40.825 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.123 * * * [progress]: [2/2] Setting up program. 0.126 * [progress]: [Phase 2 of 3] Improving. 0.127 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.127 * [simplify]: Sending expressions to egg_math: (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) 0.269 * * [progress]: iteration 1 / 4 0.269 * * * [progress]: picking best candidate 0.271 * * * * [pick]: Picked # 0.272 * * * [progress]: localizing error 0.287 * * * [progress]: generating rewritten candidates 0.287 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.309 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.341 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.352 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.446 * * * [progress]: generating series expansions 0.446 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.447 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.447 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.447 * [taylor]: Taking taylor expansion of 0.5 in k 0.447 * [backup-simplify]: Simplify 0.5 into 0.5 0.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.447 * [taylor]: Taking taylor expansion of 1.0 in k 0.447 * [backup-simplify]: Simplify 1.0 into 1.0 0.448 * [taylor]: Taking taylor expansion of k in k 0.448 * [backup-simplify]: Simplify 0 into 0 0.448 * [backup-simplify]: Simplify 1 into 1 0.448 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.448 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.448 * [taylor]: Taking taylor expansion of 2.0 in k 0.448 * [backup-simplify]: Simplify 2.0 into 2.0 0.448 * [taylor]: Taking taylor expansion of (* n PI) in k 0.448 * [taylor]: Taking taylor expansion of n in k 0.448 * [backup-simplify]: Simplify n into n 0.448 * [taylor]: Taking taylor expansion of PI in k 0.448 * [backup-simplify]: Simplify PI into PI 0.448 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.448 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.448 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.449 * [backup-simplify]: Simplify (- 0) into 0 0.449 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.450 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.450 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.450 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.450 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.450 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.450 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.450 * [taylor]: Taking taylor expansion of 0.5 in n 0.450 * [backup-simplify]: Simplify 0.5 into 0.5 0.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.450 * [taylor]: Taking taylor expansion of 1.0 in n 0.450 * [backup-simplify]: Simplify 1.0 into 1.0 0.450 * [taylor]: Taking taylor expansion of k in n 0.450 * [backup-simplify]: Simplify k into k 0.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.450 * [taylor]: Taking taylor expansion of 2.0 in n 0.450 * [backup-simplify]: Simplify 2.0 into 2.0 0.450 * [taylor]: Taking taylor expansion of (* n PI) in n 0.450 * [taylor]: Taking taylor expansion of n in n 0.451 * [backup-simplify]: Simplify 0 into 0 0.451 * [backup-simplify]: Simplify 1 into 1 0.451 * [taylor]: Taking taylor expansion of PI in n 0.451 * [backup-simplify]: Simplify PI into PI 0.451 * [backup-simplify]: Simplify (* 0 PI) into 0 0.452 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.453 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.455 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.456 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.456 * [backup-simplify]: Simplify (- k) into (- k) 0.456 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.456 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.457 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.457 * [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)))) 0.458 * [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))))) 0.458 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.458 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.458 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.458 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.458 * [taylor]: Taking taylor expansion of 0.5 in n 0.458 * [backup-simplify]: Simplify 0.5 into 0.5 0.458 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.458 * [taylor]: Taking taylor expansion of 1.0 in n 0.458 * [backup-simplify]: Simplify 1.0 into 1.0 0.458 * [taylor]: Taking taylor expansion of k in n 0.458 * [backup-simplify]: Simplify k into k 0.462 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.462 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.462 * [taylor]: Taking taylor expansion of 2.0 in n 0.462 * [backup-simplify]: Simplify 2.0 into 2.0 0.462 * [taylor]: Taking taylor expansion of (* n PI) in n 0.462 * [taylor]: Taking taylor expansion of n in n 0.462 * [backup-simplify]: Simplify 0 into 0 0.462 * [backup-simplify]: Simplify 1 into 1 0.462 * [taylor]: Taking taylor expansion of PI in n 0.462 * [backup-simplify]: Simplify PI into PI 0.463 * [backup-simplify]: Simplify (* 0 PI) into 0 0.463 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.464 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.465 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.466 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.466 * [backup-simplify]: Simplify (- k) into (- k) 0.466 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.466 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.467 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.467 * [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)))) 0.468 * [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))))) 0.468 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.468 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.468 * [taylor]: Taking taylor expansion of 0.5 in k 0.468 * [backup-simplify]: Simplify 0.5 into 0.5 0.468 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.468 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.468 * [taylor]: Taking taylor expansion of 1.0 in k 0.468 * [backup-simplify]: Simplify 1.0 into 1.0 0.468 * [taylor]: Taking taylor expansion of k in k 0.469 * [backup-simplify]: Simplify 0 into 0 0.469 * [backup-simplify]: Simplify 1 into 1 0.469 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.469 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.469 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.469 * [taylor]: Taking taylor expansion of 2.0 in k 0.469 * [backup-simplify]: Simplify 2.0 into 2.0 0.469 * [taylor]: Taking taylor expansion of PI in k 0.469 * [backup-simplify]: Simplify PI into PI 0.469 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.470 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.470 * [taylor]: Taking taylor expansion of (log n) in k 0.470 * [taylor]: Taking taylor expansion of n in k 0.470 * [backup-simplify]: Simplify n into n 0.470 * [backup-simplify]: Simplify (log n) into (log n) 0.470 * [backup-simplify]: Simplify (- 0) into 0 0.470 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.471 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.472 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.472 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.473 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.474 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.474 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.476 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.476 * [backup-simplify]: Simplify (- 0) into 0 0.477 * [backup-simplify]: Simplify (+ 0 0) into 0 0.477 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.478 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.479 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.480 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.480 * [taylor]: Taking taylor expansion of 0 in k 0.480 * [backup-simplify]: Simplify 0 into 0 0.480 * [backup-simplify]: Simplify 0 into 0 0.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.481 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.482 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.482 * [backup-simplify]: Simplify (+ 0 0) into 0 0.482 * [backup-simplify]: Simplify (- 1) into -1 0.483 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.484 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.485 * [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)))) 0.487 * [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)))))) 0.489 * [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)))))) 0.490 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.490 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.492 * [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 0.493 * [backup-simplify]: Simplify (- 0) into 0 0.493 * [backup-simplify]: Simplify (+ 0 0) into 0 0.493 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.494 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.495 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.497 * [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 0.497 * [taylor]: Taking taylor expansion of 0 in k 0.497 * [backup-simplify]: Simplify 0 into 0 0.497 * [backup-simplify]: Simplify 0 into 0 0.497 * [backup-simplify]: Simplify 0 into 0 0.497 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.500 * [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 0.502 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.503 * [backup-simplify]: Simplify (+ 0 0) into 0 0.503 * [backup-simplify]: Simplify (- 0) into 0 0.503 * [backup-simplify]: Simplify (+ 0 0) into 0 0.505 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.508 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.512 * [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)))))) 0.518 * [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)))))) 0.529 * [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)))))) 0.530 * [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)))) 0.530 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.530 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.530 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.530 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.530 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.531 * [taylor]: Taking taylor expansion of 0.5 in k 0.531 * [backup-simplify]: Simplify 0.5 into 0.5 0.531 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.531 * [taylor]: Taking taylor expansion of 1.0 in k 0.531 * [backup-simplify]: Simplify 1.0 into 1.0 0.531 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.531 * [taylor]: Taking taylor expansion of k in k 0.531 * [backup-simplify]: Simplify 0 into 0 0.531 * [backup-simplify]: Simplify 1 into 1 0.531 * [backup-simplify]: Simplify (/ 1 1) into 1 0.531 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.531 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.531 * [taylor]: Taking taylor expansion of 2.0 in k 0.531 * [backup-simplify]: Simplify 2.0 into 2.0 0.531 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.531 * [taylor]: Taking taylor expansion of PI in k 0.531 * [backup-simplify]: Simplify PI into PI 0.531 * [taylor]: Taking taylor expansion of n in k 0.531 * [backup-simplify]: Simplify n into n 0.532 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.532 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.532 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.532 * [backup-simplify]: Simplify (- 1) into -1 0.533 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.533 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.533 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.534 * [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))))) 0.534 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.534 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.534 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.534 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.534 * [taylor]: Taking taylor expansion of 0.5 in n 0.534 * [backup-simplify]: Simplify 0.5 into 0.5 0.534 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.534 * [taylor]: Taking taylor expansion of 1.0 in n 0.534 * [backup-simplify]: Simplify 1.0 into 1.0 0.534 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.534 * [taylor]: Taking taylor expansion of k in n 0.534 * [backup-simplify]: Simplify k into k 0.534 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.534 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.534 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.534 * [taylor]: Taking taylor expansion of 2.0 in n 0.534 * [backup-simplify]: Simplify 2.0 into 2.0 0.534 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.534 * [taylor]: Taking taylor expansion of PI in n 0.534 * [backup-simplify]: Simplify PI into PI 0.534 * [taylor]: Taking taylor expansion of n in n 0.534 * [backup-simplify]: Simplify 0 into 0 0.534 * [backup-simplify]: Simplify 1 into 1 0.535 * [backup-simplify]: Simplify (/ PI 1) into PI 0.535 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.536 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.537 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.537 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.537 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.540 * [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)))) 0.541 * [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))))) 0.541 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.541 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.542 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.542 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.542 * [taylor]: Taking taylor expansion of 0.5 in n 0.542 * [backup-simplify]: Simplify 0.5 into 0.5 0.542 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.542 * [taylor]: Taking taylor expansion of 1.0 in n 0.542 * [backup-simplify]: Simplify 1.0 into 1.0 0.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.542 * [taylor]: Taking taylor expansion of k in n 0.542 * [backup-simplify]: Simplify k into k 0.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.542 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.542 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.542 * [taylor]: Taking taylor expansion of 2.0 in n 0.542 * [backup-simplify]: Simplify 2.0 into 2.0 0.542 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.542 * [taylor]: Taking taylor expansion of PI in n 0.542 * [backup-simplify]: Simplify PI into PI 0.542 * [taylor]: Taking taylor expansion of n in n 0.542 * [backup-simplify]: Simplify 0 into 0 0.542 * [backup-simplify]: Simplify 1 into 1 0.543 * [backup-simplify]: Simplify (/ PI 1) into PI 0.543 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.544 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.545 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.545 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.545 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.548 * [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)))) 0.549 * [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))))) 0.549 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.549 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.549 * [taylor]: Taking taylor expansion of 0.5 in k 0.549 * [backup-simplify]: Simplify 0.5 into 0.5 0.550 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.550 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.550 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.550 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.550 * [taylor]: Taking taylor expansion of 2.0 in k 0.550 * [backup-simplify]: Simplify 2.0 into 2.0 0.550 * [taylor]: Taking taylor expansion of PI in k 0.550 * [backup-simplify]: Simplify PI into PI 0.550 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.551 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.552 * [taylor]: Taking taylor expansion of (log n) in k 0.552 * [taylor]: Taking taylor expansion of n in k 0.552 * [backup-simplify]: Simplify n into n 0.552 * [backup-simplify]: Simplify (log n) into (log n) 0.552 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.552 * [taylor]: Taking taylor expansion of 1.0 in k 0.552 * [backup-simplify]: Simplify 1.0 into 1.0 0.552 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.552 * [taylor]: Taking taylor expansion of k in k 0.552 * [backup-simplify]: Simplify 0 into 0 0.552 * [backup-simplify]: Simplify 1 into 1 0.552 * [backup-simplify]: Simplify (/ 1 1) into 1 0.552 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.553 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.554 * [backup-simplify]: Simplify (- 1) into -1 0.554 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.555 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.556 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.558 * [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))))) 0.559 * [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))))) 0.560 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.561 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.563 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.563 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.564 * [backup-simplify]: Simplify (- 0) into 0 0.564 * [backup-simplify]: Simplify (+ 0 0) into 0 0.565 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.567 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.569 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.569 * [taylor]: Taking taylor expansion of 0 in k 0.570 * [backup-simplify]: Simplify 0 into 0 0.570 * [backup-simplify]: Simplify 0 into 0 0.570 * [backup-simplify]: Simplify 0 into 0 0.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.572 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.575 * [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 0.576 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.576 * [backup-simplify]: Simplify (- 0) into 0 0.576 * [backup-simplify]: Simplify (+ 0 0) into 0 0.577 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.580 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.583 * [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 0.583 * [taylor]: Taking taylor expansion of 0 in k 0.583 * [backup-simplify]: Simplify 0 into 0 0.583 * [backup-simplify]: Simplify 0 into 0 0.583 * [backup-simplify]: Simplify 0 into 0 0.583 * [backup-simplify]: Simplify 0 into 0 0.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.586 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.599 * [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 0.599 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.600 * [backup-simplify]: Simplify (- 0) into 0 0.600 * [backup-simplify]: Simplify (+ 0 0) into 0 0.601 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.605 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.608 * [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 0.608 * [taylor]: Taking taylor expansion of 0 in k 0.608 * [backup-simplify]: Simplify 0 into 0 0.608 * [backup-simplify]: Simplify 0 into 0 0.609 * [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)))) 0.610 * [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))) 0.610 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.610 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.610 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.610 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.611 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.611 * [taylor]: Taking taylor expansion of 0.5 in k 0.611 * [backup-simplify]: Simplify 0.5 into 0.5 0.611 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.611 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.611 * [taylor]: Taking taylor expansion of k in k 0.611 * [backup-simplify]: Simplify 0 into 0 0.611 * [backup-simplify]: Simplify 1 into 1 0.611 * [backup-simplify]: Simplify (/ 1 1) into 1 0.611 * [taylor]: Taking taylor expansion of 1.0 in k 0.611 * [backup-simplify]: Simplify 1.0 into 1.0 0.611 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.611 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.611 * [taylor]: Taking taylor expansion of -2.0 in k 0.611 * [backup-simplify]: Simplify -2.0 into -2.0 0.611 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.611 * [taylor]: Taking taylor expansion of PI in k 0.611 * [backup-simplify]: Simplify PI into PI 0.611 * [taylor]: Taking taylor expansion of n in k 0.611 * [backup-simplify]: Simplify n into n 0.611 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.611 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.611 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.612 * [backup-simplify]: Simplify (+ 1 0) into 1 0.612 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.612 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.612 * [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)))))) 0.612 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.612 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.612 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.612 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.612 * [taylor]: Taking taylor expansion of 0.5 in n 0.612 * [backup-simplify]: Simplify 0.5 into 0.5 0.612 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.612 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.612 * [taylor]: Taking taylor expansion of k in n 0.612 * [backup-simplify]: Simplify k into k 0.612 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.612 * [taylor]: Taking taylor expansion of 1.0 in n 0.612 * [backup-simplify]: Simplify 1.0 into 1.0 0.612 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.613 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.613 * [taylor]: Taking taylor expansion of -2.0 in n 0.613 * [backup-simplify]: Simplify -2.0 into -2.0 0.613 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.613 * [taylor]: Taking taylor expansion of PI in n 0.613 * [backup-simplify]: Simplify PI into PI 0.613 * [taylor]: Taking taylor expansion of n in n 0.613 * [backup-simplify]: Simplify 0 into 0 0.613 * [backup-simplify]: Simplify 1 into 1 0.613 * [backup-simplify]: Simplify (/ PI 1) into PI 0.613 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.614 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.614 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.614 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.616 * [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)))) 0.616 * [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))))) 0.616 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.616 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.616 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.616 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.616 * [taylor]: Taking taylor expansion of 0.5 in n 0.616 * [backup-simplify]: Simplify 0.5 into 0.5 0.617 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.617 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.617 * [taylor]: Taking taylor expansion of k in n 0.617 * [backup-simplify]: Simplify k into k 0.617 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.617 * [taylor]: Taking taylor expansion of 1.0 in n 0.617 * [backup-simplify]: Simplify 1.0 into 1.0 0.617 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.617 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.617 * [taylor]: Taking taylor expansion of -2.0 in n 0.617 * [backup-simplify]: Simplify -2.0 into -2.0 0.617 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.617 * [taylor]: Taking taylor expansion of PI in n 0.617 * [backup-simplify]: Simplify PI into PI 0.617 * [taylor]: Taking taylor expansion of n in n 0.617 * [backup-simplify]: Simplify 0 into 0 0.617 * [backup-simplify]: Simplify 1 into 1 0.617 * [backup-simplify]: Simplify (/ PI 1) into PI 0.617 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.618 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.618 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.618 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.619 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.620 * [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)))) 0.621 * [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))))) 0.621 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.621 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.621 * [taylor]: Taking taylor expansion of 0.5 in k 0.621 * [backup-simplify]: Simplify 0.5 into 0.5 0.621 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.621 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.621 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.621 * [taylor]: Taking taylor expansion of k in k 0.621 * [backup-simplify]: Simplify 0 into 0 0.621 * [backup-simplify]: Simplify 1 into 1 0.621 * [backup-simplify]: Simplify (/ 1 1) into 1 0.621 * [taylor]: Taking taylor expansion of 1.0 in k 0.621 * [backup-simplify]: Simplify 1.0 into 1.0 0.621 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.621 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.621 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.621 * [taylor]: Taking taylor expansion of -2.0 in k 0.621 * [backup-simplify]: Simplify -2.0 into -2.0 0.621 * [taylor]: Taking taylor expansion of PI in k 0.621 * [backup-simplify]: Simplify PI into PI 0.622 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.622 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.622 * [taylor]: Taking taylor expansion of (log n) in k 0.622 * [taylor]: Taking taylor expansion of n in k 0.622 * [backup-simplify]: Simplify n into n 0.622 * [backup-simplify]: Simplify (log n) into (log n) 0.623 * [backup-simplify]: Simplify (+ 1 0) into 1 0.623 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.623 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.624 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.625 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.625 * [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))))) 0.626 * [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))))) 0.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.627 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.628 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.628 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.628 * [backup-simplify]: Simplify (+ 0 0) into 0 0.629 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.630 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.632 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.632 * [taylor]: Taking taylor expansion of 0 in k 0.632 * [backup-simplify]: Simplify 0 into 0 0.632 * [backup-simplify]: Simplify 0 into 0 0.632 * [backup-simplify]: Simplify 0 into 0 0.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.633 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.635 * [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 0.635 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.635 * [backup-simplify]: Simplify (+ 0 0) into 0 0.636 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.638 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.639 * [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 0.639 * [taylor]: Taking taylor expansion of 0 in k 0.639 * [backup-simplify]: Simplify 0 into 0 0.639 * [backup-simplify]: Simplify 0 into 0 0.639 * [backup-simplify]: Simplify 0 into 0 0.639 * [backup-simplify]: Simplify 0 into 0 0.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.641 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.644 * [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 0.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.644 * [backup-simplify]: Simplify (+ 0 0) into 0 0.645 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.647 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.650 * [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 0.650 * [taylor]: Taking taylor expansion of 0 in k 0.650 * [backup-simplify]: Simplify 0 into 0 0.650 * [backup-simplify]: Simplify 0 into 0 0.652 * [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)))))) 0.652 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.652 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.652 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.653 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.653 * [taylor]: Taking taylor expansion of 2.0 in n 0.653 * [backup-simplify]: Simplify 2.0 into 2.0 0.653 * [taylor]: Taking taylor expansion of (* n PI) in n 0.653 * [taylor]: Taking taylor expansion of n in n 0.653 * [backup-simplify]: Simplify 0 into 0 0.653 * [backup-simplify]: Simplify 1 into 1 0.653 * [taylor]: Taking taylor expansion of PI in n 0.653 * [backup-simplify]: Simplify PI into PI 0.653 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.653 * [taylor]: Taking taylor expansion of 2.0 in n 0.653 * [backup-simplify]: Simplify 2.0 into 2.0 0.653 * [taylor]: Taking taylor expansion of (* n PI) in n 0.653 * [taylor]: Taking taylor expansion of n in n 0.653 * [backup-simplify]: Simplify 0 into 0 0.653 * [backup-simplify]: Simplify 1 into 1 0.653 * [taylor]: Taking taylor expansion of PI in n 0.653 * [backup-simplify]: Simplify PI into PI 0.654 * [backup-simplify]: Simplify (* 0 PI) into 0 0.654 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.654 * [backup-simplify]: Simplify 0 into 0 0.656 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.657 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.659 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.660 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.661 * [backup-simplify]: Simplify 0 into 0 0.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.663 * [backup-simplify]: Simplify 0 into 0 0.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.666 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.666 * [backup-simplify]: Simplify 0 into 0 0.667 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.669 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.672 * [backup-simplify]: Simplify 0 into 0 0.675 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.677 * [backup-simplify]: Simplify 0 into 0 0.677 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.678 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.678 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.678 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.678 * [taylor]: Taking taylor expansion of 2.0 in n 0.678 * [backup-simplify]: Simplify 2.0 into 2.0 0.678 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.678 * [taylor]: Taking taylor expansion of PI in n 0.678 * [backup-simplify]: Simplify PI into PI 0.678 * [taylor]: Taking taylor expansion of n in n 0.678 * [backup-simplify]: Simplify 0 into 0 0.678 * [backup-simplify]: Simplify 1 into 1 0.679 * [backup-simplify]: Simplify (/ PI 1) into PI 0.679 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.679 * [taylor]: Taking taylor expansion of 2.0 in n 0.679 * [backup-simplify]: Simplify 2.0 into 2.0 0.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.679 * [taylor]: Taking taylor expansion of PI in n 0.679 * [backup-simplify]: Simplify PI into PI 0.679 * [taylor]: Taking taylor expansion of n in n 0.679 * [backup-simplify]: Simplify 0 into 0 0.679 * [backup-simplify]: Simplify 1 into 1 0.679 * [backup-simplify]: Simplify (/ PI 1) into PI 0.680 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.680 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.681 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.682 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.682 * [backup-simplify]: Simplify 0 into 0 0.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.684 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.684 * [backup-simplify]: Simplify 0 into 0 0.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.687 * [backup-simplify]: Simplify 0 into 0 0.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.689 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.689 * [backup-simplify]: Simplify 0 into 0 0.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.692 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.692 * [backup-simplify]: Simplify 0 into 0 0.693 * [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 0.695 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.695 * [backup-simplify]: Simplify 0 into 0 0.696 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.696 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.696 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.696 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.696 * [taylor]: Taking taylor expansion of -2.0 in n 0.696 * [backup-simplify]: Simplify -2.0 into -2.0 0.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.696 * [taylor]: Taking taylor expansion of PI in n 0.696 * [backup-simplify]: Simplify PI into PI 0.697 * [taylor]: Taking taylor expansion of n in n 0.697 * [backup-simplify]: Simplify 0 into 0 0.697 * [backup-simplify]: Simplify 1 into 1 0.697 * [backup-simplify]: Simplify (/ PI 1) into PI 0.697 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.697 * [taylor]: Taking taylor expansion of -2.0 in n 0.697 * [backup-simplify]: Simplify -2.0 into -2.0 0.697 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.697 * [taylor]: Taking taylor expansion of PI in n 0.697 * [backup-simplify]: Simplify PI into PI 0.697 * [taylor]: Taking taylor expansion of n in n 0.697 * [backup-simplify]: Simplify 0 into 0 0.697 * [backup-simplify]: Simplify 1 into 1 0.698 * [backup-simplify]: Simplify (/ PI 1) into PI 0.698 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.699 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.701 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.701 * [backup-simplify]: Simplify 0 into 0 0.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.703 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.703 * [backup-simplify]: Simplify 0 into 0 0.704 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.705 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.705 * [backup-simplify]: Simplify 0 into 0 0.706 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.708 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.708 * [backup-simplify]: Simplify 0 into 0 0.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.711 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.711 * [backup-simplify]: Simplify 0 into 0 0.712 * [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 0.714 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.714 * [backup-simplify]: Simplify 0 into 0 0.715 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.715 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.715 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.715 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.715 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.715 * [taylor]: Taking taylor expansion of 1.0 in k 0.715 * [backup-simplify]: Simplify 1.0 into 1.0 0.715 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.715 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.715 * [taylor]: Taking taylor expansion of k in k 0.715 * [backup-simplify]: Simplify 0 into 0 0.715 * [backup-simplify]: Simplify 1 into 1 0.716 * [backup-simplify]: Simplify (/ 1 1) into 1 0.716 * [backup-simplify]: Simplify (sqrt 0) into 0 0.718 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.718 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.718 * [taylor]: Taking taylor expansion of 1.0 in k 0.718 * [backup-simplify]: Simplify 1.0 into 1.0 0.718 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.718 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.718 * [taylor]: Taking taylor expansion of k in k 0.718 * [backup-simplify]: Simplify 0 into 0 0.718 * [backup-simplify]: Simplify 1 into 1 0.718 * [backup-simplify]: Simplify (/ 1 1) into 1 0.719 * [backup-simplify]: Simplify (sqrt 0) into 0 0.720 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.720 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.720 * [backup-simplify]: Simplify 0 into 0 0.721 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.721 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.722 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.728 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.730 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.730 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.730 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.733 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.734 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.734 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.735 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.735 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.735 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.735 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.735 * [taylor]: Taking taylor expansion of 1.0 in k 0.735 * [backup-simplify]: Simplify 1.0 into 1.0 0.735 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.735 * [taylor]: Taking taylor expansion of k in k 0.735 * [backup-simplify]: Simplify 0 into 0 0.735 * [backup-simplify]: Simplify 1 into 1 0.736 * [backup-simplify]: Simplify (sqrt 0) into 0 0.736 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.736 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.736 * [taylor]: Taking taylor expansion of 1.0 in k 0.736 * [backup-simplify]: Simplify 1.0 into 1.0 0.736 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.736 * [taylor]: Taking taylor expansion of k in k 0.736 * [backup-simplify]: Simplify 0 into 0 0.736 * [backup-simplify]: Simplify 1 into 1 0.737 * [backup-simplify]: Simplify (sqrt 0) into 0 0.737 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.738 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.738 * [backup-simplify]: Simplify 0 into 0 0.739 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.739 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.741 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.742 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.742 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.744 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.745 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.746 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.747 * [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)))))))) 0.747 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.747 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.747 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.747 * [taylor]: Taking taylor expansion of 1.0 in k 0.747 * [backup-simplify]: Simplify 1.0 into 1.0 0.747 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.747 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.747 * [taylor]: Taking taylor expansion of -1 in k 0.747 * [backup-simplify]: Simplify -1 into -1 0.747 * [taylor]: Taking taylor expansion of k in k 0.747 * [backup-simplify]: Simplify 0 into 0 0.747 * [backup-simplify]: Simplify 1 into 1 0.747 * [backup-simplify]: Simplify (/ -1 1) into -1 0.748 * [backup-simplify]: Simplify (sqrt 0) into 0 0.748 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.749 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.749 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.749 * [taylor]: Taking taylor expansion of 1.0 in k 0.749 * [backup-simplify]: Simplify 1.0 into 1.0 0.749 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.749 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.749 * [taylor]: Taking taylor expansion of -1 in k 0.749 * [backup-simplify]: Simplify -1 into -1 0.749 * [taylor]: Taking taylor expansion of k in k 0.749 * [backup-simplify]: Simplify 0 into 0 0.749 * [backup-simplify]: Simplify 1 into 1 0.749 * [backup-simplify]: Simplify (/ -1 1) into -1 0.749 * [backup-simplify]: Simplify (sqrt 0) into 0 0.750 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.750 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.750 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.754 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.756 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.757 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.762 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.766 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.766 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.767 * [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))))) 0.767 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.768 * [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))))) 0.768 * [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 0.768 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.768 * [taylor]: Taking taylor expansion of 1.0 in n 0.768 * [backup-simplify]: Simplify 1.0 into 1.0 0.768 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.768 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.769 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.769 * [taylor]: Taking taylor expansion of k in n 0.769 * [backup-simplify]: Simplify k into k 0.769 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.769 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.769 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.769 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.769 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.769 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.769 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.769 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.769 * [taylor]: Taking taylor expansion of 0.5 in n 0.769 * [backup-simplify]: Simplify 0.5 into 0.5 0.769 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.769 * [taylor]: Taking taylor expansion of 1.0 in n 0.769 * [backup-simplify]: Simplify 1.0 into 1.0 0.769 * [taylor]: Taking taylor expansion of k in n 0.769 * [backup-simplify]: Simplify k into k 0.769 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.769 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.769 * [taylor]: Taking taylor expansion of 2.0 in n 0.769 * [backup-simplify]: Simplify 2.0 into 2.0 0.769 * [taylor]: Taking taylor expansion of (* n PI) in n 0.770 * [taylor]: Taking taylor expansion of n in n 0.770 * [backup-simplify]: Simplify 0 into 0 0.770 * [backup-simplify]: Simplify 1 into 1 0.770 * [taylor]: Taking taylor expansion of PI in n 0.770 * [backup-simplify]: Simplify PI into PI 0.770 * [backup-simplify]: Simplify (* 0 PI) into 0 0.771 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.772 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.774 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.775 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.775 * [backup-simplify]: Simplify (- k) into (- k) 0.775 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.775 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.777 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.778 * [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)))) 0.779 * [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))))) 0.779 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.779 * [taylor]: Taking taylor expansion of 1.0 in k 0.779 * [backup-simplify]: Simplify 1.0 into 1.0 0.779 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.779 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.779 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.779 * [taylor]: Taking taylor expansion of k in k 0.779 * [backup-simplify]: Simplify 0 into 0 0.779 * [backup-simplify]: Simplify 1 into 1 0.779 * [backup-simplify]: Simplify (/ 1 1) into 1 0.780 * [backup-simplify]: Simplify (sqrt 0) into 0 0.781 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.781 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.781 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.781 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.781 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.781 * [taylor]: Taking taylor expansion of 0.5 in k 0.781 * [backup-simplify]: Simplify 0.5 into 0.5 0.781 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.781 * [taylor]: Taking taylor expansion of 1.0 in k 0.782 * [backup-simplify]: Simplify 1.0 into 1.0 0.782 * [taylor]: Taking taylor expansion of k in k 0.782 * [backup-simplify]: Simplify 0 into 0 0.782 * [backup-simplify]: Simplify 1 into 1 0.782 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.782 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.782 * [taylor]: Taking taylor expansion of 2.0 in k 0.782 * [backup-simplify]: Simplify 2.0 into 2.0 0.782 * [taylor]: Taking taylor expansion of (* n PI) in k 0.782 * [taylor]: Taking taylor expansion of n in k 0.782 * [backup-simplify]: Simplify n into n 0.782 * [taylor]: Taking taylor expansion of PI in k 0.782 * [backup-simplify]: Simplify PI into PI 0.782 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.782 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.782 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.782 * [backup-simplify]: Simplify (- 0) into 0 0.783 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.783 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.783 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.784 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.784 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.784 * [taylor]: Taking taylor expansion of 1.0 in k 0.784 * [backup-simplify]: Simplify 1.0 into 1.0 0.784 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.784 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.784 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.784 * [taylor]: Taking taylor expansion of k in k 0.784 * [backup-simplify]: Simplify 0 into 0 0.784 * [backup-simplify]: Simplify 1 into 1 0.784 * [backup-simplify]: Simplify (/ 1 1) into 1 0.785 * [backup-simplify]: Simplify (sqrt 0) into 0 0.786 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.786 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.786 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.786 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.786 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.786 * [taylor]: Taking taylor expansion of 0.5 in k 0.786 * [backup-simplify]: Simplify 0.5 into 0.5 0.786 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.786 * [taylor]: Taking taylor expansion of 1.0 in k 0.786 * [backup-simplify]: Simplify 1.0 into 1.0 0.786 * [taylor]: Taking taylor expansion of k in k 0.786 * [backup-simplify]: Simplify 0 into 0 0.786 * [backup-simplify]: Simplify 1 into 1 0.786 