50.004 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.168 * * * [progress]: [2/2] Setting up program. 0.173 * [progress]: [Phase 2 of 3] Improving. 0.174 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 2.362 * * [progress]: iteration 1 / 4 2.362 * * * [progress]: picking best candidate 2.394 * * * * [pick]: Picked # 2.394 * * * [progress]: localizing error 2.412 * * * [progress]: generating rewritten candidates 2.412 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.441 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 2.459 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 2.465 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 2.525 * * * [progress]: generating series expansions 2.525 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.526 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 2.526 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 2.526 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.526 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.526 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.526 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.526 * [taylor]: Taking taylor expansion of 0.5 in k 2.526 * [backup-simplify]: Simplify 0.5 into 0.5 2.526 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.526 * [taylor]: Taking taylor expansion of 1.0 in k 2.526 * [backup-simplify]: Simplify 1.0 into 1.0 2.526 * [taylor]: Taking taylor expansion of k in k 2.526 * [backup-simplify]: Simplify 0 into 0 2.526 * [backup-simplify]: Simplify 1 into 1 2.526 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.526 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.526 * [taylor]: Taking taylor expansion of 2.0 in k 2.526 * [backup-simplify]: Simplify 2.0 into 2.0 2.526 * [taylor]: Taking taylor expansion of (* n PI) in k 2.526 * [taylor]: Taking taylor expansion of n in k 2.526 * [backup-simplify]: Simplify n into n 2.526 * [taylor]: Taking taylor expansion of PI in k 2.527 * [backup-simplify]: Simplify PI into PI 2.527 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.527 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.527 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.527 * [backup-simplify]: Simplify (- 0) into 0 2.527 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.528 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.528 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.528 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.528 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.528 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.528 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.528 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.528 * [taylor]: Taking taylor expansion of 0.5 in n 2.528 * [backup-simplify]: Simplify 0.5 into 0.5 2.528 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.528 * [taylor]: Taking taylor expansion of 1.0 in n 2.528 * [backup-simplify]: Simplify 1.0 into 1.0 2.528 * [taylor]: Taking taylor expansion of k in n 2.528 * [backup-simplify]: Simplify k into k 2.528 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.528 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.528 * [taylor]: Taking taylor expansion of 2.0 in n 2.528 * [backup-simplify]: Simplify 2.0 into 2.0 2.528 * [taylor]: Taking taylor expansion of (* n PI) in n 2.528 * [taylor]: Taking taylor expansion of n in n 2.528 * [backup-simplify]: Simplify 0 into 0 2.528 * [backup-simplify]: Simplify 1 into 1 2.528 * [taylor]: Taking taylor expansion of PI in n 2.528 * [backup-simplify]: Simplify PI into PI 2.528 * [backup-simplify]: Simplify (* 0 PI) into 0 2.529 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.530 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.531 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.531 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.531 * [backup-simplify]: Simplify (- k) into (- k) 2.531 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.531 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.532 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.533 * [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)))) 2.534 * [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))))) 2.534 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.534 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.534 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.534 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.534 * [taylor]: Taking taylor expansion of 0.5 in n 2.534 * [backup-simplify]: Simplify 0.5 into 0.5 2.534 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.534 * [taylor]: Taking taylor expansion of 1.0 in n 2.534 * [backup-simplify]: Simplify 1.0 into 1.0 2.534 * [taylor]: Taking taylor expansion of k in n 2.534 * [backup-simplify]: Simplify k into k 2.534 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.534 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.534 * [taylor]: Taking taylor expansion of 2.0 in n 2.534 * [backup-simplify]: Simplify 2.0 into 2.0 2.534 * [taylor]: Taking taylor expansion of (* n PI) in n 2.534 * [taylor]: Taking taylor expansion of n in n 2.534 * [backup-simplify]: Simplify 0 into 0 2.534 * [backup-simplify]: Simplify 1 into 1 2.534 * [taylor]: Taking taylor expansion of PI in n 2.534 * [backup-simplify]: Simplify PI into PI 2.534 * [backup-simplify]: Simplify (* 0 PI) into 0 2.535 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.536 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.537 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.537 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.537 * [backup-simplify]: Simplify (- k) into (- k) 2.537 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.537 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.538 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.539 * [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)))) 2.540 * [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))))) 2.540 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.540 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.540 * [taylor]: Taking taylor expansion of 0.5 in k 2.540 * [backup-simplify]: Simplify 0.5 into 0.5 2.540 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.540 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.540 * [taylor]: Taking taylor expansion of 1.0 in k 2.540 * [backup-simplify]: Simplify 1.0 into 1.0 2.540 * [taylor]: Taking taylor expansion of k in k 2.540 * [backup-simplify]: Simplify 0 into 0 2.540 * [backup-simplify]: Simplify 1 into 1 2.540 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.540 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.540 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.540 * [taylor]: Taking taylor expansion of 2.0 in k 2.540 * [backup-simplify]: Simplify 2.0 into 2.0 2.540 * [taylor]: Taking taylor expansion of PI in k 2.540 * [backup-simplify]: Simplify PI into PI 2.540 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.541 