994 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.994 * [taylor]: Taking taylor expansion of 1.0 in k 12.994 * [backup-simplify]: Simplify 1.0 into 1.0 12.994 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.994 * [taylor]: Taking taylor expansion of k in k 12.994 * [backup-simplify]: Simplify 0 into 0 12.994 * [backup-simplify]: Simplify 1 into 1 12.994 * [backup-simplify]: Simplify (sqrt 0) into 0 12.995 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.995 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 12.995 * [taylor]: Taking taylor expansion of 1.0 in k 12.995 * [backup-simplify]: Simplify 1.0 into 1.0 12.995 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.996 * [taylor]: Taking taylor expansion of k in k 12.996 * [backup-simplify]: Simplify 0 into 0 12.996 * [backup-simplify]: Simplify 1 into 1 12.996 * [backup-simplify]: Simplify (sqrt 0) into 0 12.997 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.998 * [backup-simplify]: Simplify (* 1.0 0) into 0 12.998 * [backup-simplify]: Simplify 0 into 0 12.999 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 12.999 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.003 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.005 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 13.005 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.009 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.011 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 13.011 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.013 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 13.013 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 13.013 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 13.013 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.013 * [taylor]: Taking taylor expansion of 1.0 in k 13.013 * [backup-simplify]: Simplify 1.0 into 1.0 13.013 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.013 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.013 * [taylor]: Taking taylor expansion of -1 in k 13.013 * [backup-simplify]: Simplify -1 into -1 13.013 * [taylor]: Taking taylor expansion of k in k 13.013 * [backup-simplify]: Simplify 0 into 0 13.014 * [backup-simplify]: Simplify 1 into 1 13.014 * [backup-simplify]: Simplify (/ -1 1) into -1 13.014 * [backup-simplify]: Simplify (sqrt 0) into 0 13.016 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.016 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.016 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 13.016 * [taylor]: Taking taylor expansion of 1.0 in k 13.016 * [backup-simplify]: Simplify 1.0 into 1.0 13.016 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 13.016 * [taylor]: Taking taylor expansion of (/ -1 k) in k 13.016 * [taylor]: Taking taylor expansion of -1 in k 13.016 * [backup-simplify]: Simplify -1 into -1 13.016 * [taylor]: Taking taylor expansion of k in k 13.016 * [backup-simplify]: Simplify 0 into 0 13.016 * [backup-simplify]: Simplify 1 into 1 13.017 * [backup-simplify]: Simplify (/ -1 1) into -1 13.017 * [backup-simplify]: Simplify (sqrt 0) into 0 13.018 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 13.019 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 13.019 * [backup-simplify]: Simplify +nan.0 into +nan.0 13.020 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 13.022 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 13.025 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 13.025 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.030 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 13.033 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 13.034 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 13.035 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 13.035 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 2) 13.035 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.035 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 13.035 * [taylor]: Taking taylor expansion of (* n PI) in n 13.035 * [taylor]: Taking taylor expansion of n in n 13.035 * [backup-simplify]: Simplify 0 into 0 13.035 * [backup-simplify]: Simplify 1 into 1 13.035 * [taylor]: Taking taylor expansion of PI in n 13.035 * [backup-simplify]: Simplify PI into PI 13.035 * [taylor]: Taking taylor expansion of (* n PI) in n 13.035 * [taylor]: Taking taylor expansion of n in n 13.035 * [backup-simplify]: Simplify 0 into 0 13.035 * [backup-simplify]: Simplify 1 into 1 13.035 * [taylor]: Taking taylor expansion of PI in n 13.035 * [backup-simplify]: Simplify PI into PI 13.036 * [backup-simplify]: Simplify (* 0 PI) into 0 13.036 * [backup-simplify]: Simplify 0 into 0 13.037 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.037 * [backup-simplify]: Simplify PI into PI 13.038 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.038 * [backup-simplify]: Simplify 0 into 0 13.039 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.040 * [backup-simplify]: Simplify 0 into 0 13.041 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.041 * [backup-simplify]: Simplify 0 into 0 13.042 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.042 * [backup-simplify]: Simplify 0 into 0 13.044 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.044 * [backup-simplify]: Simplify 0 into 0 13.046 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.046 * [backup-simplify]: Simplify 0 into 0 13.046 * [backup-simplify]: Simplify (* PI n) into (* n PI) 13.046 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 13.046 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 13.046 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.046 * [taylor]: Taking taylor expansion of PI in n 13.046 * [backup-simplify]: Simplify PI into PI 13.046 * [taylor]: Taking taylor expansion of n in n 13.046 * [backup-simplify]: Simplify 0 into 0 13.046 * [backup-simplify]: Simplify 1 into 1 13.047 * [backup-simplify]: Simplify (/ PI 1) into PI 13.047 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.047 * [taylor]: Taking taylor expansion of PI in n 13.047 * [backup-simplify]: Simplify PI into PI 13.047 * [taylor]: Taking taylor expansion of n in n 13.047 * [backup-simplify]: Simplify 0 into 0 13.047 * [backup-simplify]: Simplify 1 into 1 13.047 * [backup-simplify]: Simplify (/ PI 1) into PI 13.047 * [backup-simplify]: Simplify PI into PI 13.048 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.048 * [backup-simplify]: Simplify 0 into 0 13.049 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.049 * [backup-simplify]: Simplify 0 into 0 13.058 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.058 * [backup-simplify]: Simplify 0 into 0 13.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.060 * [backup-simplify]: Simplify 0 into 0 13.061 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.061 * [backup-simplify]: Simplify 0 into 0 13.062 * [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 13.062 * [backup-simplify]: Simplify 0 into 0 13.062 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 13.062 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 13.062 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 13.062 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 13.062 * [taylor]: Taking taylor expansion of -1 in n 13.062 * [backup-simplify]: Simplify -1 into -1 13.062 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.062 * [taylor]: Taking taylor expansion of PI in n 13.062 * [backup-simplify]: Simplify PI into PI 13.062 * [taylor]: Taking taylor expansion of n in n 13.062 * [backup-simplify]: Simplify 0 into 0 13.062 * [backup-simplify]: Simplify 1 into 1 13.063 * [backup-simplify]: Simplify (/ PI 1) into PI 13.063 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 13.063 * [taylor]: Taking taylor expansion of -1 in n 13.063 * [backup-simplify]: Simplify -1 into -1 13.063 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.063 * [taylor]: Taking taylor expansion of PI in n 13.063 * [backup-simplify]: Simplify PI into PI 13.063 * [taylor]: Taking taylor expansion of n in n 13.063 * [backup-simplify]: Simplify 0 into 0 13.063 * [backup-simplify]: Simplify 1 into 1 13.064 * [backup-simplify]: Simplify (/ PI 1) into PI 13.064 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 13.065 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 13.066 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.066 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 13.066 * [backup-simplify]: Simplify 0 into 0 13.067 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.068 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 13.068 * [backup-simplify]: Simplify 0 into 0 13.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.070 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.070 * [backup-simplify]: Simplify 0 into 0 13.070 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.071 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.071 * [backup-simplify]: Simplify 0 into 0 13.072 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.073 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.073 * [backup-simplify]: Simplify 0 into 0 13.073 * [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 13.074 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.074 * [backup-simplify]: Simplify 0 into 0 13.075 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 13.075 * * * [progress]: simplifying candidates 13.078 * [simplify]: Simplifying: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (+ (log 2.0) (+ (log n) (log PI))) (/ (- 1.0 k) 2.0)) (* (+ (log 2.0) (log (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (pow (* 2.0 (* n PI)) (/ k 2.0)) (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0))) (pow (* 2.0 (* n PI)) (/ 1 1)) (pow (* 2.0 (* n PI)) 1) (pow (* 2.0 (* n PI)) (- 1.0 k)) (pow 2.0 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0)) (log (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) 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(* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 13.083 * * [simplify]: Extracting # 0 : cost 0 13.083 * * [simplify]: Extracting # 1 : cost 0 13.084 * * [simplify]: Extracting # 2 : cost 0 13.084 * * [simplify]: Extracting # 3 : cost 0 13.085 * * [simplify]: Extracting # 4 : cost 0 13.086 * * [simplify]: Extracting # 5 : cost 0 13.086 * * [simplify]: Extracting # 6 : cost 0 13.087 * * [simplify]: Extracting # 7 : cost 0 13.087 * * [simplify]: Extracting # 8 : cost 0 13.088 * * [simplify]: Extracting # 9 : cost 0 13.089 * * [simplify]: Extracting # 10 : cost 0 13.089 * * [simplify]: Extracting # 11 : cost 0 13.090 * * [simplify]: Extracting # 12 : cost 0 13.090 * * [simplify]: Extracting # 13 : cost 0 13.091 * * [simplify]: iteration 0 : 398 enodes (cost 2712 ) 13.273 * * [simplify]: Extracting # 0 : cost 0 13.277 * * [simplify]: Extracting # 1 : cost 0 13.280 * * [simplify]: Extracting # 2 : cost 0 13.282 * * [simplify]: Extracting # 3 : cost 0 13.285 * * [simplify]: Extracting # 4 : cost 0 13.288 * * [simplify]: Extracting # 5 : cost 0 13.291 * * [simplify]: Extracting # 6 : cost 0 13.294 * * [simplify]: iteration 1 : 1018 enodes (cost 2503 ) 14.015 * * [simplify]: Extracting # 0 : cost 0 14.021 * * [simplify]: Extracting # 1 : cost 0 14.029 * * [simplify]: Extracting # 2 : cost 0 14.036 * * [simplify]: Extracting # 3 : cost 0 14.044 * * [simplify]: Extracting # 4 : cost 0 14.051 * * [simplify]: iteration 2 : 2797 enodes (cost 2409 ) 15.181 * * [simplify]: Extracting # 0 : cost 0 15.188 * * [simplify]: Extracting # 1 : cost 0 15.194 * * [simplify]: Extracting # 2 : cost 0 15.211 * * [simplify]: Extracting # 3 : cost 0 15.218 * * [simplify]: Extracting # 4 : cost 0 15.224 * * [simplify]: iteration done: 5001 enodes (cost 2403 ) 15.226 * [simplify]: Simplified to: (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0)) (* (log (* 2.0 (* n PI))) (/ (- 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2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* PI (* 2.0 n)) (- 1.0 k)) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* (sqrt k) k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (log (* n PI)) (log (* n PI)) (exp (* n PI)) (pow (* n PI) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* n PI) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (fma (* 0.125 (pow k 2)) (fma (pow (* n (* 2.0 PI)) 0.5) (pow (log (* 2.0 PI)) 2) (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.5))) (fma (* 0.25 (pow k 2)) (* (* (log (* 2.0 PI)) (log n)) (pow (* n (* 2.0 PI)) 0.5)) (pow (* n (* 2.0 PI)) 0.5))) (* (* 0.5 k) (fma (pow (* n (* 2.0 PI)) 0.5) (log n) (* (pow (* n (* 2.0 PI)) 0.5) (log (* 2.0 PI)))))) (pow (pow (* n (* 2.0 PI)) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma (* (* 0.03125 (pow k 2)) (pow (* n (* 2.0 PI)) 0.25)) (pow (log (* 2.0 PI)) 2) (fma (* (* (pow (* n (* 2.0 PI)) 0.25) (log n)) (* (pow k 2) (log (* 2.0 PI)))) 0.0625 (fma (pow k 2) (* (* (pow (log n) 2) (pow (* n (* 2.0 PI)) 0.25)) 0.03125) (pow (* n (* 2.0 PI)) 0.25)))) (* (* 0.25 k) (fma (pow (* n (* 2.0 PI)) 0.25) (log n) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma (- k) +nan.0 (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* n PI) (* n PI) (* n PI) 15.227 * * * [progress]: adding candidates to table 16.484 * * [progress]: iteration 4 / 4 16.485 * * * [progress]: picking best candidate 16.521 * * * * [pick]: Picked # 16.521 * * * [progress]: localizing error 16.570 * * * [progress]: generating rewritten candidates 16.570 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 16.582 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 16.638 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 16.651 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 2 1) 16.682 * * * [progress]: generating series expansions 16.682 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 16.682 * [backup-simplify]: Simplify (pow (* n PI) (/ (- 1.0 k) 2.0)) into (pow (* n PI) (* 0.5 (- 1.0 k))) 16.682 * [approximate]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in (n k) around 0 16.683 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in k 16.683 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in k 16.683 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in k 16.683 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 16.683 * [taylor]: Taking taylor expansion of 0.5 in k 16.683 * [backup-simplify]: Simplify 0.5 into 0.5 16.683 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.683 * [taylor]: Taking taylor expansion of 1.0 in k 16.683 * [backup-simplify]: Simplify 1.0 into 1.0 16.683 * [taylor]: Taking taylor expansion of k in k 16.683 * [backup-simplify]: Simplify 0 into 0 16.683 * [backup-simplify]: Simplify 1 into 1 16.683 * [taylor]: Taking taylor expansion of (log (* n PI)) in k 16.683 * [taylor]: Taking taylor expansion of (* n PI) in k 16.683 * [taylor]: Taking taylor expansion of n in k 16.683 * [backup-simplify]: Simplify n into n 16.683 * [taylor]: Taking taylor expansion of PI in k 16.683 * [backup-simplify]: Simplify PI into PI 16.683 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.683 * [backup-simplify]: Simplify (log (* n PI)) into (log (* n PI)) 16.684 * [backup-simplify]: Simplify (- 0) into 0 16.684 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.685 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 16.685 * [backup-simplify]: Simplify (* 0.5 (log (* n PI))) into (* 0.5 (log (* n PI))) 16.685 * [backup-simplify]: Simplify (exp (* 0.5 (log (* n PI)))) into (pow (* n PI) 0.5) 16.685 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 16.685 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 16.685 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 16.685 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.685 * [taylor]: Taking taylor expansion of 0.5 in n 16.685 * [backup-simplify]: Simplify 0.5 into 0.5 16.685 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.685 * [taylor]: Taking taylor expansion of 1.0 in n 16.685 * [backup-simplify]: Simplify 1.0 into 1.0 16.685 * [taylor]: Taking taylor expansion of k in n 16.685 * [backup-simplify]: Simplify k into k 16.685 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 16.685 * [taylor]: Taking taylor expansion of (* n PI) in n 16.685 * [taylor]: Taking taylor expansion of n in n 16.685 * [backup-simplify]: Simplify 0 into 0 16.685 * [backup-simplify]: Simplify 1 into 1 16.685 * [taylor]: Taking taylor expansion of PI in n 16.685 * [backup-simplify]: Simplify PI into PI 16.686 * [backup-simplify]: Simplify (* 0 PI) into 0 16.687 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.688 * [backup-simplify]: Simplify (log PI) into (log PI) 16.688 * [backup-simplify]: Simplify (- k) into (- k) 16.688 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.688 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.689 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.689 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log n) (log PI))) into (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) 16.690 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) 16.690 * [taylor]: Taking taylor expansion of (pow (* n PI) (* 0.5 (- 1.0 k))) in n 16.690 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* n PI)))) in n 16.690 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* n PI))) in n 16.690 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 16.690 * [taylor]: Taking taylor expansion of 0.5 in n 16.690 * [backup-simplify]: Simplify 0.5 into 0.5 16.690 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.690 * [taylor]: Taking taylor expansion of 1.0 in n 16.690 * [backup-simplify]: Simplify 1.0 into 1.0 16.690 * [taylor]: Taking taylor expansion of k in n 16.690 * [backup-simplify]: Simplify k into k 16.690 * [taylor]: Taking taylor expansion of (log (* n PI)) in n 16.690 * [taylor]: Taking taylor expansion of (* n PI) in n 16.690 * [taylor]: Taking taylor expansion of n in n 16.690 * [backup-simplify]: Simplify 0 into 0 16.690 * [backup-simplify]: Simplify 1 into 1 16.690 * [taylor]: Taking taylor expansion of PI in n 16.690 * [backup-simplify]: Simplify PI into PI 16.691 * [backup-simplify]: Simplify (* 0 PI) into 0 16.692 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.693 * [backup-simplify]: Simplify (log PI) into (log PI) 16.693 * [backup-simplify]: Simplify (- k) into (- k) 16.693 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.693 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 16.694 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.694 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log n) (log PI))) into (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) 16.695 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) 16.695 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) in k 16.695 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log n) (log PI)))) in k 16.695 * [taylor]: Taking taylor expansion of 0.5 in k 16.695 * [backup-simplify]: Simplify 0.5 into 0.5 16.695 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log n) (log PI))) in k 16.696 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.696 * [taylor]: Taking taylor expansion of 1.0 in k 16.696 * [backup-simplify]: Simplify 1.0 into 1.0 16.696 * [taylor]: Taking taylor expansion of k in k 16.696 * [backup-simplify]: Simplify 0 into 0 16.696 * [backup-simplify]: Simplify 1 into 1 16.696 * [taylor]: Taking taylor expansion of (+ (log n) (log PI)) in k 16.696 * [taylor]: Taking taylor expansion of (log n) in k 16.696 * [taylor]: Taking taylor expansion of n in k 16.696 * [backup-simplify]: Simplify n into n 16.696 * [backup-simplify]: Simplify (log n) into (log n) 16.696 * [taylor]: Taking taylor expansion of (log PI) in k 16.696 * [taylor]: Taking taylor expansion of PI in k 16.696 * [backup-simplify]: Simplify PI into PI 16.696 * [backup-simplify]: Simplify (log PI) into (log PI) 16.697 * [backup-simplify]: Simplify (- 0) into 0 16.697 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.698 * [backup-simplify]: Simplify (+ (log n) (log PI)) into (+ (log n) (log PI)) 16.698 * [backup-simplify]: Simplify (* 1.0 (+ (log n) (log PI))) into (* 1.0 (+ (log n) (log PI))) 16.698 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log n) (log PI)))) into (* 0.5 (+ (log n) (log PI))) 16.699 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log n) (log PI)))) into (exp (* 0.5 (+ (log n) (log PI)))) 16.700 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log n) (log PI)))) into (exp (* 0.5 (+ (log n) (log PI)))) 16.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.702 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 16.703 * [backup-simplify]: Simplify (- 0) into 0 16.703 * [backup-simplify]: Simplify (+ 0 0) into 0 16.703 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 16.704 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.705 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log n) (log PI)))) into 0 16.706 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.706 * [taylor]: Taking taylor expansion of 0 in k 16.706 * [backup-simplify]: Simplify 0 into 0 16.706 * [backup-simplify]: Simplify 0 into 0 16.707 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.708 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 16.709 * [backup-simplify]: Simplify (+ 0 0) into 0 16.709 * [backup-simplify]: Simplify (- 1) into -1 16.710 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.710 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log n) (log PI)))) into (- (+ (log PI) (log n))) 16.711 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log n) (log PI))))) into (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 16.713 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) 16.715 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) into (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) 16.717 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.727 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 16.728 * [backup-simplify]: Simplify (- 0) into 0 16.728 * [backup-simplify]: Simplify (+ 0 0) into 0 16.729 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.729 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log PI)) into (+ (log n) (log PI)) 16.731 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log PI))))) into 0 16.733 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log n) (log PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.733 * [taylor]: Taking taylor expansion of 0 in k 16.733 * [backup-simplify]: Simplify 0 into 0 16.733 * [backup-simplify]: Simplify 0 into 0 16.733 * [backup-simplify]: Simplify 0 into 0 16.734 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.736 