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.786 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.786 * [taylor]: Taking taylor expansion of 2.0 in k 0.786 * [backup-simplify]: Simplify 2.0 into 2.0 0.787 * [taylor]: Taking taylor expansion of (* n PI) in k 0.787 * [taylor]: Taking taylor expansion of n in k 0.787 * [backup-simplify]: Simplify n into n 0.787 * [taylor]: Taking taylor expansion of PI in k 0.787 * [backup-simplify]: Simplify PI into PI 0.787 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.787 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.787 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.787 * [backup-simplify]: Simplify (- 0) into 0 0.788 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.788 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.788 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.788 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.789 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.789 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.789 * [taylor]: Taking taylor expansion of 0 in n 0.789 * [backup-simplify]: Simplify 0 into 0 0.789 * [backup-simplify]: Simplify 0 into 0 0.790 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.791 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.792 * [backup-simplify]: Simplify (- 1) into -1 0.792 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.794 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.794 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.795 * [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))) 0.797 * [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))) 0.799 * [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))) 0.799 * [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 0.799 * [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 0.799 * [taylor]: Taking taylor expansion of +nan.0 in n 0.799 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.799 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.800 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.800 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.800 * [taylor]: Taking taylor expansion of 0.5 in n 0.800 * [backup-simplify]: Simplify 0.5 into 0.5 0.800 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.800 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.800 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.800 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.800 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.800 * [taylor]: Taking taylor expansion of 1.0 in n 0.800 * [backup-simplify]: Simplify 1.0 into 1.0 0.800 * [taylor]: Taking taylor expansion of (log PI) in n 0.801 * [taylor]: Taking taylor expansion of PI in n 0.801 * [backup-simplify]: Simplify PI into PI 0.801 * [backup-simplify]: Simplify (log PI) into (log PI) 0.802 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.804 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.804 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.804 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.804 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.804 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.804 * [taylor]: Taking taylor expansion of 1.0 in n 0.804 * [backup-simplify]: Simplify 1.0 into 1.0 0.804 * [taylor]: Taking taylor expansion of (log n) in n 0.804 * [taylor]: Taking taylor expansion of n in n 0.804 * [backup-simplify]: Simplify 0 into 0 0.804 * [backup-simplify]: Simplify 1 into 1 0.804 * [backup-simplify]: Simplify (log 1) into 0 0.805 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.805 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.805 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.805 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.805 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.805 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.805 * [taylor]: Taking taylor expansion of 1.0 in n 0.805 * [backup-simplify]: Simplify 1.0 into 1.0 0.805 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.805 * [taylor]: Taking taylor expansion of 2.0 in n 0.805 * [backup-simplify]: Simplify 2.0 into 2.0 0.806 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.807 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.808 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.809 * [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) 0.810 * [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) 0.811 * [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)) 0.813 * [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))) 0.814 * [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) 0.816 * [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)) 0.817 * [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))) 0.819 * [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))) 0.819 * [backup-simplify]: Simplify 0 into 0 0.820 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.821 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.822 * [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 0.823 * [backup-simplify]: Simplify (- 0) into 0 0.823 * [backup-simplify]: Simplify (+ 0 0) into 0 0.824 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.825 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.827 * [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))) 0.827 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.830 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.834 * [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)))))))) 0.840 * [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)))))))) 0.840 * [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 0.840 * [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 0.840 * [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 0.840 * [taylor]: Taking taylor expansion of +nan.0 in n 0.840 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.840 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.840 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.840 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.840 * [taylor]: Taking taylor expansion of 0.5 in n 0.840 * [backup-simplify]: Simplify 0.5 into 0.5 0.840 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.840 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.840 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.840 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.840 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.840 * [taylor]: Taking taylor expansion of 1.0 in n 0.840 * [backup-simplify]: Simplify 1.0 into 1.0 0.840 * [taylor]: Taking taylor expansion of (log PI) in n 0.840 * [taylor]: Taking taylor expansion of PI in n 0.840 * [backup-simplify]: Simplify PI into PI 0.841 * [backup-simplify]: Simplify (log PI) into (log PI) 0.842 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.844 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.844 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.844 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.844 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.844 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.844 * [taylor]: Taking taylor expansion of 1.0 in n 0.844 * [backup-simplify]: Simplify 1.0 into 1.0 0.844 * [taylor]: Taking taylor expansion of (log n) in n 0.844 * [taylor]: Taking taylor expansion of n in n 0.844 * [backup-simplify]: Simplify 0 into 0 0.844 * [backup-simplify]: Simplify 1 into 1 0.844 * [backup-simplify]: Simplify (log 1) into 0 0.845 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.845 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.845 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.845 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.845 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.845 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.845 * [taylor]: Taking taylor expansion of 1.0 in n 0.845 * [backup-simplify]: Simplify 1.0 into 1.0 0.845 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.845 * [taylor]: Taking taylor expansion of 2.0 in n 0.845 * [backup-simplify]: Simplify 2.0 into 2.0 0.846 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.847 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.848 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.849 * [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) 0.851 * [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) 0.852 * [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)) 0.854 * [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))) 0.855 * [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) 0.855 * [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 0.855 * [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 0.855 * [taylor]: Taking taylor expansion of +nan.0 in n 0.855 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.855 * [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 0.855 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.856 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.856 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.856 * [taylor]: Taking taylor expansion of 0.5 in n 0.856 * [backup-simplify]: Simplify 0.5 into 0.5 0.856 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.856 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.856 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.856 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.856 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.856 * [taylor]: Taking taylor expansion of 1.0 in n 0.856 * [backup-simplify]: Simplify 1.0 into 1.0 0.856 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.856 * [taylor]: Taking taylor expansion of 2.0 in n 0.856 * [backup-simplify]: Simplify 2.0 into 2.0 0.856 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.857 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.859 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.859 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.859 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.859 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.859 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.859 * [taylor]: Taking taylor expansion of 1.0 in n 0.859 * [backup-simplify]: Simplify 1.0 into 1.0 0.859 * [taylor]: Taking taylor expansion of (log PI) in n 0.859 * [taylor]: Taking taylor expansion of PI in n 0.859 * [backup-simplify]: Simplify PI into PI 0.860 * [backup-simplify]: Simplify (log PI) into (log PI) 0.861 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.862 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.863 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.863 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.863 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.863 * [taylor]: Taking taylor expansion of 1.0 in n 0.863 * [backup-simplify]: Simplify 1.0 into 1.0 0.863 * [taylor]: Taking taylor expansion of (log n) in n 0.863 * [taylor]: Taking taylor expansion of n in n 0.863 * [backup-simplify]: Simplify 0 into 0 0.863 * [backup-simplify]: Simplify 1 into 1 0.863 * [backup-simplify]: Simplify (log 1) into 0 0.871 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.871 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.872 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.873 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.874 * [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) 0.875 * [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)) 0.877 * [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))) 0.879 * [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) 0.879 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.879 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.879 * [taylor]: Taking taylor expansion of 2.0 in n 0.879 * [backup-simplify]: Simplify 2.0 into 2.0 0.879 * [taylor]: Taking taylor expansion of (* n PI) in n 0.879 * [taylor]: Taking taylor expansion of n in n 0.879 * [backup-simplify]: Simplify 0 into 0 0.879 * [backup-simplify]: Simplify 1 into 1 0.879 * [taylor]: Taking taylor expansion of PI in n 0.879 * [backup-simplify]: Simplify PI into PI 0.880 * [backup-simplify]: Simplify (* 0 PI) into 0 0.880 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.882 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.884 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.885 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.886 * [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)) 0.888 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.890 * [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)) 0.893 * [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))) 0.896 * [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)))))) 0.901 * [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)))))))) 0.908 * [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)))))))) 0.914 * [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)))))))) 0.916 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.917 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.918 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.920 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.920 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.921 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.922 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.922 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.924 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.925 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.926 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.928 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.930 * [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 0.932 * [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 0.933 * [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 0.934 * [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 0.935 * [backup-simplify]: Simplify (- 0) into 0 0.935 * [backup-simplify]: Simplify 0 into 0 0.935 * [backup-simplify]: Simplify 0 into 0 0.935 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.936 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.938 * [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 0.938 * [backup-simplify]: Simplify (- 0) into 0 0.938 * [backup-simplify]: Simplify (+ 0 0) into 0 0.939 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.940 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.941 * [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))) 0.941 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.944 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.947 * [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)))))))) 0.954 * [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)))))))) 0.954 * [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 0.954 * [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 0.954 * [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 0.954 * [taylor]: Taking taylor expansion of +nan.0 in n 0.954 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.954 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.954 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.954 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.954 * [taylor]: Taking taylor expansion of 0.5 in n 0.954 * [backup-simplify]: Simplify 0.5 into 0.5 0.954 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.954 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.954 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.954 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.954 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.954 * [taylor]: Taking taylor expansion of 1.0 in n 0.954 * [backup-simplify]: Simplify 1.0 into 1.0 0.954 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.954 * [taylor]: Taking taylor expansion of 2.0 in n 0.954 * [backup-simplify]: Simplify 2.0 into 2.0 0.955 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.955 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.956 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.956 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.956 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.956 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.956 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.956 * [taylor]: Taking taylor expansion of 1.0 in n 0.956 * [backup-simplify]: Simplify 1.0 into 1.0 0.956 * [taylor]: Taking taylor expansion of (log n) in n 0.956 * [taylor]: Taking taylor expansion of n in n 0.956 * [backup-simplify]: Simplify 0 into 0 0.956 * [backup-simplify]: Simplify 1 into 1 0.957 * [backup-simplify]: Simplify (log 1) into 0 0.957 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.957 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.957 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.957 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.957 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.957 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.957 * [taylor]: Taking taylor expansion of 1.0 in n 0.957 * [backup-simplify]: Simplify 1.0 into 1.0 0.957 * [taylor]: Taking taylor expansion of (log PI) in n 0.957 * [taylor]: Taking taylor expansion of PI in n 0.957 * [backup-simplify]: Simplify PI into PI 0.957 * [backup-simplify]: Simplify (log PI) into (log PI) 0.958 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.959 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.960 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.961 * [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) 0.962 * [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)) 0.964 * [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))) 0.965 * [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) 0.965 * [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 0.965 * [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 0.965 * [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 0.965 * [taylor]: Taking taylor expansion of +nan.0 in n 0.965 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.965 * [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 0.965 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.965 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.965 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.965 * [taylor]: Taking taylor expansion of 0.5 in n 0.966 * [backup-simplify]: Simplify 0.5 into 0.5 0.966 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.966 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.966 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.966 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.966 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.966 * [taylor]: Taking taylor expansion of 1.0 in n 0.966 * [backup-simplify]: Simplify 1.0 into 1.0 0.966 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.966 * [taylor]: Taking taylor expansion of 2.0 in n 0.966 * [backup-simplify]: Simplify 2.0 into 2.0 0.966 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.967 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.969 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.969 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.969 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.969 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.969 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.969 * [taylor]: Taking taylor expansion of 1.0 in n 0.969 * [backup-simplify]: Simplify 1.0 into 1.0 0.969 * [taylor]: Taking taylor expansion of (log PI) in n 0.969 * [taylor]: Taking taylor expansion of PI in n 0.969 * [backup-simplify]: Simplify PI into PI 0.970 * [backup-simplify]: Simplify (log PI) into (log PI) 0.971 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.972 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.972 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.972 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.972 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.973 * [taylor]: Taking taylor expansion of 1.0 in n 0.973 * [backup-simplify]: Simplify 1.0 into 1.0 0.973 * [taylor]: Taking taylor expansion of (log n) in n 0.973 * [taylor]: Taking taylor expansion of n in n 0.973 * [backup-simplify]: Simplify 0 into 0 0.973 * [backup-simplify]: Simplify 1 into 1 0.973 * [backup-simplify]: Simplify (log 1) into 0 0.973 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.974 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.974 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.974 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.976 * [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) 0.977 * [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)) 0.978 * [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))) 0.980 * [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) 0.980 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.980 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.980 * [taylor]: Taking taylor expansion of 2.0 in n 0.980 * [backup-simplify]: Simplify 2.0 into 2.0 0.980 * [taylor]: Taking taylor expansion of (* n PI) in n 0.980 * [taylor]: Taking taylor expansion of n in n 0.980 * [backup-simplify]: Simplify 0 into 0 0.980 * [backup-simplify]: Simplify 1 into 1 0.980 * [taylor]: Taking taylor expansion of PI in n 0.980 * [backup-simplify]: Simplify PI into PI 0.981 * [backup-simplify]: Simplify (* 0 PI) into 0 0.981 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.983 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.985 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.986 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.986 * [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 0.986 * [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 0.986 * [taylor]: Taking taylor expansion of +nan.0 in n 0.986 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.986 * [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 0.986 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.986 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.986 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.986 * [taylor]: Taking taylor expansion of 0.5 in n 0.986 * [backup-simplify]: Simplify 0.5 into 0.5 0.986 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.986 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.986 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.987 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.987 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.987 * [taylor]: Taking taylor expansion of 1.0 in n 0.987 * [backup-simplify]: Simplify 1.0 into 1.0 0.987 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.987 * [taylor]: Taking taylor expansion of 2.0 in n 0.987 * [backup-simplify]: Simplify 2.0 into 2.0 0.987 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.988 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.990 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.990 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.990 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.990 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.990 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.990 * [taylor]: Taking taylor expansion of 1.0 in n 0.990 * [backup-simplify]: Simplify 1.0 into 1.0 0.990 * [taylor]: Taking taylor expansion of (log PI) in n 0.990 * [taylor]: Taking taylor expansion of PI in n 0.990 * [backup-simplify]: Simplify PI into PI 0.990 * [backup-simplify]: Simplify (log PI) into (log PI) 0.991 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.993 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.993 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.993 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.993 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.993 * [taylor]: Taking taylor expansion of 1.0 in n 0.993 * [backup-simplify]: Simplify 1.0 into 1.0 0.993 * [taylor]: Taking taylor expansion of (log n) in n 0.993 * [taylor]: Taking taylor expansion of n in n 0.993 * [backup-simplify]: Simplify 0 into 0 0.993 * [backup-simplify]: Simplify 1 into 1 0.994 * [backup-simplify]: Simplify (log 1) into 0 0.994 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.994 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.994 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.995 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.996 * [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) 0.998 * [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)) 0.999 * [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))) 1.001 * [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) 1.001 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 1.001 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.001 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.001 * [taylor]: Taking taylor expansion of 2.0 in n 1.001 * [backup-simplify]: Simplify 2.0 into 2.0 1.001 * [taylor]: Taking taylor expansion of (* n PI) in n 1.001 * [taylor]: Taking taylor expansion of n in n 1.001 * [backup-simplify]: Simplify 0 into 0 1.001 * [backup-simplify]: Simplify 1 into 1 1.001 * [taylor]: Taking taylor expansion of PI in n 1.001 * [backup-simplify]: Simplify PI into PI 1.001 * [backup-simplify]: Simplify (* 0 PI) into 0 1.002 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.003 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.005 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.013 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.015 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.016 * [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)) 1.018 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.020 * [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)) 1.023 * [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))) 1.024 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.026 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 1.027 * [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)) 1.029 * [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))) 1.031 * [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)))))))) 1.038 * [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)))))))))))) 1.047 * [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)))))))))))) 1.060 * [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)))))))))))))) 1.073 * [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)))))))))))))) 1.083 * [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)))))))))))))) 1.102 * [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)))))))))))))))))))))) 1.104 * [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)))))) 1.104 * [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 1.104 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 1.104 * [taylor]: Taking taylor expansion of 1.0 in n 1.104 * [backup-simplify]: Simplify 1.0 into 1.0 1.104 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 1.104 * [taylor]: Taking taylor expansion of (sqrt k) in n 1.104 * [taylor]: Taking taylor expansion of k in n 1.104 * [backup-simplify]: Simplify k into k 1.104 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 1.104 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 1.104 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.104 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.104 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.105 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.105 * [taylor]: Taking taylor expansion of 0.5 in n 1.105 * [backup-simplify]: Simplify 0.5 into 0.5 1.105 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.105 * [taylor]: Taking taylor expansion of 1.0 in n 1.105 * [backup-simplify]: Simplify 1.0 into 1.0 1.105 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.105 * [taylor]: Taking taylor expansion of k in n 1.105 * [backup-simplify]: Simplify k into k 1.105 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.105 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.105 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.105 * [taylor]: Taking taylor expansion of 2.0 in n 1.105 * [backup-simplify]: Simplify 2.0 into 2.0 1.105 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.105 * [taylor]: Taking taylor expansion of PI in n 1.105 * [backup-simplify]: Simplify PI into PI 1.105 * [taylor]: Taking taylor expansion of n in n 1.105 * [backup-simplify]: Simplify 0 into 0 1.105 * [backup-simplify]: Simplify 1 into 1 1.106 * [backup-simplify]: Simplify (/ PI 1) into PI 1.106 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.107 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.107 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.107 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.108 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.110 * [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)))) 1.111 * [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))))) 1.111 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 1.111 * [taylor]: Taking taylor expansion of 1.0 in k 1.111 * [backup-simplify]: Simplify 1.0 into 1.0 1.111 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 1.111 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.111 * [taylor]: Taking taylor expansion of k in k 1.111 * [backup-simplify]: Simplify 0 into 0 1.111 * [backup-simplify]: Simplify 1 into 1 1.112 * [backup-simplify]: Simplify (sqrt 0) into 0 1.112 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.112 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.112 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.113 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.113 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.113 * [taylor]: Taking taylor expansion of 0.5 in k 1.113 * [backup-simplify]: Simplify 0.5 into 0.5 1.113 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.113 * [taylor]: Taking taylor expansion of 1.0 in k 1.113 * [backup-simplify]: Simplify 1.0 into 1.0 1.113 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.113 * [taylor]: Taking taylor expansion of k in k 1.113 * [backup-simplify]: Simplify 0 into 0 1.113 * [backup-simplify]: Simplify 1 into 1 1.113 * [backup-simplify]: Simplify (/ 1 1) into 1 1.113 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.113 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.113 * [taylor]: Taking taylor expansion of 2.0 in k 1.113 * [backup-simplify]: Simplify 2.0 into 2.0 1.113 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.113 * [taylor]: Taking taylor expansion of PI in k 1.113 * [backup-simplify]: Simplify PI into PI 1.113 * [taylor]: Taking taylor expansion of n in k 1.113 * [backup-simplify]: Simplify n into n 1.113 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.113 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.113 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.113 * [backup-simplify]: Simplify (- 1) into -1 1.114 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.114 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.114 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.114 * [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))))) 1.114 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 1.114 * [taylor]: Taking taylor expansion of 1.0 in k 1.114 * [backup-simplify]: Simplify 1.0 into 1.0 1.114 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 1.114 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.114 * [taylor]: Taking taylor expansion of k in k 1.114 * [backup-simplify]: Simplify 0 into 0 1.114 * [backup-simplify]: Simplify 1 into 1 1.115 * [backup-simplify]: Simplify (sqrt 0) into 0 1.115 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.115 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.115 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.115 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.116 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.116 * [taylor]: Taking taylor expansion of 0.5 in k 1.116 * [backup-simplify]: Simplify 0.5 into 0.5 1.116 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.116 * [taylor]: Taking taylor expansion of 1.0 in k 1.116 * [backup-simplify]: Simplify 1.0 into 1.0 1.116 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.116 * [taylor]: Taking taylor expansion of k in k 1.116 * [backup-simplify]: Simplify 0 into 0 1.116 * [backup-simplify]: Simplify 1 into 1 1.116 * [backup-simplify]: Simplify (/ 1 1) into 1 1.116 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.116 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.116 * [taylor]: Taking taylor expansion of 2.0 in k 1.116 * [backup-simplify]: Simplify 2.0 into 2.0 1.116 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.116 * [taylor]: Taking taylor expansion of PI in k 1.116 * [backup-simplify]: Simplify PI into PI 1.116 * [taylor]: Taking taylor expansion of n in k 1.116 * [backup-simplify]: Simplify n into n 1.116 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.116 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.116 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.116 * [backup-simplify]: Simplify (- 1) into -1 1.117 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.117 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.117 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.117 * [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))))) 1.117 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 1.118 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.118 * [taylor]: Taking taylor expansion of 0 in n 1.118 * [backup-simplify]: Simplify 0 into 0 1.118 * [backup-simplify]: Simplify 0 into 0 1.122 * [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))))))) 1.123 * [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))))))) 1.123 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 1.123 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 1.123 * [taylor]: Taking taylor expansion of +nan.0 in n 1.123 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.123 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 1.123 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 1.123 * [taylor]: Taking taylor expansion of 0.5 in n 1.123 * [backup-simplify]: Simplify 0.5 into 0.5 1.123 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 1.123 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.123 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.123 * [taylor]: Taking taylor expansion of 2.0 in n 1.123 * [backup-simplify]: Simplify 2.0 into 2.0 1.123 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.123 * [taylor]: Taking taylor expansion of PI in n 1.123 * [backup-simplify]: Simplify PI into PI 1.123 * [taylor]: Taking taylor expansion of n in n 1.123 * [backup-simplify]: Simplify 0 into 0 1.123 * [backup-simplify]: Simplify 1 into 1 1.124 * [backup-simplify]: Simplify (/ PI 1) into PI 1.124 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.125 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.125 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.125 * [taylor]: Taking taylor expansion of 1.0 in n 1.125 * [backup-simplify]: Simplify 1.0 into 1.0 1.125 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.125 * [taylor]: Taking taylor expansion of k in n 1.125 * [backup-simplify]: Simplify k into k 1.125 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.126 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.126 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.127 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 1.127 * [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)))) 1.128 * [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))))) 1.129 * [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)))))) 1.130 * [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))))))) 1.131 * [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))))))) 1.131 * [backup-simplify]: Simplify 0 into 0 1.133 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.133 * [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))))))) 1.134 * [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))))))) 1.134 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 1.134 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 1.134 * [taylor]: Taking taylor expansion of +nan.0 in n 1.134 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.134 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 1.134 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 1.134 * [taylor]: Taking taylor expansion of 0.5 in n 1.134 * [backup-simplify]: Simplify 0.5 into 0.5 1.134 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 1.134 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.134 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.134 * [taylor]: Taking taylor expansion of 2.0 in n 1.134 * [backup-simplify]: Simplify 2.0 into 2.0 1.134 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.134 * [taylor]: Taking taylor expansion of PI in n 1.134 * [backup-simplify]: Simplify PI into PI 1.134 * [taylor]: Taking taylor expansion of n in n 1.134 * [backup-simplify]: Simplify 0 into 0 1.134 * [backup-simplify]: Simplify 1 into 1 1.135 * [backup-simplify]: Simplify (/ PI 1) into PI 1.135 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.136 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.136 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.136 * [taylor]: Taking taylor expansion of 1.0 in n 1.136 * [backup-simplify]: Simplify 1.0 into 1.0 1.136 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.136 * [taylor]: Taking taylor expansion of k in n 1.136 * [backup-simplify]: Simplify k into k 1.136 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.137 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.137 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.138 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 1.138 * [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)))) 1.139 * [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))))) 1.141 * [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)))))) 1.142 * [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))))))) 1.143 * [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))))))) 1.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.145 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.145 * [backup-simplify]: Simplify (- 0) into 0 1.146 * [backup-simplify]: Simplify (+ 0 0) into 0 1.147 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.147 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.149 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.150 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.152 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 1.154 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.155 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 1.156 * [backup-simplify]: Simplify (- 0) into 0 1.156 * [backup-simplify]: Simplify 0 into 0 1.156 * [backup-simplify]: Simplify 0 into 0 1.158 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.159 * [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))))))) 1.160 * [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))))))) 1.160 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 1.160 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 1.160 * [taylor]: Taking taylor expansion of +nan.0 in n 1.160 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.160 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 1.160 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 1.160 * [taylor]: Taking taylor expansion of 0.5 in n 1.160 * [backup-simplify]: Simplify 0.5 into 0.5 1.160 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 1.160 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.160 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.160 * [taylor]: Taking taylor expansion of 2.0 in n 1.160 * [backup-simplify]: Simplify 2.0 into 2.0 1.160 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.160 * [taylor]: Taking taylor expansion of PI in n 1.160 * [backup-simplify]: Simplify PI into PI 1.160 * [taylor]: Taking taylor expansion of n in n 1.160 * [backup-simplify]: Simplify 0 into 0 1.160 * [backup-simplify]: Simplify 1 into 1 1.161 * [backup-simplify]: Simplify (/ PI 1) into PI 1.161 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.162 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.162 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.162 * [taylor]: Taking taylor expansion of 1.0 in n 1.162 * [backup-simplify]: Simplify 1.0 into 1.0 1.162 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.162 * [taylor]: Taking taylor expansion of k in n 1.162 * [backup-simplify]: Simplify k into k 1.162 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.163 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.163 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.164 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 1.164 * [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)))) 1.165 * [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))))) 1.166 * [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)))))) 1.167 * [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))))))) 1.167 * [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))))))) 1.170 * [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)))))))) 1.171 * [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)))) 1.171 * [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 1.171 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 1.171 * [taylor]: Taking taylor expansion of 1.0 in n 1.171 * [backup-simplify]: Simplify 1.0 into 1.0 1.171 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 1.171 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.171 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.171 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.171 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.171 * [taylor]: Taking taylor expansion of 0.5 in n 1.171 * [backup-simplify]: Simplify 0.5 into 0.5 1.171 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.171 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.171 * [taylor]: Taking taylor expansion of k in n 1.171 * [backup-simplify]: Simplify k into k 1.171 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.171 * [taylor]: Taking taylor expansion of 1.0 in n 1.171 * [backup-simplify]: Simplify 1.0 into 1.0 1.171 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.171 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.171 * [taylor]: Taking taylor expansion of -2.0 in n 1.171 * [backup-simplify]: Simplify -2.0 into -2.0 1.171 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.171 * [taylor]: Taking taylor expansion of PI in n 1.171 * [backup-simplify]: Simplify PI into PI 1.171 * [taylor]: Taking taylor expansion of n in n 1.171 * [backup-simplify]: Simplify 0 into 0 1.171 * [backup-simplify]: Simplify 1 into 1 1.172 * [backup-simplify]: Simplify (/ PI 1) into PI 1.172 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.173 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.173 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.173 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.174 * [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)))) 1.175 * [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))))) 1.175 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 1.175 * [taylor]: Taking taylor expansion of (/ -1 k) in n 1.175 * [taylor]: Taking taylor expansion of -1 in n 1.175 * [backup-simplify]: Simplify -1 into -1 1.175 * [taylor]: Taking taylor expansion of k in n 1.175 * [backup-simplify]: Simplify k into k 1.175 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 1.175 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1.175 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1.175 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1.176 * [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))) 1.176 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 1.176 * [taylor]: Taking taylor expansion of 1.0 in k 1.176 * [backup-simplify]: Simplify 1.0 into 1.0 1.176 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 1.176 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.176 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.176 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.176 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.176 * [taylor]: Taking taylor expansion of 0.5 in k 1.176 * [backup-simplify]: Simplify 0.5 into 0.5 1.176 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.176 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.177 * [taylor]: Taking taylor expansion of k in k 1.177 * [backup-simplify]: Simplify 0 into 0 1.177 * [backup-simplify]: Simplify 1 into 1 1.177 * [backup-simplify]: Simplify (/ 1 1) into 1 1.177 * [taylor]: Taking taylor expansion of 1.0 in k 1.177 * [backup-simplify]: Simplify 1.0 into 1.0 1.177 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.177 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.177 * [taylor]: Taking taylor expansion of -2.0 in k 1.177 * [backup-simplify]: Simplify -2.0 into -2.0 1.177 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.177 * [taylor]: Taking taylor expansion of PI in k 1.177 * [backup-simplify]: Simplify PI into PI 1.177 * [taylor]: Taking taylor expansion of n in k 1.177 * [backup-simplify]: Simplify n into n 1.177 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.177 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.177 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.177 * [backup-simplify]: Simplify (+ 1 0) into 1 1.178 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.178 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.178 * [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)))))) 1.178 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.178 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.178 * [taylor]: Taking taylor expansion of -1 in k 1.178 * [backup-simplify]: Simplify -1 into -1 1.178 * [taylor]: Taking taylor expansion of k in k 1.178 * [backup-simplify]: Simplify 0 into 0 1.178 * [backup-simplify]: Simplify 1 into 1 1.178 * [backup-simplify]: Simplify (/ -1 1) into -1 1.179 * [backup-simplify]: Simplify (sqrt 0) into 0 1.179 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.179 * [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))))))) 1.180 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 1.180 * [taylor]: Taking taylor expansion of 1.0 in k 1.180 * [backup-simplify]: Simplify 1.0 into 1.0 1.180 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 1.180 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.180 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.180 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.180 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.180 * [taylor]: Taking taylor expansion of 0.5 in k 1.180 * [backup-simplify]: Simplify 0.5 into 0.5 1.180 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.180 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.180 * [taylor]: Taking taylor expansion of k in k 1.180 * [backup-simplify]: Simplify 0 into 0 1.180 * [backup-simplify]: Simplify 1 into 1 1.180 * [backup-simplify]: Simplify (/ 1 1) into 1 1.180 * [taylor]: Taking taylor expansion of 1.0 in k 1.180 * [backup-simplify]: Simplify 1.0 into 1.0 1.180 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.180 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.180 * [taylor]: Taking taylor expansion of -2.0 in k 1.180 * [backup-simplify]: Simplify -2.0 into -2.0 1.180 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.180 * [taylor]: Taking taylor expansion of PI in k 1.180 * [backup-simplify]: Simplify PI into PI 1.180 * [taylor]: Taking taylor expansion of n in k 1.180 * [backup-simplify]: Simplify n into n 1.180 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.180 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.180 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.181 * [backup-simplify]: Simplify (+ 1 0) into 1 1.181 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.181 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.181 * [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)))))) 1.181 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.181 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.181 * [taylor]: Taking taylor expansion of -1 in k 1.181 * [backup-simplify]: Simplify -1 into -1 1.181 * [taylor]: Taking taylor expansion of k in k 1.181 * [backup-simplify]: Simplify 0 into 0 1.181 * [backup-simplify]: Simplify 1 into 1 1.182 * [backup-simplify]: Simplify (/ -1 1) into -1 1.182 * [backup-simplify]: Simplify (sqrt 0) into 0 1.183 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.183 * [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))))))) 1.184 * [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))))))) 1.184 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 1.184 * [taylor]: Taking taylor expansion of +nan.0 in n 1.184 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.184 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 1.184 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 1.184 * [taylor]: Taking taylor expansion of 0.5 in n 1.184 * [backup-simplify]: Simplify 0.5 into 0.5 1.184 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 1.184 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.184 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.184 * [taylor]: Taking taylor expansion of k in n 1.184 * [backup-simplify]: Simplify k into k 1.184 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.184 * [taylor]: Taking taylor expansion of 1.0 in n 1.184 * [backup-simplify]: Simplify 1.0 into 1.0 1.184 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.184 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.184 * [taylor]: Taking taylor expansion of -2.0 in n 1.184 * [backup-simplify]: Simplify -2.0 into -2.0 1.184 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.184 * [taylor]: Taking taylor expansion of PI in n 1.184 * [backup-simplify]: Simplify PI into PI 1.184 * [taylor]: Taking taylor expansion of n in n 1.184 * [backup-simplify]: Simplify 0 into 0 1.184 * [backup-simplify]: Simplify 1 into 1 1.185 * [backup-simplify]: Simplify (/ PI 1) into PI 1.185 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.186 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.187 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.188 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.189 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 1.191 * [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)))) 1.192 * [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))))) 1.193 * [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)))))) 1.194 * [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)))))) 1.195 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.199 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.200 * [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)))))))) 1.200 * [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)))))))) 1.201 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 1.201 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 1.201 * [taylor]: Taking taylor expansion of +nan.0 in n 1.201 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.201 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 1.201 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 1.201 * [taylor]: Taking taylor expansion of 0.5 in n 1.201 * [backup-simplify]: Simplify 0.5 into 0.5 1.201 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 1.201 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.201 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.201 * [taylor]: Taking taylor expansion of k in n 1.201 * [backup-simplify]: Simplify k into k 1.201 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.201 * [taylor]: Taking taylor expansion of 1.0 in n 1.201 * [backup-simplify]: Simplify 1.0 into 1.0 1.201 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.201 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.201 * [taylor]: Taking taylor expansion of -2.0 in n 1.201 * [backup-simplify]: Simplify -2.0 into -2.0 1.201 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.201 * [taylor]: Taking taylor expansion of PI in n 1.201 * [backup-simplify]: Simplify PI into PI 1.201 * [taylor]: Taking taylor expansion of n in n 1.201 * [backup-simplify]: Simplify 0 into 0 1.201 * [backup-simplify]: Simplify 1 into 1 1.202 * [backup-simplify]: Simplify (/ PI 1) into PI 1.202 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.204 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.204 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.205 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.206 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 1.208 * [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)))) 1.209 * [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))))) 1.210 * [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)))))) 1.212 * [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))))))) 1.213 * [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))))))) 1.