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.541 * [taylor]: Taking taylor expansion of (log n) in k 2.541 * [taylor]: Taking taylor expansion of n in k 2.541 * [backup-simplify]: Simplify n into n 2.541 * [backup-simplify]: Simplify (log n) into (log n) 2.541 * [backup-simplify]: Simplify (- 0) into 0 2.542 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.542 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.543 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.544 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 2.544 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.545 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 2.546 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.546 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.547 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.548 * [backup-simplify]: Simplify (- 0) into 0 2.548 * [backup-simplify]: Simplify (+ 0 0) into 0 2.548 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 2.549 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.553 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.555 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.555 * [taylor]: Taking taylor expansion of 0 in k 2.555 * [backup-simplify]: Simplify 0 into 0 2.555 * [backup-simplify]: Simplify 0 into 0 2.555 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.556 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.557 * [backup-simplify]: Simplify (+ 0 0) into 0 2.557 * [backup-simplify]: Simplify (- 1) into -1 2.558 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.558 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.560 * [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)))) 2.562 * [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)))))) 2.565 * [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)))))) 2.566 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.571 * [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 2.571 * [backup-simplify]: Simplify (- 0) into 0 2.572 * [backup-simplify]: Simplify (+ 0 0) into 0 2.573 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.574 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.576 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.579 * [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 2.579 * [taylor]: Taking taylor expansion of 0 in k 2.579 * [backup-simplify]: Simplify 0 into 0 2.579 * [backup-simplify]: Simplify 0 into 0 2.579 * [backup-simplify]: Simplify 0 into 0 2.580 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.583 * [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 2.585 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.586 * [backup-simplify]: Simplify (+ 0 0) into 0 2.586 * [backup-simplify]: Simplify (- 0) into 0 2.587 * [backup-simplify]: Simplify (+ 0 0) into 0 2.589 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.592 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.596 * [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)))))) 2.601 * [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)))))) 2.612 * [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)))))) 2.613 * [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)))) 2.613 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 2.613 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.613 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.613 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.613 * [taylor]: Taking taylor expansion of 0.5 in k 2.614 * [backup-simplify]: Simplify 0.5 into 0.5 2.614 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.614 * [taylor]: Taking taylor expansion of 1.0 in k 2.614 * [backup-simplify]: Simplify 1.0 into 1.0 2.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.614 * [taylor]: Taking taylor expansion of k in k 2.614 * [backup-simplify]: Simplify 0 into 0 2.614 * [backup-simplify]: Simplify 1 into 1 2.614 * [backup-simplify]: Simplify (/ 1 1) into 1 2.614 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.614 * [taylor]: Taking taylor expansion of 2.0 in k 2.614 * [backup-simplify]: Simplify 2.0 into 2.0 2.614 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.614 * [taylor]: Taking taylor expansion of PI in k 2.614 * [backup-simplify]: Simplify PI into PI 2.614 * [taylor]: Taking taylor expansion of n in k 2.614 * [backup-simplify]: Simplify n into n 2.614 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.615 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.615 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.615 * [backup-simplify]: Simplify (- 1) into -1 2.615 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.616 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.616 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.616 * [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))))) 2.616 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.616 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.617 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.617 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.617 * [taylor]: Taking taylor expansion of 0.5 in n 2.617 * [backup-simplify]: Simplify 0.5 into 0.5 2.617 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.617 * [taylor]: Taking taylor expansion of 1.0 in n 2.617 * [backup-simplify]: Simplify 1.0 into 1.0 2.617 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.617 * [taylor]: Taking taylor expansion of k in n 2.617 * [backup-simplify]: Simplify k into k 2.617 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.617 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.617 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.617 * [taylor]: Taking taylor expansion of 2.0 in n 2.617 * [backup-simplify]: Simplify 2.0 into 2.0 2.617 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.617 * [taylor]: Taking taylor expansion of PI in n 2.617 * [backup-simplify]: Simplify PI into PI 2.617 * [taylor]: Taking taylor expansion of n in n 2.617 * [backup-simplify]: Simplify 0 into 0 2.617 * [backup-simplify]: Simplify 1 into 1 2.618 * [backup-simplify]: Simplify (/ PI 1) into PI 2.618 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.619 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.619 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.619 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.619 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.621 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.622 * [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)))) 2.623 * [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))))) 2.623 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.623 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.623 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.623 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.623 * [taylor]: Taking taylor expansion of 0.5 in n 2.623 * [backup-simplify]: Simplify 0.5 into 0.5 2.623 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.624 * [taylor]: Taking taylor expansion of 1.0 in n 2.624 * [backup-simplify]: Simplify 1.0 into 1.0 2.624 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.624 * [taylor]: Taking taylor expansion of k in n 2.624 * [backup-simplify]: Simplify k into k 2.624 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.624 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.624 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.624 * [taylor]: Taking taylor expansion of 2.0 in n 2.624 * [backup-simplify]: Simplify 2.0 into 2.0 2.624 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.624 * [taylor]: Taking taylor expansion of PI in n 2.624 * [backup-simplify]: Simplify PI into PI 2.624 * [taylor]: Taking taylor expansion of n in n 2.624 * [backup-simplify]: Simplify 0 into 0 2.624 * [backup-simplify]: Simplify 1 into 1 2.625 * [backup-simplify]: Simplify (/ PI 1) into PI 2.625 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.626 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.626 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.626 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.626 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.629 * [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)))) 2.630 * [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))))) 2.631 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.631 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.631 * [taylor]: Taking taylor expansion of 0.5 in k 2.631 * [backup-simplify]: Simplify 0.5 into 0.5 2.631 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.631 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.631 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.631 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.631 * [taylor]: Taking taylor expansion of 2.0 in k 2.631 * [backup-simplify]: Simplify 2.0 into 2.0 2.631 * [taylor]: Taking taylor expansion of PI in k 2.631 * [backup-simplify]: Simplify PI into PI 2.632 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.633 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.633 * [taylor]: Taking taylor expansion of (log n) in k 2.633 * [taylor]: Taking taylor expansion of n in k 2.633 * [backup-simplify]: Simplify n into n 2.633 * [backup-simplify]: Simplify (log n) into (log n) 2.633 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.633 * [taylor]: Taking taylor expansion of 1.0 in k 2.633 * [backup-simplify]: Simplify 1.0 into 1.0 2.633 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.633 * [taylor]: Taking taylor expansion of k in k 2.633 * [backup-simplify]: Simplify 0 into 0 2.633 * [backup-simplify]: Simplify 1 into 1 2.633 * [backup-simplify]: Simplify (/ 1 1) into 1 2.633 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.635 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.635 * [backup-simplify]: Simplify (- 1) into -1 2.635 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.637 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.638 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 2.639 * [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))))) 2.640 * [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))))) 2.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.644 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.645 * [backup-simplify]: Simplify (- 0) into 0 2.645 * [backup-simplify]: Simplify (+ 0 0) into 0 2.646 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.647 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.648 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.649 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.649 * [taylor]: Taking taylor expansion of 0 in k 2.649 * [backup-simplify]: Simplify 0 into 0 2.649 * [backup-simplify]: Simplify 0 into 0 2.649 * [backup-simplify]: Simplify 0 into 0 2.650 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.652 * [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 2.652 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.652 * [backup-simplify]: Simplify (- 0) into 0 2.653 * [backup-simplify]: Simplify (+ 0 0) into 0 2.653 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.654 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.655 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.657 * [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 2.657 * [taylor]: Taking taylor expansion of 0 in k 2.657 * [backup-simplify]: Simplify 0 into 0 2.657 * [backup-simplify]: Simplify 0 into 0 2.657 * [backup-simplify]: Simplify 0 into 0 2.657 * [backup-simplify]: Simplify 0 into 0 2.657 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.658 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.661 * [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 2.662 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.662 * [backup-simplify]: Simplify (- 0) into 0 2.662 * [backup-simplify]: Simplify (+ 0 0) into 0 2.663 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.665 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.667 * [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 2.667 * [taylor]: Taking taylor expansion of 0 in k 2.667 * [backup-simplify]: Simplify 0 into 0 2.667 * [backup-simplify]: Simplify 0 into 0 2.668 * [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)))) 2.668 * [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))) 2.668 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 2.668 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.668 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.668 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.668 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.668 * [taylor]: Taking taylor expansion of 0.5 in k 2.668 * [backup-simplify]: Simplify 0.5 into 0.5 2.668 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.668 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.668 * [taylor]: Taking taylor expansion of k in k 2.668 * [backup-simplify]: Simplify 0 into 0 2.668 * [backup-simplify]: Simplify 1 into 1 2.669 * [backup-simplify]: Simplify (/ 1 1) into 1 2.669 * [taylor]: Taking taylor expansion of 1.0 in k 2.669 * [backup-simplify]: Simplify 1.0 into 1.0 2.669 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.669 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.669 * [taylor]: Taking taylor expansion of -2.0 in k 2.669 * [backup-simplify]: Simplify -2.0 into -2.0 2.669 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.669 * [taylor]: Taking taylor expansion of PI in k 2.669 * [backup-simplify]: Simplify PI into PI 2.669 * [taylor]: Taking taylor expansion of n in k 2.669 * [backup-simplify]: Simplify n into n 2.669 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.669 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.669 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.669 * [backup-simplify]: Simplify (+ 1 0) into 1 2.669 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.670 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.670 * [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)))))) 2.670 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.670 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.670 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.670 * [taylor]: Taking taylor expansion of 0.5 in n 2.670 * [backup-simplify]: Simplify 0.5 into 0.5 2.670 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.670 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.670 * [taylor]: Taking taylor expansion of k in n 2.670 * [backup-simplify]: Simplify k into k 2.670 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.670 * [taylor]: Taking taylor expansion of 1.0 in n 2.670 * [backup-simplify]: Simplify 1.0 into 1.0 2.670 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.670 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.670 * [taylor]: Taking taylor expansion of -2.0 in n 2.670 * [backup-simplify]: Simplify -2.0 into -2.0 2.670 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.670 * [taylor]: Taking taylor expansion of PI in n 2.670 * [backup-simplify]: Simplify PI into PI 2.670 * [taylor]: Taking taylor expansion of n in n 2.670 * [backup-simplify]: Simplify 0 into 0 2.670 * [backup-simplify]: Simplify 1 into 1 2.670 * [backup-simplify]: Simplify (/ PI 1) into PI 2.671 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.671 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.671 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.672 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.673 * [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)))) 2.674 * [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))))) 2.674 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.674 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.674 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.674 * [taylor]: Taking taylor expansion of 0.5 in n 2.674 * [backup-simplify]: Simplify 0.5 into 0.5 2.674 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.674 * [taylor]: Taking taylor expansion of k in n 2.674 * [backup-simplify]: Simplify k into k 2.674 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.674 * [taylor]: Taking taylor expansion of 1.0 in n 2.674 * [backup-simplify]: Simplify 1.0 into 1.0 2.674 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.674 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.674 * [taylor]: Taking taylor expansion of -2.0 in n 2.674 * [backup-simplify]: Simplify -2.0 into -2.0 2.674 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.675 * [taylor]: Taking taylor expansion of PI in n 2.675 * [backup-simplify]: Simplify PI into PI 2.675 * [taylor]: Taking taylor expansion of n in n 2.675 * [backup-simplify]: Simplify 0 into 0 2.675 * [backup-simplify]: Simplify 1 into 1 2.675 * [backup-simplify]: Simplify (/ PI 1) into PI 2.675 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.676 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.676 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.676 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.682 * [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)))) 2.683 * [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))))) 2.683 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.683 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.683 * [taylor]: Taking taylor expansion of 0.5 in k 2.683 * [backup-simplify]: Simplify 0.5 into 0.5 2.683 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.683 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.683 * [taylor]: Taking taylor expansion of k in k 2.683 * [backup-simplify]: Simplify 0 into 0 2.683 * [backup-simplify]: Simplify 1 into 1 2.683 * [backup-simplify]: Simplify (/ 1 1) into 1 2.683 * [taylor]: Taking taylor expansion of 1.0 in k 2.684 * [backup-simplify]: Simplify 1.0 into 1.0 2.684 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.684 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.684 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.684 * [taylor]: Taking taylor expansion of -2.0 in k 2.684 * [backup-simplify]: Simplify -2.0 into -2.0 2.684 * [taylor]: Taking taylor expansion of PI in k 2.684 * [backup-simplify]: Simplify PI into PI 2.684 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.685 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.685 * [taylor]: Taking taylor expansion of (log n) in k 2.685 * [taylor]: Taking taylor expansion of n in k 2.685 * [backup-simplify]: Simplify n into n 2.685 * [backup-simplify]: Simplify (log n) into (log n) 2.686 * [backup-simplify]: Simplify (+ 1 0) into 1 2.686 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.687 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.688 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.689 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 2.690 * [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))))) 2.691 * [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))))) 2.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.693 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.694 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.694 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.695 * [backup-simplify]: Simplify (+ 0 0) into 0 2.695 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.698 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.699 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.699 * [taylor]: Taking taylor expansion of 0 in k 2.699 * [backup-simplify]: Simplify 0 into 0 2.700 * [backup-simplify]: Simplify 0 into 0 2.700 * [backup-simplify]: Simplify 0 into 0 2.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.701 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.705 * [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 2.705 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.706 * [backup-simplify]: Simplify (+ 0 0) into 0 2.707 * [backup-simplify]: Simplify (+ (* 0.5 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)) 2.710 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.713 * [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 2.713 * [taylor]: Taking taylor expansion of 0 in k 2.713 * [backup-simplify]: Simplify 0 into 0 2.713 * [backup-simplify]: Simplify 0 into 0 2.713 * [backup-simplify]: Simplify 0 into 0 2.713 * [backup-simplify]: Simplify 0 into 0 2.