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 16.736 * [backup-simplify]: Simplify (+ 0 0) into 0 16.736 * [backup-simplify]: Simplify (- 0) into 0 16.736 * [backup-simplify]: Simplify (+ 0 0) into 0 16.737 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log n) (log PI))))) into 0 16.738 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log PI) (log n)))) (* 0 (* 1.0 (+ (log n) (log PI)))))) into 0 16.740 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* (/ (pow (- (+ (* 0.5 (log n)) (* 0.5 (log PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.125 (pow (log PI) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) 16.742 * [backup-simplify]: Simplify (* (+ (* 0.125 (pow (log PI) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) into (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) 16.747 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log PI) 2)) (* 0.25 (* (log n) (log PI))))) (exp (* 0.5 (+ (log n) (log PI))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.5 (log n)) (* 0.5 (log PI))))) (* k 1)) (exp (* 0.5 (+ (log n) (log PI)))))) into (- (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log n) 2)))) (* 0.25 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (* (log n) (log PI)))))))) (+ (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log PI)))) (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log n)))))) 16.747 * [backup-simplify]: Simplify (pow (* (/ 1 n) PI) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) 16.747 * [approximate]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 16.747 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in k 16.747 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in k 16.747 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in k 16.747 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 16.747 * [taylor]: Taking taylor expansion of 0.5 in k 16.747 * [backup-simplify]: Simplify 0.5 into 0.5 16.747 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.747 * [taylor]: Taking taylor expansion of 1.0 in k 16.747 * [backup-simplify]: Simplify 1.0 into 1.0 16.747 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.747 * [taylor]: Taking taylor expansion of k in k 16.747 * [backup-simplify]: Simplify 0 into 0 16.747 * [backup-simplify]: Simplify 1 into 1 16.747 * [backup-simplify]: Simplify (/ 1 1) into 1 16.747 * [taylor]: Taking taylor expansion of (log (/ PI n)) in k 16.747 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.747 * [taylor]: Taking taylor expansion of PI in k 16.747 * [backup-simplify]: Simplify PI into PI 16.747 * [taylor]: Taking taylor expansion of n in k 16.747 * [backup-simplify]: Simplify n into n 16.748 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.748 * [backup-simplify]: Simplify (log (/ PI n)) into (log (/ PI n)) 16.748 * [backup-simplify]: Simplify (- 1) into -1 16.748 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.748 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 16.748 * [backup-simplify]: Simplify (* -0.5 (log (/ PI n))) into (* -0.5 (log (/ PI n))) 16.749 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) into (exp (* 0.5 (* (log (/ PI n)) (- 1.0 (/ 1 k))))) 16.749 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.749 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 16.749 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 16.749 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.749 * [taylor]: Taking taylor expansion of 0.5 in n 16.749 * [backup-simplify]: Simplify 0.5 into 0.5 16.749 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.749 * [taylor]: Taking taylor expansion of 1.0 in n 16.749 * [backup-simplify]: Simplify 1.0 into 1.0 16.749 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.749 * [taylor]: Taking taylor expansion of k in n 16.749 * [backup-simplify]: Simplify k into k 16.749 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.749 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 16.749 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.749 * [taylor]: Taking taylor expansion of PI in n 16.749 * [backup-simplify]: Simplify PI into PI 16.749 * [taylor]: Taking taylor expansion of n in n 16.749 * [backup-simplify]: Simplify 0 into 0 16.749 * [backup-simplify]: Simplify 1 into 1 16.749 * [backup-simplify]: Simplify (/ PI 1) into PI 16.750 * [backup-simplify]: Simplify (log PI) into (log PI) 16.750 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.750 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.750 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.751 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.751 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) 16.751 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.751 * [taylor]: Taking taylor expansion of (pow (/ PI n) (* 0.5 (- 1.0 (/ 1 k)))) in n 16.751 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n)))) in n 16.751 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (/ PI n))) in n 16.751 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 16.752 * [taylor]: Taking taylor expansion of 0.5 in n 16.752 * [backup-simplify]: Simplify 0.5 into 0.5 16.752 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.752 * [taylor]: Taking taylor expansion of 1.0 in n 16.752 * [backup-simplify]: Simplify 1.0 into 1.0 16.752 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.752 * [taylor]: Taking taylor expansion of k in n 16.752 * [backup-simplify]: Simplify k into k 16.752 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.752 * [taylor]: Taking taylor expansion of (log (/ PI n)) in n 16.752 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.752 * [taylor]: Taking taylor expansion of PI in n 16.752 * [backup-simplify]: Simplify PI into PI 16.752 * [taylor]: Taking taylor expansion of n in n 16.752 * [backup-simplify]: Simplify 0 into 0 16.752 * [backup-simplify]: Simplify 1 into 1 16.752 * [backup-simplify]: Simplify (/ PI 1) into PI 16.752 * [backup-simplify]: Simplify (log PI) into (log PI) 16.752 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.753 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.753 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 16.753 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.754 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log PI) (log n))) into (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) 16.754 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.754 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) in k 16.754 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k)))) in k 16.754 * [taylor]: Taking taylor expansion of 0.5 in k 16.754 * [backup-simplify]: Simplify 0.5 into 0.5 16.754 * [taylor]: Taking taylor expansion of (* (- (log PI) (log n)) (- 1.0 (/ 1 k))) in k 16.754 * [taylor]: Taking taylor expansion of (- (log PI) (log n)) in k 16.754 * [taylor]: Taking taylor expansion of (log PI) in k 16.754 * [taylor]: Taking taylor expansion of PI in k 16.754 * [backup-simplify]: Simplify PI into PI 16.754 * [backup-simplify]: Simplify (log PI) into (log PI) 16.754 * [taylor]: Taking taylor expansion of (log n) in k 16.755 * [taylor]: Taking taylor expansion of n in k 16.755 * [backup-simplify]: Simplify n into n 16.755 * [backup-simplify]: Simplify (log n) into (log n) 16.755 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.755 * [taylor]: Taking taylor expansion of 1.0 in k 16.755 * [backup-simplify]: Simplify 1.0 into 1.0 16.755 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.755 * [taylor]: Taking taylor expansion of k in k 16.755 * [backup-simplify]: Simplify 0 into 0 16.755 * [backup-simplify]: Simplify 1 into 1 16.755 * [backup-simplify]: Simplify (/ 1 1) into 1 16.755 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.755 * [backup-simplify]: Simplify (+ (log PI) (- (log n))) into (- (log PI) (log n)) 16.756 * [backup-simplify]: Simplify (- 1) into -1 16.756 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.756 * [backup-simplify]: Simplify (* (- (log PI) (log n)) -1) into (* -1 (- (log PI) (log n))) 16.757 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log PI) (log n)))) into (* -0.5 (- (log PI) (log n))) 16.757 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.758 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) 16.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.761 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 16.761 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.761 * [backup-simplify]: Simplify (- 0) into 0 16.762 * [backup-simplify]: Simplify (+ 0 0) into 0 16.762 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.763 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.764 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log PI) (log n)))) into 0 16.765 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.765 * [taylor]: Taking taylor expansion of 0 in k 16.765 * [backup-simplify]: Simplify 0 into 0 16.765 * [backup-simplify]: Simplify 0 into 0 16.765 * [backup-simplify]: Simplify 0 into 0 16.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.769 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow PI 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow PI 1)))) 2) into 0 16.770 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.770 * [backup-simplify]: Simplify (- 0) into 0 16.771 * [backup-simplify]: Simplify (+ 0 0) into 0 16.772 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.773 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log PI) (log n))))) into 0 16.774 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.774 * [taylor]: Taking taylor expansion of 0 in k 16.774 * [backup-simplify]: Simplify 0 into 0 16.774 * [backup-simplify]: Simplify 0 into 0 16.774 * [backup-simplify]: Simplify 0 into 0 16.774 * [backup-simplify]: Simplify 0 into 0 16.