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.215 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.217 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.217 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.217 * [backup-simplify]: Simplify (+ 0 0) into 0 1.219 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.220 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.222 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 1.224 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.226 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 1.226 * [backup-simplify]: Simplify 0 into 0 1.227 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.231 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.233 * [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)))))))) 1.234 * [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)))))))) 1.234 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 1.234 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 1.234 * [taylor]: Taking taylor expansion of +nan.0 in n 1.234 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.234 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 1.235 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 1.235 * [taylor]: Taking taylor expansion of 0.5 in n 1.235 * [backup-simplify]: Simplify 0.5 into 0.5 1.235 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 1.235 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.235 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.235 * [taylor]: Taking taylor expansion of k in n 1.235 * [backup-simplify]: Simplify k into k 1.235 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.235 * [taylor]: Taking taylor expansion of 1.0 in n 1.235 * [backup-simplify]: Simplify 1.0 into 1.0 1.235 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.235 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.235 * [taylor]: Taking taylor expansion of -2.0 in n 1.235 * [backup-simplify]: Simplify -2.0 into -2.0 1.235 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.235 * [taylor]: Taking taylor expansion of PI in n 1.235 * [backup-simplify]: Simplify PI into PI 1.235 * [taylor]: Taking taylor expansion of n in n 1.235 * [backup-simplify]: Simplify 0 into 0 1.235 * [backup-simplify]: Simplify 1 into 1 1.236 * [backup-simplify]: Simplify (/ PI 1) into PI 1.236 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.237 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.237 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.239 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.240 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 1.242 * [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)))) 1.243 * [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))))) 1.244 * [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)))))) 1.245 * [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))))))) 1.254 * [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))))))) 1.259 * [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)))))))))))) 1.259 * * * [progress]: simplifying candidates 1.263 * [simplify]: Simplifying: (* (+ (+ (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)) (* (* 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) (- (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) 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(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 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(sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (+ (- (log h2) (log (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (- (log h2) (log (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (+ (log (/ h2 (sqrt h1))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (+ (log (* h0 h4)) (log h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (* (log (* (* h0 h4) h3)) (/ (- h2 h1) h0))) (+ (log (/ h2 (sqrt h1))) (log (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (log (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (exp (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (* (* h2 h2) h2) (* (* (sqrt h1) (sqrt h1)) (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (/ h2 (sqrt h1))) (/ h2 (sqrt h1))) (* (* (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (cbrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (* (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (sqrt (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* h2 (pow (* (* h0 h4) h3) (/ h2 h0))) (* (sqrt h1) (pow (* (* h0 h4) h3) (/ h1 h0))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (/ h2 (sqrt h1)) (pow (* h0 h4) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (* (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (cbrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))))) (* (/ h2 (sqrt h1)) (sqrt (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)))) (* (/ h2 (sqrt h1)) 1) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (sqrt (/ h2 (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (cbrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ (sqrt h2) (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (cbrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (cbrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt (sqrt h1))) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ 1 (sqrt h1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (* (/ h2 (sqrt h1)) (pow (* (* h0 h4) h3) (/ h2 h0))) (* h2 (pow (* (* h0 h4) h3) (/ (- h2 h1) h0))) (- (+ (* h7 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h7 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (+ (* h6 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (- (+ (* h9 h1) (- (+ (* h9 (pow h1 2)) (- h9))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- (* h9 (/ 1 (pow h1 3)))))))) (- (+ (* h9 (/ 1 (pow h1 2))) (- (+ (* h9 (/ 1 h1)) (- h9))))) (- (+ (* h9 (* (* (pow h1 2) (pow (log (* h0 h4)) 2)) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log (* h0 h4))) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (* (log (* h0 h4)) (log h3))) (pow (* (pow h4 h2) (* (pow h0 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log (* h0 h4))) (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5))) (- (+ (* h9 (* (* (pow h1 2) (pow (log h3) 2)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (* (* h1 (log h3)) (pow (* (pow h0 h2) (* (pow h4 h2) (pow h3 h2))) h5))) (- (+ (* h9 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)) (- (+ (* h9 (* (pow h1 2) (pow (* (pow h4 h2) (* (pow h3 h2) (pow h0 h2))) h5))) (- (* h9 (* h1 (pow (* (pow h0 h2) (* (pow h3 h2) (pow h4 h2))) h5)))))))))))))))))))))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 3))) (- (+ (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) h1)) (- (* h9 (/ (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (pow h1 2)))))))) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) h1)) (- (+ (* h9 (/ (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (pow h1 2))) (- (* h9 (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))))))))) 1.375 * * * [progress]: adding candidates to table 2.026 * * [progress]: iteration 2 / 4 2.026 * * * [progress]: picking best candidate 2.071 * * * * [pick]: Picked # 2.071 * * * [progress]: localizing error 2.096 * * * [progress]: generating rewritten candidates 2.096 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.136 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 2.195 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 2.228 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 2.258 * * * [progress]: generating series expansions 2.258 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.259 * [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))) 2.259 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.259 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.259 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.259 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.259 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.259 * [taylor]: Taking taylor expansion of 0.25 in k 2.259 * [backup-simplify]: Simplify 0.25 into 0.25 2.259 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.259 * [taylor]: Taking taylor expansion of 1.0 in k 2.259 * [backup-simplify]: Simplify 1.0 into 1.0 2.259 * [taylor]: Taking taylor expansion of k in k 2.259 * [backup-simplify]: Simplify 0 into 0 2.259 * [backup-simplify]: Simplify 1 into 1 2.259 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.259 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.259 * [taylor]: Taking taylor expansion of 2.0 in k 2.259 * [backup-simplify]: Simplify 2.0 into 2.0 2.259 * [taylor]: Taking taylor expansion of (* n PI) in k 2.259 * [taylor]: Taking taylor expansion of n in k 2.259 * [backup-simplify]: Simplify n into n 2.259 * [taylor]: Taking taylor expansion of PI in k 2.260 * [backup-simplify]: Simplify PI into PI 2.260 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.260 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.260 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.260 * [backup-simplify]: Simplify (- 0) into 0 2.260 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.261 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.261 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.261 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.261 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.261 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.261 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.261 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.261 * [taylor]: Taking taylor expansion of 0.25 in n 2.261 * [backup-simplify]: Simplify 0.25 into 0.25 2.261 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.261 * [taylor]: Taking taylor expansion of 1.0 in n 2.261 * [backup-simplify]: Simplify 1.0 into 1.0 2.261 * [taylor]: Taking taylor expansion of k in n 2.261 * [backup-simplify]: Simplify k into k 2.261 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.261 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.261 * [taylor]: Taking taylor expansion of 2.0 in n 2.261 * [backup-simplify]: Simplify 2.0 into 2.0 2.261 * [taylor]: Taking taylor expansion of (* n PI) in n 2.261 * [taylor]: Taking taylor expansion of n in n 2.261 * [backup-simplify]: Simplify 0 into 0 2.261 * [backup-simplify]: Simplify 1 into 1 2.261 * [taylor]: Taking taylor expansion of PI in n 2.261 * [backup-simplify]: Simplify PI into PI 2.262 * [backup-simplify]: Simplify (* 0 PI) into 0 2.262 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.263 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.264 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.266 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.266 * [backup-simplify]: Simplify (- k) into (- k) 2.266 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.266 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.267 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.269 * [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)))) 2.270 * [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))))) 2.270 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.270 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.270 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.270 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.270 * [taylor]: Taking taylor expansion of 0.25 in n 2.270 * [backup-simplify]: Simplify 0.25 into 0.25 2.270 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.270 * [taylor]: Taking taylor expansion of 1.0 in n 2.270 * [backup-simplify]: Simplify 1.0 into 1.0 2.270 * [taylor]: Taking taylor expansion of k in n 2.270 * [backup-simplify]: Simplify k into k 2.270 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.270 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.270 * [taylor]: Taking taylor expansion of 2.0 in n 2.271 * [backup-simplify]: Simplify 2.0 into 2.0 2.271 * [taylor]: Taking taylor expansion of (* n PI) in n 2.271 * [taylor]: Taking taylor expansion of n in n 2.271 * [backup-simplify]: Simplify 0 into 0 2.271 * [backup-simplify]: Simplify 1 into 1 2.271 * [taylor]: Taking taylor expansion of PI in n 2.271 * [backup-simplify]: Simplify PI into PI 2.271 * [backup-simplify]: Simplify (* 0 PI) into 0 2.272 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.273 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.275 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.276 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.276 * [backup-simplify]: Simplify (- k) into (- k) 2.276 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.276 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.278 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.279 * [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)))) 2.280 * [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))))) 2.280 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.281 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.281 * [taylor]: Taking taylor expansion of 0.25 in k 2.281 * [backup-simplify]: Simplify 0.25 into 0.25 2.281 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.281 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.281 * [taylor]: Taking taylor expansion of 1.0 in k 2.281 * [backup-simplify]: Simplify 1.0 into 1.0 2.281 * [taylor]: Taking taylor expansion of k in k 2.281 * [backup-simplify]: Simplify 0 into 0 2.281 * [backup-simplify]: Simplify 1 into 1 2.281 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.281 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.281 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.281 * [taylor]: Taking taylor expansion of 2.0 in k 2.281 * [backup-simplify]: Simplify 2.0 into 2.0 2.281 * [taylor]: Taking taylor expansion of PI in k 2.281 * [backup-simplify]: Simplify PI into PI 2.282 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.283 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.283 * [taylor]: Taking taylor expansion of (log n) in k 2.283 * [taylor]: Taking taylor expansion of n in k 2.283 * [backup-simplify]: Simplify n into n 2.283 * [backup-simplify]: Simplify (log n) into (log n) 2.283 * [backup-simplify]: Simplify (- 0) into 0 2.284 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.285 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.286 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.288 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.289 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.290 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.291 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.292 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.301 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.302 * [backup-simplify]: Simplify (- 0) into 0 2.302 * [backup-simplify]: Simplify (+ 0 0) into 0 2.303 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.305 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.307 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.309 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.309 * [taylor]: Taking taylor expansion of 0 in k 2.309 * [backup-simplify]: Simplify 0 into 0 2.309 * [backup-simplify]: Simplify 0 into 0 2.310 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.312 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.313 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.313 * [backup-simplify]: Simplify (+ 0 0) into 0 2.314 * [backup-simplify]: Simplify (- 1) into -1 2.314 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.316 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.318 * [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)))) 2.321 * [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)))))) 2.324 * [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)))))) 2.326 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.327 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.331 * [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 2.331 * [backup-simplify]: Simplify (- 0) into 0 2.332 * [backup-simplify]: Simplify (+ 0 0) into 0 2.333 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.334 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.336 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.338 * [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 2.339 * [taylor]: Taking taylor expansion of 0 in k 2.339 * [backup-simplify]: Simplify 0 into 0 2.339 * [backup-simplify]: Simplify 0 into 0 2.339 * [backup-simplify]: Simplify 0 into 0 2.340 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.343 * [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 2.345 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.346 * [backup-simplify]: Simplify (+ 0 0) into 0 2.346 * [backup-simplify]: Simplify (- 0) into 0 2.346 * [backup-simplify]: Simplify (+ 0 0) into 0 2.349 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.351 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.355 * [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))))) 2.361 * [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))))) 2.372 * [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)))))) 2.373 * [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)))) 2.373 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.373 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.373 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.373 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.373 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.373 * [taylor]: Taking taylor expansion of 0.25 in k 2.373 * [backup-simplify]: Simplify 0.25 into 0.25 2.374 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.374 * [taylor]: Taking taylor expansion of 1.0 in k 2.374 * [backup-simplify]: Simplify 1.0 into 1.0 2.374 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.374 * [taylor]: Taking taylor expansion of k in k 2.374 * [backup-simplify]: Simplify 0 into 0 2.374 * [backup-simplify]: Simplify 1 into 1 2.374 * [backup-simplify]: Simplify (/ 1 1) into 1 2.374 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.374 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.374 * [taylor]: Taking taylor expansion of 2.0 in k 2.374 * [backup-simplify]: Simplify 2.0 into 2.0 2.374 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.374 * [taylor]: Taking taylor expansion of PI in k 2.374 * [backup-simplify]: Simplify PI into PI 2.374 * [taylor]: Taking taylor expansion of n in k 2.374 * [backup-simplify]: Simplify n into n 2.374 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.375 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.375 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.375 * [backup-simplify]: Simplify (- 1) into -1 2.376 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.376 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.376 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.376 * [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))))) 2.376 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.377 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.377 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.377 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.377 * [taylor]: Taking taylor expansion of 0.25 in n 2.377 * [backup-simplify]: Simplify 0.25 into 0.25 2.377 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.377 * [taylor]: Taking taylor expansion of 1.0 in n 2.377 * [backup-simplify]: Simplify 1.0 into 1.0 2.377 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.377 * [taylor]: Taking taylor expansion of k in n 2.377 * [backup-simplify]: Simplify k into k 2.377 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.377 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.377 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.377 * [taylor]: Taking taylor expansion of 2.0 in n 2.377 * [backup-simplify]: Simplify 2.0 into 2.0 2.377 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.377 * [taylor]: Taking taylor expansion of PI in n 2.377 * [backup-simplify]: Simplify PI into PI 2.377 * [taylor]: Taking taylor expansion of n in n 2.377 * [backup-simplify]: Simplify 0 into 0 2.377 * [backup-simplify]: Simplify 1 into 1 2.378 * [backup-simplify]: Simplify (/ PI 1) into PI 2.378 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.379 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.379 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.380 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.380 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.381 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.382 * [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)))) 2.384 * [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))))) 2.384 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.384 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.384 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.384 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.384 * [taylor]: Taking taylor expansion of 0.25 in n 2.384 * [backup-simplify]: Simplify 0.25 into 0.25 2.384 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.384 * [taylor]: Taking taylor expansion of 1.0 in n 2.384 * [backup-simplify]: Simplify 1.0 into 1.0 2.384 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.384 * [taylor]: Taking taylor expansion of k in n 2.384 * [backup-simplify]: Simplify k into k 2.384 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.384 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.384 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.384 * [taylor]: Taking taylor expansion of 2.0 in n 2.384 * [backup-simplify]: Simplify 2.0 into 2.0 2.384 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.384 * [taylor]: Taking taylor expansion of PI in n 2.385 * [backup-simplify]: Simplify PI into PI 2.385 * [taylor]: Taking taylor expansion of n in n 2.385 * [backup-simplify]: Simplify 0 into 0 2.385 * [backup-simplify]: Simplify 1 into 1 2.385 * [backup-simplify]: Simplify (/ PI 1) into PI 2.386 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.387 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.387 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.387 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.387 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.389 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.390 * [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)))) 2.391 * [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))))) 2.391 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.391 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.391 * [taylor]: Taking taylor expansion of 0.25 in k 2.391 * [backup-simplify]: Simplify 0.25 into 0.25 2.391 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.391 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.391 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.391 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.391 * [taylor]: Taking taylor expansion of 2.0 in k 2.391 * [backup-simplify]: Simplify 2.0 into 2.0 2.392 * [taylor]: Taking taylor expansion of PI in k 2.392 * [backup-simplify]: Simplify PI into PI 2.392 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.393 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.393 * [taylor]: Taking taylor expansion of (log n) in k 2.393 * [taylor]: Taking taylor expansion of n in k 2.393 * [backup-simplify]: Simplify n into n 2.393 * [backup-simplify]: Simplify (log n) into (log n) 2.393 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.393 * [taylor]: Taking taylor expansion of 1.0 in k 2.393 * [backup-simplify]: Simplify 1.0 into 1.0 2.393 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.393 * [taylor]: Taking taylor expansion of k in k 2.393 * [backup-simplify]: Simplify 0 into 0 2.394 * [backup-simplify]: Simplify 1 into 1 2.394 * [backup-simplify]: Simplify (/ 1 1) into 1 2.394 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.395 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.395 * [backup-simplify]: Simplify (- 1) into -1 2.396 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.397 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.398 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.400 * [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))))) 2.401 * [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))))) 2.402 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.403 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.404 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.405 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.405 * [backup-simplify]: Simplify (- 0) into 0 2.405 * [backup-simplify]: Simplify (+ 0 0) into 0 2.406 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.407 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.409 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.411 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.411 * [taylor]: Taking taylor expansion of 0 in k 2.411 * [backup-simplify]: Simplify 0 into 0 2.411 * [backup-simplify]: Simplify 0 into 0 2.411 * [backup-simplify]: Simplify 0 into 0 2.412 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.413 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.417 * [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 2.417 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.418 * [backup-simplify]: Simplify (- 0) into 0 2.418 * [backup-simplify]: Simplify (+ 0 0) into 0 2.419 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.420 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.422 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.425 * [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 2.425 * [taylor]: Taking taylor expansion of 0 in k 2.425 * [backup-simplify]: Simplify 0 into 0 2.425 * [backup-simplify]: Simplify 0 into 0 2.425 * [backup-simplify]: Simplify 0 into 0 2.425 * [backup-simplify]: Simplify 0 into 0 2.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.427 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.434 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.434 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.434 * [backup-simplify]: Simplify (- 0) into 0 2.435 * [backup-simplify]: Simplify (+ 0 0) into 0 2.436 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.440 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.443 * [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 2.443 * [taylor]: Taking taylor expansion of 0 in k 2.443 * [backup-simplify]: Simplify 0 into 0 2.443 * [backup-simplify]: Simplify 0 into 0 2.444 * [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)))) 2.445 * [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))) 2.445 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.445 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.445 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.445 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.445 * [taylor]: Taking taylor expansion of 0.25 in k 2.445 * [backup-simplify]: Simplify 0.25 into 0.25 2.445 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.445 * [taylor]: Taking taylor expansion of k in k 2.445 * [backup-simplify]: Simplify 0 into 0 2.445 * [backup-simplify]: Simplify 1 into 1 2.446 * [backup-simplify]: Simplify (/ 1 1) into 1 2.446 * [taylor]: Taking taylor expansion of 1.0 in k 2.446 * [backup-simplify]: Simplify 1.0 into 1.0 2.446 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.446 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.446 * [taylor]: Taking taylor expansion of -2.0 in k 2.446 * [backup-simplify]: Simplify -2.0 into -2.0 2.446 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.446 * [taylor]: Taking taylor expansion of PI in k 2.446 * [backup-simplify]: Simplify PI into PI 2.446 * [taylor]: Taking taylor expansion of n in k 2.446 * [backup-simplify]: Simplify n into n 2.446 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.446 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.446 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.447 * [backup-simplify]: Simplify (+ 1 0) into 1 2.447 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.447 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.447 * [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)))))) 2.448 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.448 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.448 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.448 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.448 * [taylor]: Taking taylor expansion of 0.25 in n 2.448 * [backup-simplify]: Simplify 0.25 into 0.25 2.448 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.448 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.448 * [taylor]: Taking taylor expansion of k in n 2.448 * [backup-simplify]: Simplify k into k 2.448 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.448 * [taylor]: Taking taylor expansion of 1.0 in n 2.448 * [backup-simplify]: Simplify 1.0 into 1.0 2.448 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.448 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.448 * [taylor]: Taking taylor expansion of -2.0 in n 2.448 * [backup-simplify]: Simplify -2.0 into -2.0 2.448 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.448 * [taylor]: Taking taylor expansion of PI in n 2.448 * [backup-simplify]: Simplify PI into PI 2.448 * [taylor]: Taking taylor expansion of n in n 2.448 * [backup-simplify]: Simplify 0 into 0 2.449 * [backup-simplify]: Simplify 1 into 1 2.449 * [backup-simplify]: Simplify (/ PI 1) into PI 2.449 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.450 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.450 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.451 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.452 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.453 * [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)))) 2.460 * [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))))) 2.461 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.461 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.461 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.461 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.461 * [taylor]: Taking taylor expansion of 0.25 in n 2.461 * [backup-simplify]: Simplify 0.25 into 0.25 2.461 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.461 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.461 * [taylor]: Taking taylor expansion of k in n 2.461 * [backup-simplify]: Simplify k into k 2.461 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.461 * [taylor]: Taking taylor expansion of 1.0 in n 2.461 * [backup-simplify]: Simplify 1.0 into 1.0 2.461 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.461 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.461 * [taylor]: Taking taylor expansion of -2.0 in n 2.461 * [backup-simplify]: Simplify -2.0 into -2.0 2.461 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.461 * [taylor]: Taking taylor expansion of PI in n 2.461 * [backup-simplify]: Simplify PI into PI 2.461 * [taylor]: Taking taylor expansion of n in n 2.461 * [backup-simplify]: Simplify 0 into 0 2.461 * [backup-simplify]: Simplify 1 into 1 2.461 * [backup-simplify]: Simplify (/ PI 1) into PI 2.462 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.462 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.462 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.462 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.463 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.464 * [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)))) 2.465 * [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))))) 2.465 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.465 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.465 * [taylor]: Taking taylor expansion of 0.25 in k 2.465 * [backup-simplify]: Simplify 0.25 into 0.25 2.465 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.465 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.465 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.465 * [taylor]: Taking taylor expansion of k in k 2.465 * [backup-simplify]: Simplify 0 into 0 2.465 * [backup-simplify]: Simplify 1 into 1 2.465 * [backup-simplify]: Simplify (/ 1 1) into 1 2.465 * [taylor]: Taking taylor expansion of 1.0 in k 2.465 * [backup-simplify]: Simplify 1.0 into 1.0 2.465 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.465 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.465 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.465 * [taylor]: Taking taylor expansion of -2.0 in k 2.465 * [backup-simplify]: Simplify -2.0 into -2.0 2.465 * [taylor]: Taking taylor expansion of PI in k 2.465 * [backup-simplify]: Simplify PI into PI 2.466 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.466 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.466 * [taylor]: Taking taylor expansion of (log n) in k 2.466 * [taylor]: Taking taylor expansion of n in k 2.466 * [backup-simplify]: Simplify n into n 2.466 * [backup-simplify]: Simplify (log n) into (log n) 2.467 * [backup-simplify]: Simplify (+ 1 0) into 1 2.467 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.467 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.468 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.469 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.469 * [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))))) 2.470 * [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))))) 2.471 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.471 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.472 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.472 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.473 * [backup-simplify]: Simplify (+ 0 0) into 0 2.473 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.475 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.476 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.476 * [taylor]: Taking taylor expansion of 0 in k 2.476 * [backup-simplify]: Simplify 0 into 0 2.476 * [backup-simplify]: Simplify 0 into 0 2.476 * [backup-simplify]: Simplify 0 into 0 2.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.477 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.479 * [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 2.480 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.480 * [backup-simplify]: Simplify (+ 0 0) into 0 2.481 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.484 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.487 * [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 2.487 * [taylor]: Taking taylor expansion of 0 in k 2.487 * [backup-simplify]: Simplify 0 into 0 2.487 * [backup-simplify]: Simplify 0 into 0 2.487 * [backup-simplify]: Simplify 0 into 0 2.487 * [backup-simplify]: Simplify 0 into 0 2.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.489 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.495 * [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 2.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.496 * [backup-simplify]: Simplify (+ 0 0) into 0 2.497 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.499 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.501 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.503 * [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 2.504 * [taylor]: Taking taylor expansion of 0 in k 2.504 * [backup-simplify]: Simplify 0 into 0 2.504 * [backup-simplify]: Simplify 0 into 0 2.505 * [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)))))) 2.505 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 2.506 * [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))) 2.506 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.506 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.506 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.506 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.506 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.506 * [taylor]: Taking taylor expansion of 0.25 in k 2.506 * [backup-simplify]: Simplify 0.25 into 0.25 2.506 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.506 * [taylor]: Taking taylor expansion of 1.0 in k 2.506 * [backup-simplify]: Simplify 1.0 into 1.0 2.506 * [taylor]: Taking taylor expansion of k in k 2.506 * [backup-simplify]: Simplify 0 into 0 2.506 * [backup-simplify]: Simplify 1 into 1 2.506 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.506 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.507 * [taylor]: Taking taylor expansion of 2.0 in k 2.507 * [backup-simplify]: Simplify 2.0 into 2.0 2.507 * [taylor]: Taking taylor expansion of (* n PI) in k 2.507 * [taylor]: Taking taylor expansion of n in k 2.507 * [backup-simplify]: Simplify n into n 2.507 * [taylor]: Taking taylor expansion of PI in k 2.507 * [backup-simplify]: Simplify PI into PI 2.507 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.507 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.507 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.507 * [backup-simplify]: Simplify (- 0) into 0 2.508 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.508 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.508 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.509 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.509 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.509 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.509 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.509 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.509 * [taylor]: Taking taylor expansion of 0.25 in n 2.509 * [backup-simplify]: Simplify 0.25 into 0.25 2.509 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.509 * [taylor]: Taking taylor expansion of 1.0 in n 2.509 * [backup-simplify]: Simplify 1.0 into 1.0 2.509 * [taylor]: Taking taylor expansion of k in n 2.509 * [backup-simplify]: Simplify k into k 2.509 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.509 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.509 * [taylor]: Taking taylor expansion of 2.0 in n 2.509 * [backup-simplify]: Simplify 2.0 into 2.0 2.509 * [taylor]: Taking taylor expansion of (* n PI) in n 2.509 * [taylor]: Taking taylor expansion of n in n 2.509 * [backup-simplify]: Simplify 0 into 0 2.509 * [backup-simplify]: Simplify 1 into 1 2.509 * [taylor]: Taking taylor expansion of PI in n 2.509 * [backup-simplify]: Simplify PI into PI 2.510 * [backup-simplify]: Simplify (* 0 PI) into 0 2.510 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.512 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.513 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.514 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.514 * [backup-simplify]: Simplify (- k) into (- k) 2.514 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.515 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.516 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.517 * [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)))) 2.519 * [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))))) 2.519 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.519 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.519 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.519 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.519 * [taylor]: Taking taylor expansion of 0.25 in n 2.519 * [backup-simplify]: Simplify 0.25 into 0.25 2.519 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.519 * [taylor]: Taking taylor expansion of 1.0 in n 2.519 * [backup-simplify]: Simplify 1.0 into 1.0 2.519 * [taylor]: Taking taylor expansion of k in n 2.519 * [backup-simplify]: Simplify k into k 2.519 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.519 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.519 * [taylor]: Taking taylor expansion of 2.0 in n 2.519 * [backup-simplify]: Simplify 2.0 into 2.0 2.519 * [taylor]: Taking taylor expansion of (* n PI) in n 2.519 * [taylor]: Taking taylor expansion of n in n 2.519 * [backup-simplify]: Simplify 0 into 0 2.519 * [backup-simplify]: Simplify 1 into 1 2.519 * [taylor]: Taking taylor expansion of PI in n 2.520 * [backup-simplify]: Simplify PI into PI 2.520 * [backup-simplify]: Simplify (* 0 PI) into 0 2.521 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.522 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.524 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.525 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.525 * [backup-simplify]: Simplify (- k) into (- k) 2.525 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.525 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.527 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.528 * [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)))) 2.529 * [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))))) 2.529 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.530 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.530 * [taylor]: Taking taylor expansion of 0.25 in k 2.530 * [backup-simplify]: Simplify 0.25 into 0.25 2.530 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.530 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.530 * [taylor]: Taking taylor expansion of 1.0 in k 2.530 * [backup-simplify]: Simplify 1.0 into 1.0 2.530 * [taylor]: Taking taylor expansion of k in k 2.530 * [backup-simplify]: Simplify 0 into 0 2.530 * [backup-simplify]: Simplify 1 into 1 2.530 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.530 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.530 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.530 * [taylor]: Taking taylor expansion of 2.0 in k 2.530 * [backup-simplify]: Simplify 2.0 into 2.0 2.530 * [taylor]: Taking taylor expansion of PI in k 2.530 * [backup-simplify]: Simplify PI into PI 2.531 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.532 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.532 * [taylor]: Taking taylor expansion of (log n) in k 2.532 * [taylor]: Taking taylor expansion of n in k 2.532 * [backup-simplify]: Simplify n into n 2.532 * [backup-simplify]: Simplify (log n) into (log n) 2.532 * [backup-simplify]: Simplify (- 0) into 0 2.533 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.534 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.535 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.536 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.537 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.538 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.539 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.541 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.542 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.543 * [backup-simplify]: Simplify (- 0) into 0 2.543 * [backup-simplify]: Simplify (+ 0 0) into 0 2.544 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.545 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.546 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.548 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.548 * [taylor]: Taking taylor expansion of 0 in k 2.548 * [backup-simplify]: Simplify 0 into 0 2.548 * [backup-simplify]: Simplify 0 into 0 2.549 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.551 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.552 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.552 * [backup-simplify]: Simplify (+ 0 0) into 0 2.553 * [backup-simplify]: Simplify (- 1) into -1 2.553 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.555 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.557 * [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)))) 2.560 * [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)))))) 2.563 * [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)))))) 2.565 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.566 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.570 * [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 2.570 * [backup-simplify]: Simplify (- 0) into 0 2.571 * [backup-simplify]: Simplify (+ 0 0) into 0 2.572 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.573 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.575 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.577 * [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 2.577 * [taylor]: Taking taylor expansion of 0 in k 2.577 * [backup-simplify]: Simplify 0 into 0 2.577 * [backup-simplify]: Simplify 0 into 0 2.578 * [backup-simplify]: Simplify 0 into 0 2.