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.715 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.721 * [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 2.722 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.722 * [backup-simplify]: Simplify (+ 0 0) into 0 2.724 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.725 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.727 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.730 * [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 2.730 * [taylor]: Taking taylor expansion of 0 in k 2.731 * [backup-simplify]: Simplify 0 into 0 2.731 * [backup-simplify]: Simplify 0 into 0 2.732 * [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)))))) 2.732 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 2.733 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.733 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.733 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 (* n PI) in n 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 2.733 * [taylor]: Taking taylor expansion of PI in n 2.733 * [backup-simplify]: Simplify PI into PI 2.733 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 (* n PI) in n 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 2.733 * [taylor]: Taking taylor expansion of PI in n 2.733 * [backup-simplify]: Simplify PI into PI 2.734 * [backup-simplify]: Simplify (* 0 PI) into 0 2.734 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.734 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.737 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.738 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.739 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.740 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.740 * [backup-simplify]: Simplify 0 into 0 2.741 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.743 * [backup-simplify]: Simplify 0 into 0 2.743 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.744 * [backup-simplify]: Simplify 0 into 0 2.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.746 * [backup-simplify]: Simplify 0 into 0 2.747 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.748 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.748 * [backup-simplify]: Simplify 0 into 0 2.749 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.750 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.750 * [backup-simplify]: Simplify 0 into 0 2.750 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.751 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.751 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.751 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.751 * [taylor]: Taking taylor expansion of 2.0 in n 2.751 * [backup-simplify]: Simplify 2.0 into 2.0 2.751 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.751 * [taylor]: Taking taylor expansion of PI in n 2.751 * [backup-simplify]: Simplify PI into PI 2.751 * [taylor]: Taking taylor expansion of n in n 2.751 * [backup-simplify]: Simplify 0 into 0 2.751 * [backup-simplify]: Simplify 1 into 1 2.751 * [backup-simplify]: Simplify (/ PI 1) into PI 2.751 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.751 * [taylor]: Taking taylor expansion of 2.0 in n 2.751 * [backup-simplify]: Simplify 2.0 into 2.0 2.751 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.751 * [taylor]: Taking taylor expansion of PI in n 2.751 * [backup-simplify]: Simplify PI into PI 2.751 * [taylor]: Taking taylor expansion of n in n 2.751 * [backup-simplify]: Simplify 0 into 0 2.751 * [backup-simplify]: Simplify 1 into 1 2.752 * [backup-simplify]: Simplify (/ PI 1) into PI 2.752 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.752 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.753 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.753 * [backup-simplify]: Simplify (+ (* 2.0 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)))) into 0 2.755 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.755 * [backup-simplify]: Simplify 0 into 0 2.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 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)))) into 0 2.757 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.757 * [backup-simplify]: Simplify 0 into 0 2.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 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 PI)))))) into 0 2.759 * [backup-simplify]: Simplify 0 into 0 2.760 * [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 2.761 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.761 * [backup-simplify]: Simplify 0 into 0 2.761 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.761 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.761 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.761 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) 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 (/ PI n) in n 2.761 * [taylor]: Taking taylor expansion of PI in n 2.762 * [backup-simplify]: Simplify PI into PI 2.762 * [taylor]: Taking taylor expansion of n in n 2.762 * [backup-simplify]: Simplify 0 into 0 2.762 * [backup-simplify]: Simplify 1 into 1 2.762 * [backup-simplify]: Simplify (/ PI 1) into PI 2.762 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.762 * [taylor]: Taking taylor expansion of -2.0 in n 2.762 * [backup-simplify]: Simplify -2.0 into -2.0 2.762 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.762 * [taylor]: Taking taylor expansion of PI in n 2.762 * [backup-simplify]: Simplify PI into PI 2.762 * [taylor]: Taking taylor expansion of n in n 2.762 * [backup-simplify]: Simplify 0 into 0 2.762 * [backup-simplify]: Simplify 1 into 1 2.762 * [backup-simplify]: Simplify (/ PI 1) into PI 2.763 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.763 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.764 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.764 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.764 * [backup-simplify]: Simplify 0 into 0 2.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.765 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.765 * [backup-simplify]: Simplify 0 into 0 2.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.767 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.767 * [backup-simplify]: Simplify 0 into 0 2.767 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.768 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.768 * [backup-simplify]: Simplify 0 into 0 2.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.769 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.769 * [backup-simplify]: Simplify 0 into 0 2.770 * [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 2.771 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.771 * [backup-simplify]: Simplify 0 into 0 2.771 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.772 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 2.772 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 2.772 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 2.772 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.772 * [taylor]: Taking taylor expansion of 1.0 in k 2.772 * [backup-simplify]: Simplify 1.0 into 1.0 2.772 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.772 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.772 * [taylor]: Taking taylor expansion of k in k 2.772 * [backup-simplify]: Simplify 0 into 0 2.772 * [backup-simplify]: Simplify 1 into 1 2.772 * [backup-simplify]: Simplify (/ 1 1) into 1 2.772 * [backup-simplify]: Simplify (sqrt 0) into 0 2.773 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.773 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 2.774 * [taylor]: Taking taylor