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.778 * [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 16.778 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.778 * [backup-simplify]: Simplify (- 0) into 0 16.779 * [backup-simplify]: Simplify (+ 0 0) into 0 16.779 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.780 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log PI)) into (- (log PI) (log n)) 16.781 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log PI) (log n)))))) into 0 16.782 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log PI) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.782 * [taylor]: Taking taylor expansion of 0 in k 16.782 * [backup-simplify]: Simplify 0 into 0 16.782 * [backup-simplify]: Simplify 0 into 0 16.783 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log PI) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) 16.783 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) PI) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 16.783 * [approximate]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 16.783 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 16.783 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in k 16.783 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in k 16.783 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 16.783 * [taylor]: Taking taylor expansion of 0.5 in k 16.783 * [backup-simplify]: Simplify 0.5 into 0.5 16.783 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.783 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.783 * [taylor]: Taking taylor expansion of k in k 16.783 * [backup-simplify]: Simplify 0 into 0 16.783 * [backup-simplify]: Simplify 1 into 1 16.784 * [backup-simplify]: Simplify (/ 1 1) into 1 16.784 * [taylor]: Taking taylor expansion of 1.0 in k 16.784 * [backup-simplify]: Simplify 1.0 into 1.0 16.784 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in k 16.784 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in k 16.784 * [taylor]: Taking taylor expansion of -1 in k 16.784 * [backup-simplify]: Simplify -1 into -1 16.784 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.784 * [taylor]: Taking taylor expansion of PI in k 16.784 * [backup-simplify]: Simplify PI into PI 16.784 * [taylor]: Taking taylor expansion of n in k 16.784 * [backup-simplify]: Simplify n into n 16.784 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.784 * [backup-simplify]: Simplify (* -1 (/ PI n)) into (* -1 (/ PI n)) 16.784 * [backup-simplify]: Simplify (log (* -1 (/ PI n))) into (log (* -1 (/ PI n))) 16.784 * [backup-simplify]: Simplify (+ 1 0) into 1 16.784 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 16.785 * [backup-simplify]: Simplify (* 0.5 (log (* -1 (/ PI n)))) into (* 0.5 (log (* -1 (/ PI n)))) 16.785 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -1 (/ PI n)))))) 16.785 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 16.785 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 16.785 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 16.785 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 16.785 * [taylor]: Taking taylor expansion of 0.5 in n 16.785 * [backup-simplify]: Simplify 0.5 into 0.5 16.785 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.785 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.785 * [taylor]: Taking taylor expansion of k in n 16.785 * [backup-simplify]: Simplify k into k 16.785 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.785 * [taylor]: Taking taylor expansion of 1.0 in n 16.785 * [backup-simplify]: Simplify 1.0 into 1.0 16.785 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 16.785 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 16.785 * [taylor]: Taking taylor expansion of -1 in n 16.785 * [backup-simplify]: Simplify -1 into -1 16.785 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.785 * [taylor]: Taking taylor expansion of PI in n 16.785 * [backup-simplify]: Simplify PI into PI 16.785 * [taylor]: Taking taylor expansion of n in n 16.785 * [backup-simplify]: Simplify 0 into 0 16.785 * [backup-simplify]: Simplify 1 into 1 16.785 * [backup-simplify]: Simplify (/ PI 1) into PI 16.786 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.786 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 16.786 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.787 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 16.787 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.788 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 16.789 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.789 * [taylor]: Taking taylor expansion of (pow (* -1 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 16.789 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n))))) in n 16.789 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -1 (/ PI n)))) in n 16.789 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 16.789 * [taylor]: Taking taylor expansion of 0.5 in n 16.789 * [backup-simplify]: Simplify 0.5 into 0.5 16.789 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 16.789 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.789 * [taylor]: Taking taylor expansion of k in n 16.789 * [backup-simplify]: Simplify k into k 16.789 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.789 * [taylor]: Taking taylor expansion of 1.0 in n 16.789 * [backup-simplify]: Simplify 1.0 into 1.0 16.789 * [taylor]: Taking taylor expansion of (log (* -1 (/ PI n))) in n 16.789 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 16.789 * [taylor]: Taking taylor expansion of -1 in n 16.789 * [backup-simplify]: Simplify -1 into -1 16.789 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.789 * [taylor]: Taking taylor expansion of PI in n 16.789 * [backup-simplify]: Simplify PI into PI 16.789 * [taylor]: Taking taylor expansion of n in n 16.789 * [backup-simplify]: Simplify 0 into 0 16.789 * [backup-simplify]: Simplify 1 into 1 16.790 * [backup-simplify]: Simplify (/ PI 1) into PI 16.790 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.791 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 16.791 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 16.791 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 16.792 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.792 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -1 PI)) (log n))) into (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) 16.793 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.793 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k 16.793 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0))) in k 16.793 * [taylor]: Taking taylor expansion of 0.5 in k 16.793 * [backup-simplify]: Simplify 0.5 into 0.5 16.793 * [taylor]: Taking taylor expansion of (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)) in k 16.793 * [taylor]: Taking taylor expansion of (- (log (* -1 PI)) (log n)) in k 16.793 * [taylor]: Taking taylor expansion of (log (* -1 PI)) in k 16.793 * [taylor]: Taking taylor expansion of (* -1 PI) in k 16.794 * [taylor]: Taking taylor expansion of -1 in k 16.794 * [backup-simplify]: Simplify -1 into -1 16.794 * [taylor]: Taking taylor expansion of PI in k 16.794 * [backup-simplify]: Simplify PI into PI 16.794 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 16.794 * [backup-simplify]: Simplify (log (* -1 PI)) into (log (* -1 PI)) 16.795 * [taylor]: Taking taylor expansion of (log n) in k 16.795 * [taylor]: Taking taylor expansion of n in k 16.795 * [backup-simplify]: Simplify n into n 16.795 * [backup-simplify]: Simplify (log n) into (log n) 16.795 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 16.795 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.795 * [taylor]: Taking taylor expansion of k in k 16.795 * [backup-simplify]: Simplify 0 into 0 16.795 * [backup-simplify]: Simplify 1 into 1 16.795 * [backup-simplify]: Simplify (/ 1 1) into 1 16.795 * [taylor]: Taking taylor expansion of 1.0 in k 16.795 * [backup-simplify]: Simplify 1.0 into 1.0 16.795 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.796 * [backup-simplify]: Simplify (+ (log (* -1 PI)) (- (log n))) into (- (log (* -1 PI)) (log n)) 16.796 * [backup-simplify]: Simplify (+ 1 0) into 1 16.797 * [backup-simplify]: Simplify (* (- (log (* -1 PI)) (log n)) 1) into (- (log (* -1 PI)) (log n)) 16.798 * [backup-simplify]: Simplify (* 0.5 (- (log (* -1 PI)) (log n))) into (* 0.5 (- (log (* -1 PI)) (log n))) 16.798 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.799 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) 16.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.800 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 16.801 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -1 PI) 1)))) 1) into 0 16.801 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.801 * [backup-simplify]: Simplify (+ 0 0) into 0 16.802 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 16.803 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.803 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -1 PI)) (log n)))) into 0 16.805 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 16.805 * [taylor]: Taking taylor expansion of 0 in k 16.805 * [backup-simplify]: Simplify 0 into 0 16.805 * [backup-simplify]: Simplify 0 into 0 16.805 * [backup-simplify]: Simplify 0 into 0 16.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.807 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 16.811 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -1 PI) 1)))) 2) into 0 16.811 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.811 * [backup-simplify]: Simplify (+ 0 0) into 0 16.812 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 16.814 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.816 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n))))) into 0 16.818 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.819 * [taylor]: Taking taylor expansion of 0 in k 16.819 * [backup-simplify]: Simplify 0 into 0 16.819 * [backup-simplify]: Simplify 0 into 0 16.819 * [backup-simplify]: Simplify 0 into 0 16.819 * [backup-simplify]: Simplify 0 into 0 16.820 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.821 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.824 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -1 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -1 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -1 PI) 1)))) 6) into 0 16.824 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.824 * [backup-simplify]: Simplify (+ 0 0) into 0 16.825 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 16.826 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -1 PI))) into (- (log (* -1 PI)) (log n)) 16.828 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -1 PI)) (log n)))))) into 0 16.829 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -1 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.829 * [taylor]: Taking taylor expansion of 0 in k 16.829 * [backup-simplify]: Simplify 0 into 0 16.829 * [backup-simplify]: Simplify 0 into 0 16.830 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -1 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -1 PI)) (log (/ -1 n)))))) 16.830 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 16.831 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 16.831 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 16.831 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 16.831 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 16.831 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 16.831 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 16.831 * [taylor]: Taking taylor expansion of 0.25 in k 16.831 * [backup-simplify]: Simplify 0.25 into 0.25 16.831 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.831 * [taylor]: Taking taylor expansion of 1.0 in k 16.831 * [backup-simplify]: Simplify 1.0 into 1.0 16.831 * [taylor]: Taking taylor expansion of k in k 16.831 * [backup-simplify]: Simplify 0 into 0 16.831 * [backup-simplify]: Simplify 1 into 1 16.831 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 16.831 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 16.831 * [taylor]: Taking taylor expansion of 2.0 in k 16.831 * [backup-simplify]: Simplify 2.0 into 2.0 16.831 * [taylor]: Taking taylor expansion of (* n PI) in k 16.831 * [taylor]: Taking taylor expansion of n in k 16.831 * [backup-simplify]: Simplify n into n 16.831 * [taylor]: Taking taylor expansion of PI in k 16.831 * [backup-simplify]: Simplify PI into PI 16.831 * [backup-simplify]: Simplify (* n PI) into (* n PI) 16.831 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 16.831 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 16.832 * [backup-simplify]: Simplify (- 0) into 0 16.832 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.832 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 16.832 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 