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.582 * [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 2.584 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.585 * [backup-simplify]: Simplify (+ 0 0) into 0 2.585 * [backup-simplify]: Simplify (- 0) into 0 2.586 * [backup-simplify]: Simplify (+ 0 0) into 0 2.588 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.591 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.593 * [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))))) 2.603 * [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))))) 2.609 * [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)))))) 2.609 * [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)))) 2.609 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.609 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.609 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.609 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.609 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.609 * [taylor]: Taking taylor expansion of 0.25 in k 2.609 * [backup-simplify]: Simplify 0.25 into 0.25 2.609 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.609 * [taylor]: Taking taylor expansion of 1.0 in k 2.609 * [backup-simplify]: Simplify 1.0 into 1.0 2.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.609 * [taylor]: Taking taylor expansion of k in k 2.609 * [backup-simplify]: Simplify 0 into 0 2.610 * [backup-simplify]: Simplify 1 into 1 2.610 * [backup-simplify]: Simplify (/ 1 1) into 1 2.610 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.610 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.610 * [taylor]: Taking taylor expansion of 2.0 in k 2.610 * [backup-simplify]: Simplify 2.0 into 2.0 2.610 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.610 * [taylor]: Taking taylor expansion of PI in k 2.610 * [backup-simplify]: Simplify PI into PI 2.610 * [taylor]: Taking taylor expansion of n in k 2.610 * [backup-simplify]: Simplify n into n 2.610 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.610 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.610 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.610 * [backup-simplify]: Simplify (- 1) into -1 2.611 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.611 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.611 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.611 * [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))))) 2.611 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.611 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.611 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.611 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.611 * [taylor]: Taking taylor expansion of 0.25 in n 2.611 * [backup-simplify]: Simplify 0.25 into 0.25 2.611 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.611 * [taylor]: Taking taylor expansion of 1.0 in n 2.611 * [backup-simplify]: Simplify 1.0 into 1.0 2.611 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.611 * [taylor]: Taking taylor expansion of k in n 2.611 * [backup-simplify]: Simplify k into k 2.611 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.611 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.611 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.611 * [taylor]: Taking taylor expansion of 2.0 in n 2.611 * [backup-simplify]: Simplify 2.0 into 2.0 2.611 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.611 * [taylor]: Taking taylor expansion of PI in n 2.611 * [backup-simplify]: Simplify PI into PI 2.612 * [taylor]: Taking taylor expansion of n in n 2.612 * [backup-simplify]: Simplify 0 into 0 2.612 * [backup-simplify]: Simplify 1 into 1 2.612 * [backup-simplify]: Simplify (/ PI 1) into PI 2.612 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.613 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.613 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.613 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.613 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.614 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.615 * [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)))) 2.615 * [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))))) 2.615 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.615 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.615 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.615 * [taylor]: Taking taylor expansion of 0.25 in n 2.615 * [backup-simplify]: Simplify 0.25 into 0.25 2.615 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.615 * [taylor]: Taking taylor expansion of 1.0 in n 2.616 * [backup-simplify]: Simplify 1.0 into 1.0 2.616 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.616 * [taylor]: Taking taylor expansion of k in n 2.616 * [backup-simplify]: Simplify k into k 2.616 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.616 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.616 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.616 * [taylor]: Taking taylor expansion of 2.0 in n 2.616 * [backup-simplify]: Simplify 2.0 into 2.0 2.616 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.616 * [taylor]: Taking taylor expansion of PI in n 2.616 * [backup-simplify]: Simplify PI into PI 2.616 * [taylor]: Taking taylor expansion of n in n 2.616 * [backup-simplify]: Simplify 0 into 0 2.616 * [backup-simplify]: Simplify 1 into 1 2.616 * [backup-simplify]: Simplify (/ PI 1) into PI 2.616 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.617 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.617 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.617 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.617 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.619 * [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)))) 2.620 * [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))))) 2.620 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.620 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.620 * [taylor]: Taking taylor expansion of 0.25 in k 2.620 * [backup-simplify]: Simplify 0.25 into 0.25 2.620 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.620 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.620 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.620 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.620 * [taylor]: Taking taylor expansion of 2.0 in k 2.620 * [backup-simplify]: Simplify 2.0 into 2.0 2.620 * [taylor]: Taking taylor expansion of PI in k 2.620 * [backup-simplify]: Simplify PI into PI 2.620 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.621 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.621 * [taylor]: Taking taylor expansion of (log n) in k 2.621 * [taylor]: Taking taylor expansion of n in k 2.621 * [backup-simplify]: Simplify n into n 2.621 * [backup-simplify]: Simplify (log n) into (log n) 2.621 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.621 * [taylor]: Taking taylor expansion of 1.0 in k 2.621 * [backup-simplify]: Simplify 1.0 into 1.0 2.621 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.621 * [taylor]: Taking taylor expansion of k in k 2.621 * [backup-simplify]: Simplify 0 into 0 2.621 * [backup-simplify]: Simplify 1 into 1 2.621 * [backup-simplify]: Simplify (/ 1 1) into 1 2.621 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.622 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.622 * [backup-simplify]: Simplify (- 1) into -1 2.623 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.623 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.624 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.625 * [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))))) 2.625 * [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))))) 2.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.626 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.628 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.628 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.628 * [backup-simplify]: Simplify (- 0) into 0 2.629 * [backup-simplify]: Simplify (+ 0 0) into 0 2.630 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.631 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.633 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.635 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.635 * [taylor]: Taking taylor expansion of 0 in k 2.635 * [backup-simplify]: Simplify 0 into 0 2.635 * [backup-simplify]: Simplify 0 into 0 2.635 * [backup-simplify]: Simplify 0 into 0 2.635 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.636 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.638 * [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 2.638 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.638 * [backup-simplify]: Simplify (- 0) into 0 2.639 * [backup-simplify]: Simplify (+ 0 0) into 0 2.639 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.641 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.642 * [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 2.642 * [taylor]: Taking taylor expansion of 0 in k 2.643 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify 0 into 0 2.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.644 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.647 * [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 2.647 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.648 * [backup-simplify]: Simplify (- 0) into 0 2.648 * [backup-simplify]: Simplify (+ 0 0) into 0 2.649 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.651 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.653 * [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 2.653 * [taylor]: Taking taylor expansion of 0 in k 2.653 * [backup-simplify]: Simplify 0 into 0 2.653 * [backup-simplify]: Simplify 0 into 0 2.654 * [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)))) 2.655 * [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))) 2.655 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.655 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.655 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.655 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.655 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.655 * [taylor]: Taking taylor expansion of 0.25 in k 2.655 * [backup-simplify]: Simplify 0.25 into 0.25 2.655 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.655 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.655 * [taylor]: Taking taylor expansion of k in k 2.655 * [backup-simplify]: Simplify 0 into 0 2.655 * [backup-simplify]: Simplify 1 into 1 2.655 * [backup-simplify]: Simplify (/ 1 1) into 1 2.655 * [taylor]: Taking taylor expansion of 1.0 in k 2.655 * [backup-simplify]: Simplify 1.0 into 1.0 2.655 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.655 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.655 * [taylor]: Taking taylor expansion of -2.0 in k 2.655 * [backup-simplify]: Simplify -2.0 into -2.0 2.655 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.655 * [taylor]: Taking taylor expansion of PI in k 2.655 * [backup-simplify]: Simplify PI into PI 2.655 * [taylor]: Taking taylor expansion of n in k 2.655 * [backup-simplify]: Simplify n into n 2.655 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.655 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.655 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.656 * [backup-simplify]: Simplify (+ 1 0) into 1 2.656 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.656 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.656 * [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)))))) 2.656 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.656 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.656 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.656 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.656 * [taylor]: Taking taylor expansion of 0.25 in n 2.656 * [backup-simplify]: Simplify 0.25 into 0.25 2.656 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.656 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.656 * [taylor]: Taking taylor expansion of k in n 2.656 * [backup-simplify]: Simplify k into k 2.656 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.657 * [taylor]: Taking taylor expansion of 1.0 in n 2.657 * [backup-simplify]: Simplify 1.0 into 1.0 2.657 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.657 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.657 * [taylor]: Taking taylor expansion of -2.0 in n 2.657 * [backup-simplify]: Simplify -2.0 into -2.0 2.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.657 * [taylor]: Taking taylor expansion of PI in n 2.657 * [backup-simplify]: Simplify PI into PI 2.657 * [taylor]: Taking taylor expansion of n in n 2.657 * [backup-simplify]: Simplify 0 into 0 2.657 * [backup-simplify]: Simplify 1 into 1 2.657 * [backup-simplify]: Simplify (/ PI 1) into PI 2.657 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.658 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.658 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.658 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.659 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.660 * [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)))) 2.661 * [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))))) 2.661 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.661 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.661 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.661 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.661 * [taylor]: Taking taylor expansion of 0.25 in n 2.661 * [backup-simplify]: Simplify 0.25 into 0.25 2.661 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.661 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.661 * [taylor]: Taking taylor expansion of k in n 2.661 * [backup-simplify]: Simplify k into k 2.661 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.661 * [taylor]: Taking taylor expansion of 1.0 in n 2.661 * [backup-simplify]: Simplify 1.0 into 1.0 2.661 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.661 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.661 * [taylor]: Taking taylor expansion of -2.0 in n 2.661 * [backup-simplify]: Simplify -2.0 into -2.0 2.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.661 * [taylor]: Taking taylor expansion of PI in n 2.661 * [backup-simplify]: Simplify PI into PI 2.661 * [taylor]: Taking taylor expansion of n in n 2.661 * [backup-simplify]: Simplify 0 into 0 2.661 * [backup-simplify]: Simplify 1 into 1 2.661 * [backup-simplify]: Simplify (/ PI 1) into PI 2.662 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.662 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.662 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.663 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.664 * [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)))) 2.665 * [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))))) 2.665 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.665 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.665 * [taylor]: Taking taylor expansion of 0.25 in k 2.665 * [backup-simplify]: Simplify 0.25 into 0.25 2.665 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.665 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.665 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.665 * [taylor]: Taking taylor expansion of k in k 2.665 * [backup-simplify]: Simplify 0 into 0 2.665 * [backup-simplify]: Simplify 1 into 1 2.665 * [backup-simplify]: Simplify (/ 1 1) into 1 2.665 * [taylor]: Taking taylor expansion of 1.0 in k 2.665 * [backup-simplify]: Simplify 1.0 into 1.0 2.665 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.665 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.665 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.665 * [taylor]: Taking taylor expansion of -2.0 in k 2.666 * [backup-simplify]: Simplify -2.0 into -2.0 2.666 * [taylor]: Taking taylor expansion of PI in k 2.666 * [backup-simplify]: Simplify PI into PI 2.666 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.666 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.666 * [taylor]: Taking taylor expansion of (log n) in k 2.667 * [taylor]: Taking taylor expansion of n in k 2.667 * [backup-simplify]: Simplify n into n 2.667 * [backup-simplify]: Simplify (log n) into (log n) 2.667 * [backup-simplify]: Simplify (+ 1 0) into 1 2.667 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.668 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.669 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.670 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.672 * [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))))) 2.673 * [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))))) 2.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.675 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.677 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.677 * [backup-simplify]: Simplify (+ 0 0) into 0 2.678 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.680 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.682 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.682 * [taylor]: Taking taylor expansion of 0 in k 2.682 * [backup-simplify]: Simplify 0 into 0 2.682 * [backup-simplify]: Simplify 0 into 0 2.682 * [backup-simplify]: Simplify 0 into 0 2.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.684 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.688 * [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 2.688 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.689 * [backup-simplify]: Simplify (+ 0 0) into 0 2.690 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.691 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.693 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.696 * [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 2.696 * [taylor]: Taking taylor expansion of 0 in k 2.696 * [backup-simplify]: Simplify 0 into 0 2.696 * [backup-simplify]: Simplify 0 into 0 2.696 * [backup-simplify]: Simplify 0 into 0 2.696 * [backup-simplify]: Simplify 0 into 0 2.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.698 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.705 * [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 2.705 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.705 * [backup-simplify]: Simplify (+ 0 0) into 0 2.707 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.708 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.711 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.718 * [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 2.718 * [taylor]: Taking taylor expansion of 0 in k 2.718 * [backup-simplify]: Simplify 0 into 0 2.718 * [backup-simplify]: Simplify 0 into 0 2.719 * [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)))))) 2.719 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 2.719 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.720 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.720 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.720 * [taylor]: Taking taylor expansion of 2.0 in n 2.720 * [backup-simplify]: Simplify 2.0 into 2.0 2.720 * [taylor]: Taking taylor expansion of (* n PI) in n 2.720 * [taylor]: Taking taylor expansion of n in n 2.720 * [backup-simplify]: Simplify 0 into 0 2.720 * [backup-simplify]: Simplify 1 into 1 2.720 * [taylor]: Taking taylor expansion of PI in n 2.720 * [backup-simplify]: Simplify PI into PI 2.720 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.720 * [taylor]: Taking taylor expansion of 2.0 in n 2.720 * [backup-simplify]: Simplify 2.0 into 2.0 2.720 * [taylor]: Taking taylor expansion of (* n PI) in n 2.720 * [taylor]: Taking taylor expansion of n in n 2.720 * [backup-simplify]: Simplify 0 into 0 2.720 * [backup-simplify]: Simplify 1 into 1 2.720 * [taylor]: Taking taylor expansion of PI in n 2.720 * [backup-simplify]: Simplify PI into PI 2.720 * [backup-simplify]: Simplify (* 0 PI) into 0 2.720 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.721 * [backup-simplify]: Simplify 0 into 0 2.721 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.722 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.723 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.723 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.724 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.724 * [backup-simplify]: Simplify 0 into 0 2.725 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.725 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.725 * [backup-simplify]: Simplify 0 into 0 2.726 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.727 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.727 * [backup-simplify]: Simplify 0 into 0 2.728 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.729 * [backup-simplify]: Simplify 0 into 0 2.729 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.730 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.730 * [backup-simplify]: Simplify 0 into 0 2.731 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.733 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.733 * [backup-simplify]: Simplify 0 into 0 2.733 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.733 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.733 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.733 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.733 * [taylor]: Taking taylor expansion of 2.0 in n 2.733 * [backup-simplify]: Simplify 2.0 into 2.0 2.733 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.733 * [taylor]: Taking taylor expansion of PI in n 2.733 * [backup-simplify]: Simplify PI into PI 2.733 * [taylor]: Taking taylor expansion of n in n 2.733 * [backup-simplify]: Simplify 0 into 0 2.733 * [backup-simplify]: Simplify 1 into 1 2.734 * [backup-simplify]: Simplify (/ PI 1) into PI 2.734 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.734 * [taylor]: Taking taylor expansion of 2.0 in n 2.734 * [backup-simplify]: Simplify 2.0 into 2.0 2.734 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.734 * [taylor]: Taking taylor expansion of PI in n 2.734 * [backup-simplify]: Simplify PI into PI 2.734 * [taylor]: Taking taylor expansion of n in n 2.734 * [backup-simplify]: Simplify 0 into 0 2.734 * [backup-simplify]: Simplify 1 into 1 2.734 * [backup-simplify]: Simplify (/ PI 1) into PI 2.735 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.735 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.736 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.737 * [backup-simplify]: Simplify 0 into 0 2.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.738 * [backup-simplify]: Simplify 0 into 0 2.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.740 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.740 * [backup-simplify]: Simplify 0 into 0 2.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.742 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.742 * [backup-simplify]: Simplify 0 into 0 2.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.743 * [backup-simplify]: Simplify 0 into 0 2.743 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.744 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.744 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.744 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.744 * [taylor]: Taking taylor expansion of -2.0 in n 2.744 * [backup-simplify]: Simplify -2.0 into -2.0 2.744 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.744 * [taylor]: Taking taylor expansion of PI in n 2.744 * [backup-simplify]: Simplify PI into PI 2.744 * [taylor]: Taking taylor expansion of n in n 2.744 * [backup-simplify]: Simplify 0 into 0 2.744 * [backup-simplify]: Simplify 1 into 1 2.744 * [backup-simplify]: Simplify (/ PI 1) into PI 2.744 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.744 * [taylor]: Taking taylor expansion of -2.0 in n 2.744 * [backup-simplify]: Simplify -2.0 into -2.0 2.744 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.744 * [taylor]: Taking taylor expansion of PI in n 2.744 * [backup-simplify]: Simplify PI into PI 2.744 * [taylor]: Taking taylor expansion of n in n 2.744 * [backup-simplify]: Simplify 0 into 0 2.745 * [backup-simplify]: Simplify 1 into 1 2.745 * [backup-simplify]: Simplify (/ PI 1) into PI 2.745 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.745 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.746 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.746 * [backup-simplify]: Simplify 0 into 0 2.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.748 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.748 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.751 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.751 * [backup-simplify]: Simplify 0 into 0 2.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.753 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.753 * [backup-simplify]: Simplify 0 into 0 2.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.756 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.756 * [backup-simplify]: Simplify 0 into 0 2.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.759 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.759 * [backup-simplify]: Simplify 0 into 0 2.760 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.760 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 2.760 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.760 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.760 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.760 * [taylor]: Taking taylor expansion of 2.0 in n 2.760 * [backup-simplify]: Simplify 2.0 into 2.0 2.760 * [taylor]: Taking taylor expansion of (* n PI) in n 2.761 * [taylor]: Taking taylor expansion of n in n 2.761 * [backup-simplify]: Simplify 0 into 0 2.761 * [backup-simplify]: Simplify 1 into 1 2.761 * [taylor]: Taking taylor expansion of PI in n 2.761 * [backup-simplify]: Simplify PI into PI 2.761 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.761 * [taylor]: Taking taylor expansion of 2.0 in n 2.761 * [backup-simplify]: Simplify 2.0 into 2.0 2.761 * [taylor]: Taking taylor expansion of (* n PI) in n 2.761 * [taylor]: Taking taylor expansion of n in n 2.761 * [backup-simplify]: Simplify 0 into 0 2.761 * [backup-simplify]: Simplify 1 into 1 2.761 * [taylor]: Taking taylor expansion of PI in n 2.761 * [backup-simplify]: Simplify PI into PI 2.761 * [backup-simplify]: Simplify (* 0 PI) into 0 2.762 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.762 * [backup-simplify]: Simplify 0 into 0 2.763 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.765 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.766 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.767 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.768 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.768 * [backup-simplify]: Simplify 0 into 0 2.770 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.771 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.771 * [backup-simplify]: Simplify 0 into 0 2.772 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.774 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.774 * [backup-simplify]: Simplify 0 into 0 2.775 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.776 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.776 * [backup-simplify]: Simplify 0 into 0 2.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.778 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.778 * [backup-simplify]: Simplify 0 into 0 2.779 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.780 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.780 * [backup-simplify]: Simplify 0 into 0 2.780 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.781 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.781 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.781 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.781 * [taylor]: Taking taylor expansion of 2.0 in n 2.781 * [backup-simplify]: Simplify 2.0 into 2.0 2.781 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.781 * [taylor]: Taking taylor expansion of PI in n 2.781 * [backup-simplify]: Simplify PI into PI 2.781 * [taylor]: Taking taylor expansion of n in n 2.781 * [backup-simplify]: Simplify 0 into 0 2.781 * [backup-simplify]: Simplify 1 into 1 2.781 * [backup-simplify]: Simplify (/ PI 1) into PI 2.781 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.781 * [taylor]: Taking taylor expansion of 2.0 in n 2.781 * [backup-simplify]: Simplify 2.0 into 2.0 2.781 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.781 * [taylor]: Taking taylor expansion of PI in n 2.781 * [backup-simplify]: Simplify PI into PI 2.781 * [taylor]: Taking taylor expansion of n in n 2.781 * [backup-simplify]: Simplify 0 into 0 2.781 * [backup-simplify]: Simplify 1 into 1 2.782 * [backup-simplify]: Simplify (/ PI 1) into PI 2.782 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.782 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.783 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.783 * [backup-simplify]: Simplify 0 into 0 2.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.785 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.785 * [backup-simplify]: Simplify 0 into 0 2.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.786 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.786 * [backup-simplify]: Simplify 0 into 0 2.787 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.787 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.787 * [backup-simplify]: Simplify 0 into 0 2.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.789 * [backup-simplify]: Simplify 0 into 0 2.789 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.791 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.791 * [backup-simplify]: Simplify 0 into 0 2.791 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.791 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.792 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.792 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.792 * [taylor]: Taking taylor expansion of -2.0 in n 2.792 * [backup-simplify]: Simplify -2.0 into -2.0 2.792 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.792 * [taylor]: Taking taylor expansion of PI in n 2.792 * [backup-simplify]: Simplify PI into PI 2.792 * [taylor]: Taking taylor expansion of n in n 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [backup-simplify]: Simplify (/ PI 1) into PI 2.792 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.792 * [taylor]: Taking taylor expansion of -2.0 in n 2.792 * [backup-simplify]: Simplify -2.0 into -2.0 2.792 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.792 * [taylor]: Taking taylor expansion of PI in n 2.792 * [backup-simplify]: Simplify PI into PI 2.792 * [taylor]: Taking taylor expansion of n in n 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [backup-simplify]: Simplify (/ PI 1) into PI 2.793 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.793 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.794 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.795 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.795 * [backup-simplify]: Simplify 0 into 0 2.796 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.797 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.797 * [backup-simplify]: Simplify 0 into 0 2.798 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.798 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.798 * [backup-simplify]: Simplify 0 into 0 2.799 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.801 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.801 * [backup-simplify]: Simplify 0 into 0 2.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.804 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.804 * [backup-simplify]: Simplify 0 into 0 2.804 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.804 * * * [progress]: simplifying candidates 2.810 * [simplify]: Simplifying: (* (+ (+ (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) 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h3) (/ (sqrt (/ (- h2 h1) h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (sqrt (/ (- h2 h1) h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (* (cbrt (- h2 h1)) (cbrt (- h2 h1))) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (sqrt (- h2 h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ (+ (sqrt h2) (sqrt h1)) 1) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (* (cbrt h0) (cbrt h0))) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 (sqrt h0)) 1)) (pow (* (* h0 h4) h3) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (/ 1 1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (/ 1 1) 1)) (pow (* (* h0 h4) h3) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ 1 (sqrt 2))) (pow (* (* h0 h4) h3) (/ 1 1)) (pow (* (* h0 h4) h3) (/ (- h2 h1) (* (cbrt 2) (cbrt 2)))) (pow (* (* h0 h4) h3) (/ (- h2 h1) (sqrt 2))) (pow (* (* h0 h4) h3) (/ (- h2 h1) 1)) (pow (* (* h0 h4) h3) 1) (pow (* (* h0 h4) h3) (/ (- h2 h1) h0)) (pow (* h0 h4) (/ (/ (- h2 h1) h0) 2)) (pow h3 (/ (/ (- h2 h1) h0) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (exp (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2)) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (- h2 h1) h0) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (* (* h0 h4) h3) (* (* h0 h4) h3) (+ (+ (log h0) (log h4)) (log h3)) (+ (log (* h0 h4)) (log h3)) (log (* (* h0 h4) h3)) (exp (* (* h0 h4) h3)) (* (* (* (* h0 h0) h0) (* (* h4 h4) h4)) (* (* h3 h3) h3)) (* (* (* (* h0 h4) (* h0 h4)) (* h0 h4)) (* (* h3 h3) h3)) (* (cbrt (* (* h0 h4) h3)) (cbrt (* (* h0 h4) h3))) (cbrt (* (* h0 h4) h3)) (* (* (* (* h0 h4) h3) (* (* h0 h4) h3)) (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (sqrt (* (* h0 h4) h3)) (* (* h0 h4) (* (cbrt h3) (cbrt h3))) (* (* h0 h4) (sqrt h3)) (* (* h0 h4) 1) (* h4 h3) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) 2.884 * * * [progress]: adding candidates to table 4.003 * * [progress]: iteration 3 / 4 4.003 * * * [progress]: picking best candidate 4.027 * * * * [pick]: Picked # 4.027 * * * [progress]: localizing error 4.075 * * * [progress]: generating rewritten candidates 4.075 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 4.111 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2) 4.170 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1) 4.224 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2) 4.358 * * * [progress]: generating series expansions 4.358 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 4.359 * [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))) 4.359 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 4.359 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 4.359 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.359 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.359 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 4.359 * [taylor]: Taking taylor expansion of 0.25 in k 4.359 * [backup-simplify]: Simplify 0.25 into 0.25 4.359 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.359 * [taylor]: Taking taylor expansion of 1.0 in k 4.359 * [backup-simplify]: Simplify 1.0 into 1.0 4.359 * [taylor]: Taking taylor expansion of k in k 4.359 * [backup-simplify]: Simplify 0 into 0 4.359 * [backup-simplify]: Simplify 1 into 1 4.359 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.359 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.359 * [taylor]: Taking taylor expansion of 2.0 in k 4.359 * [backup-simplify]: Simplify 2.0 into 2.0 4.359 * [taylor]: Taking taylor expansion of (* n PI) in k 4.359 * [taylor]: Taking taylor expansion of n in k 4.359 * [backup-simplify]: Simplify n into n 4.359 * [taylor]: Taking taylor expansion of PI in k 4.359 * [backup-simplify]: Simplify PI into PI 4.359 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.359 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.359 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.359 * [backup-simplify]: Simplify (- 0) into 0 4.360 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.360 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 4.360 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 4.360 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 4.360 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.360 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.360 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.360 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.360 * [taylor]: Taking taylor expansion of 0.25 in n 4.360 * [backup-simplify]: Simplify 0.25 into 0.25 4.360 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.360 * [taylor]: Taking taylor expansion of 1.0 in n 4.361 * [backup-simplify]: Simplify 1.0 into 1.0 4.361 * [taylor]: Taking taylor expansion of k in n 4.361 * [backup-simplify]: Simplify k into k 4.361 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.361 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.361 * [taylor]: Taking taylor expansion of 2.0 in n 4.361 * [backup-simplify]: Simplify 2.0 into 2.0 4.361 * [taylor]: Taking taylor expansion of (* n PI) in n 4.361 * [taylor]: Taking taylor expansion of n in n 4.361 * [backup-simplify]: Simplify 0 into 0 4.361 * [backup-simplify]: Simplify 1 into 1 4.361 * [taylor]: Taking taylor expansion of PI in n 4.361 * [backup-simplify]: Simplify PI into PI 4.361 * [backup-simplify]: Simplify (* 0 PI) into 0 4.361 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.363 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.364 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.364 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.364 * [backup-simplify]: Simplify (- k) into (- k) 4.364 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.364 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.365 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.366 * [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)))) 4.367 * [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))))) 4.367 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 4.367 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.367 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.367 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 4.367 * [taylor]: Taking taylor expansion of 0.25 in n 4.367 * [backup-simplify]: Simplify 0.25 into 0.25 4.367 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.367 * [taylor]: Taking taylor expansion of 1.0 in n 4.367 * [backup-simplify]: Simplify 1.0 into 1.0 4.367 * [taylor]: Taking taylor expansion of k in n 4.367 * [backup-simplify]: Simplify k into k 4.367 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.367 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.367 * [taylor]: Taking taylor expansion of 2.0 in n 4.367 * [backup-simplify]: Simplify 2.0 into 2.0 4.367 * [taylor]: Taking taylor expansion of (* n PI) in n 4.367 * [taylor]: Taking taylor expansion of n in n 4.367 * [backup-simplify]: Simplify 0 into 0 4.367 * [backup-simplify]: Simplify 1 into 1 4.367 * [taylor]: Taking taylor expansion of PI in n 4.367 * [backup-simplify]: Simplify PI into PI 4.367 * [backup-simplify]: Simplify (* 0 PI) into 0 4.368 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.369 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.370 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.370 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.370 * [backup-simplify]: Simplify (- k) into (- k) 4.370 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.370 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 4.371 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.372 * [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)))) 4.373 * [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))))) 4.373 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.373 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.373 * [taylor]: Taking taylor expansion of 0.25 in k 4.373 * [backup-simplify]: Simplify 0.25 into 0.25 4.373 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.373 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.373 * [taylor]: Taking taylor expansion of 1.0 in k 4.373 * [backup-simplify]: Simplify 1.0 into 1.0 4.373 * [taylor]: Taking taylor expansion of k in k 4.373 * [backup-simplify]: Simplify 0 into 0 4.373 * [backup-simplify]: Simplify 1 into 1 4.373 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.373 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.373 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.373 * [taylor]: Taking taylor expansion of 2.0 in k 4.373 * [backup-simplify]: Simplify 2.0 into 2.0 4.373 * [taylor]: Taking taylor expansion of PI in k 4.373 * [backup-simplify]: Simplify PI into PI 4.373 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.374 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.374 * [taylor]: Taking taylor expansion of (log n) in k 4.374 * [taylor]: Taking taylor expansion of n in k 4.374 * [backup-simplify]: Simplify n into n 4.374 * [backup-simplify]: Simplify (log n) into (log n) 4.374 * [backup-simplify]: Simplify (- 0) into 0 4.375 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.375 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.376 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.377 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 4.377 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.378 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 4.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.379 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.380 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.381 * [backup-simplify]: Simplify (- 0) into 0 4.381 * [backup-simplify]: Simplify (+ 0 0) into 0 4.381 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 4.382 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.383 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.385 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.385 * [taylor]: Taking taylor expansion of 0 in k 4.385 * [backup-simplify]: Simplify 0 into 0 4.385 * [backup-simplify]: Simplify 0 into 0 4.