expansion of 1.0 in k 2.774 * [backup-simplify]: Simplify 1.0 into 1.0 2.774 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.774 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.774 * [taylor]: Taking taylor expansion of k in k 2.774 * [backup-simplify]: Simplify 0 into 0 2.774 * [backup-simplify]: Simplify 1 into 1 2.774 * [backup-simplify]: Simplify (/ 1 1) into 1 2.774 * [backup-simplify]: Simplify (sqrt 0) into 0 2.775 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.775 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.775 * [backup-simplify]: Simplify 0 into 0 2.776 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.776 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.777 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.779 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.781 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.781 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.782 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.786 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.788 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.789 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.790 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 2.790 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 2.790 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 2.790 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.790 * [taylor]: Taking taylor expansion of 1.0 in k 2.790 * [backup-simplify]: Simplify 1.0 into 1.0 2.790 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.790 * [taylor]: Taking taylor expansion of k in k 2.790 * [backup-simplify]: Simplify 0 into 0 2.790 * [backup-simplify]: Simplify 1 into 1 2.791 * [backup-simplify]: Simplify (sqrt 0) into 0 2.792 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.792 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 2.792 * [taylor]: Taking taylor expansion of 1.0 in k 2.792 * [backup-simplify]: Simplify 1.0 into 1.0 2.792 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.792 * [taylor]: Taking taylor expansion of k in k 2.792 * [backup-simplify]: Simplify 0 into 0 2.792 * [backup-simplify]: Simplify 1 into 1 2.792 * [backup-simplify]: Simplify (sqrt 0) into 0 2.794 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.794 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.794 * [backup-simplify]: Simplify 0 into 0 2.795 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 2.796 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.804 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.806 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 2.807 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.811 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.812 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 2.812 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.813 * [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)))))))) 2.813 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 2.814 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 2.814 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.814 * [taylor]: Taking taylor expansion of 1.0 in k 2.814 * [backup-simplify]: Simplify 1.0 into 1.0 2.814 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.814 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.814 * [taylor]: Taking taylor expansion of -1 in k 2.814 * [backup-simplify]: Simplify -1 into -1 2.814 * [taylor]: Taking taylor expansion of k in k 2.814 * [backup-simplify]: Simplify 0 into 0 2.814 * [backup-simplify]: Simplify 1 into 1 2.814 * [backup-simplify]: Simplify (/ -1 1) into -1 2.814 * [backup-simplify]: Simplify (sqrt 0) into 0 2.815 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.815 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.815 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 2.815 * [taylor]: Taking taylor expansion of 1.0 in k 2.815 * [backup-simplify]: Simplify 1.0 into 1.0 2.815 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.815 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.815 * [taylor]: Taking taylor expansion of -1 in k 2.815 * [backup-simplify]: Simplify -1 into -1 2.816 * [taylor]: Taking taylor expansion of k in k 2.816 * [backup-simplify]: Simplify 0 into 0 2.816 * [backup-simplify]: Simplify 1 into 1 2.816 * [backup-simplify]: Simplify (/ -1 1) into -1 2.816 * [backup-simplify]: Simplify (sqrt 0) into 0 2.817 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.817 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 2.817 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.820 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.821 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 2.821 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.824 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.827 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 2.827 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 2.828 * [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))))) 2.828 * * * * [progress]: [ 4 / 4 ] generating series at (2) 2.828 * [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))))) 2.828 * [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 2.828 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 2.828 * [taylor]: Taking taylor expansion of 1.0 in n 2.828 * [backup-simplify]: Simplify 1.0 into 1.0 2.828 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 2.828 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 2.828 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.828 * [taylor]: Taking taylor expansion of k in n 2.828 * [backup-simplify]: Simplify k into k 2.829 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.829 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 2.829 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.829 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 2.829 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 2.829 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.829 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.829 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 2.829 * [taylor]: Taking taylor expansion of 0.5 in n 2.829 * [backup-simplify]: Simplify 0.5 into 0.5 2.829 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.829 * [taylor]: Taking taylor expansion of 1.0 in n 2.829 * [backup-simplify]: Simplify 1.0 into 1.0 2.829 * [taylor]: Taking taylor expansion of k in n 2.829 * [backup-simplify]: Simplify k into k 2.829 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.829 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.829 * [taylor]: Taking taylor expansion of 2.0 in n 2.829 * [backup-simplify]: Simplify 2.0 into 2.0 2.829 * [taylor]: Taking taylor expansion of (* n PI) in n 2.829 * [taylor]: Taking taylor expansion of n in n 2.829 * [backup-simplify]: Simplify 0 into 0 2.829 * [backup-simplify]: Simplify 1 into 1 2.829 * [taylor]: Taking taylor expansion of PI in n 2.829 * [backup-simplify]: Simplify PI