16.832 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 16.832 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 16.832 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.832 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.832 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 16.832 * [taylor]: Taking taylor expansion of 0.25 in n 16.832 * [backup-simplify]: Simplify 0.25 into 0.25 16.832 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.832 * [taylor]: Taking taylor expansion of 1.0 in n 16.832 * [backup-simplify]: Simplify 1.0 into 1.0 16.832 * [taylor]: Taking taylor expansion of k in n 16.832 * [backup-simplify]: Simplify k into k 16.833 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.833 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.833 * [taylor]: Taking taylor expansion of 2.0 in n 16.833 * [backup-simplify]: Simplify 2.0 into 2.0 16.833 * [taylor]: Taking taylor expansion of (* n PI) in n 16.833 * [taylor]: Taking taylor expansion of n in n 16.833 * [backup-simplify]: Simplify 0 into 0 16.833 * [backup-simplify]: Simplify 1 into 1 16.833 * [taylor]: Taking taylor expansion of PI in n 16.833 * [backup-simplify]: Simplify PI into PI 16.833 * [backup-simplify]: Simplify (* 0 PI) into 0 16.833 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.834 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.835 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.842 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.842 * [backup-simplify]: Simplify (- k) into (- k) 16.842 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.842 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 16.843 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.844 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 16.844 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 16.844 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 16.845 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 16.845 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 16.845 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 16.845 * [taylor]: Taking taylor expansion of 0.25 in n 16.845 * [backup-simplify]: Simplify 0.25 into 0.25 16.845 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 16.845 * [taylor]: Taking taylor expansion of 1.0 in n 16.845 * [backup-simplify]: Simplify 1.0 into 1.0 16.845 * [taylor]: Taking taylor expansion of k in n 16.845 * [backup-simplify]: Simplify k into k 16.845 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 16.845 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 16.845 * [taylor]: Taking taylor expansion of 2.0 in n 16.845 * [backup-simplify]: Simplify 2.0 into 2.0 16.845 * [taylor]: Taking taylor expansion of (* n PI) in n 16.845 * [taylor]: Taking taylor expansion of n in n 16.845 * [backup-simplify]: Simplify 0 into 0 16.845 * [backup-simplify]: Simplify 1 into 1 16.845 * [taylor]: Taking taylor expansion of PI in n 16.845 * [backup-simplify]: Simplify PI into PI 16.845 * [backup-simplify]: Simplify (* 0 PI) into 0 16.846 * [backup-simplify]: Simplify (* 2.0 0) into 0 16.847 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 16.848 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 16.848 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.848 * [backup-simplify]: Simplify (- k) into (- k) 16.848 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 16.848 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 16.849 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.850 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 16.851 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 16.851 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 16.851 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 16.851 * [taylor]: Taking taylor expansion of 0.25 in k 16.851 * [backup-simplify]: Simplify 0.25 into 0.25 16.851 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 16.851 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 16.851 * [taylor]: Taking taylor expansion of 1.0 in k 16.851 * [backup-simplify]: Simplify 1.0 into 1.0 16.851 * [taylor]: Taking taylor expansion of k in k 16.851 * [backup-simplify]: Simplify 0 into 0 16.851 * [backup-simplify]: Simplify 1 into 1 16.851 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 16.851 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.852 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.852 * [taylor]: Taking taylor expansion of 2.0 in k 16.852 * [backup-simplify]: Simplify 2.0 into 2.0 16.852 * [taylor]: Taking taylor expansion of PI in k 16.852 * [backup-simplify]: Simplify PI into PI 16.852 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.853 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.853 * [taylor]: Taking taylor expansion of (log n) in k 16.853 * [taylor]: Taking taylor expansion of n in k 16.853 * [backup-simplify]: Simplify n into n 16.853 * [backup-simplify]: Simplify (log n) into (log n) 16.853 * [backup-simplify]: Simplify (- 0) into 0 16.853 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 16.854 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 16.855 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 16.855 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 16.856 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 16.857 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 16.857 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 16.858 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 16.859 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.859 * [backup-simplify]: Simplify (- 0) into 0 16.860 * [backup-simplify]: Simplify (+ 0 0) into 0 16.860 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 16.861 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.862 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 16.863 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.863 * [taylor]: Taking taylor expansion of 0 in k 16.863 * [backup-simplify]: Simplify 0 into 0 16.863 * [backup-simplify]: Simplify 0 into 0 16.863 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.864 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.865 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 16.865 * [backup-simplify]: Simplify (+ 0 0) into 0 16.865 * [backup-simplify]: Simplify (- 1) into -1 16.866 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.867 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 16.868 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 16.870 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 16.872 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 16.873 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 16.873 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 16.875 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.876 * [backup-simplify]: Simplify (- 0) into 0 16.876 * [backup-simplify]: Simplify (+ 0 0) into 0 16.877 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 16.879 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 16.880 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.883 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.883 * [taylor]: Taking taylor expansion of 0 in k 16.883 * [backup-simplify]: Simplify 0 into 0 16.883 * [backup-simplify]: Simplify 0 into 0 16.883 * [backup-simplify]: Simplify 0 into 0 16.884 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.888 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.890 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 16.890 * [backup-simplify]: Simplify (+ 0 0) into 0 16.891 * [backup-simplify]: Simplify (- 0) into 0 16.891 * [backup-simplify]: Simplify (+ 0 0) into 0 16.893 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 16.896 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 16.901 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 16.906 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 16.917 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 16.919 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 16.919 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 16.919 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 16.919 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 16.919 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 16.919 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 16.919 * [taylor]: Taking taylor expansion of 0.25 in k 16.919 * [backup-simplify]: Simplify 0.25 into 0.25 16.919 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.919 * [taylor]: Taking taylor expansion of 1.0 in k 16.919 * [backup-simplify]: Simplify 1.0 into 1.0 16.919 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.919 * [taylor]: Taking taylor expansion of k in k 16.919 * [backup-simplify]: Simplify 0 into 0 16.919 * [backup-simplify]: Simplify 1 into 1 16.920 * [backup-simplify]: Simplify (/ 1 1) into 1 16.920 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 16.920 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 16.920 * [taylor]: Taking taylor expansion of 2.0 in k 16.920 * [backup-simplify]: Simplify 2.0 into 2.0 16.920 * [taylor]: Taking taylor expansion of (/ PI n) in k 16.920 * [taylor]: Taking taylor expansion of PI in k 16.920 * [backup-simplify]: Simplify PI into PI 16.920 * [taylor]: Taking taylor expansion of n in k 16.920 * [backup-simplify]: Simplify n into n 16.920 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 16.920 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 16.920 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 16.921 * [backup-simplify]: Simplify (- 1) into -1 16.921 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.922 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 16.922 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 16.922 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 16.922 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 16.922 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.922 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.922 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 16.922 * [taylor]: Taking taylor expansion of 0.25 in n 16.922 * [backup-simplify]: Simplify 0.25 into 0.25 16.922 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.922 * [taylor]: Taking taylor expansion of 1.0 in n 16.922 * [backup-simplify]: Simplify 1.0 into 1.0 16.922 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.922 * [taylor]: Taking taylor expansion of k in n 16.922 * [backup-simplify]: Simplify k into k 16.922 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.922 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.922 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.923 * [taylor]: Taking taylor expansion of 2.0 in n 16.923 * [backup-simplify]: Simplify 2.0 into 2.0 16.923 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.923 * [taylor]: Taking taylor expansion of PI in n 16.923 * [backup-simplify]: Simplify PI into PI 16.923 * [taylor]: Taking taylor expansion of n in n 16.923 * [backup-simplify]: Simplify 0 into 0 16.923 * [backup-simplify]: Simplify 1 into 1 16.923 * [backup-simplify]: Simplify (/ PI 1) into PI 16.924 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.925 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.925 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.925 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.925 