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.388 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.389 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.389 * [backup-simplify]: Simplify (+ 0 0) into 0 4.390 * [backup-simplify]: Simplify (- 1) into -1 4.390 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.392 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.394 * [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)))) 4.396 * [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)))))) 4.398 * [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)))))) 4.408 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.409 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.411 * [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 4.412 * [backup-simplify]: Simplify (- 0) into 0 4.412 * [backup-simplify]: Simplify (+ 0 0) into 0 4.413 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.414 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.414 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.416 * [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 4.416 * [taylor]: Taking taylor expansion of 0 in k 4.416 * [backup-simplify]: Simplify 0 into 0 4.416 * [backup-simplify]: Simplify 0 into 0 4.416 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.419 * [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 4.421 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.421 * [backup-simplify]: Simplify (+ 0 0) into 0 4.422 * [backup-simplify]: Simplify (- 0) into 0 4.422 * [backup-simplify]: Simplify (+ 0 0) into 0 4.424 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.427 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.431 * [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))))) 4.437 * [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))))) 4.444 * [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)))))) 4.445 * [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)))) 4.445 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 4.445 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 4.445 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.445 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.445 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 4.445 * [taylor]: Taking taylor expansion of 0.25 in k 4.445 * [backup-simplify]: Simplify 0.25 into 0.25 4.445 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.445 * [taylor]: Taking taylor expansion of 1.0 in k 4.445 * [backup-simplify]: Simplify 1.0 into 1.0 4.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.445 * [taylor]: Taking taylor expansion of k in k 4.445 * [backup-simplify]: Simplify 0 into 0 4.445 * [backup-simplify]: Simplify 1 into 1 4.445 * [backup-simplify]: Simplify (/ 1 1) into 1 4.445 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.445 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.445 * [taylor]: Taking taylor expansion of 2.0 in k 4.445 * [backup-simplify]: Simplify 2.0 into 2.0 4.445 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.445 * [taylor]: Taking taylor expansion of PI in k 4.445 * [backup-simplify]: Simplify PI into PI 4.445 * [taylor]: Taking taylor expansion of n in k 4.445 * [backup-simplify]: Simplify n into n 4.445 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.445 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.445 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.446 * [backup-simplify]: Simplify (- 1) into -1 4.446 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.446 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 4.446 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 4.446 * [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))))) 4.446 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.446 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.446 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.446 * [taylor]: Taking taylor expansion of 0.25 in n 4.447 * [backup-simplify]: Simplify 0.25 into 0.25 4.447 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.447 * [taylor]: Taking taylor expansion of 1.0 in n 4.447 * [backup-simplify]: Simplify 1.0 into 1.0 4.447 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.447 * [taylor]: Taking taylor expansion of k in n 4.447 * [backup-simplify]: Simplify k into k 4.447 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.447 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.447 * [taylor]: Taking taylor expansion of 2.0 in n 4.447 * [backup-simplify]: Simplify 2.0 into 2.0 4.447 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.447 * [taylor]: Taking taylor expansion of PI in n 4.447 * [backup-simplify]: Simplify PI into PI 4.447 * [taylor]: Taking taylor expansion of n in n 4.447 * [backup-simplify]: Simplify 0 into 0 4.447 * [backup-simplify]: Simplify 1 into 1 4.447 * [backup-simplify]: Simplify (/ PI 1) into PI 4.447 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.448 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.448 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.448 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.448 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.449 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.450 * [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)))) 4.451 * [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))))) 4.451 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 4.451 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.451 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.451 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 4.451 * [taylor]: Taking taylor expansion of 0.25 in n 4.451 * [backup-simplify]: Simplify 0.25 into 0.25 4.451 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.451 * [taylor]: Taking taylor expansion of 1.0 in n 4.451 * [backup-simplify]: Simplify 1.0 into 1.0 4.451 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.451 * [taylor]: Taking taylor expansion of k in n 4.451 * [backup-simplify]: Simplify k into k 4.451 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.451 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.451 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.451 * [taylor]: Taking taylor expansion of 2.0 in n 4.451 * [backup-simplify]: Simplify 2.0 into 2.0 4.451 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.451 * [taylor]: Taking taylor expansion of PI in n 4.451 * [backup-simplify]: Simplify PI into PI 4.451 * [taylor]: Taking taylor expansion of n in n 4.451 * [backup-simplify]: Simplify 0 into 0 4.451 * [backup-simplify]: Simplify 1 into 1 4.452 * [backup-simplify]: Simplify (/ PI 1) into PI 4.452 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.452 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.453 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.453 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.453 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 4.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.454 * [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)))) 4.455 * [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))))) 4.455 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.455 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.455 * [taylor]: Taking taylor expansion of 0.25 in k 4.455 * [backup-simplify]: Simplify 0.25 into 0.25 4.455 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.455 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.455 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.455 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.455 * [taylor]: Taking taylor expansion of 2.0 in k 4.455 * [backup-simplify]: Simplify 2.0 into 2.0 4.455 * [taylor]: Taking taylor expansion of PI in k 4.455 * [backup-simplify]: Simplify PI into PI 4.456 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.456 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.456 * [taylor]: Taking taylor expansion of (log n) in k 4.456 * [taylor]: Taking taylor expansion of n in k 4.456 * [backup-simplify]: Simplify n into n 4.456 * [backup-simplify]: Simplify (log n) into (log n) 4.456 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.456 * [taylor]: Taking taylor expansion of 1.0 in k 4.456 * [backup-simplify]: Simplify 1.0 into 1.0 4.456 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.457 * [taylor]: Taking taylor expansion of k in k 4.457 * [backup-simplify]: Simplify 0 into 0 4.457 * [backup-simplify]: Simplify 1 into 1 4.457 * [backup-simplify]: Simplify (/ 1 1) into 1 4.457 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.457 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.458 * [backup-simplify]: Simplify (- 1) into -1 4.458 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.459 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.459 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 4.460 * [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))))) 4.461 * [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))))) 4.462 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.463 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.463 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.463 * [backup-simplify]: Simplify (- 0) into 0 4.464 * [backup-simplify]: Simplify (+ 0 0) into 0 4.464 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.465 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.465 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.467 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.467 * [taylor]: Taking taylor expansion of 0 in k 4.467 * [backup-simplify]: Simplify 0 into 0 4.467 * [backup-simplify]: Simplify 0 into 0 4.467 * [backup-simplify]: Simplify 0 into 0 4.468 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.470 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.473 * [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 4.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.474 * [backup-simplify]: Simplify (- 0) into 0 4.475 * [backup-simplify]: Simplify (+ 0 0) into 0 4.476 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.477 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.479 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.481 * [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 4.482 * [taylor]: Taking taylor expansion of 0 in k 4.482 * [backup-simplify]: Simplify 0 into 0 4.482 * [backup-simplify]: Simplify 0 into 0 4.482 * [backup-simplify]: Simplify 0 into 0 4.482 * [backup-simplify]: Simplify 0 into 0 4.483 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.484 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.490 * [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 4.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.491 * [backup-simplify]: Simplify (- 0) into 0 4.491 * [backup-simplify]: Simplify (+ 0 0) into 0 4.492 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.494 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.496 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.499 * [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 4.499 * [taylor]: Taking taylor expansion of 0 in k 4.499 * [backup-simplify]: Simplify 0 into 0 4.499 * [backup-simplify]: Simplify 0 into 0 4.500 * [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)))) 4.501 * [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))) 4.501 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 4.501 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 4.501 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.501 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.501 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 4.501 * [taylor]: Taking taylor expansion of 0.25 in k 4.501 * [backup-simplify]: Simplify 0.25 into 0.25 4.501 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.501 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.502 * [taylor]: Taking taylor expansion of k in k 4.502 * [backup-simplify]: Simplify 0 into 0 4.502 * [backup-simplify]: Simplify 1 into 1 4.502 * [backup-simplify]: Simplify (/ 1 1) into 1 4.502 * [taylor]: Taking taylor expansion of 1.0 in k 4.502 * [backup-simplify]: Simplify 1.0 into 1.0 4.502 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.502 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.502 * [taylor]: Taking taylor expansion of -2.0 in k 4.502 * [backup-simplify]: Simplify -2.0 into -2.0 4.502 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.502 * [taylor]: Taking taylor expansion of PI in k 4.502 * [backup-simplify]: Simplify PI into PI 4.502 * [taylor]: Taking taylor expansion of n in k 4.502 * [backup-simplify]: Simplify n into n 4.502 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.502 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.503 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.503 * [backup-simplify]: Simplify (+ 1 0) into 1 4.503 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 4.503 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 4.504 * [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)))))) 4.504 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.504 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.504 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.504 * [taylor]: Taking taylor expansion of 0.25 in n 4.504 * [backup-simplify]: Simplify 0.25 into 0.25 4.504 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.504 * [taylor]: Taking taylor expansion of k in n 4.504 * [backup-simplify]: Simplify k into k 4.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.504 * [taylor]: Taking taylor expansion of 1.0 in n 4.504 * [backup-simplify]: Simplify 1.0 into 1.0 4.504 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.504 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.504 * [taylor]: Taking taylor expansion of -2.0 in n 4.504 * [backup-simplify]: Simplify -2.0 into -2.0 4.504 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.504 * [taylor]: Taking taylor expansion of PI in n 4.504 * [backup-simplify]: Simplify PI into PI 4.504 * [taylor]: Taking taylor expansion of n in n 4.504 * [backup-simplify]: Simplify 0 into 0 4.504 * [backup-simplify]: Simplify 1 into 1 4.505 * [backup-simplify]: Simplify (/ PI 1) into PI 4.505 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.506 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.506 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.507 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.509 * [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)))) 4.510 * [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))))) 4.510 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 4.510 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.511 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.511 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 4.511 * [taylor]: Taking taylor expansion of 0.25 in n 4.511 * [backup-simplify]: Simplify 0.25 into 0.25 4.511 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.511 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.511 * [taylor]: Taking taylor expansion of k in n 4.511 * [backup-simplify]: Simplify k into k 4.511 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.511 * [taylor]: Taking taylor expansion of 1.0 in n 4.511 * [backup-simplify]: Simplify 1.0 into 1.0 4.511 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.511 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.511 * [taylor]: Taking taylor expansion of -2.0 in n 4.511 * [backup-simplify]: Simplify -2.0 into -2.0 4.511 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.511 * [taylor]: Taking taylor expansion of PI in n 4.511 * [backup-simplify]: Simplify PI into PI 4.511 * [taylor]: Taking taylor expansion of n in n 4.511 * [backup-simplify]: Simplify 0 into 0 4.511 * [backup-simplify]: Simplify 1 into 1 4.512 * [backup-simplify]: Simplify (/ PI 1) into PI 4.512 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.513 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.513 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.513 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 4.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.516 * [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)))) 4.517 * [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))))) 4.517 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.517 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.517 * [taylor]: Taking taylor expansion of 0.25 in k 4.517 * [backup-simplify]: Simplify 0.25 into 0.25 4.517 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.517 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.517 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.517 * [taylor]: Taking taylor expansion of k in k 4.517 * [backup-simplify]: Simplify 0 into 0 4.517 * [backup-simplify]: Simplify 1 into 1 4.518 * [backup-simplify]: Simplify (/ 1 1) into 1 4.518 * [taylor]: Taking taylor expansion of 1.0 in k 4.518 * [backup-simplify]: Simplify 1.0 into 1.0 4.518 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.518 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.518 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.518 * [taylor]: Taking taylor expansion of -2.0 in k 4.518 * [backup-simplify]: Simplify -2.0 into -2.0 4.518 * [taylor]: Taking taylor expansion of PI in k 4.518 * [backup-simplify]: Simplify PI into PI 4.519 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.520 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.520 * [taylor]: Taking taylor expansion of (log n) in k 4.520 * [taylor]: Taking taylor expansion of n in k 4.520 * [backup-simplify]: Simplify n into n 4.520 * [backup-simplify]: Simplify (log n) into (log n) 4.520 * [backup-simplify]: Simplify (+ 1 0) into 1 4.520 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.522 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.524 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.525 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 4.526 * [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))))) 4.527 * [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))))) 4.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.529 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.531 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.531 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.532 * [backup-simplify]: Simplify (+ 0 0) into 0 4.532 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.534 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.543 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.545 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.546 * [taylor]: Taking taylor expansion of 0 in k 4.546 * [backup-simplify]: Simplify 0 into 0 4.546 * [backup-simplify]: Simplify 0 into 0 4.546 * [backup-simplify]: Simplify 0 into 0 4.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.548 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.552 * [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 4.552 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.552 * [backup-simplify]: Simplify (+ 0 0) into 0 4.553 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.557 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.560 * [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 4.560 * [taylor]: Taking taylor expansion of 0 in k 4.560 * [backup-simplify]: Simplify 0 into 0 4.560 * [backup-simplify]: Simplify 0 into 0 4.560 * [backup-simplify]: Simplify 0 into 0 4.560 * [backup-simplify]: Simplify 0 into 0 4.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.562 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.569 * [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 4.569 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.570 * [backup-simplify]: Simplify (+ 0 0) into 0 4.571 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.573 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.575 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.578 * [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 4.578 * [taylor]: Taking taylor expansion of 0 in k 4.578 * [backup-simplify]: Simplify 0 into 0 4.578 * [backup-simplify]: Simplify 0 into 0 4.579 * [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)))))) 4.579 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2) 4.580 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.580 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.580 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.580 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.581 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.581 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.581 * [taylor]: Taking taylor expansion of 0.125 in k 4.581 * [backup-simplify]: Simplify 0.125 into 0.125 4.581 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.581 * [taylor]: Taking taylor expansion of 1.0 in k 4.581 * [backup-simplify]: Simplify 1.0 into 1.0 4.581 * [taylor]: Taking taylor expansion of k in k 4.581 * [backup-simplify]: Simplify 0 into 0 4.581 * [backup-simplify]: Simplify 1 into 1 4.581 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.581 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.581 * [taylor]: Taking taylor expansion of 2.0 in k 4.581 * [backup-simplify]: Simplify 2.0 into 2.0 4.581 * [taylor]: Taking taylor expansion of (* n PI) in k 4.581 * [taylor]: Taking taylor expansion of n in k 4.581 * [backup-simplify]: Simplify n into n 4.581 * [taylor]: Taking taylor expansion of PI in k 4.581 * [backup-simplify]: Simplify PI into PI 4.581 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.581 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.581 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.582 * [backup-simplify]: Simplify (- 0) into 0 4.582 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.583 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.583 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.583 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.583 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.583 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.583 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.583 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.583 * [taylor]: Taking taylor expansion of 0.125 in n 4.583 * [backup-simplify]: Simplify 0.125 into 0.125 4.583 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.583 * [taylor]: Taking taylor expansion of 1.0 in n 4.583 * [backup-simplify]: Simplify 1.0 into 1.0 4.583 * [taylor]: Taking taylor expansion of k in n 4.583 * [backup-simplify]: Simplify k into k 4.583 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.583 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.583 * [taylor]: Taking taylor expansion of 2.0 in n 4.583 * [backup-simplify]: Simplify 2.0 into 2.0 4.583 * [taylor]: Taking taylor expansion of (* n PI) in n 4.583 * [taylor]: Taking taylor expansion of n in n 4.583 * [backup-simplify]: Simplify 0 into 0 4.583 * [backup-simplify]: Simplify 1 into 1 4.583 * [taylor]: Taking taylor expansion of PI in n 4.583 * [backup-simplify]: Simplify PI into PI 4.584 * [backup-simplify]: Simplify (* 0 PI) into 0 4.584 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.585 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.586 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.586 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.586 * [backup-simplify]: Simplify (- k) into (- k) 4.586 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.586 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.588 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.589 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.589 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.589 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.589 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.589 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.589 * [taylor]: Taking taylor expansion of 0.125 in n 4.589 * [backup-simplify]: Simplify 0.125 into 0.125 4.589 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.589 * [taylor]: Taking taylor expansion of 1.0 in n 4.589 * [backup-simplify]: Simplify 1.0 into 1.0 4.589 * [taylor]: Taking taylor expansion of k in n 4.589 * [backup-simplify]: Simplify k into k 4.589 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.589 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.589 * [taylor]: Taking taylor expansion of 2.0 in n 4.589 * [backup-simplify]: Simplify 2.0 into 2.0 4.589 * [taylor]: Taking taylor expansion of (* n PI) in n 4.589 * [taylor]: Taking taylor expansion of n in n 4.589 * [backup-simplify]: Simplify 0 into 0 4.589 * [backup-simplify]: Simplify 1 into 1 4.589 * [taylor]: Taking taylor expansion of PI in n 4.589 * [backup-simplify]: Simplify PI into PI 4.589 * [backup-simplify]: Simplify (* 0 PI) into 0 4.590 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.591 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.592 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.593 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.593 * [backup-simplify]: Simplify (- k) into (- k) 4.593 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.593 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.594 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.595 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.595 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.595 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.595 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.595 * [taylor]: Taking taylor expansion of 0.125 in k 4.595 * [backup-simplify]: Simplify 0.125 into 0.125 4.596 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.596 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.596 * [taylor]: Taking taylor expansion of 1.0 in k 4.596 * [backup-simplify]: Simplify 1.0 into 1.0 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 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.596 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.596 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.596 * [taylor]: Taking taylor expansion of 2.0 in k 4.596 * [backup-simplify]: Simplify 2.0 into 2.0 4.596 * [taylor]: Taking taylor expansion of PI in k 4.596 * [backup-simplify]: Simplify PI into PI 4.596 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.597 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.597 * [taylor]: Taking taylor expansion of (log n) in k 4.597 * [taylor]: Taking taylor expansion of n in k 4.597 * [backup-simplify]: Simplify n into n 4.597 * [backup-simplify]: Simplify (log n) into (log n) 4.597 * [backup-simplify]: Simplify (- 0) into 0 4.597 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.598 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.599 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.599 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.600 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.601 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.601 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.602 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.603 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.603 * [backup-simplify]: Simplify (- 0) into 0 4.603 * [backup-simplify]: Simplify (+ 0 0) into 0 4.604 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.604 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.605 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.606 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.606 * [taylor]: Taking taylor expansion of 0 in k 4.606 * [backup-simplify]: Simplify 0 into 0 4.606 * [backup-simplify]: Simplify 0 into 0 4.607 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.608 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.608 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.609 * [backup-simplify]: Simplify (+ 0 0) into 0 4.609 * [backup-simplify]: Simplify (- 1) into -1 4.609 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.610 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.611 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.613 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.615 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.616 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.617 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.619 * [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 4.619 * [backup-simplify]: Simplify (- 0) into 0 4.619 * [backup-simplify]: Simplify (+ 0 0) into 0 4.620 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.622 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.623 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.626 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.626 * [taylor]: Taking taylor expansion of 0 in k 4.626 * [backup-simplify]: Simplify 0 into 0 4.626 * [backup-simplify]: Simplify 0 into 0 4.626 * [backup-simplify]: Simplify 0 into 0 4.627 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.631 * [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 4.633 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.633 * [backup-simplify]: Simplify (+ 0 0) into 0 4.634 * [backup-simplify]: Simplify (- 0) into 0 4.634 * [backup-simplify]: Simplify (+ 0 0) into 0 4.636 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.639 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.644 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.648 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.654 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.655 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.655 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.655 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.655 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.655 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.655 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.655 * [taylor]: Taking taylor expansion of 0.125 in k 4.655 * [backup-simplify]: Simplify 0.125 into 0.125 4.655 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.655 * [taylor]: Taking taylor expansion of 1.0 in k 4.655 * [backup-simplify]: Simplify 1.0 into 1.0 4.655 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.655 * [taylor]: Taking taylor expansion of k in k 4.655 * [backup-simplify]: Simplify 0 into 0 4.655 * [backup-simplify]: Simplify 1 into 1 4.656 * [backup-simplify]: Simplify (/ 1 1) into 1 4.656 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.656 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.656 * [taylor]: Taking taylor expansion of 2.0 in k 4.656 * [backup-simplify]: Simplify 2.0 into 2.0 4.656 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.656 * [taylor]: Taking taylor expansion of PI in k 4.656 * [backup-simplify]: Simplify PI into PI 4.656 * [taylor]: Taking taylor expansion of n in k 4.656 * [backup-simplify]: Simplify n into n 4.656 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.656 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.656 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.656 * [backup-simplify]: Simplify (- 1) into -1 4.657 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.657 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.657 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.657 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.657 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.657 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.657 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.657 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.657 * [taylor]: Taking taylor expansion of 0.125 in n 4.657 * [backup-simplify]: Simplify 0.125 into 0.125 4.657 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.657 * [taylor]: Taking taylor expansion of 1.0 in n 4.657 * [backup-simplify]: Simplify 1.0 into 1.0 4.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.657 * [taylor]: Taking taylor expansion of k in n 4.657 * [backup-simplify]: Simplify k into k 4.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.657 * [taylor]: Taking taylor expansion of 2.0 in n 4.657 * [backup-simplify]: Simplify 2.0 into 2.0 4.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.657 * [taylor]: Taking taylor expansion of PI in n 4.657 * [backup-simplify]: Simplify PI into PI 4.657 * [taylor]: Taking taylor expansion of n in n 4.657 * [backup-simplify]: Simplify 0 into 0 4.657 * [backup-simplify]: Simplify 1 into 1 4.658 * [backup-simplify]: Simplify (/ PI 1) into PI 4.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.659 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.659 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.659 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.659 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.661 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.668 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.668 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.668 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.668 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.668 * [taylor]: Taking taylor expansion of 0.125 in n 4.668 * [backup-simplify]: Simplify 0.125 into 0.125 4.668 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.668 * [taylor]: Taking taylor expansion of 1.0 in n 4.668 * [backup-simplify]: Simplify 1.0 into 1.0 4.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.668 * [taylor]: Taking taylor expansion of k in n 4.668 * [backup-simplify]: Simplify k into k 4.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.668 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.668 * [taylor]: Taking taylor expansion of 2.0 in n 4.668 * [backup-simplify]: Simplify 2.0 into 2.0 4.668 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.668 * [taylor]: Taking taylor expansion of PI in n 4.668 * [backup-simplify]: Simplify PI into PI 4.668 * [taylor]: Taking taylor expansion of n in n 4.668 * [backup-simplify]: Simplify 0 into 0 4.668 * [backup-simplify]: Simplify 1 into 1 4.669 * [backup-simplify]: Simplify (/ PI 1) into PI 4.669 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.670 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.670 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.670 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.670 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.671 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.671 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.672 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.672 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.672 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.672 * [taylor]: Taking taylor expansion of 0.125 in k 4.672 * [backup-simplify]: Simplify 0.125 into 0.125 4.672 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.672 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.672 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.672 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.672 * [taylor]: Taking taylor expansion of 2.0 in k 4.672 * [backup-simplify]: Simplify 2.0 into 2.0 4.672 * [taylor]: Taking taylor expansion of PI in k 4.673 * [backup-simplify]: Simplify PI into PI 4.673 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.673 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.674 * [taylor]: Taking taylor expansion of (log n) in k 4.674 * [taylor]: Taking taylor expansion of n in k 4.674 * [backup-simplify]: Simplify n into n 4.674 * [backup-simplify]: Simplify (log n) into (log n) 4.674 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.674 * [taylor]: Taking taylor expansion of 1.0 in k 4.674 * [backup-simplify]: Simplify 1.0 into 1.0 4.674 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.674 * [taylor]: Taking taylor expansion of k in k 4.674 * [backup-simplify]: Simplify 0 into 0 4.674 * [backup-simplify]: Simplify 1 into 1 4.674 * [backup-simplify]: Simplify (/ 1 1) into 1 4.674 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.675 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.675 * [backup-simplify]: Simplify (- 1) into -1 4.675 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.676 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.676 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.677 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.678 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.680 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.681 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.681 * [backup-simplify]: Simplify (- 0) into 0 4.681 * [backup-simplify]: Simplify (+ 0 0) into 0 4.681 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.683 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.685 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.685 * [taylor]: Taking taylor expansion of 0 in k 4.685 * [backup-simplify]: Simplify 0 into 0 4.685 * [backup-simplify]: Simplify 0 into 0 4.685 * [backup-simplify]: Simplify 0 into 0 4.687 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.691 * [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 4.691 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.692 * [backup-simplify]: Simplify (- 0) into 0 4.692 * [backup-simplify]: Simplify (+ 0 0) into 0 4.693 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.697 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.699 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.700 * [taylor]: Taking taylor expansion of 0 in k 4.700 * [backup-simplify]: Simplify 0 into 0 4.700 * [backup-simplify]: Simplify 0 into 0 4.700 * [backup-simplify]: Simplify 0 into 0 4.700 * [backup-simplify]: Simplify 0 into 0 4.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.708 * [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 4.708 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.709 * [backup-simplify]: Simplify (- 0) into 0 4.709 * [backup-simplify]: Simplify (+ 0 0) into 0 4.711 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.712 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.714 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.717 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (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 4.717 * [taylor]: Taking taylor expansion of 0 in k 4.718 * [backup-simplify]: Simplify 0 into 0 4.718 * [backup-simplify]: Simplify 0 into 0 4.719 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.720 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.720 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.720 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.720 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.720 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.720 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.720 * [taylor]: Taking taylor expansion of 0.125 in k 4.720 * [backup-simplify]: Simplify 0.125 into 0.125 4.720 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.720 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.720 * [taylor]: Taking taylor expansion of k in k 4.720 * [backup-simplify]: Simplify 0 into 0 4.720 * [backup-simplify]: Simplify 1 into 1 4.721 * [backup-simplify]: Simplify (/ 1 1) into 1 4.721 * [taylor]: Taking taylor expansion of 1.0 in k 4.721 * [backup-simplify]: Simplify 1.0 into 1.0 4.721 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.721 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.721 * [taylor]: Taking taylor expansion of -2.0 in k 4.721 * [backup-simplify]: Simplify -2.0 into -2.0 4.721 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.721 * [taylor]: Taking taylor expansion of PI in k 4.721 * [backup-simplify]: Simplify PI into PI 4.721 * [taylor]: Taking taylor expansion of n in k 4.721 * [backup-simplify]: Simplify n into n 4.721 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.721 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.722 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.722 * [backup-simplify]: Simplify (+ 1 0) into 1 4.723 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.723 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.723 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.723 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.723 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.723 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.723 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.723 * [taylor]: Taking taylor expansion of 0.125 in n 4.723 * [backup-simplify]: Simplify 0.125 into 0.125 4.723 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.723 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.723 * [taylor]: Taking taylor expansion of k in n 4.723 * [backup-simplify]: Simplify k into k 4.723 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.724 * [taylor]: Taking taylor expansion of 1.0 in n 4.724 * [backup-simplify]: Simplify 1.0 into 1.0 4.724 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.724 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.724 * [taylor]: Taking taylor expansion of -2.0 in n 4.724 * [backup-simplify]: Simplify -2.0 into -2.0 4.724 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.724 * [taylor]: Taking taylor expansion of PI in n 4.724 * [backup-simplify]: Simplify PI into PI 4.724 * [taylor]: Taking taylor expansion of n in n 4.724 * [backup-simplify]: Simplify 0 into 0 4.724 * [backup-simplify]: Simplify 1 into 1 4.725 * [backup-simplify]: Simplify (/ PI 1) into PI 4.725 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.726 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.726 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.726 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.728 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.729 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.731 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.731 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.731 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.731 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.731 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.731 * [taylor]: Taking taylor expansion of 0.125 in n 4.731 * [backup-simplify]: Simplify 0.125 into 0.125 4.731 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.731 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.731 * [taylor]: Taking taylor expansion of k in n 4.731 * [backup-simplify]: Simplify k into k 4.731 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 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 (/ PI n))) in n 4.732 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.732 * [taylor]: Taking taylor expansion of -2.0 in n 4.732 * [backup-simplify]: Simplify -2.0 into -2.0 4.732 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.732 * [taylor]: Taking taylor expansion of PI in n 4.732 * [backup-simplify]: Simplify PI into PI 4.732 * [taylor]: Taking taylor expansion of n in n 4.732 * [backup-simplify]: Simplify 0 into 0 4.732 * [backup-simplify]: Simplify 1 into 1 4.732 * [backup-simplify]: Simplify (/ PI 1) into PI 4.733 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.734 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.734 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.734 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.737 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.738 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.739 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.739 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.739 * [taylor]: Taking taylor expansion of 0.125 in k 4.739 * [backup-simplify]: Simplify 0.125 into 0.125 4.739 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.739 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.739 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.739 * [taylor]: Taking taylor expansion of k in k 4.739 * [backup-simplify]: Simplify 0 into 0 4.739 * [backup-simplify]: Simplify 1 into 1 4.739 * [backup-simplify]: Simplify (/ 1 1) into 1 4.739 * [taylor]: Taking taylor expansion of 1.0 in k 4.739 * [backup-simplify]: Simplify 1.0 into 1.0 4.739 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.739 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.740 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.740 * [taylor]: Taking taylor expansion of -2.0 in k 4.740 * [backup-simplify]: Simplify -2.0 into -2.0 4.740 * [taylor]: Taking taylor expansion of PI in k 4.740 * [backup-simplify]: Simplify PI into PI 4.740 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.741 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.741 * [taylor]: Taking taylor expansion of (log n) in k 4.741 * [taylor]: Taking taylor expansion of n in k 4.741 * [backup-simplify]: Simplify n into n 4.741 * [backup-simplify]: Simplify (log n) into (log n) 4.742 * [backup-simplify]: Simplify (+ 1 0) into 1 4.742 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.743 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.744 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.745 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.747 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.748 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.750 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.752 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.752 * [backup-simplify]: Simplify (+ 0 0) into 0 4.752 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.754 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.755 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.757 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.757 * [taylor]: Taking taylor expansion of 0 in k 4.757 * [backup-simplify]: Simplify 0 into 0 4.757 * [backup-simplify]: Simplify 0 into 0 4.757 * [backup-simplify]: Simplify 0 into 0 4.