into PI 2.829 * [backup-simplify]: Simplify (* 0 PI) into 0 2.830 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.831 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.832 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.832 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.832 * [backup-simplify]: Simplify (- k) into (- k) 2.832 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.832 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 2.833 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.834 * [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)))) 2.835 * [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))))) 2.835 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.835 * [taylor]: Taking taylor expansion of 1.0 in k 2.835 * [backup-simplify]: Simplify 1.0 into 1.0 2.835 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.835 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.835 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.835 * [taylor]: Taking taylor expansion of k in k 2.835 * [backup-simplify]: Simplify 0 into 0 2.835 * [backup-simplify]: Simplify 1 into 1 2.835 * [backup-simplify]: Simplify (/ 1 1) into 1 2.835 * [backup-simplify]: Simplify (sqrt 0) into 0 2.836 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.836 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.836 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.836 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.836 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.836 * [taylor]: Taking taylor expansion of 0.5 in k 2.836 * [backup-simplify]: Simplify 0.5 into 0.5 2.836 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.836 * [taylor]: Taking taylor expansion of 1.0 in k 2.836 * [backup-simplify]: Simplify 1.0 into 1.0 2.836 * [taylor]: Taking taylor expansion of k in k 2.836 * [backup-simplify]: Simplify 0 into 0 2.836 * [backup-simplify]: Simplify 1 into 1 2.836 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.836 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.836 * [taylor]: Taking taylor expansion of 2.0 in k 2.836 * [backup-simplify]: Simplify 2.0 into 2.0 2.836 * [taylor]: Taking taylor expansion of (* n PI) in k 2.836 * [taylor]: Taking taylor expansion of n in k 2.836 * [backup-simplify]: Simplify n into n 2.836 * [taylor]: Taking taylor expansion of PI in k 2.837 * [backup-simplify]: Simplify PI into PI 2.837 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.837 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.837 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.837 * [backup-simplify]: Simplify (- 0) into 0 2.837 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.837 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.838 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.838 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.838 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 2.838 * [taylor]: Taking taylor expansion of 1.0 in k 2.838 * [backup-simplify]: Simplify 1.0 into 1.0 2.838 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 2.838 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 2.838 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.838 * [taylor]: Taking taylor expansion of k in k 2.838 * [backup-simplify]: Simplify 0 into 0 2.838 * [backup-simplify]: Simplify 1 into 1 2.838 * [backup-simplify]: Simplify (/ 1 1) into 1 2.838 * [backup-simplify]: Simplify (sqrt 0) into 0 2.839 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.839 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 2.839 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.839 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.839 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 2.839 * [taylor]: Taking taylor expansion of 0.5 in k 2.839 * [backup-simplify]: Simplify 0.5 into 0.5 2.839 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.839 * [taylor]: Taking taylor expansion of 1.0 in k 2.839 * [backup-simplify]: Simplify 1.0 into 1.0 2.839 * [taylor]: Taking taylor expansion of k in k 2.839 * [backup-simplify]: Simplify 0 into 0 2.839 * [backup-simplify]: Simplify 1 into 1 2.839 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.839 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.839 * [taylor]: Taking taylor expansion of 2.0 in k 2.839 * [backup-simplify]: Simplify 2.0 into 2.0 2.839 * [taylor]: Taking taylor expansion of (* n PI) in k 2.839 * [taylor]: Taking taylor expansion of n in k 2.839 * [backup-simplify]: Simplify n into n 2.839 * [taylor]: Taking taylor expansion of PI in k 2.839 * [backup-simplify]: Simplify PI into PI 2.840 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.840 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.840 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.840 * [backup-simplify]: Simplify (- 0) into 0 2.840 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.840 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 2.840 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 2.841 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 2.841 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 2.841 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.841 * [taylor]: Taking taylor expansion of 0 in n 2.841 * [backup-simplify]: Simplify 0 into 0 2.841 * [backup-simplify]: Simplify 0 into 0 2.842 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 2.842 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 2.842 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 2.843 * [backup-simplify]: Simplify (- 1) into -1 2.843 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.845 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 2.846 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 2.846 * [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))) 2.848 * [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))) 2.850 * [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))) 2.850 * [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 2.850 * [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 2.850 * [taylor]: Taking taylor expansion of +nan.0 in n 2.850 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.850 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.850 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.850 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.850 * [taylor]: Taking taylor expansion of 0.5 in n 2.850 * [backup-simplify]: Simplify 0.5 into 0.5 2.850 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.850 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.850 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.850 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.850 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.850 * [taylor]: Taking taylor expansion of 1.0 in n 2.850 * [backup-simplify]: Simplify 1.0 into 1.0 2.850 * [taylor]: Taking taylor expansion of (log PI) in n 2.850 * [taylor]: Taking taylor expansion of PI in n 2.850 * [backup-simplify]: Simplify PI into PI 2.851 * [backup-simplify]: Simplify (log PI) into (log PI) 2.852 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.853 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.853 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.853 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.853 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.853 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.853 * [taylor]: Taking taylor expansion of 1.0 in n 2.853 * [backup-simplify]: Simplify 1.0 into 1.0 2.853 * [taylor]: Taking taylor expansion of (log n) in n 2.853 * [taylor]: Taking taylor expansion of n in n 2.853 * [backup-simplify]: Simplify 0 into 0 2.853 * [backup-simplify]: Simplify 1 into 1 2.854 * [backup-simplify]: Simplify (log 1) into 0 2.