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 16.927 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.928 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.929 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.929 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 16.930 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 16.930 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 16.930 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 16.930 * [taylor]: Taking taylor expansion of 0.25 in n 16.930 * [backup-simplify]: Simplify 0.25 into 0.25 16.930 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 16.930 * [taylor]: Taking taylor expansion of 1.0 in n 16.930 * [backup-simplify]: Simplify 1.0 into 1.0 16.930 * [taylor]: Taking taylor expansion of (/ 1 k) in n 16.930 * [taylor]: Taking taylor expansion of k in n 16.930 * [backup-simplify]: Simplify k into k 16.930 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 16.930 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 16.930 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 16.930 * [taylor]: Taking taylor expansion of 2.0 in n 16.930 * [backup-simplify]: Simplify 2.0 into 2.0 16.930 * [taylor]: Taking taylor expansion of (/ PI n) in n 16.930 * [taylor]: Taking taylor expansion of PI in n 16.930 * [backup-simplify]: Simplify PI into PI 16.930 * [taylor]: Taking taylor expansion of n in n 16.930 * [backup-simplify]: Simplify 0 into 0 16.930 * [backup-simplify]: Simplify 1 into 1 16.931 * [backup-simplify]: Simplify (/ PI 1) into PI 16.932 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.933 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.933 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 16.933 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 16.933 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 16.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.936 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 16.937 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.937 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 16.937 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 16.937 * [taylor]: Taking taylor expansion of 0.25 in k 16.937 * [backup-simplify]: Simplify 0.25 into 0.25 16.937 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 16.937 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 16.937 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 16.937 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 16.938 * [taylor]: Taking taylor expansion of 2.0 in k 16.938 * [backup-simplify]: Simplify 2.0 into 2.0 16.938 * [taylor]: Taking taylor expansion of PI in k 16.938 * [backup-simplify]: Simplify PI into PI 16.938 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 16.939 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 16.939 * [taylor]: Taking taylor expansion of (log n) in k 16.939 * [taylor]: Taking taylor expansion of n in k 16.939 * [backup-simplify]: Simplify n into n 16.939 * [backup-simplify]: Simplify (log n) into (log n) 16.939 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 16.939 * [taylor]: Taking taylor expansion of 1.0 in k 16.939 * [backup-simplify]: Simplify 1.0 into 1.0 16.939 * [taylor]: Taking taylor expansion of (/ 1 k) in k 16.940 * [taylor]: Taking taylor expansion of k in k 16.940 * [backup-simplify]: Simplify 0 into 0 16.940 * [backup-simplify]: Simplify 1 into 1 16.940 * [backup-simplify]: Simplify (/ 1 1) into 1 16.940 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 16.941 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 16.942 * [backup-simplify]: Simplify (- 1) into -1 16.942 * [backup-simplify]: Simplify (+ 0 -1) into -1 16.943 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 16.944 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 16.946 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.947 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 16.948 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 16.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 16.951 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 16.951 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 16.952 * [backup-simplify]: Simplify (- 0) into 0 16.952 * [backup-simplify]: Simplify (+ 0 0) into 0 16.953 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 16.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.956 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 16.958 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 16.958 * [taylor]: Taking taylor expansion of 0 in k 16.958 * [backup-simplify]: Simplify 0 into 0 16.958 * [backup-simplify]: Simplify 0 into 0 16.958 * [backup-simplify]: Simplify 0 into 0 16.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 16.963 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 16.964 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.964 * [backup-simplify]: Simplify (- 0) into 0 16.965 * [backup-simplify]: Simplify (+ 0 0) into 0 16.965 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 16.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.969 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 16.971 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 16.971 * [taylor]: Taking taylor expansion of 0 in k 16.971 * [backup-simplify]: Simplify 0 into 0 16.972 * [backup-simplify]: Simplify 0 into 0 16.972 * [backup-simplify]: Simplify 0 into 0 16.972 * [backup-simplify]: Simplify 0 into 0 16.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 16.982 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 16.989 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 16.989 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 16.990 * [backup-simplify]: Simplify (- 0) into 0 16.990 * [backup-simplify]: Simplify (+ 0 0) into 0 16.991 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 16.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 16.995 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 16.998 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 16.998 * [taylor]: Taking taylor expansion of 0 in k 16.998 * [backup-simplify]: Simplify 0 into 0 16.998 * [backup-simplify]: Simplify 0 into 0 17.000 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 17.001 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 17.001 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 17.001 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 17.001 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 17.001 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 17.001 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 17.001 * [taylor]: Taking taylor expansion of 0.25 in k 17.001 * [backup-simplify]: Simplify 0.25 into 0.25 17.001 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.001 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.001 * [taylor]: Taking taylor expansion of k in k 17.001 * [backup-simplify]: Simplify 0 into 0 17.001 * [backup-simplify]: Simplify 1 into 1 17.002 * [backup-simplify]: Simplify (/ 1 1) into 1 17.002 * [taylor]: Taking taylor expansion of 1.0 in k 17.002 * [backup-simplify]: Simplify 1.0 into 1.0 17.002 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 17.002 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 17.002 * [taylor]: Taking taylor expansion of -2.0 in k 17.002 * [backup-simplify]: Simplify -2.0 into -2.0 17.002 * [taylor]: Taking taylor expansion of (/ PI n) in k 17.002 * [taylor]: Taking taylor expansion of PI in k 17.002 * [backup-simplify]: Simplify PI into PI 17.002 * [taylor]: Taking taylor expansion of n in k 17.002 * [backup-simplify]: Simplify n into n 17.002 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 17.002 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 17.002 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 17.003 * [backup-simplify]: Simplify (+ 1 0) into 1 17.003 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 17.003 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 17.004 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 17.004 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 17.004 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.004 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.004 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 17.004 * [taylor]: Taking taylor expansion of 0.25 in n 17.004 * [backup-simplify]: Simplify 0.25 into 0.25 17.004 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.004 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.004 * [taylor]: Taking taylor expansion of k in n 17.004 * [backup-simplify]: Simplify k into k 17.004 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.004 * [taylor]: Taking taylor expansion of 1.0 in n 17.004 * [backup-simplify]: Simplify 1.0 into 1.0 17.004 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.004 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.004 * [taylor]: Taking taylor expansion of -2.0 in n 17.004 * [backup-simplify]: Simplify -2.0 into -2.0 17.004 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.004 * [taylor]: Taking taylor expansion of PI in n 17.004 * [backup-simplify]: Simplify PI into PI 17.004 * [taylor]: Taking taylor expansion of n in n 17.004 * [backup-simplify]: Simplify 0 into 0 17.004 * [backup-simplify]: Simplify 1 into 1 17.005 * [backup-simplify]: Simplify (/ PI 1) into PI 17.005 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.007 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.007 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.007 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 17.008 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.009 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 17.011 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.011 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 17.011 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 17.011 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 17.011 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 17.011 * [taylor]: Taking taylor expansion of 0.25 in n 17.011 * [backup-simplify]: Simplify 0.25 into 0.25 17.011 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 17.011 * [taylor]: Taking taylor expansion of (/ 1 k) in n 17.011 * [taylor]: Taking taylor expansion of k in n 17.011 * [backup-simplify]: Simplify k into k 17.011 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 17.011 * [taylor]: Taking taylor expansion of 1.0 in n 17.011 * [backup-simplify]: Simplify 1.0 into 1.0 17.011 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 17.011 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 17.011 * [taylor]: Taking taylor expansion of -2.0 in n 17.011 * [backup-simplify]: Simplify -2.0 into -2.0 17.011 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.011 * [taylor]: Taking taylor expansion of PI in n 17.011 * [backup-simplify]: Simplify PI into PI 17.011 * [taylor]: Taking taylor expansion of n in n 17.011 * [backup-simplify]: Simplify 0 into 0 17.011 * [backup-simplify]: Simplify 1 into 1 17.012 * [backup-simplify]: Simplify (/ PI 1) into PI 17.012 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.013 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.014 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 17.014 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 17.015 