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.760 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.763 * [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 4.763 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.764 * [backup-simplify]: Simplify (+ 0 0) into 0 4.765 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.766 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.767 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.770 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.770 * [taylor]: Taking taylor expansion of 0 in k 4.770 * [backup-simplify]: Simplify 0 into 0 4.770 * [backup-simplify]: Simplify 0 into 0 4.770 * [backup-simplify]: Simplify 0 into 0 4.770 * [backup-simplify]: Simplify 0 into 0 4.772 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.773 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.779 * [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 4.779 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.779 * [backup-simplify]: Simplify (+ 0 0) into 0 4.781 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.782 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.784 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.787 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 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 4.788 * [taylor]: Taking taylor expansion of 0 in k 4.788 * [backup-simplify]: Simplify 0 into 0 4.788 * [backup-simplify]: Simplify 0 into 0 4.789 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.789 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1) 4.790 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) into (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 4.790 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in (n k) around 0 4.790 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 4.790 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.790 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.790 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 4.790 * [taylor]: Taking taylor expansion of 0.125 in k 4.790 * [backup-simplify]: Simplify 0.125 into 0.125 4.790 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.790 * [taylor]: Taking taylor expansion of 1.0 in k 4.790 * [backup-simplify]: Simplify 1.0 into 1.0 4.790 * [taylor]: Taking taylor expansion of k in k 4.790 * [backup-simplify]: Simplify 0 into 0 4.790 * [backup-simplify]: Simplify 1 into 1 4.790 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.790 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.790 * [taylor]: Taking taylor expansion of 2.0 in k 4.790 * [backup-simplify]: Simplify 2.0 into 2.0 4.790 * [taylor]: Taking taylor expansion of (* n PI) in k 4.790 * [taylor]: Taking taylor expansion of n in k 4.790 * [backup-simplify]: Simplify n into n 4.790 * [taylor]: Taking taylor expansion of PI in k 4.790 * [backup-simplify]: Simplify PI into PI 4.790 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.791 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.791 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.791 * [backup-simplify]: Simplify (- 0) into 0 4.792 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.792 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 4.792 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 4.792 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 4.792 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.792 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.792 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.792 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.793 * [taylor]: Taking taylor expansion of 0.125 in n 4.793 * [backup-simplify]: Simplify 0.125 into 0.125 4.793 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.793 * [taylor]: Taking taylor expansion of 1.0 in n 4.793 * [backup-simplify]: Simplify 1.0 into 1.0 4.793 * [taylor]: Taking taylor expansion of k in n 4.793 * [backup-simplify]: Simplify k into k 4.793 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.793 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.793 * [taylor]: Taking taylor expansion of 2.0 in n 4.793 * [backup-simplify]: Simplify 2.0 into 2.0 4.793 * [taylor]: Taking taylor expansion of (* n PI) in n 4.793 * [taylor]: Taking taylor expansion of n in n 4.793 * [backup-simplify]: Simplify 0 into 0 4.793 * [backup-simplify]: Simplify 1 into 1 4.793 * [taylor]: Taking taylor expansion of PI in n 4.793 * [backup-simplify]: Simplify PI into PI 4.793 * [backup-simplify]: Simplify (* 0 PI) into 0 4.794 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.795 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.797 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.798 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.798 * [backup-simplify]: Simplify (- k) into (- k) 4.798 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.798 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.800 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.801 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.802 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.802 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 4.802 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.802 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.803 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 4.803 * [taylor]: Taking taylor expansion of 0.125 in n 4.803 * [backup-simplify]: Simplify 0.125 into 0.125 4.803 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.803 * [taylor]: Taking taylor expansion of 1.0 in n 4.803 * [backup-simplify]: Simplify 1.0 into 1.0 4.803 * [taylor]: Taking taylor expansion of k in n 4.803 * [backup-simplify]: Simplify k into k 4.803 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.803 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.803 * [taylor]: Taking taylor expansion of 2.0 in n 4.803 * [backup-simplify]: Simplify 2.0 into 2.0 4.803 * [taylor]: Taking taylor expansion of (* n PI) in n 4.803 * [taylor]: Taking taylor expansion of n in n 4.803 * [backup-simplify]: Simplify 0 into 0 4.803 * [backup-simplify]: Simplify 1 into 1 4.803 * [taylor]: Taking taylor expansion of PI in n 4.803 * [backup-simplify]: Simplify PI into PI 4.804 * [backup-simplify]: Simplify (* 0 PI) into 0 4.804 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.806 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.807 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.808 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.808 * [backup-simplify]: Simplify (- k) into (- k) 4.808 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.809 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 4.810 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.811 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.821 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.821 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.821 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.821 * [taylor]: Taking taylor expansion of 0.125 in k 4.821 * [backup-simplify]: Simplify 0.125 into 0.125 4.821 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.821 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.821 * [taylor]: Taking taylor expansion of 1.0 in k 4.821 * [backup-simplify]: Simplify 1.0 into 1.0 4.822 * [taylor]: Taking taylor expansion of k in k 4.822 * [backup-simplify]: Simplify 0 into 0 4.822 * [backup-simplify]: Simplify 1 into 1 4.822 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.822 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.822 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.822 * [taylor]: Taking taylor expansion of 2.0 in k 4.822 * [backup-simplify]: Simplify 2.0 into 2.0 4.822 * [taylor]: Taking taylor expansion of PI in k 4.822 * [backup-simplify]: Simplify PI into PI 4.822 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.824 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.824 * [taylor]: Taking taylor expansion of (log n) in k 4.824 * [taylor]: Taking taylor expansion of n in k 4.824 * [backup-simplify]: Simplify n into n 4.824 * [backup-simplify]: Simplify (log n) into (log n) 4.824 * [backup-simplify]: Simplify (- 0) into 0 4.825 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.826 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.827 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.829 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 4.830 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.831 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 4.832 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.834 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.836 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.836 * [backup-simplify]: Simplify (- 0) into 0 4.836 * [backup-simplify]: Simplify (+ 0 0) into 0 4.837 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 4.838 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.840 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.842 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.842 * [taylor]: Taking taylor expansion of 0 in k 4.842 * [backup-simplify]: Simplify 0 into 0 4.842 * [backup-simplify]: Simplify 0 into 0 4.843 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.845 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.846 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.846 * [backup-simplify]: Simplify (+ 0 0) into 0 4.846 * [backup-simplify]: Simplify (- 1) into -1 4.847 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.848 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.851 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 4.854 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.857 * [backup-simplify]: Simplify (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 4.859 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.860 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.863 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.864 * [backup-simplify]: Simplify (- 0) into 0 4.864 * [backup-simplify]: Simplify (+ 0 0) into 0 4.865 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.866 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.868 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.871 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.871 * [taylor]: Taking taylor expansion of 0 in k 4.871 * [backup-simplify]: Simplify 0 into 0 4.871 * [backup-simplify]: Simplify 0 into 0 4.871 * [backup-simplify]: Simplify 0 into 0 4.872 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.876 * [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 4.878 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.878 * [backup-simplify]: Simplify (+ 0 0) into 0 4.878 * [backup-simplify]: Simplify (- 0) into 0 4.879 * [backup-simplify]: Simplify (+ 0 0) into 0 4.881 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.884 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.888 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.894 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 4.905 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* k 1)) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.0078125 (* (pow k 2) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (* 0.015625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))))))) (+ (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.125 (* k (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (log (* 2.0 PI))))))) 4.906 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) into (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 4.906 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in (n k) around 0 4.906 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 4.906 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.906 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.906 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 4.906 * [taylor]: Taking taylor expansion of 0.125 in k 4.906 * [backup-simplify]: Simplify 0.125 into 0.125 4.906 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.906 * [taylor]: Taking taylor expansion of 1.0 in k 4.906 * [backup-simplify]: Simplify 1.0 into 1.0 4.906 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.906 * [taylor]: Taking taylor expansion of k in k 4.906 * [backup-simplify]: Simplify 0 into 0 4.906 * [backup-simplify]: Simplify 1 into 1 4.907 * [backup-simplify]: Simplify (/ 1 1) into 1 4.907 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.907 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.907 * [taylor]: Taking taylor expansion of 2.0 in k 4.907 * [backup-simplify]: Simplify 2.0 into 2.0 4.907 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.907 * [taylor]: Taking taylor expansion of PI in k 4.907 * [backup-simplify]: Simplify PI into PI 4.907 * [taylor]: Taking taylor expansion of n in k 4.907 * [backup-simplify]: Simplify n into n 4.907 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.907 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.907 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.908 * [backup-simplify]: Simplify (- 1) into -1 4.908 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.909 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 4.909 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 4.909 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.909 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.909 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.909 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.909 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.909 * [taylor]: Taking taylor expansion of 0.125 in n 4.909 * [backup-simplify]: Simplify 0.125 into 0.125 4.910 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.910 * [taylor]: Taking taylor expansion of 1.0 in n 4.910 * [backup-simplify]: Simplify 1.0 into 1.0 4.910 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.910 * [taylor]: Taking taylor expansion of k in n 4.910 * [backup-simplify]: Simplify k into k 4.910 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.910 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.910 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.910 * [taylor]: Taking taylor expansion of 2.0 in n 4.910 * [backup-simplify]: Simplify 2.0 into 2.0 4.910 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.910 * [taylor]: Taking taylor expansion of PI in n 4.910 * [backup-simplify]: Simplify PI into PI 4.910 * [taylor]: Taking taylor expansion of n in n 4.910 * [backup-simplify]: Simplify 0 into 0 4.910 * [backup-simplify]: Simplify 1 into 1 4.911 * [backup-simplify]: Simplify (/ PI 1) into PI 4.911 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.912 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.913 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.913 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.913 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.916 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.917 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.917 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 4.917 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.917 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.917 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 4.917 * [taylor]: Taking taylor expansion of 0.125 in n 4.917 * [backup-simplify]: Simplify 0.125 into 0.125 4.917 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.917 * [taylor]: Taking taylor expansion of 1.0 in n 4.917 * [backup-simplify]: Simplify 1.0 into 1.0 4.917 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.917 * [taylor]: Taking taylor expansion of k in n 4.917 * [backup-simplify]: Simplify k into k 4.917 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.917 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.917 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.918 * [taylor]: Taking taylor expansion of 2.0 in n 4.918 * [backup-simplify]: Simplify 2.0 into 2.0 4.918 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.918 * [taylor]: Taking taylor expansion of PI in n 4.918 * [backup-simplify]: Simplify PI into PI 4.918 * [taylor]: Taking taylor expansion of n in n 4.918 * [backup-simplify]: Simplify 0 into 0 4.918 * [backup-simplify]: Simplify 1 into 1 4.918 * [backup-simplify]: Simplify (/ PI 1) into PI 4.919 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.920 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.920 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.920 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.920 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 4.922 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.923 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.924 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.925 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.925 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.925 * [taylor]: Taking taylor expansion of 0.125 in k 4.925 * [backup-simplify]: Simplify 0.125 into 0.125 4.925 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.925 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.925 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.925 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.925 * [taylor]: Taking taylor expansion of 2.0 in k 4.925 * [backup-simplify]: Simplify 2.0 into 2.0 4.925 * [taylor]: Taking taylor expansion of PI in k 4.925 * [backup-simplify]: Simplify PI into PI 4.926 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.927 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.927 * [taylor]: Taking taylor expansion of (log n) in k 4.927 * [taylor]: Taking taylor expansion of n in k 4.927 * [backup-simplify]: Simplify n into n 4.927 * [backup-simplify]: Simplify (log n) into (log n) 4.927 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.927 * [taylor]: Taking taylor expansion of 1.0 in k 4.927 * [backup-simplify]: Simplify 1.0 into 1.0 4.927 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.927 * [taylor]: Taking taylor expansion of k in k 4.927 * [backup-simplify]: Simplify 0 into 0 4.927 * [backup-simplify]: Simplify 1 into 1 4.927 * [backup-simplify]: Simplify (/ 1 1) into 1 4.928 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.929 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.929 * [backup-simplify]: Simplify (- 1) into -1 4.929 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.931 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.932 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 4.933 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.935 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.936 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.936 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.938 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.938 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.939 * [backup-simplify]: Simplify (- 0) into 0 4.939 * [backup-simplify]: Simplify (+ 0 0) into 0 4.940 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.943 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.944 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.945 * [taylor]: Taking taylor expansion of 0 in k 4.945 * [backup-simplify]: Simplify 0 into 0 4.945 * [backup-simplify]: Simplify 0 into 0 4.945 * [backup-simplify]: Simplify 0 into 0 4.946 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.947 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.950 * [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 4.951 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.951 * [backup-simplify]: Simplify (- 0) into 0 4.951 * [backup-simplify]: Simplify (+ 0 0) into 0 4.952 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.955 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.957 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.957 * [taylor]: Taking taylor expansion of 0 in k 4.957 * [backup-simplify]: Simplify 0 into 0 4.957 * [backup-simplify]: Simplify 0 into 0 4.957 * [backup-simplify]: Simplify 0 into 0 4.957 * [backup-simplify]: Simplify 0 into 0 4.957 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.958 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.961 * [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 4.962 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.962 * [backup-simplify]: Simplify (- 0) into 0 4.962 * [backup-simplify]: Simplify (+ 0 0) into 0 4.963 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.965 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.973 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (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 4.973 * [taylor]: Taking taylor expansion of 0 in k 4.973 * [backup-simplify]: Simplify 0 into 0 4.973 * [backup-simplify]: Simplify 0 into 0 4.974 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.974 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) into (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 4.974 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in (n k) around 0 4.974 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 4.974 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.974 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.974 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 4.974 * [taylor]: Taking taylor expansion of 0.125 in k 4.974 * [backup-simplify]: Simplify 0.125 into 0.125 4.974 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.974 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.974 * [taylor]: Taking taylor expansion of k in k 4.974 * [backup-simplify]: Simplify 0 into 0 4.974 * [backup-simplify]: Simplify 1 into 1 4.975 * [backup-simplify]: Simplify (/ 1 1) into 1 4.975 * [taylor]: Taking taylor expansion of 1.0 in k 4.975 * [backup-simplify]: Simplify 1.0 into 1.0 4.975 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.975 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.975 * [taylor]: Taking taylor expansion of -2.0 in k 4.975 * [backup-simplify]: Simplify -2.0 into -2.0 4.975 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.975 * [taylor]: Taking taylor expansion of PI in k 4.975 * [backup-simplify]: Simplify PI into PI 4.975 * [taylor]: Taking taylor expansion of n in k 4.975 * [backup-simplify]: Simplify n into n 4.975 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.975 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.975 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.975 * [backup-simplify]: Simplify (+ 1 0) into 1 4.975 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 4.976 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 4.976 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.976 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.976 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.976 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.976 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.976 * [taylor]: Taking taylor expansion of 0.125 in n 4.976 * [backup-simplify]: Simplify 0.125 into 0.125 4.976 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.976 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.976 * [taylor]: Taking taylor expansion of k in n 4.976 * [backup-simplify]: Simplify k into k 4.976 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.976 * [taylor]: Taking taylor expansion of 1.0 in n 4.976 * [backup-simplify]: Simplify 1.0 into 1.0 4.976 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.976 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.976 * [taylor]: Taking taylor expansion of -2.0 in n 4.976 * [backup-simplify]: Simplify -2.0 into -2.0 4.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.976 * [taylor]: Taking taylor expansion of PI in n 4.976 * [backup-simplify]: Simplify PI into PI 4.976 * [taylor]: Taking taylor expansion of n in n 4.976 * [backup-simplify]: Simplify 0 into 0 4.976 * [backup-simplify]: Simplify 1 into 1 4.976 * [backup-simplify]: Simplify (/ PI 1) into PI 4.977 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.977 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.977 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.978 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.979 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.980 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.980 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 4.980 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.980 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.980 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 4.980 * [taylor]: Taking taylor expansion of 0.125 in n 4.980 * [backup-simplify]: Simplify 0.125 into 0.125 4.980 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.980 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.980 * [taylor]: Taking taylor expansion of k in n 4.980 * [backup-simplify]: Simplify k into k 4.980 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.980 * [taylor]: Taking taylor expansion of 1.0 in n 4.980 * [backup-simplify]: Simplify 1.0 into 1.0 4.980 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.980 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.980 * [taylor]: Taking taylor expansion of -2.0 in n 4.980 * [backup-simplify]: Simplify -2.0 into -2.0 4.980 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.980 * [taylor]: Taking taylor expansion of PI in n 4.980 * [backup-simplify]: Simplify PI into PI 4.980 * [taylor]: Taking taylor expansion of n in n 4.980 * [backup-simplify]: Simplify 0 into 0 4.980 * [backup-simplify]: Simplify 1 into 1 4.981 * [backup-simplify]: Simplify (/ PI 1) into PI 4.981 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.982 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.982 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.982 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 4.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.983 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.984 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.984 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.984 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.984 * [taylor]: Taking taylor expansion of 0.125 in k 4.984 * [backup-simplify]: Simplify 0.125 into 0.125 4.984 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.984 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.985 * [taylor]: Taking taylor expansion of k in k 4.985 * [backup-simplify]: Simplify 0 into 0 4.985 * [backup-simplify]: Simplify 1 into 1 4.985 * [backup-simplify]: Simplify (/ 1 1) into 1 4.985 * [taylor]: Taking taylor expansion of 1.0 in k 4.985 * [backup-simplify]: Simplify 1.0 into 1.0 4.985 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.985 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.985 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.985 * [taylor]: Taking taylor expansion of -2.0 in k 4.985 * [backup-simplify]: Simplify -2.0 into -2.0 4.985 * [taylor]: Taking taylor expansion of PI in k 4.985 * [backup-simplify]: Simplify PI into PI 4.985 * [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 * [taylor]: Taking taylor expansion of (log n) in k 4.986 * [taylor]: Taking taylor expansion of n in k 4.986 * [backup-simplify]: Simplify n into n 4.986 * [backup-simplify]: Simplify (log n) into (log n) 4.986 * [backup-simplify]: Simplify (+ 1 0) into 1 4.986 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.987 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.988 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.988 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 4.989 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.990 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.991 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.992 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.992 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.992 * [backup-simplify]: Simplify (+ 0 0) into 0 4.992 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.994 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.995 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.996 * [taylor]: Taking taylor expansion of 0 in k 4.996 * [backup-simplify]: Simplify 0 into 0 4.996 * [backup-simplify]: Simplify 0 into 0 4.996 * [backup-simplify]: Simplify 0 into 0 4.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.998 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.001 * [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 5.002 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.002 * [backup-simplify]: Simplify (+ 0 0) into 0 5.003 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 5.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.006 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 5.009 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.009 * [taylor]: Taking taylor expansion of 0 in k 5.009 * [backup-simplify]: Simplify 0 into 0 5.009 * [backup-simplify]: Simplify 0 into 0 5.009 * [backup-simplify]: Simplify 0 into 0 5.009 * [backup-simplify]: Simplify 0 into 0 5.010 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.011 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.017 * [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 5.018 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.018 * [backup-simplify]: Simplify (+ 0 0) into 0 5.019 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 5.021 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.023 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 5.026 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 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 5.026 * [taylor]: Taking taylor expansion of 0 in k 5.026 * [backup-simplify]: Simplify 0 into 0 5.026 * [backup-simplify]: Simplify 0 into 0 5.027 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 5.027 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2) 5.029 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))) into (pow (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 2) 5.029 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 2) in (n k) around 0 5.029 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 2) in k 5.029 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in k 5.029 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 5.029 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 5.029 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in k 5.029 * [taylor]: Taking taylor expansion of 0.125 in k 5.029 * [backup-simplify]: Simplify 0.125 into 0.125 5.029 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.029 * [taylor]: Taking taylor expansion of 1.0 in k 5.030 * [backup-simplify]: Simplify 1.0 into 1.0 5.030 * [taylor]: Taking taylor expansion of k in k 5.030 * [backup-simplify]: Simplify 0 into 0 5.030 * [backup-simplify]: Simplify 1 into 1 5.030 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 5.030 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 5.030 * [taylor]: Taking taylor expansion of 2.0 in k 5.030 * [backup-simplify]: Simplify 2.0 into 2.0 5.030 * [taylor]: Taking taylor expansion of (* n PI) in k 5.030 * [taylor]: Taking taylor expansion of n in k 5.030 * [backup-simplify]: Simplify n into n 5.030 * [taylor]: Taking taylor expansion of PI in k 5.030 * [backup-simplify]: Simplify PI into PI 5.030 * [backup-simplify]: Simplify (* n PI) into (* n PI) 5.030 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 5.030 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 5.031 * [backup-simplify]: Simplify (- 0) into 0 5.031 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.032 * [backup-simplify]: Simplify (* 0.125 1.0) into 0.125 5.032 * [backup-simplify]: Simplify (* 0.125 (log (* 2.0 (* n PI)))) into (* 0.125 (log (* 2.0 (* n PI)))) 5.032 * [backup-simplify]: Simplify (exp (* 0.125 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.125) 5.032 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 2) in n 5.032 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 5.032 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.032 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.032 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 5.032 * [taylor]: Taking taylor expansion of 0.125 in n 5.032 * [backup-simplify]: Simplify 0.125 into 0.125 5.032 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.032 * [taylor]: Taking taylor expansion of 1.0 in n 5.032 * [backup-simplify]: Simplify 1.0 into 1.0 5.032 * [taylor]: Taking taylor expansion of k in n 5.032 * [backup-simplify]: Simplify k into k 5.032 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.032 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.033 * [taylor]: Taking taylor expansion of 2.0 in n 5.033 * [backup-simplify]: Simplify 2.0 into 2.0 5.033 * [taylor]: Taking taylor expansion of (* n PI) in n 5.033 * [taylor]: Taking taylor expansion of n in n 5.033 * [backup-simplify]: Simplify 0 into 0 5.033 * [backup-simplify]: Simplify 1 into 1 5.033 * [taylor]: Taking taylor expansion of PI in n 5.033 * [backup-simplify]: Simplify PI into PI 5.033 * [backup-simplify]: Simplify (* 0 PI) into 0 5.034 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.035 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.037 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.038 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.038 * [backup-simplify]: Simplify (- k) into (- k) 5.038 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.038 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 5.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.041 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.042 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.042 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) 2) in n 5.042 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.125 (- 1.0 k))) in n 5.042 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.042 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.043 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 k)) in n 5.043 * [taylor]: Taking taylor expansion of 0.125 in n 5.043 * [backup-simplify]: Simplify 0.125 into 0.125 5.043 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.043 * [taylor]: Taking taylor expansion of 1.0 in n 5.043 * [backup-simplify]: Simplify 1.0 into 1.0 5.043 * [taylor]: Taking taylor expansion of k in n 5.043 * [backup-simplify]: Simplify k into k 5.043 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.043 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.043 * [taylor]: Taking taylor expansion of 2.0 in n 5.043 * [backup-simplify]: Simplify 2.0 into 2.0 5.043 * [taylor]: Taking taylor expansion of (* n PI) in n 5.043 * [taylor]: Taking taylor expansion of n in n 5.043 * [backup-simplify]: Simplify 0 into 0 5.043 * [backup-simplify]: Simplify 1 into 1 5.043 * [taylor]: Taking taylor expansion of PI in n 5.043 * [backup-simplify]: Simplify PI into PI 5.044 * [backup-simplify]: Simplify (* 0 PI) into 0 5.044 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.045 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.047 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.048 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.048 * [backup-simplify]: Simplify (- k) into (- k) 5.048 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.048 * [backup-simplify]: Simplify (* 0.125 (- 1.0 k)) into (* 0.125 (- 1.0 k)) 5.050 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.051 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.052 * [backup-simplify]: Simplify (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.055 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (pow (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) 5.055 * [taylor]: Taking taylor expansion of (pow (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 5.055 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 5.055 * [taylor]: Taking taylor expansion of (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 5.055 * [taylor]: Taking taylor expansion of 0.125 in k 5.055 * [backup-simplify]: Simplify 0.125 into 0.125 5.055 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 5.055 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.055 * [taylor]: Taking taylor expansion of 1.0 in k 5.055 * [backup-simplify]: Simplify 1.0 into 1.0 5.055 * [taylor]: Taking taylor expansion of k in k 5.055 * [backup-simplify]: Simplify 0 into 0 5.055 * [backup-simplify]: Simplify 1 into 1 5.055 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 5.055 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.055 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.055 * [taylor]: Taking taylor expansion of 2.0 in k 5.055 * [backup-simplify]: Simplify 2.0 into 2.0 5.055 * [taylor]: Taking taylor expansion of PI in k 5.055 * [backup-simplify]: Simplify PI into PI 5.056 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.057 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.057 * [taylor]: Taking taylor expansion of (log n) in k 5.057 * [taylor]: Taking taylor expansion of n in k 5.057 * [backup-simplify]: Simplify n into n 5.057 * [backup-simplify]: Simplify (log n) into (log n) 5.058 * [backup-simplify]: Simplify (- 0) into 0 5.058 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.059 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 5.060 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 5.061 * [backup-simplify]: Simplify (* 0.125 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.125 (+ (log (* 2.0 PI)) (log n))) 5.063 * [backup-simplify]: Simplify (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 5.065 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))) into (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) 5.066 * [backup-simplify]: Simplify (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) into (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) 5.067 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 5.068 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 5.070 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.071 * [backup-simplify]: Simplify (- 0) into 0 5.071 * [backup-simplify]: Simplify (+ 0 0) into 0 5.071 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 k))) into 0 5.072 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.073 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 5.074 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.076 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into 0 5.076 * [taylor]: Taking taylor expansion of 0 in k 5.076 * [backup-simplify]: Simplify 0 into 0 5.076 * [backup-simplify]: Simplify 0 into 0 5.076 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.077 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.078 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 5.078 * [backup-simplify]: Simplify (+ 0 0) into 0 5.078 * [backup-simplify]: Simplify (- 1) into -1 5.079 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.080 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 5.081 * [backup-simplify]: Simplify (+ (* 0.125 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 5.083 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 1) 1)))) into (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) 5.089 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))))) (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log (* 2.0 PI)))) (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) 5.091 * [backup-simplify]: Simplify (- (+ (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log (* 2.0 PI)))) (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) into (- (+ (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log (* 2.0 PI)))) (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) 5.092 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 5.099 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 5.103 * [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 5.103 * [backup-simplify]: Simplify (- 0) into 0 5.104 * [backup-simplify]: Simplify (+ 0 0) into 0 5.104 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 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 (+ (* (* 0.125 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.109 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.111 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 5.111 * [taylor]: Taking taylor expansion of 0 in k 5.111 * [backup-simplify]: Simplify 0 into 0 5.111 * [backup-simplify]: Simplify 0 into 0 5.111 * [backup-simplify]: Simplify 0 into 0 5.112 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.114 * [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 5.115 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 5.116 * [backup-simplify]: Simplify (+ 0 0) into 0 5.116 * [backup-simplify]: Simplify (- 0) into 0 5.116 * [backup-simplify]: Simplify (+ 0 0) into 0 5.117 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.119 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 5.122 * [backup-simplify]: Simplify (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) 5.134 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n))))))) (+ (* (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n))))) (* -1 (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (log (* 2.0 PI))) (* 0.125 (log n)))))) (* (* (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0078125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.0078125 (pow (log n) 2)) (* 0.015625 (* (log (* 2.0 PI)) (log n)))))) (exp (* 0.125 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (+ (* 0.03125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2))) (* 0.03125 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 5.142 * [backup-simplify]: Simplify (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (+ (* 0.03125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2))) (* 0.03125 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) into (+ (* 0.03125 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.03125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2))))) 5.156 * [backup-simplify]: Simplify (+ (* (+ (* 0.03125 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.03125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log (* 2.0 PI)))) (* 0.25 (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) (* k 1)) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2)))) (+ (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (log n) (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2)))))))) (+ (* 0.25 (* k (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log (* 2.0 PI))))) (* 0.25 (* k (* (pow (exp (* 0.125 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))))) 5.158 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (/ (- 1.0 (/ 1 k)) 2.0) 2) 2))) into (pow (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 2) 5.158 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 5.158 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 2) in k 5.158 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in k 5.158 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.158 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.158 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in k 5.158 * [taylor]: Taking taylor expansion of 0.125 in k 5.158 * [backup-simplify]: Simplify 0.125 into 0.125 5.158 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.158 * [taylor]: Taking taylor expansion of 1.0 in k 5.158 * [backup-simplify]: Simplify 1.0 into 1.0 5.158 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.158 * [taylor]: Taking taylor expansion of k in k 5.158 * [backup-simplify]: Simplify 0 into 0 5.158 * [backup-simplify]: Simplify 1 into 1 5.159 * [backup-simplify]: Simplify (/ 1 1) into 1 5.159 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.159 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.159 * [taylor]: Taking taylor expansion of 2.0 in k 5.159 * [backup-simplify]: Simplify 2.0 into 2.0 5.159 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.159 * [taylor]: Taking taylor expansion of PI in k 5.159 * [backup-simplify]: Simplify PI into PI 5.159 * [taylor]: Taking taylor expansion of n in k 5.159 * [backup-simplify]: Simplify n into n 5.159 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.159 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 5.159 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 5.160 * [backup-simplify]: Simplify (- 1) into -1 5.160 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.161 * [backup-simplify]: Simplify (* 0.125 -1) into -0.125 5.161 * [backup-simplify]: Simplify (* -0.125 (log (* 2.0 (/ PI n)))) into (* -0.125 (log (* 2.0 (/ PI n)))) 5.161 * [backup-simplify]: Simplify (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.125 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 5.161 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 2) in n 5.161 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 5.161 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.161 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.161 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 5.161 * [taylor]: Taking taylor expansion of 0.125 in n 5.161 * [backup-simplify]: Simplify 0.125 into 0.125 5.161 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.161 * [taylor]: Taking taylor expansion of 1.0 in n 5.161 * [backup-simplify]: Simplify 1.0 into 1.0 5.162 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.162 * [taylor]: Taking taylor expansion of k in n 5.162 * [backup-simplify]: Simplify k into k 5.162 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.162 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.162 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.162 * [taylor]: Taking taylor expansion of 2.0 in n 5.162 * [backup-simplify]: Simplify 2.0 into 2.0 5.162 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.162 * [taylor]: Taking taylor expansion of PI in n 5.162 * [backup-simplify]: Simplify PI into PI 5.162 * [taylor]: Taking taylor expansion of n in n 5.162 * [backup-simplify]: Simplify 0 into 0 5.162 * [backup-simplify]: Simplify 1 into 1 5.163 * [backup-simplify]: Simplify (/ PI 1) into PI 5.163 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.164 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.165 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.165 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.165 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 5.166 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.167 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.169 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.169 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) 2) in n 5.169 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.125 (- 1.0 (/ 1 k)))) in n 5.169 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.169 * [taylor]: Taking taylor expansion of (* (* 0.125 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.169 * [taylor]: Taking taylor expansion of (* 0.125 (- 1.0 (/ 1 k))) in n 5.169 * [taylor]: Taking taylor expansion of 0.125 in n 5.169 * [backup-simplify]: Simplify 0.125 into 0.125 5.169 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.169 * [taylor]: Taking taylor expansion of 1.0 in n 5.169 * [backup-simplify]: Simplify 1.0 into 1.0 5.169 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.169 * [taylor]: Taking taylor expansion of k in n 5.169 * [backup-simplify]: Simplify k into k 5.169 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.169 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.169 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.169 * [taylor]: Taking taylor expansion of 2.0 in n 5.169 * [backup-simplify]: Simplify 2.0 into 2.0 5.169 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.169 * [taylor]: Taking taylor expansion of PI in n 5.169 * [backup-simplify]: Simplify PI into PI 5.169 * [taylor]: Taking taylor expansion of n in n 5.169 * [backup-simplify]: Simplify 0 into 0 5.169 * [backup-simplify]: Simplify 1 into 1 5.170 * [backup-simplify]: Simplify (/ PI 1) into PI 5.170 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.171 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.171 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.172 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.172 * [backup-simplify]: Simplify (* 0.125 (- 1.0 (/ 1 k))) into (* 0.125 (- 1.0 (/ 1 k))) 5.173 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.174 * [backup-simplify]: Simplify (* (* 0.125 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.176 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.178 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 5.178 * [taylor]: Taking taylor expansion of (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 5.179 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 5.179 * [taylor]: Taking taylor expansion of (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 5.179 * [taylor]: Taking taylor expansion of 0.125 in k 5.179 * [backup-simplify]: Simplify 0.125 into 0.125 5.179 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 5.179 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 5.179 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.179 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.179 * [taylor]: Taking taylor expansion of 2.0 in k 5.179 * [backup-simplify]: Simplify 2.0 into 2.0 5.179 * [taylor]: Taking taylor expansion of PI in k 5.179 * [backup-simplify]: Simplify PI into PI 5.179 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.180 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.180 * [taylor]: Taking taylor expansion of (log n) in k 5.180 * [taylor]: Taking taylor expansion of n in k 5.181 * [backup-simplify]: Simplify n into n 5.181 * [backup-simplify]: Simplify (log n) into (log n) 5.181 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.181 * [taylor]: Taking taylor expansion of 1.0 in k 5.181 * [backup-simplify]: Simplify 1.0 into 1.0 5.181 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.181 * [taylor]: Taking taylor expansion of k in k 5.181 * [backup-simplify]: Simplify 0 into 0 5.181 * [backup-simplify]: Simplify 1 into 1 5.181 * [backup-simplify]: Simplify (/ 1 1) into 1 5.181 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.183 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 5.183 * [backup-simplify]: Simplify (- 1) into -1 5.183 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.185 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 5.186 * [backup-simplify]: Simplify (* 0.125 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.125 (- (log (* 2.0 PI)) (log n))) 5.187 * [backup-simplify]: Simplify (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.190 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 5.191 * [backup-simplify]: Simplify (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) into (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 5.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.193 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.195 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.195 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.195 * [backup-simplify]: Simplify (- 0) into 0 5.196 * [backup-simplify]: Simplify (+ 0 0) into 0 5.196 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (- 1.0 (/ 1 k)))) into 0 5.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.199 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 5.200 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.201 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 5.201 * [taylor]: Taking taylor expansion of 0 in k 5.201 * [backup-simplify]: Simplify 0 into 0 5.201 * [backup-simplify]: Simplify 0 into 0 5.203 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 5.203 * [backup-simplify]: Simplify 0 into 0 5.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.204 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.206 * [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 5.206 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.207 * [backup-simplify]: Simplify (- 0) into 0 5.207 * [backup-simplify]: Simplify (+ 0 0) into 0 5.207 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 5.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.209 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 5.211 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.212 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 5.212 * [taylor]: Taking taylor expansion of 0 in k 5.212 * [backup-simplify]: Simplify 0 into 0 5.212 * [backup-simplify]: Simplify 0 into 0 5.212 * [backup-simplify]: Simplify 0 into 0 5.214 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 5.214 * [backup-simplify]: Simplify 0 into 0 5.215 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.215 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.224 * [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 5.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.225 * [backup-simplify]: Simplify (- 0) into 0 5.225 * [backup-simplify]: Simplify (+ 0 0) into 0 5.226 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 5.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.229 * [backup-simplify]: Simplify (+ (* (* 0.125 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 5.232 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (- (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 5.235 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 5.235 * [taylor]: Taking taylor expansion of 0 in k 5.235 * [backup-simplify]: Simplify 0 into 0 5.235 * [backup-simplify]: Simplify 0 into 0 5.236 * [backup-simplify]: Simplify (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) 2) into (pow (exp (* 0.125 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2) 5.238 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2)) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2) 2))) into (pow (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 2) 5.238 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 5.238 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 2) in k 5.238 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in k 5.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.238 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.238 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in k 5.238 * [taylor]: Taking taylor expansion of 0.125 in k 5.238 * [backup-simplify]: Simplify 0.125 into 0.125 5.238 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.238 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.238 * [taylor]: Taking taylor expansion of k in k 5.238 * [backup-simplify]: Simplify 0 into 0 5.238 * [backup-simplify]: Simplify 1 into 1 5.239 * [backup-simplify]: Simplify (/ 1 1) into 1 5.239 * [taylor]: Taking taylor expansion of 1.0 in k 5.239 * [backup-simplify]: Simplify 1.0 into 1.0 5.239 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.239 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.239 * [taylor]: Taking taylor expansion of -2.0 in k 5.239 * [backup-simplify]: Simplify -2.0 into -2.0 5.239 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.239 * [taylor]: Taking taylor expansion of PI in k 5.239 * [backup-simplify]: Simplify PI into PI 5.239 * [taylor]: Taking taylor expansion of n in k 5.239 * [backup-simplify]: Simplify n into n 5.239 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.239 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.239 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.240 * [backup-simplify]: Simplify (+ 1 0) into 1 5.240 * [backup-simplify]: Simplify (* 0.125 1) into 0.125 5.240 * [backup-simplify]: Simplify (* 0.125 (log (* -2.0 (/ PI n)))) into (* 0.125 (log (* -2.0 (/ PI n)))) 5.240 * [backup-simplify]: Simplify (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.240 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 2) in n 5.240 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 5.240 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.240 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.240 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 5.240 * [taylor]: Taking taylor expansion of 0.125 in n 5.241 * [backup-simplify]: Simplify 0.125 into 0.125 5.241 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.241 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.241 * [taylor]: Taking taylor expansion of k in n 5.241 * [backup-simplify]: Simplify k into k 5.241 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.241 * [taylor]: Taking taylor expansion of 1.0 in n 5.241 * [backup-simplify]: Simplify 1.0 into 1.0 5.241 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.241 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.241 * [taylor]: Taking taylor expansion of -2.0 in n 5.241 * [backup-simplify]: Simplify -2.0 into -2.0 5.241 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.241 * [taylor]: Taking taylor expansion of PI in n 5.241 * [backup-simplify]: Simplify PI into PI 5.241 * [taylor]: Taking taylor expansion of n in n 5.241 * [backup-simplify]: Simplify 0 into 0 5.241 * [backup-simplify]: Simplify 1 into 1 5.241 * [backup-simplify]: Simplify (/ PI 1) into PI 5.242 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.243 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.243 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.243 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 5.245 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.246 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.247 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.247 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) 2) in n 5.247 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.125 (+ (/ 1 k) 1.0))) in n 5.247 * [taylor]: Taking taylor expansion of (exp (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.247 * [taylor]: Taking taylor expansion of (* (* 0.125 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.247 * [taylor]: Taking taylor expansion of (* 0.125 (+ (/ 1 k) 1.0)) in n 5.247 * [taylor]: Taking taylor expansion of 0.125 in n 5.247 * [backup-simplify]: Simplify 0.125 into 0.125 5.247 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.247 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.247 * [taylor]: Taking taylor expansion of k in n 5.247 * [backup-simplify]: Simplify k into k 5.247 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.247 * [taylor]: Taking taylor expansion of 1.0 in n 5.247 * [backup-simplify]: Simplify 1.0 into 1.0 5.247 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.247 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.247 * [taylor]: Taking taylor expansion of -2.0 in n 5.247 * [backup-simplify]: Simplify -2.0 into -2.0 5.247 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.248 * [taylor]: Taking taylor expansion of PI in n 5.248 * [backup-simplify]: Simplify PI into PI 5.248 * [taylor]: Taking taylor expansion of n in n 5.248 * [backup-simplify]: Simplify 0 into 0 5.248 * [backup-simplify]: Simplify 1 into 1 5.248 * [backup-simplify]: Simplify (/ PI 1) into PI 5.248 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.249 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.250 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.250 * [backup-simplify]: Simplify (* 0.125 (+ (/ 1 k) 1.0)) into (* 0.125 (+ (/ 1 k) 1.0)) 5.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.252 * [backup-simplify]: Simplify (* (* 0.125 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.253 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.255 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 5.256 * [taylor]: Taking taylor expansion of (pow (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 5.256 * [taylor]: Taking taylor expansion of (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 5.256 * [taylor]: Taking taylor expansion of (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 5.256 * [taylor]: Taking taylor expansion of 0.125 in k 5.256 * [backup-simplify]: Simplify 0.125 into 0.125 5.256 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 5.256 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.256 * [taylor]: Taking taylor expansion of k in k 5.256 * [backup-simplify]: Simplify 0 into 0 5.256 * [backup-simplify]: Simplify 1 into 1 5.256 * [backup-simplify]: Simplify (/ 1 1) into 1 5.256 * [taylor]: Taking taylor expansion of 1.0 in k 5.256 * [backup-simplify]: Simplify 1.0 into 1.0 5.256 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 5.256 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 5.256 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 5.256 * [taylor]: Taking taylor expansion of -2.0 in k 5.256 * [backup-simplify]: Simplify -2.0 into -2.0 5.256 * [taylor]: Taking taylor expansion of PI in k 5.256 * [backup-simplify]: Simplify PI into PI 5.257 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.258 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.258 * [taylor]: Taking taylor expansion of (log n) in k 5.258 * [taylor]: Taking taylor expansion of n in k 5.258 * [backup-simplify]: Simplify n into n 5.258 * [backup-simplify]: Simplify (log n) into (log n) 5.258 * [backup-simplify]: Simplify (+ 1 0) into 1 5.258 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.259 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 5.260 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 5.261 * [backup-simplify]: Simplify (* 0.125 (- (log (* -2.0 PI)) (log n))) into (* 0.125 (- (log (* -2.0 PI)) (log n))) 5.263 * [backup-simplify]: Simplify (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.265 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 5.266 * [backup-simplify]: Simplify (pow (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) into (pow (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 5.267 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.268 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.269 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 5.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.270 * [backup-simplify]: Simplify (+ 0 0) into 0 5.270 * [backup-simplify]: Simplify (+ (* 0.125 0) (* 0 (+ (/ 1 k) 1.0))) into 0 5.272 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.273 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 5.275 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.277 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 5.277 * [taylor]: Taking taylor expansion of 0 in k 5.277 * [backup-simplify]: Simplify 0 into 0 5.277 * [backup-simplify]: Simplify 0 into 0 5.279 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 5.279 * [backup-simplify]: Simplify 0 into 0 5.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.280 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.282 * [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 5.283 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.283 * [backup-simplify]: Simplify (+ 0 0) into 0 5.283 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 5.284 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.285 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 5.287 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.289 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 5.289 * [taylor]: Taking taylor expansion of 0 in k 5.289 * [backup-simplify]: Simplify 0 into 0 5.289 * [backup-simplify]: Simplify 0 into 0 5.289 * [backup-simplify]: Simplify 0 into 0 5.291 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 5.291 * [backup-simplify]: Simplify 0 into 0 5.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.293 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.299 * [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 5.300 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.300 * [backup-simplify]: Simplify (+ 0 0) into 0 5.301 * [backup-simplify]: Simplify (+ (* 0.125 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 5.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.305 * [backup-simplify]: Simplify (+ (* (* 0.125 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 5.307 * [backup-simplify]: Simplify (* (exp (* 0.125 (* (+ (/ 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 5.310 * [backup-simplify]: Simplify (+ (* (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.125 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0 5.310 * [taylor]: Taking taylor expansion of 0 in k 5.310 * [backup-simplify]: Simplify 0 into 0 5.310 * [backup-simplify]: Simplify 0 into 0 5.311 * [backup-simplify]: Simplify (pow (exp (* 0.125 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 0.125 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) 5.311 * * * [progress]: simplifying candidates 5.321 * [simplify]: Simplifying: (* (+ (+ (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)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (/ (- 1.0 k) 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(* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2))) (+ (* (log (* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (log (* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2))) (+ (* (log (* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2)) (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (+ (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (+ (+ (log h0) (log h4)) (log h3)) (/ (/ (/ (- h2 h1) h0) 2) 2))) (+ (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (+ (log (* h0 h4)) (log h3)) (/ (/ (/ (- h2 h1) h0) 2) 2))) (+ (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (log (* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2))) (+ (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (log (* (* h0 h4) h3)) (/ (/ (/ (- h2 h1) h0) 2) 2))) (+ (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (log (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (log (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (exp (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (* (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (cbrt (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (cbrt (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))))) (cbrt (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (* (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (sqrt (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (sqrt (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (pow (* (* h0 h4) h3) (/ (/ (/ h2 h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ h2 h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ h1 h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ h1 h0) 2) 2))) (* (pow (* h0 h4) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* h0 h4) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow h3 (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow h3 (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* 1 1) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* 2 (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* h0 h4) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) 1) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2))) (* (pow h3 (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (cbrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (sqrt (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (/ (- h2 h1) h0) 2) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ h2 h0) 2) 2))) (* (pow (* (* h0 h4) h3) (/ (/ (/ h2 h0) 2) 2)) (pow (* (* h0 h4) h3) (/ (/ (/ (- h2 h1) h0) 2) 2))) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (+ (* h11 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))) (+ (* h11 (* (pow h1 2) (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (* h10 (* (pow h1 2) (* (log (* h0 h4)) (* (log h3) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))))))) (+ (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log (* h0 h4))))))) (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (+ (* h11 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))) (+ (* h11 (* (pow h1 2) (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2)))) (* h10 (* (pow h1 2) (* (log (* h0 h4)) (* (log h3) (exp (* h9 (+ (log (* h0 h4)) (log h3))))))))))) (+ (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log h3)))) (* h9 (* h1 (* (exp (* h9 (+ (log (* h0 h4)) (log h3)))) (log (* h0 h4))))))) (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (pow h1 2) (* (pow (exp (* h9 (+ (log (* h0 h4)) (log h3)))) 2) (pow (log h3) 2)))) (+ (pow (exp (* h9 (+ (log (* h0 h4)) (log h3)))) 2) (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (pow (exp (* h9 (+ (log (* h0 h4)) (log h3)))) 2)))) (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (log h3) (pow (exp (* h9 (+ (log (* h0 h4)) (log h3)))) 2)))))))) (+ (* h5 (* h1 (* (pow (exp (* h9 (+ (log (* h0 h4)) (log h3)))) 2) (log (* h0 h4))))) (* h5 (* h1 (* (pow (exp (* h9 (+ (log (* h0 h4)) (log h3)))) 2) (log h3)))))) (pow (exp (* h9 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) 2) (pow (exp (* h9 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) 2) 5.422 * * * [progress]: adding candidates to table 9.030 * * [progress]: iteration 4 / 4 9.030 * * * [progress]: picking best candidate 9.066 * * * * [pick]: Picked # 9.066 * * * [progress]: localizing error 9.105 * * * [progress]: generating rewritten candidates 9.105 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 9.139 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2) 9.155 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 9.201 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 9.220 * * * [progress]: generating series expansions 9.220 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 9.221 * [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))) 9.221 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.221 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.221 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.221 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.221 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.221 * [taylor]: Taking taylor expansion of 0.25 in k 9.221 * [backup-simplify]: Simplify 0.25 into 0.25 9.221 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.221 * [taylor]: Taking taylor expansion of 1.0 in k 9.222 * [backup-simplify]: Simplify 1.0 into 1.0 9.222 * [taylor]: Taking taylor expansion of k in k 9.222 * [backup-simplify]: Simplify 0 into 0 9.222 * [backup-simplify]: Simplify 1 into 1 9.222 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.222 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.222 * [taylor]: Taking taylor expansion of 2.0 in k 9.222 * [backup-simplify]: Simplify 2.0 into 2.0 9.222 * [taylor]: Taking taylor expansion of (* n PI) in k 9.222 * [taylor]: Taking taylor expansion of n in k 9.222 * [backup-simplify]: Simplify n into n 9.222 * [taylor]: Taking taylor expansion of PI in k 9.222 * [backup-simplify]: Simplify PI into PI 9.222 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.222 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.222 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.222 * [backup-simplify]: Simplify (- 0) into 0 9.223 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.223 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.223 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.223 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.223 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.223 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.223 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.223 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.223 * [taylor]: Taking taylor expansion of 0.25 in n 9.223 * [backup-simplify]: Simplify 0.25 into 0.25 9.223 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.223 * [taylor]: Taking taylor expansion of 1.0 in n 9.223 * [backup-simplify]: Simplify 1.0 into 1.0 9.223 * [taylor]: Taking taylor expansion of k in n 9.223 * [backup-simplify]: Simplify k into k 9.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.223 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.223 * [taylor]: Taking taylor expansion of 2.0 in n 9.223 * [backup-simplify]: Simplify 2.0 into 2.0 9.223 * [taylor]: Taking taylor expansion of (* n PI) in n 9.223 * [taylor]: Taking taylor expansion of n in n 9.223 * [backup-simplify]: Simplify 0 into 0 9.223 * [backup-simplify]: Simplify 1 into 1 9.223 * [taylor]: Taking taylor expansion of PI in n 9.223 * [backup-simplify]: Simplify PI into PI 9.224 * [backup-simplify]: Simplify (* 0 PI) into 0 9.224 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.225 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.226 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.227 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.227 * [backup-simplify]: Simplify (- k) into (- k) 9.227 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.227 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.228 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.228 * [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)))) 9.229 * [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))))) 9.229 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.229 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.229 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.229 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.229 * [taylor]: Taking taylor expansion of 0.25 in n 9.229 * [backup-simplify]: Simplify 0.25 into 0.25 9.229 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.229 * [taylor]: Taking taylor expansion of 1.0 in n 9.229 * [backup-simplify]: Simplify 1.0 into 1.0 9.229 * [taylor]: Taking taylor expansion of k in n 9.229 * [backup-simplify]: Simplify k into k 9.229 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.229 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.229 * [taylor]: Taking taylor expansion of 2.0 in n 9.229 * [backup-simplify]: Simplify 2.0 into 2.0 9.230 * [taylor]: Taking taylor expansion of (* n PI) in n 9.230 * [taylor]: Taking taylor expansion of n in n 9.230 * [backup-simplify]: Simplify 0 into 0 9.230 * [backup-simplify]: Simplify 1 into 1 9.230 * [taylor]: Taking taylor expansion of PI in n 9.230 * [backup-simplify]: Simplify PI into PI 9.230 * [backup-simplify]: Simplify (* 0 PI) into 0 9.230 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.231 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.232 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.233 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.233 * [backup-simplify]: Simplify (- k) into (- k) 9.233 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.233 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.234 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.234 * [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)))) 9.235 * [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))))) 9.235 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.235 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.235 * [taylor]: Taking taylor expansion of 0.25 in k 9.235 * [backup-simplify]: Simplify 0.25 into 0.25 9.235 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.235 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.235 * [taylor]: Taking taylor expansion of 1.0 in k 9.235 * [backup-simplify]: Simplify 1.0 into 1.0 9.235 * [taylor]: Taking taylor expansion of k in k 9.235 * [backup-simplify]: Simplify 0 into 0 9.235 * [backup-simplify]: Simplify 1 into 1 9.235 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.235 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.235 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.235 * [taylor]: Taking taylor expansion of 2.0 in k 9.235 * [backup-simplify]: Simplify 2.0 into 2.0 9.235 * [taylor]: Taking taylor expansion of PI in k 9.236 * [backup-simplify]: Simplify PI into PI 9.236 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.236 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.236 * [taylor]: Taking taylor expansion of (log n) in k 9.236 * [taylor]: Taking taylor expansion of n in k 9.237 * [backup-simplify]: Simplify n into n 9.237 * [backup-simplify]: Simplify (log n) into (log n) 9.237 * [backup-simplify]: Simplify (- 0) into 0 9.237 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.238 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.238 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.239 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.240 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.240 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.241 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.243 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.243 * [backup-simplify]: Simplify (- 0) into 0 9.243 * [backup-simplify]: Simplify (+ 0 0) into 0 9.243 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.245 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.246 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.246 * [taylor]: Taking taylor expansion of 0 in k 9.246 * [backup-simplify]: Simplify 0 into 0 9.246 * [backup-simplify]: Simplify 0 into 0 9.247 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.248 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.248 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.249 * [backup-simplify]: Simplify (+ 0 0) into 0 9.249 * [backup-simplify]: Simplify (- 1) into -1 9.249 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.250 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.252 * [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)))) 9.256 * [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)))))) 9.259 * [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)))))) 9.260 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.262 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.265 * [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 9.266 * [backup-simplify]: Simplify (- 0) into 0 9.266 * [backup-simplify]: Simplify (+ 0 0) into 0 9.267 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.268 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.270 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.273 * [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 9.273 * [taylor]: Taking taylor expansion of 0 in k 9.273 * [backup-simplify]: Simplify 0 into 0 9.273 * [backup-simplify]: Simplify 0 into 0 9.273 * [backup-simplify]: Simplify 0 into 0 9.274 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.278 * [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 9.280 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.280 * [backup-simplify]: Simplify (+ 0 0) into 0 9.281 * [backup-simplify]: Simplify (- 0) into 0 9.281 * [backup-simplify]: Simplify (+ 0 0) into 0 9.294 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.297 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.301 * [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))))) 9.307 * [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))))) 9.318 * [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)))))) 9.319 * [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)))) 9.319 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.319 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.319 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.319 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.319 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.319 * [taylor]: Taking taylor expansion of 0.25 in k 9.319 * [backup-simplify]: Simplify 0.25 into 0.25 9.319 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.319 * [taylor]: Taking taylor expansion of 1.0 in k 9.319 * [backup-simplify]: Simplify 1.0 into 1.0 9.319 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.319 * [taylor]: Taking taylor expansion of k in k 9.320 * [backup-simplify]: Simplify 0 into 0 9.320 * [backup-simplify]: Simplify 1 into 1 9.320 * [backup-simplify]: Simplify (/ 1 1) into 1 9.320 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.320 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.320 * [taylor]: Taking taylor expansion of 2.0 in k 9.320 * [backup-simplify]: Simplify 2.0 into 2.0 9.320 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.320 * [taylor]: Taking taylor expansion of PI in k 9.320 * [backup-simplify]: Simplify PI into PI 9.320 * [taylor]: Taking taylor expansion of n in k 9.320 * [backup-simplify]: Simplify n into n 9.320 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.320 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.321 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.321 * [backup-simplify]: Simplify (- 1) into -1 9.321 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.322 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.322 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.322 * [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))))) 9.322 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.322 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.322 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.322 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.322 * [taylor]: Taking taylor expansion of 0.25 in n 9.323 * [backup-simplify]: Simplify 0.25 into 0.25 9.323 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.323 * [taylor]: Taking taylor expansion of 1.0 in n 9.323 * [backup-simplify]: Simplify 1.0 into 1.0 9.323 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.323 * [taylor]: Taking taylor expansion of k in n 9.323 * [backup-simplify]: Simplify k into k 9.323 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.323 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.323 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.323 * [taylor]: Taking taylor expansion of 2.0 in n 9.323 * [backup-simplify]: Simplify 2.0 into 2.0 9.323 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.323 * [taylor]: Taking taylor expansion of PI in n 9.323 * [backup-simplify]: Simplify PI into PI 9.323 * [taylor]: Taking taylor expansion of n in n 9.323 * [backup-simplify]: Simplify 0 into 0 9.323 * [backup-simplify]: Simplify 1 into 1 9.323 * [backup-simplify]: Simplify (/ PI 1) into PI 9.324 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.324 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.324 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.324 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.325 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.325 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.326 * [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)))) 9.327 * [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))))) 9.327 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.327 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.327 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.327 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.327 * [taylor]: Taking taylor expansion of 0.25 in n 9.327 * [backup-simplify]: Simplify 0.25 into 0.25 9.327 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.327 * [taylor]: Taking taylor expansion of 1.0 in n 9.327 * [backup-simplify]: Simplify 1.0 into 1.0 9.327 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.327 * [taylor]: Taking taylor expansion of k in n 9.327 * [backup-simplify]: Simplify k into k 9.327 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.327 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.327 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.327 * [taylor]: Taking taylor expansion of 2.0 in n 9.327 * [backup-simplify]: Simplify 2.0 into 2.0 9.327 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.327 * [taylor]: Taking taylor expansion of PI in n 9.327 * [backup-simplify]: Simplify PI into PI 9.327 * [taylor]: Taking taylor expansion of n in n 9.327 * [backup-simplify]: Simplify 0 into 0 9.327 * [backup-simplify]: Simplify 1 into 1 9.328 * [backup-simplify]: Simplify (/ PI 1) into PI 9.328 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.329 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.329 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.329 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.329 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.331 * [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)))) 9.331 * [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))))) 9.331 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.331 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.331 * [taylor]: Taking taylor expansion of 0.25 in k 9.332 * [backup-simplify]: Simplify 0.25 into 0.25 9.332 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.332 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.332 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.332 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.332 * [taylor]: Taking taylor expansion of 2.0 in k 9.332 * [backup-simplify]: Simplify 2.0 into 2.0 9.332 * [taylor]: Taking taylor expansion of PI in k 9.332 * [backup-simplify]: Simplify PI into PI 9.332 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.333 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.333 * [taylor]: Taking taylor expansion of (log n) in k 9.333 * [taylor]: Taking taylor expansion of n in k 9.333 * [backup-simplify]: Simplify n into n 9.333 * [backup-simplify]: Simplify (log n) into (log n) 9.333 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.333 * [taylor]: Taking taylor expansion of 1.0 in k 9.333 * [backup-simplify]: Simplify 1.0 into 1.0 9.333 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.333 * [taylor]: Taking taylor expansion of k in k 9.333 * [backup-simplify]: Simplify 0 into 0 9.333 * [backup-simplify]: Simplify 1 into 1 9.333 * [backup-simplify]: Simplify (/ 1 1) into 1 9.333 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.334 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.334 * [backup-simplify]: Simplify (- 1) into -1 9.334 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.335 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.336 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.336 * [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))))) 9.337 * [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))))) 9.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.338 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.339 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.339 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.340 * [backup-simplify]: Simplify (- 0) into 0 9.340 * [backup-simplify]: Simplify (+ 0 0) into 0 9.340 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.341 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.342 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.343 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.343 * [taylor]: Taking taylor expansion of 0 in k 9.343 * [backup-simplify]: Simplify 0 into 0 9.343 * [backup-simplify]: Simplify 0 into 0 9.343 * [backup-simplify]: Simplify 0 into 0 9.344 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.344 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.346 * [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 9.346 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.347 * [backup-simplify]: Simplify (- 0) into 0 9.347 * [backup-simplify]: Simplify (+ 0 0) into 0 9.347 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.349 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.351 * [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 9.351 * [taylor]: Taking taylor expansion of 0 in k 9.351 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify 0 into 0 9.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.352 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.355 * [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 9.356 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.356 * [backup-simplify]: Simplify (- 0) into 0 9.356 * [backup-simplify]: Simplify (+ 0 0) into 0 9.357 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.358 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.359 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.361 * [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 9.361 * [taylor]: Taking taylor expansion of 0 in k 9.361 * [backup-simplify]: Simplify 0 into 0 9.361 * [backup-simplify]: Simplify 0 into 0 9.362 * [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)))) 9.362 * [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))) 9.362 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.362 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.362 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.362 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.362 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.362 * [taylor]: Taking taylor expansion of 0.25 in k 9.362 * [backup-simplify]: Simplify 0.25 into 0.25 9.362 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.362 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.362 * [taylor]: Taking taylor expansion of k in k 9.362 * [backup-simplify]: Simplify 0 into 0 9.363 * [backup-simplify]: Simplify 1 into 1 9.363 * [backup-simplify]: Simplify (/ 1 1) into 1 9.363 * [taylor]: Taking taylor expansion of 1.0 in k 9.363 * [backup-simplify]: Simplify 1.0 into 1.0 9.363 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.363 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.363 * [taylor]: Taking taylor expansion of -2.0 in k 9.363 * [backup-simplify]: Simplify -2.0 into -2.0 9.363 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.363 * [taylor]: Taking taylor expansion of PI in k 9.363 * [backup-simplify]: Simplify PI into PI 9.363 * [taylor]: Taking taylor expansion of n in k 9.363 * [backup-simplify]: Simplify n into n 9.363 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.363 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.363 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.364 * [backup-simplify]: Simplify (+ 1 0) into 1 9.364 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.364 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.364 * [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)))))) 9.364 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.364 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.364 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.364 * [taylor]: Taking taylor expansion of 0.25 in n 9.364 * [backup-simplify]: Simplify 0.25 into 0.25 9.364 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.364 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.364 * [taylor]: Taking taylor expansion of k in n 9.364 * [backup-simplify]: Simplify k into k 9.364 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.364 * [taylor]: Taking taylor expansion of 1.0 in n 9.364 * [backup-simplify]: Simplify 1.0 into 1.0 9.364 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.364 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.364 * [taylor]: Taking taylor expansion of -2.0 in n 9.365 * [backup-simplify]: Simplify -2.0 into -2.0 9.365 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.365 * [taylor]: Taking taylor expansion of PI in n 9.365 * [backup-simplify]: Simplify PI into PI 9.365 * [taylor]: Taking taylor expansion of n in n 9.365 * [backup-simplify]: Simplify 0 into 0 9.365 * [backup-simplify]: Simplify 1 into 1 9.365 * [backup-simplify]: Simplify (/ PI 1) into PI 9.365 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.366 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.366 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.366 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.367 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.368 * [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)))) 9.369 * [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))))) 9.369 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.369 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.369 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.369 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.369 * [taylor]: Taking taylor expansion of 0.25 in n 9.369 * [backup-simplify]: Simplify 0.25 into 0.25 9.369 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.369 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.369 * [taylor]: Taking taylor expansion of k in n 9.369 * [backup-simplify]: Simplify k into k 9.370 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.370 * [taylor]: Taking taylor expansion of 1.0 in n 9.370 * [backup-simplify]: Simplify 1.0 into 1.0 9.370 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.370 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.370 * [taylor]: Taking taylor expansion of -2.0 in n 9.370 * [backup-simplify]: Simplify -2.0 into -2.0 9.370 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.370 * [taylor]: Taking taylor expansion of PI in n 9.370 * [backup-simplify]: Simplify PI into PI 9.370 * [taylor]: Taking taylor expansion of n in n 9.370 * [backup-simplify]: Simplify 0 into 0 9.370 * [backup-simplify]: Simplify 1 into 1 9.370 * [backup-simplify]: Simplify (/ PI 1) into PI 9.371 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.372 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.372 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.372 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.373 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.374 * [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)))) 9.376 * [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))))) 9.376 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.376 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.376 * [taylor]: Taking taylor expansion of 0.25 in k 9.376 * [backup-simplify]: Simplify 0.25 into 0.25 9.376 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.376 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.376 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.376 * [taylor]: Taking taylor expansion of k in k 9.376 * [backup-simplify]: Simplify 0 into 0 9.376 * [backup-simplify]: Simplify 1 into 1 9.376 * [backup-simplify]: Simplify (/ 1 1) into 1 9.376 * [taylor]: Taking taylor expansion of 1.0 in k 9.376 * [backup-simplify]: Simplify 1.0 into 1.0 9.376 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.376 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.377 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.377 * [taylor]: Taking taylor expansion of -2.0 in k 9.377 * [backup-simplify]: Simplify -2.0 into -2.0 9.377 * [taylor]: Taking taylor expansion of PI in k 9.377 * [backup-simplify]: Simplify PI into PI 9.377 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.378 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.378 * [taylor]: Taking taylor expansion of (log n) in k 9.378 * [taylor]: Taking taylor expansion of n in k 9.378 * [backup-simplify]: Simplify n into n 9.378 * [backup-simplify]: Simplify (log n) into (log n) 9.379 * [backup-simplify]: Simplify (+ 1 0) into 1 9.379 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.380 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.381 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.382 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.383 * [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))))) 9.384 * [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))))) 9.385 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.386 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.387 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.388 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.388 * [backup-simplify]: Simplify (+ 0 0) into 0 9.388 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.390 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.391 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.393 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.393 * [taylor]: Taking taylor expansion of 0 in k 9.393 * [backup-simplify]: Simplify 0 into 0 9.393 * [backup-simplify]: Simplify 0 into 0 9.393 * [backup-simplify]: Simplify 0 into 0 9.394 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.396 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.399 * [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 9.400 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.400 * [backup-simplify]: Simplify (+ 0 0) into 0 9.401 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.403 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.404 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.407 * [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 9.407 * [taylor]: Taking taylor expansion of 0 in k 9.407 * [backup-simplify]: Simplify 0 into 0 9.407 * [backup-simplify]: Simplify 0 into 0 9.407 * [backup-simplify]: Simplify 0 into 0 9.407 * [backup-simplify]: Simplify 0 into 0 9.