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.016 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 17.018 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.018 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 17.018 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 17.018 * [taylor]: Taking taylor expansion of 0.25 in k 17.018 * [backup-simplify]: Simplify 0.25 into 0.25 17.018 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 17.018 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 17.018 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.018 * [taylor]: Taking taylor expansion of k in k 17.018 * [backup-simplify]: Simplify 0 into 0 17.018 * [backup-simplify]: Simplify 1 into 1 17.018 * [backup-simplify]: Simplify (/ 1 1) into 1 17.019 * [taylor]: Taking taylor expansion of 1.0 in k 17.019 * [backup-simplify]: Simplify 1.0 into 1.0 17.019 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 17.019 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 17.019 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 17.019 * [taylor]: Taking taylor expansion of -2.0 in k 17.019 * [backup-simplify]: Simplify -2.0 into -2.0 17.019 * [taylor]: Taking taylor expansion of PI in k 17.019 * [backup-simplify]: Simplify PI into PI 17.019 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 17.020 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 17.020 * [taylor]: Taking taylor expansion of (log n) in k 17.020 * [taylor]: Taking taylor expansion of n in k 17.020 * [backup-simplify]: Simplify n into n 17.020 * [backup-simplify]: Simplify (log n) into (log n) 17.021 * [backup-simplify]: Simplify (+ 1 0) into 1 17.021 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 17.022 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 17.023 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 17.024 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 17.026 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.027 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 17.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.029 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 17.031 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 17.031 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 17.031 * [backup-simplify]: Simplify (+ 0 0) into 0 17.032 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 17.033 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.035 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 17.037 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 17.037 * [taylor]: Taking taylor expansion of 0 in k 17.037 * [backup-simplify]: Simplify 0 into 0 17.037 * [backup-simplify]: Simplify 0 into 0 17.037 * [backup-simplify]: Simplify 0 into 0 17.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.039 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 17.043 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 17.043 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.044 * [backup-simplify]: Simplify (+ 0 0) into 0 17.045 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 17.046 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.048 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 17.050 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 17.050 * [taylor]: Taking taylor expansion of 0 in k 17.050 * [backup-simplify]: Simplify 0 into 0 17.050 * [backup-simplify]: Simplify 0 into 0 17.050 * [backup-simplify]: Simplify 0 into 0 17.050 * [backup-simplify]: Simplify 0 into 0 17.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.053 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.059 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 17.060 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 17.060 * [backup-simplify]: Simplify (+ 0 0) into 0 17.062 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 17.063 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 17.065 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 17.068 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 17.069 * [taylor]: Taking taylor expansion of 0 in k 17.069 * [backup-simplify]: Simplify 0 into 0 17.069 * [backup-simplify]: Simplify 0 into 0 17.070 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 17.070 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 17.070 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 17.070 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 17.070 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 17.070 * [taylor]: Taking taylor expansion of 1.0 in k 17.070 * [backup-simplify]: Simplify 1.0 into 1.0 17.070 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.070 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.070 * [taylor]: Taking taylor expansion of k in k 17.070 * [backup-simplify]: Simplify 0 into 0 17.070 * [backup-simplify]: Simplify 1 into 1 17.071 * [backup-simplify]: Simplify (/ 1 1) into 1 17.071 * [backup-simplify]: Simplify (sqrt 0) into 0 17.073 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.073 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 17.073 * [taylor]: Taking taylor expansion of 1.0 in k 17.073 * [backup-simplify]: Simplify 1.0 into 1.0 17.073 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 17.073 * [taylor]: Taking taylor expansion of (/ 1 k) in k 17.073 * [taylor]: Taking taylor expansion of k in k 17.073 * [backup-simplify]: Simplify 0 into 0 17.073 * [backup-simplify]: Simplify 1 into 1 17.073 * [backup-simplify]: Simplify (/ 1 1) into 1 17.074 * [backup-simplify]: Simplify (sqrt 0) into 0 17.075 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.076 * [backup-simplify]: Simplify (* 1.0 0) into 0 17.076 * [backup-simplify]: Simplify 0 into 0 17.077 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 17.078 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.079 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 17.082 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.084 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 17.084 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.085 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.089 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.091 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 17.092 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.093 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 17.093 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 17.093 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 17.093 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 17.093 * [taylor]: Taking taylor expansion of 1.0 in k 17.093 * [backup-simplify]: Simplify 1.0 into 1.0 17.093 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.093 * [taylor]: Taking taylor expansion of k in k 17.093 * [backup-simplify]: Simplify 0 into 0 17.093 * [backup-simplify]: Simplify 1 into 1 17.094 * [backup-simplify]: Simplify (sqrt 0) into 0 17.095 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.095 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 17.095 * [taylor]: Taking taylor expansion of 1.0 in k 17.095 * [backup-simplify]: Simplify 1.0 into 1.0 17.095 * [taylor]: Taking taylor expansion of (sqrt k) in k 17.095 * [taylor]: Taking taylor expansion of k in k 17.095 * [backup-simplify]: Simplify 0 into 0 17.095 * [backup-simplify]: Simplify 1 into 1 17.096 * [backup-simplify]: Simplify (sqrt 0) into 0 17.097 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 17.097 * [backup-simplify]: Simplify (* 1.0 0) into 0 17.097 * [backup-simplify]: Simplify 0 into 0 17.099 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 17.100 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.102 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.104 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 17.105 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.109 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.111 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 17.113 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.115 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 17.115 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 17.115 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 17.115 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 17.115 * [taylor]: Taking taylor expansion of 1.0 in k 17.115 * [backup-simplify]: Simplify 1.0 into 1.0 17.115 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.115 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.115 * [taylor]: Taking taylor expansion of -1 in k 17.115 * [backup-simplify]: Simplify -1 into -1 17.115 * [taylor]: Taking taylor expansion of k in k 17.115 * [backup-simplify]: Simplify 0 into 0 17.115 * [backup-simplify]: Simplify 1 into 1 17.116 * [backup-simplify]: Simplify (/ -1 1) into -1 17.116 * [backup-simplify]: Simplify (sqrt 0) into 0 17.118 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.118 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 17.118 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 17.118 * [taylor]: Taking taylor expansion of 1.0 in k 17.118 * [backup-simplify]: Simplify 1.0 into 1.0 17.118 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 17.118 * [taylor]: Taking taylor expansion of (/ -1 k) in k 17.118 * [taylor]: Taking taylor expansion of -1 in k 17.118 * [backup-simplify]: Simplify -1 into -1 17.118 * [taylor]: Taking taylor expansion of k in k 17.118 * [backup-simplify]: Simplify 0 into 0 17.118 * [backup-simplify]: Simplify 1 into 1 17.119 * [backup-simplify]: Simplify (/ -1 1) into -1 17.119 * [backup-simplify]: Simplify (sqrt 0) into 0 17.121 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 17.121 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 17.121 * [backup-simplify]: Simplify +nan.0 into +nan.0 17.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 17.125 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 17.128 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 17.128 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.133 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 17.146 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 17.146 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 17.147 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 17.147 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 2 1) 17.147 * [backup-simplify]: Simplify (* n PI) into (* n PI) 17.147 * [approximate]: Taking taylor expansion of (* n PI) in (n) around 0 17.147 * [taylor]: Taking taylor expansion of (* n PI) in n 17.147 * [taylor]: Taking taylor expansion of n in n 17.147 * [backup-simplify]: Simplify 0 into 0 17.147 * [backup-simplify]: Simplify 1 into 1 17.147 * [taylor]: Taking taylor expansion of PI in n 17.147 * [backup-simplify]: Simplify PI into PI 17.147 * [taylor]: Taking taylor expansion of (* n PI) in n 17.147 * [taylor]: Taking taylor expansion of n in n 17.147 * [backup-simplify]: Simplify 0 into 0 17.147 * [backup-simplify]: Simplify 1 into 1 17.147 * [taylor]: Taking taylor expansion of PI in n 17.147 * [backup-simplify]: Simplify PI into PI 17.148 * [backup-simplify]: Simplify (* 0 PI) into 0 17.148 * [backup-simplify]: Simplify 0 into 0 17.149 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 17.149 * [backup-simplify]: Simplify PI into PI 17.149 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 17.149 * [backup-simplify]: Simplify 0 into 0 17.150 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 17.150 * [backup-simplify]: Simplify 0 into 0 17.151 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.151 * [backup-simplify]: Simplify 0 into 0 17.