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.410 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.427 * [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 9.427 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.428 * [backup-simplify]: Simplify (+ 0 0) into 0 9.429 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.432 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.434 * [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 9.434 * [taylor]: Taking taylor expansion of 0 in k 9.435 * [backup-simplify]: Simplify 0 into 0 9.435 * [backup-simplify]: Simplify 0 into 0 9.436 * [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)))))) 9.436 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2) 9.436 * [backup-simplify]: Simplify (pow n (/ (/ (- 1.0 k) 2.0) 2)) into (pow n (* 0.25 (- 1.0 k))) 9.436 * [approximate]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in (n k) around 0 9.436 * [taylor]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in k 9.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log n))) in k 9.436 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log n)) in k 9.436 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.436 * [taylor]: Taking taylor expansion of 0.25 in k 9.436 * [backup-simplify]: Simplify 0.25 into 0.25 9.436 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.436 * [taylor]: Taking taylor expansion of 1.0 in k 9.436 * [backup-simplify]: Simplify 1.0 into 1.0 9.436 * [taylor]: Taking taylor expansion of k in k 9.436 * [backup-simplify]: Simplify 0 into 0 9.437 * [backup-simplify]: Simplify 1 into 1 9.437 * [taylor]: Taking taylor expansion of (log n) in k 9.437 * [taylor]: Taking taylor expansion of n in k 9.437 * [backup-simplify]: Simplify n into n 9.437 * [backup-simplify]: Simplify (log n) into (log n) 9.437 * [backup-simplify]: Simplify (- 0) into 0 9.437 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.438 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.438 * [backup-simplify]: Simplify (* 0.25 (log n)) into (* 0.25 (log n)) 9.438 * [backup-simplify]: Simplify (exp (* 0.25 (log n))) into (pow n 0.25) 9.438 * [taylor]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in n 9.438 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log n))) in n 9.438 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log n)) in n 9.438 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.438 * [taylor]: Taking taylor expansion of 0.25 in n 9.438 * [backup-simplify]: Simplify 0.25 into 0.25 9.438 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.438 * [taylor]: Taking taylor expansion of 1.0 in n 9.438 * [backup-simplify]: Simplify 1.0 into 1.0 9.438 * [taylor]: Taking taylor expansion of k in n 9.438 * [backup-simplify]: Simplify k into k 9.438 * [taylor]: Taking taylor expansion of (log n) in n 9.438 * [taylor]: Taking taylor expansion of n in n 9.438 * [backup-simplify]: Simplify 0 into 0 9.438 * [backup-simplify]: Simplify 1 into 1 9.439 * [backup-simplify]: Simplify (log 1) into 0 9.439 * [backup-simplify]: Simplify (- k) into (- k) 9.439 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.439 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.439 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 9.440 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (log n)) into (* 0.25 (* (- 1.0 k) (log n))) 9.440 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (log n)))) into (exp (* 0.25 (* (- 1.0 k) (log n)))) 9.440 * [taylor]: Taking taylor expansion of (pow n (* 0.25 (- 1.0 k))) in n 9.440 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log n))) in n 9.440 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log n)) in n 9.440 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.440 * [taylor]: Taking taylor expansion of 0.25 in n 9.440 * [backup-simplify]: Simplify 0.25 into 0.25 9.440 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.440 * [taylor]: Taking taylor expansion of 1.0 in n 9.440 * [backup-simplify]: Simplify 1.0 into 1.0 9.440 * [taylor]: Taking taylor expansion of k in n 9.440 * [backup-simplify]: Simplify k into k 9.440 * [taylor]: Taking taylor expansion of (log n) in n 9.440 * [taylor]: Taking taylor expansion of n in n 9.440 * [backup-simplify]: Simplify 0 into 0 9.440 * [backup-simplify]: Simplify 1 into 1 9.440 * [backup-simplify]: Simplify (log 1) into 0 9.440 * [backup-simplify]: Simplify (- k) into (- k) 9.441 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.441 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.441 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 9.441 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (log n)) into (* 0.25 (* (- 1.0 k) (log n))) 9.441 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (log n)))) into (exp (* 0.25 (* (- 1.0 k) (log n)))) 9.441 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (log n)))) in k 9.441 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (log n))) in k 9.442 * [taylor]: Taking taylor expansion of 0.25 in k 9.442 * [backup-simplify]: Simplify 0.25 into 0.25 9.442 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (log n)) in k 9.442 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.442 * [taylor]: Taking taylor expansion of 1.0 in k 9.442 * [backup-simplify]: Simplify 1.0 into 1.0 9.442 * [taylor]: Taking taylor expansion of k in k 9.442 * [backup-simplify]: Simplify 0 into 0 9.442 * [backup-simplify]: Simplify 1 into 1 9.442 * [taylor]: Taking taylor expansion of (log n) in k 9.442 * [taylor]: Taking taylor expansion of n in k 9.442 * [backup-simplify]: Simplify n into n 9.442 * [backup-simplify]: Simplify (log n) into (log n) 9.442 * [backup-simplify]: Simplify (- 0) into 0 9.443 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.443 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 9.443 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (log n))) into (* 0.25 (log n)) 9.443 * [backup-simplify]: Simplify (exp (* 0.25 (log n))) into (pow n 0.25) 9.443 * [backup-simplify]: Simplify (pow n 0.25) into (pow n 0.25) 9.444 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 9.445 * [backup-simplify]: Simplify (- 0) into 0 9.445 * [backup-simplify]: Simplify (+ 0 0) into 0 9.446 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.446 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 9.446 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (log n))) into 0 9.447 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.447 * [taylor]: Taking taylor expansion of 0 in k 9.447 * [backup-simplify]: Simplify 0 into 0 9.447 * [backup-simplify]: Simplify 0 into 0 9.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.448 * [backup-simplify]: Simplify (- 1) into -1 9.449 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.449 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (log n))) into (- (log n)) 9.449 * [backup-simplify]: Simplify (+ (* 0.25 (- (log n))) (* 0 (* 1.0 (log n)))) into (- (* 0.25 (log n))) 9.450 * [backup-simplify]: Simplify (* (exp (* 0.25 (log n))) (+ (* (/ (pow (- (* 0.25 (log n))) 1) 1)))) into (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) 9.450 * [backup-simplify]: Simplify (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) into (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) 9.453 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 9.453 * [backup-simplify]: Simplify (- 0) into 0 9.453 * [backup-simplify]: Simplify (+ 0 0) into 0 9.454 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 9.455 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0 9.456 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.456 * [taylor]: Taking taylor expansion of 0 in k 9.456 * [backup-simplify]: Simplify 0 into 0 9.456 * [backup-simplify]: Simplify 0 into 0 9.456 * [backup-simplify]: Simplify 0 into 0 9.457 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.458 * [backup-simplify]: Simplify (- 0) into 0 9.458 * [backup-simplify]: Simplify (+ 0 0) into 0 9.458 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (log n)))) into 0 9.459 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (log n))) (* 0 (* 1.0 (log n))))) into 0 9.459 * [backup-simplify]: Simplify (* (exp (* 0.25 (log n))) (+ (* (/ (pow (- (* 0.25 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) 9.460 * [backup-simplify]: Simplify (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) into (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) 9.460 * [backup-simplify]: Simplify (+ (* (* 0.03125 (* (pow (pow n 1.0) 0.25) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -0.25 (* (pow (pow n 1.0) 0.25) (log n))) (* k 1)) (pow n 0.25))) into (- (+ (* 0.03125 (* (* (pow k 2) (pow (log n) 2)) (pow (pow n 1.0) 0.25))) (pow n 0.25)) (* 0.25 (* (* k (log n)) (pow (pow n 1.0) 0.25)))) 9.461 * [backup-simplify]: Simplify (pow (/ 1 n) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) 9.461 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.461 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.461 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in k 9.461 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n))) in k 9.461 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.461 * [taylor]: Taking taylor expansion of 0.25 in k 9.461 * [backup-simplify]: Simplify 0.25 into 0.25 9.461 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.461 * [taylor]: Taking taylor expansion of 1.0 in k 9.461 * [backup-simplify]: Simplify 1.0 into 1.0 9.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.461 * [taylor]: Taking taylor expansion of k in k 9.461 * [backup-simplify]: Simplify 0 into 0 9.461 * [backup-simplify]: Simplify 1 into 1 9.461 * [backup-simplify]: Simplify (/ 1 1) into 1 9.461 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k 9.461 * [taylor]: Taking taylor expansion of (/ 1 n) in k 9.461 * [taylor]: Taking taylor expansion of n in k 9.461 * [backup-simplify]: Simplify n into n 9.461 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n) 9.461 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n)) 9.462 * [backup-simplify]: Simplify (- 1) into -1 9.462 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.462 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.462 * [backup-simplify]: Simplify (* -0.25 (log (/ 1 n))) into (* -0.25 (log (/ 1 n))) 9.462 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) into (exp (* 0.25 (* (log (/ 1 n)) (- 1.0 (/ 1 k))))) 9.462 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.462 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 9.462 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 9.462 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.463 * [taylor]: Taking taylor expansion of 0.25 in n 9.463 * [backup-simplify]: Simplify 0.25 into 0.25 9.463 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.463 * [taylor]: Taking taylor expansion of 1.0 in n 9.463 * [backup-simplify]: Simplify 1.0 into 1.0 9.463 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.463 * [taylor]: Taking taylor expansion of k in n 9.463 * [backup-simplify]: Simplify k into k 9.463 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.463 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 9.463 * [taylor]: Taking taylor expansion of (/ 1 n) in n 9.463 * [taylor]: Taking taylor expansion of n in n 9.463 * [backup-simplify]: Simplify 0 into 0 9.463 * [backup-simplify]: Simplify 1 into 1 9.463 * [backup-simplify]: Simplify (/ 1 1) into 1 9.463 * [backup-simplify]: Simplify (log 1) into 0 9.463 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.463 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.463 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 9.464 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.25 (* (log n) (- 1.0 (/ 1 k)))) 9.464 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 9.464 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.464 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n)))) in n 9.464 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (/ 1 n))) in n 9.464 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.464 * [taylor]: Taking taylor expansion of 0.25 in n 9.464 * [backup-simplify]: Simplify 0.25 into 0.25 9.464 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.464 * [taylor]: Taking taylor expansion of 1.0 in n 9.464 * [backup-simplify]: Simplify 1.0 into 1.0 9.464 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.464 * [taylor]: Taking taylor expansion of k in n 9.464 * [backup-simplify]: Simplify k into k 9.464 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.464 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 9.464 * [taylor]: Taking taylor expansion of (/ 1 n) in n 9.464 * [taylor]: Taking taylor expansion of n in n 9.464 * [backup-simplify]: Simplify 0 into 0 9.464 * [backup-simplify]: Simplify 1 into 1 9.465 * [backup-simplify]: Simplify (/ 1 1) into 1 9.465 * [backup-simplify]: Simplify (log 1) into 0 9.465 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.465 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.465 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.465 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 9.465 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log n))) into (* -0.25 (* (log n) (- 1.0 (/ 1 k)))) 9.466 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 9.466 * [taylor]: Taking taylor expansion of (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) in k 9.466 * [taylor]: Taking taylor expansion of (* -0.25 (* (log n) (- 1.0 (/ 1 k)))) in k 9.466 * [taylor]: Taking taylor expansion of -0.25 in k 9.466 * [backup-simplify]: Simplify -0.25 into -0.25 9.466 * [taylor]: Taking taylor expansion of (* (log n) (- 1.0 (/ 1 k))) in k 9.466 * [taylor]: Taking taylor expansion of (log n) in k 9.466 * [taylor]: Taking taylor expansion of n in k 9.466 * [backup-simplify]: Simplify n into n 9.466 * [backup-simplify]: Simplify (log n) into (log n) 9.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.466 * [taylor]: Taking taylor expansion of 1.0 in k 9.466 * [backup-simplify]: Simplify 1.0 into 1.0 9.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.466 * [taylor]: Taking taylor expansion of k in k 9.466 * [backup-simplify]: Simplify 0 into 0 9.466 * [backup-simplify]: Simplify 1 into 1 9.466 * [backup-simplify]: Simplify (/ 1 1) into 1 9.466 * [backup-simplify]: Simplify (- 1) into -1 9.467 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.467 * [backup-simplify]: Simplify (* (log n) -1) into (* -1 (log n)) 9.467 * [backup-simplify]: Simplify (* -0.25 (* -1 (log n))) into (* 0.25 (log n)) 9.467 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 9.467 * [backup-simplify]: Simplify (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) into (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) 9.468 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.468 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 9.469 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.469 * [backup-simplify]: Simplify (- 0) into 0 9.469 * [backup-simplify]: Simplify (+ 0 0) into 0 9.469 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.470 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 9.470 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log n)))) into 0 9.470 * [backup-simplify]: Simplify (* (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.470 * [taylor]: Taking taylor expansion of 0 in k 9.470 * [backup-simplify]: Simplify 0 into 0 9.470 * [backup-simplify]: Simplify 0 into 0 9.470 * [backup-simplify]: Simplify 0 into 0 9.471 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.473 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 9.473 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.473 * [backup-simplify]: Simplify (- 0) into 0 9.473 * [backup-simplify]: Simplify (+ 0 0) into 0 9.474 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.474 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 9.475 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 9.476 * [backup-simplify]: Simplify (* (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.476 * [taylor]: Taking taylor expansion of 0 in k 9.476 * [backup-simplify]: Simplify 0 into 0 9.476 * [backup-simplify]: Simplify 0 into 0 9.476 * [backup-simplify]: Simplify 0 into 0 9.476 * [backup-simplify]: Simplify 0 into 0 9.476 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.479 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 9.479 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.480 * [backup-simplify]: Simplify (- 0) into 0 9.480 * [backup-simplify]: Simplify (+ 0 0) into 0 9.481 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.481 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 9.482 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 9.483 * [backup-simplify]: Simplify (* (exp (* -0.25 (* (log n) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.483 * [taylor]: Taking taylor expansion of 0 in k 9.483 * [backup-simplify]: Simplify 0 into 0 9.483 * [backup-simplify]: Simplify 0 into 0 9.483 * [backup-simplify]: Simplify (exp (* -0.25 (* (log (/ 1 n)) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* -0.25 (* (- 1.0 k) (log (/ 1 n))))) 9.483 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) 9.483 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.483 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in k 9.483 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in k 9.483 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.483 * [taylor]: Taking taylor expansion of 0.25 in k 9.483 * [backup-simplify]: Simplify 0.25 into 0.25 9.483 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.483 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.483 * [taylor]: Taking taylor expansion of k in k 9.483 * [backup-simplify]: Simplify 0 into 0 9.483 * [backup-simplify]: Simplify 1 into 1 9.484 * [backup-simplify]: Simplify (/ 1 1) into 1 9.484 * [taylor]: Taking taylor expansion of 1.0 in k 9.484 * [backup-simplify]: Simplify 1.0 into 1.0 9.484 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k 9.484 * [taylor]: Taking taylor expansion of (/ -1 n) in k 9.484 * [taylor]: Taking taylor expansion of -1 in k 9.484 * [backup-simplify]: Simplify -1 into -1 9.484 * [taylor]: Taking taylor expansion of n in k 9.484 * [backup-simplify]: Simplify n into n 9.484 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n) 9.484 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n)) 9.484 * [backup-simplify]: Simplify (+ 1 0) into 1 9.484 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.484 * [backup-simplify]: Simplify (* 0.25 (log (/ -1 n))) into (* 0.25 (log (/ -1 n))) 9.485 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (/ -1 n))))) 9.485 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.485 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 9.485 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 9.485 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.485 * [taylor]: Taking taylor expansion of 0.25 in n 9.485 * [backup-simplify]: Simplify 0.25 into 0.25 9.485 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.485 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.485 * [taylor]: Taking taylor expansion of k in n 9.485 * [backup-simplify]: Simplify k into k 9.485 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.485 * [taylor]: Taking taylor expansion of 1.0 in n 9.485 * [backup-simplify]: Simplify 1.0 into 1.0 9.485 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 9.485 * [taylor]: Taking taylor expansion of (/ -1 n) in n 9.485 * [taylor]: Taking taylor expansion of -1 in n 9.485 * [backup-simplify]: Simplify -1 into -1 9.485 * [taylor]: Taking taylor expansion of n in n 9.485 * [backup-simplify]: Simplify 0 into 0 9.485 * [backup-simplify]: Simplify 1 into 1 9.485 * [backup-simplify]: Simplify (/ -1 1) into -1 9.486 * [backup-simplify]: Simplify (log -1) into (log -1) 9.486 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.486 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 9.487 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 9.487 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 9.487 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.487 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n)))) in n 9.487 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (/ -1 n))) in n 9.487 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.487 * [taylor]: Taking taylor expansion of 0.25 in n 9.487 * [backup-simplify]: Simplify 0.25 into 0.25 9.487 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.487 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.487 * [taylor]: Taking taylor expansion of k in n 9.487 * [backup-simplify]: Simplify k into k 9.487 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.487 * [taylor]: Taking taylor expansion of 1.0 in n 9.487 * [backup-simplify]: Simplify 1.0 into 1.0 9.487 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n 9.487 * [taylor]: Taking taylor expansion of (/ -1 n) in n 9.487 * [taylor]: Taking taylor expansion of -1 in n 9.487 * [backup-simplify]: Simplify -1 into -1 9.487 * [taylor]: Taking taylor expansion of n in n 9.487 * [backup-simplify]: Simplify 0 into 0 9.487 * [backup-simplify]: Simplify 1 into 1 9.488 * [backup-simplify]: Simplify (/ -1 1) into -1 9.488 * [backup-simplify]: Simplify (log -1) into (log -1) 9.488 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.488 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.489 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 9.489 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log -1) (log n))) into (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) 9.489 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 9.489 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) in k 9.489 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0))) in k 9.489 * [taylor]: Taking taylor expansion of 0.25 in k 9.489 * [backup-simplify]: Simplify 0.25 into 0.25 9.489 * [taylor]: Taking taylor expansion of (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)) in k 9.489 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k 9.489 * [taylor]: Taking taylor expansion of (log -1) in k 9.489 * [taylor]: Taking taylor expansion of -1 in k 9.489 * [backup-simplify]: Simplify -1 into -1 9.490 * [backup-simplify]: Simplify (log -1) into (log -1) 9.490 * [taylor]: Taking taylor expansion of (log n) in k 9.490 * [taylor]: Taking taylor expansion of n in k 9.490 * [backup-simplify]: Simplify n into n 9.490 * [backup-simplify]: Simplify (log n) into (log n) 9.490 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.490 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.490 * [taylor]: Taking taylor expansion of k in k 9.490 * [backup-simplify]: Simplify 0 into 0 9.490 * [backup-simplify]: Simplify 1 into 1 9.490 * [backup-simplify]: Simplify (/ 1 1) into 1 9.490 * [taylor]: Taking taylor expansion of 1.0 in k 9.490 * [backup-simplify]: Simplify 1.0 into 1.0 9.490 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.491 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n)) 9.491 * [backup-simplify]: Simplify (+ 1 0) into 1 9.491 * [backup-simplify]: Simplify (* (- (log -1) (log n)) 1) into (- (log -1) (log n)) 9.491 * [backup-simplify]: Simplify (* 0.25 (- (log -1) (log n))) into (* 0.25 (- (log -1) (log n))) 9.492 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 9.492 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) 9.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.494 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0 9.494 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.494 * [backup-simplify]: Simplify (+ 0 0) into 0 9.494 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 9.495 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log -1) (log n)))) into 0 9.496 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 9.496 * [taylor]: Taking taylor expansion of 0 in k 9.496 * [backup-simplify]: Simplify 0 into 0 9.496 * [backup-simplify]: Simplify 0 into 0 9.496 * [backup-simplify]: Simplify 0 into 0 9.497 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.498 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0 9.498 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.499 * [backup-simplify]: Simplify (+ 0 0) into 0 9.499 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.500 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 9.500 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0 9.501 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.501 * [taylor]: Taking taylor expansion of 0 in k 9.501 * [backup-simplify]: Simplify 0 into 0 9.501 * [backup-simplify]: Simplify 0 into 0 9.501 * [backup-simplify]: Simplify 0 into 0 9.501 * [backup-simplify]: Simplify 0 into 0 9.502 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.505 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -1 1)))) 6) into 0 9.505 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.505 * [backup-simplify]: Simplify (+ 0 0) into 0 9.506 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.507 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n)) 9.508 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0 9.509 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log -1) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.509 * [taylor]: Taking taylor expansion of 0 in k 9.509 * [backup-simplify]: Simplify 0 into 0 9.509 * [backup-simplify]: Simplify 0 into 0 9.509 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log -1) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.25 (* (- 1.0 k) (- (log -1) (log (/ -1 n)))))) 9.509 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 9.510 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.510 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.510 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.510 * [taylor]: Taking taylor expansion of 2.0 in n 9.510 * [backup-simplify]: Simplify 2.0 into 2.0 9.510 * [taylor]: Taking taylor expansion of (* n PI) in n 9.510 * [taylor]: Taking taylor expansion of n in n 9.510 * [backup-simplify]: Simplify 0 into 0 9.510 * [backup-simplify]: Simplify 1 into 1 9.510 * [taylor]: Taking taylor expansion of PI in n 9.510 * [backup-simplify]: Simplify PI into PI 9.510 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.510 * [taylor]: Taking taylor expansion of 2.0 in n 9.510 * [backup-simplify]: Simplify 2.0 into 2.0 9.510 * [taylor]: Taking taylor expansion of (* n PI) in n 9.510 * [taylor]: Taking taylor expansion of n in n 9.510 * [backup-simplify]: Simplify 0 into 0 9.510 * [backup-simplify]: Simplify 1 into 1 9.510 * [taylor]: Taking taylor expansion of PI in n 9.510 * [backup-simplify]: Simplify PI into PI 9.510 * [backup-simplify]: Simplify (* 0 PI) into 0 9.511 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.511 * [backup-simplify]: Simplify 0 into 0 9.512 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.513 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.513 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.514 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.514 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.514 * [backup-simplify]: Simplify 0 into 0 9.515 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.516 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.516 * [backup-simplify]: Simplify 0 into 0 9.517 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.518 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.518 * [backup-simplify]: Simplify 0 into 0 9.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.520 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.520 * [backup-simplify]: Simplify 0 into 0 9.521 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.522 * [backup-simplify]: Simplify 0 into 0 9.523 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.524 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.524 * [backup-simplify]: Simplify 0 into 0 9.525 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.525 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.525 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.525 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.525 * [taylor]: Taking taylor expansion of 2.0 in n 9.525 * [backup-simplify]: Simplify 2.0 into 2.0 9.525 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.525 * [taylor]: Taking taylor expansion of PI in n 9.525 * [backup-simplify]: Simplify PI into PI 9.525 * [taylor]: Taking taylor expansion of n in n 9.525 * [backup-simplify]: Simplify 0 into 0 9.525 * [backup-simplify]: Simplify 1 into 1 9.526 * [backup-simplify]: Simplify (/ PI 1) into PI 9.526 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.526 * [taylor]: Taking taylor expansion of 2.0 in n 9.526 * [backup-simplify]: Simplify 2.0 into 2.0 9.526 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.526 * [taylor]: Taking taylor expansion of PI in n 9.526 * [backup-simplify]: Simplify PI into PI 9.526 * [taylor]: Taking taylor expansion of n in n 9.526 * [backup-simplify]: Simplify 0 into 0 9.526 * [backup-simplify]: Simplify 1 into 1 9.526 * [backup-simplify]: Simplify (/ PI 1) into PI 9.526 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.527 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.527 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.528 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.528 * [backup-simplify]: Simplify 0 into 0 9.528 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.529 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.529 * [backup-simplify]: Simplify 0 into 0 9.530 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.537 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.537 * [backup-simplify]: Simplify 0 into 0 9.538 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.539 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.540 * [backup-simplify]: Simplify 0 into 0 9.541 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.542 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.542 * [backup-simplify]: Simplify 0 into 0 9.543 * [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 9.545 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.545 * [backup-simplify]: Simplify 0 into 0 9.545 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.546 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.546 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.546 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.546 * [taylor]: Taking taylor expansion of -2.0 in n 9.546 * [backup-simplify]: Simplify -2.0 into -2.0 9.546 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.546 * [taylor]: Taking taylor expansion of PI in n 9.546 * [backup-simplify]: Simplify PI into PI 9.546 * [taylor]: Taking taylor expansion of n in n 9.546 * [backup-simplify]: Simplify 0 into 0 9.546 * [backup-simplify]: Simplify 1 into 1 9.547 * [backup-simplify]: Simplify (/ PI 1) into PI 9.547 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.547 * [taylor]: Taking taylor expansion of -2.0 in n 9.547 * [backup-simplify]: Simplify -2.0 into -2.0 9.547 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.547 * [taylor]: Taking taylor expansion of PI in n 9.547 * [backup-simplify]: Simplify PI into PI 9.547 * [taylor]: Taking taylor expansion of n in n 9.547 * [backup-simplify]: Simplify 0 into 0 9.547 * [backup-simplify]: Simplify 1 into 1 9.547 * [backup-simplify]: Simplify (/ PI 1) into PI 9.548 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.548 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.549 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.550 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.550 * [backup-simplify]: Simplify 0 into 0 9.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.552 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.552 * [backup-simplify]: Simplify 0 into 0 9.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.554 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.554 * [backup-simplify]: Simplify 0 into 0 9.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.556 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.556 * [backup-simplify]: Simplify 0 into 0 9.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.559 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.559 * [backup-simplify]: Simplify 0 into 0 9.560 * [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 9.561 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.561 * [backup-simplify]: Simplify 0 into 0 9.562 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.562 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 9.562 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 9.562 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 9.562 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.562 * [taylor]: Taking taylor expansion of 1.0 in k 9.562 * [backup-simplify]: Simplify 1.0 into 1.0 9.562 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.562 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.562 * [taylor]: Taking taylor expansion of k in k 9.562 * [backup-simplify]: Simplify 0 into 0 9.562 * [backup-simplify]: Simplify 1 into 1 9.563 * [backup-simplify]: Simplify (/ 1 1) into 1 9.563 * [backup-simplify]: Simplify (sqrt 0) into 0 9.564 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.564 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 9.564 * [taylor]: Taking taylor expansion of 1.0 in k 9.565 * [backup-simplify]: Simplify 1.0 into 1.0 9.565 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 9.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.565 * [taylor]: Taking taylor expansion of k in k 9.565 * [backup-simplify]: Simplify 0 into 0 9.565 * [backup-simplify]: Simplify 1 into 1 9.565 * [backup-simplify]: Simplify (/ 1 1) into 1 9.565 * [backup-simplify]: Simplify (sqrt 0) into 0 9.566 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.567 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.567 * [backup-simplify]: Simplify 0 into 0 9.568 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.569 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.569 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.572 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.574 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.574 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.575 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.580 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.582 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.582 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.584 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 9.584 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.584 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.584 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.584 * [taylor]: Taking taylor expansion of 1.0 in k 9.584 * [backup-simplify]: Simplify 1.0 into 1.0 9.584 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.584 * [taylor]: Taking taylor expansion of k in k 9.584 * [backup-simplify]: Simplify 0 into 0 9.585 * [backup-simplify]: Simplify 1 into 1 9.585 * [backup-simplify]: Simplify (sqrt 0) into 0 9.586 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.586 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.586 * [taylor]: Taking taylor expansion of 1.0 in k 9.586 * [backup-simplify]: Simplify 1.0 into 1.0 9.587 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.587 * [taylor]: Taking taylor expansion of k in k 9.587 * [backup-simplify]: Simplify 0 into 0 9.587 * [backup-simplify]: Simplify 1 into 1 9.587 * [backup-simplify]: Simplify (sqrt 0) into 0 9.588 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.589 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.589 * [backup-simplify]: Simplify 0 into 0 9.591 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.591 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.594 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.596 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.597 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.600 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.601 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.602 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.603 * [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)))))))) 9.603 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.603 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.603 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.603 * [taylor]: Taking taylor expansion of 1.0 in k 9.603 * [backup-simplify]: Simplify 1.0 into 1.0 9.603 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.603 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.603 * [taylor]: Taking taylor expansion of -1 in k 9.603 * [backup-simplify]: Simplify -1 into -1 9.603 * [taylor]: Taking taylor expansion of k in k 9.603 * [backup-simplify]: Simplify 0 into 0 9.603 * [backup-simplify]: Simplify 1 into 1 9.603 * [backup-simplify]: Simplify (/ -1 1) into -1 9.604 * [backup-simplify]: Simplify (sqrt 0) into 0 9.604 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.605 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.605 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.605 * [taylor]: Taking taylor expansion of 1.0 in k 9.605 * [backup-simplify]: Simplify 1.0 into 1.0 9.605 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.605 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.605 * [taylor]: Taking taylor expansion of -1 in k 9.605 * [backup-simplify]: Simplify -1 into -1 9.605 * [taylor]: Taking taylor expansion of k in k 9.605 * [backup-simplify]: Simplify 0 into 0 9.605 * [backup-simplify]: Simplify 1 into 1 9.605 * [backup-simplify]: Simplify (/ -1 1) into -1 9.605 * [backup-simplify]: Simplify (sqrt 0) into 0 9.606 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.606 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.607 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.607 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.609 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.610 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.611 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.611 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.613 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.616 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.617 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.617 * [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))))) 9.617 * * * [progress]: simplifying candidates 9.621 * [simplify]: Simplifying: (* (+ (+ (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)) (* (log n) (/ (/ (- 1.0 k) 2.0) 2)) (* (log n) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ 1.0 2.0) 2)) (pow n (/ (/ k 2.0) 2)) (pow n (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow n (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow n (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow n (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow n (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow n (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow n (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow n (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow n (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow n (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow n (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow n (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow n (/ (/ 1 (sqrt 2.0)) 1)) (pow n (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 1) (sqrt 2))) (pow n (/ (/ 1 1) 1)) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow n (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow n (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow n (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow n (/ (/ 1 (sqrt 2.0)) 1)) (pow n (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow n (/ (/ 1 1) (sqrt 2))) (pow n (/ (/ 1 1) 1)) (pow n (/ 1 (* (cbrt 2) (cbrt 2)))) (pow n (/ 1 (sqrt 2))) (pow n (/ 1 1)) (pow n (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow n (/ (- 1.0 k) (sqrt 2))) (pow n (/ (- 1.0 k) 1)) (pow n 1) (pow n (/ (- 1.0 k) 2.0)) (pow (* (cbrt n) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (cbrt n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (sqrt n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (sqrt n) (/ (/ (- 1.0 k) 2.0) 2)) (pow 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow n (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow n (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow n (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow n (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow n (/ (/ (- 1.0 k) 2.0) 2))) (pow n (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow n (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (* 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) (- (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 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h1))) (/ (cbrt h2) (sqrt (sqrt h1))) (/ (* (cbrt h2) (cbrt h2)) 1) (/ (cbrt h2) (sqrt h1)) (/ (sqrt h2) (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ (sqrt h2) (cbrt (sqrt h1))) (/ (sqrt h2) (sqrt (* (cbrt h1) (cbrt h1)))) (/ (sqrt h2) (sqrt (cbrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt 1)) (/ (sqrt h2) (sqrt h1)) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) (sqrt (sqrt h1))) (/ (sqrt h2) 1) (/ (sqrt h2) (sqrt h1)) (/ 1 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (cbrt (sqrt h1))) (/ 1 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (cbrt h1))) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 (sqrt 1)) (/ h2 (sqrt h1)) (/ 1 (sqrt (sqrt h1))) (/ h2 (sqrt (sqrt h1))) (/ 1 1) (/ h2 (sqrt h1)) (/ 1 (sqrt h1)) (/ (sqrt h1) h2) (/ h2 (* (cbrt (sqrt h1)) (cbrt (sqrt h1)))) (/ h2 (sqrt (* (cbrt h1) (cbrt h1)))) (/ h2 (sqrt (sqrt h1))) (/ h2 (sqrt 1)) (/ h2 (sqrt (sqrt h1))) (/ h2 1) (/ (sqrt h1) (cbrt h2)) (/ (sqrt h1) (sqrt h2)) (/ (sqrt h1) h2) (- (+ (* h6 (* (pow h1 2) (* (pow (log (* h0 h4)) 2) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (+ (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (+ (* h7 (* (pow h1 2) (* (log (* h0 h4)) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3))))) (* h6 (* (pow h1 2) (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (pow (log h3) 2))))))) (+ (* h5 (* h1 (* (log (* h0 h4)) (exp (* h5 (+ (log (* h0 h4)) (log h3))))))) (* h5 (* h1 (* (exp (* h5 (+ (log (* h0 h4)) (log h3)))) (log h3)))))) (exp (* h5 (* (- (log (* h0 h4)) (log (/ 1 h3))) (- h2 h1)))) (exp (* h5 (* (- h2 h1) (- (log (* h8 h4)) (log (/ -1 h3)))))) (- (+ (* h6 (* (* (pow h1 2) (pow (log h3) 2)) (pow (pow h3 h2) h5))) (pow h3 h5)) (* h5 (* (* h1 (log h3)) (pow (pow h3 h2) h5)))) (exp (* h9 (* (- h2 h1) (log (/ 1 h3))))) (exp (* h5 (* (- h2 h1) (- (log -1) (log (/ -1 h3)))))) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (* h0 (* h3 h4)) (- (+ (* h10 h1) (- (+ (* h10 (pow h1 2)) (- h10))))) (- (+ (* h10 (/ 1 (pow h1 2))) (- (+ (* h10 (/ 1 h1)) (- (* h10 (/ 1 (pow h1 3)))))))) (- (+ (* h10 (/ 1 (pow h1 2))) (- (+ (* h10 (/ 1 h1)) (- h10))))) 9.702 * * * [progress]: adding candidates to table 11.061 * [progress]: [Phase 3 of 3] Extracting. 11.061 * * [regime]: Finding splitpoints for: (# # # # # # #) 11.063 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 11.063 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # #) 11.128 * * * * [regimes]: Trying to branch on n from (# # # # # # #) 11.192 * * * * [regimes]: Trying to branch on k from (# # # # # # #) 11.228 * * * [regime]: Found split indices: #