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.152 * [backup-simplify]: Simplify 0 into 0 17.153 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.153 * [backup-simplify]: Simplify 0 into 0 17.154 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 17.154 * [backup-simplify]: Simplify 0 into 0 17.154 * [backup-simplify]: Simplify (* PI n) into (* n PI) 17.154 * [backup-simplify]: Simplify (* (/ 1 n) PI) into (/ PI n) 17.154 * [approximate]: Taking taylor expansion of (/ PI n) in (n) around 0 17.154 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.154 * [taylor]: Taking taylor expansion of PI in n 17.154 * [backup-simplify]: Simplify PI into PI 17.154 * [taylor]: Taking taylor expansion of n in n 17.154 * [backup-simplify]: Simplify 0 into 0 17.154 * [backup-simplify]: Simplify 1 into 1 17.155 * [backup-simplify]: Simplify (/ PI 1) into PI 17.155 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.155 * [taylor]: Taking taylor expansion of PI in n 17.155 * [backup-simplify]: Simplify PI into PI 17.155 * [taylor]: Taking taylor expansion of n in n 17.155 * [backup-simplify]: Simplify 0 into 0 17.155 * [backup-simplify]: Simplify 1 into 1 17.155 * [backup-simplify]: Simplify (/ PI 1) into PI 17.155 * [backup-simplify]: Simplify PI into PI 17.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.156 * [backup-simplify]: Simplify 0 into 0 17.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.157 * [backup-simplify]: Simplify 0 into 0 17.157 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.157 * [backup-simplify]: Simplify 0 into 0 17.158 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.158 * [backup-simplify]: Simplify 0 into 0 17.159 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.159 * [backup-simplify]: Simplify 0 into 0 17.159 * [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 17.159 * [backup-simplify]: Simplify 0 into 0 17.159 * [backup-simplify]: Simplify (* PI (/ 1 (/ 1 n))) into (* n PI) 17.159 * [backup-simplify]: Simplify (* (/ 1 (- n)) PI) into (* -1 (/ PI n)) 17.160 * [approximate]: Taking taylor expansion of (* -1 (/ PI n)) in (n) around 0 17.160 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 17.160 * [taylor]: Taking taylor expansion of -1 in n 17.160 * [backup-simplify]: Simplify -1 into -1 17.160 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.160 * [taylor]: Taking taylor expansion of PI in n 17.160 * [backup-simplify]: Simplify PI into PI 17.160 * [taylor]: Taking taylor expansion of n in n 17.160 * [backup-simplify]: Simplify 0 into 0 17.160 * [backup-simplify]: Simplify 1 into 1 17.160 * [backup-simplify]: Simplify (/ PI 1) into PI 17.160 * [taylor]: Taking taylor expansion of (* -1 (/ PI n)) in n 17.160 * [taylor]: Taking taylor expansion of -1 in n 17.160 * [backup-simplify]: Simplify -1 into -1 17.160 * [taylor]: Taking taylor expansion of (/ PI n) in n 17.160 * [taylor]: Taking taylor expansion of PI in n 17.160 * [backup-simplify]: Simplify PI into PI 17.160 * [taylor]: Taking taylor expansion of n in n 17.160 * [backup-simplify]: Simplify 0 into 0 17.160 * [backup-simplify]: Simplify 1 into 1 17.160 * [backup-simplify]: Simplify (/ PI 1) into PI 17.161 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 17.161 * [backup-simplify]: Simplify (* -1 PI) into (* -1 PI) 17.162 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 17.162 * [backup-simplify]: Simplify (+ (* -1 0) (* 0 PI)) into 0 17.162 * [backup-simplify]: Simplify 0 into 0 17.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.163 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (* 0 PI))) into 0 17.164 * [backup-simplify]: Simplify 0 into 0 17.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.165 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 17.165 * [backup-simplify]: Simplify 0 into 0 17.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.166 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 17.166 * [backup-simplify]: Simplify 0 into 0 17.167 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 17.168 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 17.168 * [backup-simplify]: Simplify 0 into 0 17.169 * [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 17.170 * [backup-simplify]: Simplify (+ (* -1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 17.170 * [backup-simplify]: Simplify 0 into 0 17.170 * [backup-simplify]: Simplify (* (* -1 PI) (/ 1 (/ 1 (- n)))) into (* n PI) 17.170 * * * [progress]: simplifying candidates 17.173 * [simplify]: Simplifying: (expm1 (pow (* n PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (+ (log n) (log PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* (log (* n PI)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (/ (sqrt (- 1.0 k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (pow (* n PI) (/ 1 1)) (pow (* n PI) 1) (pow (* n PI) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (* (pow (* n PI) (/ (- 1.0 k) 2.0)) (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* n PI) (+ (log n) (log PI)) (log (* n PI)) (exp (* n PI)) (* (* (* n n) n) (* (* PI PI) PI)) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (* (* (* n PI) (* n PI)) (* n PI)) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) (* n 1) (* (cbrt n) PI) (* (sqrt n) PI) (* n PI) (- (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log PI) 2)))) (+ (exp (* 0.5 (+ (log n) (log PI)))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (pow (log n) 2)))) (* 0.25 (* (pow k 2) (* (exp (* 0.5 (+ (log n) (log PI)))) (* (log n) (log PI)))))))) (+ (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log PI)))) (* 0.5 (* k (* (exp (* 0.5 (+ (log n) (log PI)))) (log n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log PI) (log (/ 1 n)))))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -1 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* n PI) (* n PI) (* n PI) 17.178 * * [simplify]: Extracting # 0 : cost 0 17.178 * * [simplify]: Extracting # 1 : cost 0 17.179 * * [simplify]: Extracting # 2 : cost 0 17.179 * * [simplify]: Extracting # 3 : cost 0 17.181 * * [simplify]: Extracting # 4 : cost 0 17.182 * * [simplify]: Extracting # 5 : cost 0 17.183 * * [simplify]: Extracting # 6 : cost 0 17.185 * * [simplify]: Extracting # 7 : cost 0 17.186 * * [simplify]: Extracting # 8 : cost 0 17.187 * * [simplify]: Extracting # 9 : cost 0 17.189 * * [simplify]: Extracting # 10 : cost 0 17.190 * * [simplify]: Extracting # 11 : cost 0 17.191 * * [simplify]: Extracting # 12 : cost 0 17.192 * * [simplify]: Extracting # 13 : cost 0 17.194 * * [simplify]: iteration 0 : 401 enodes (cost 2593 ) 17.381 * * [simplify]: Extracting # 0 : cost 0 17.384 * * [simplify]: Extracting # 1 : cost 0 17.387 * * [simplify]: Extracting # 2 : cost 0 17.390 * * [simplify]: Extracting # 3 : cost 0 17.393 * * [simplify]: Extracting # 4 : cost 0 17.395 * * [simplify]: Extracting # 5 : cost 0 17.398 * * [simplify]: Extracting # 6 : cost 0 17.401 * * [simplify]: iteration 1 : 1023 enodes (cost 2390 ) 17.933 * * [simplify]: Extracting # 0 : cost 0 17.936 * * [simplify]: Extracting # 1 : cost 0 17.942 * * [simplify]: Extracting # 2 : cost 0 17.955 * * [simplify]: Extracting # 3 : cost 0 17.963 * * [simplify]: Extracting # 4 : cost 0 17.971 * * [simplify]: iteration 2 : 2853 enodes (cost 2297 ) 19.166 * * [simplify]: Extracting # 0 : cost 0 19.180 * * [simplify]: Extracting # 1 : cost 0 19.191 * * [simplify]: Extracting # 2 : cost 0 19.204 * * [simplify]: Extracting # 3 : cost 0 19.228 * * [simplify]: Extracting # 4 : cost 0 19.240 * * [simplify]: iteration done: 5000 enodes (cost 2291 ) 19.243 * [simplify]: Simplified to: (expm1 (pow (* n PI) (/ (- 1.0 k) 2.0))) (log1p (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* n PI) (/ 1.0 2.0)) (pow (* n PI) (/ k 2.0)) (pow (* n PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* n PI) (sqrt (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n PI) (sqrt (- 1.0 k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* PI n) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* PI n) (+ (sqrt 1.0) (sqrt k))) (pow (* n PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* n PI) (/ 1 (sqrt 2.0))) (* PI n) (* PI n) (pow (* PI n) (- 1.0 k)) (pow n (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)) (log (pow (* n PI) (/ (- 1.0 k) 2.0))) (exp (pow (* n PI) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (pow (* n PI) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (sqrt (pow (* n PI) (/ (- 1.0 k) 2.0))) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* n PI) (/ (/ (- 1.0 k) 2.0) 2)) (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (- 1.0 k) (* 2 2.0)) (/ (- 1.0 k) (* 2 2.0)) (/ (- 1.0 k) (* 2 2.0)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2))) (pow (* n (* 2.0 PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (sqrt (- 1.0 k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (pow (* n (* 2.0 PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* n (* 2.0 PI)) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* n (* 2.0 PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (- 1.0 k)) (* (* 2.0 PI) n) (pow (* n (* 2.0 PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (pow (* n (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (/ (pow 1.0 3) k) (sqrt k)) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (expm1 (* n PI)) (log1p (* n PI)) (* PI n) (log (* PI n)) (log (* PI n)) (exp (* n PI)) (pow (* PI n) 3) (* (cbrt (* n PI)) (cbrt (* n PI))) (cbrt (* n PI)) (pow (* PI n) 3) (sqrt (* n PI)) (sqrt (* n PI)) (* (sqrt n) (sqrt PI)) (* (sqrt n) (sqrt PI)) (* n (* (cbrt PI) (cbrt PI))) (* n (sqrt PI)) n (* (cbrt n) PI) (* (sqrt n) PI) (* PI n) (- (fma (pow k 2) (* (* (pow (log PI) 2) (pow (* PI n) 0.5)) 0.125) (fma (* 0.125 (* (pow (log n) 2) (pow (* PI n) 0.5))) (pow k 2) (fma (* 0.25 (* k (* (pow (* PI n) 0.5) k))) (* (log n) (log PI)) (pow (* PI n) 0.5)))) (* 0.5 (* (* (pow (* PI n) 0.5) k) (log (* PI n))))) (pow (pow (* PI n) 0.5) (- 1.0 k)) (pow (exp 0.5) (* (- (log (- PI)) (log (/ -1 n))) (- 1.0 k))) (fma (pow k 2) (* (* (pow (* n (* 2.0 PI)) 0.25) (pow (log (* 2.0 PI)) 2)) 0.03125) (- (fma (* 0.0625 (* (log (* 2.0 PI)) (* (pow (* n (* 2.0 PI)) 0.25) (log n)))) (pow k 2) (fma 0.03125 (* (* (pow k 2) (pow (* n (* 2.0 PI)) 0.25)) (pow (log n) 2)) (pow (* n (* 2.0 PI)) 0.25))) (* (* 0.25 k) (fma (pow (* n (* 2.0 PI)) 0.25) (log n) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (fma +nan.0 (- k) (- (* +nan.0 (pow k 2)) +nan.0)) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2))) (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0)) (* PI n) (* PI n) (* PI n) 19.246 * * * [progress]: adding candidates to table 20.670 * [progress]: [Phase 3 of 3] Extracting. 20.670 * * [regime]: Finding splitpoints for: (# # # # # # #) 20.676 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 20.676 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 20.757 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # #) 20.793 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 20.838 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 20.878 * * * [regime]: Found split indices: #