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.854 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.854 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.854 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.854 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.854 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.854 * [taylor]: Taking taylor expansion of 1.0 in n 2.854 * [backup-simplify]: Simplify 1.0 into 1.0 2.855 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.855 * [taylor]: Taking taylor expansion of 2.0 in n 2.855 * [backup-simplify]: Simplify 2.0 into 2.0 2.855 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.856 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.857 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.858 * [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) 2.859 * [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) 2.861 * [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)) 2.862 * [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))) 2.863 * [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) 2.865 * [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)) 2.866 * [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))) 2.867 * [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))) 2.867 * [backup-simplify]: Simplify 0 into 0 2.868 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 2.869 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 2.871 * [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 2.871 * [backup-simplify]: Simplify (- 0) into 0 2.871 * [backup-simplify]: Simplify (+ 0 0) into 0 2.872 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 2.873 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 2.875 * [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))) 2.876 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 2.879 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.883 * [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)))))))) 2.888 * [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)))))))) 2.888 * [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 2.888 * [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 2.888 * [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 2.888 * [taylor]: Taking taylor expansion of +nan.0 in n 2.888 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.889 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 2.889 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 2.889 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 2.889 * [taylor]: Taking taylor expansion of 0.5 in n 2.889 * [backup-simplify]: Simplify 0.5 into 0.5 2.889 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 2.889 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 2.889 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.889 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.889 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.889 * [taylor]: Taking taylor expansion of 1.0 in n 2.889 * [backup-simplify]: Simplify 1.0 into 1.0 2.889 * [taylor]: Taking taylor expansion of (log PI) in n 2.889 * [taylor]: Taking taylor expansion of PI in n 2.889 * [backup-simplify]: Simplify PI into PI 2.889 * [backup-simplify]: Simplify (log PI) into (log PI) 2.890 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.892 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.892 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 2.892 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.892 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.892 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.892 * [taylor]: Taking taylor expansion of 1.0 in n 2.892 * [backup-simplify]: Simplify 1.0 into 1.0 2.892 * [taylor]: Taking taylor expansion of (log n) in n 2.892 * [taylor]: Taking taylor expansion of n in n 2.892 * [backup-simplify]: Simplify 0 into 0 2.893 * [backup-simplify]: Simplify 1 into 1 2.893 * [backup-simplify]: Simplify (log 1) into 0 2.893 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.893 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.894 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.894 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.894 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.894 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.894 * [taylor]: Taking taylor expansion of 1.0 in n 2.894 * [backup-simplify]: Simplify 1.0 into 1.0 2.894 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.894 * [taylor]: Taking taylor expansion of 2.0 in n 2.894 * [backup-simplify]: Simplify 2.0 into 2.0 2.894 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.895 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.897 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.898 * [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) 2.899 * [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) 2.901 * [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)) 2.902 * [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))) 2.904 * [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) 2.904 * [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 2.904 * [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 2.904 * [taylor]: Taking taylor expansion of +nan.0 in n 2.904 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.904 * [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 2.904 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.904 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.904 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.904 * [taylor]: Taking taylor expansion of 0.5 in n 2.904 * [backup-simplify]: Simplify 0.5 into 0.5 2.904 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.904 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.904 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.904 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.904 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.904 * [taylor]: Taking taylor expansion of 1.0 in n 2.904 * [backup-simplify]: Simplify 1.0 into 1.0 2.904 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.904 * [taylor]: Taking taylor expansion of 2.0 in n 2.904 * [backup-simplify]: Simplify 2.0 into 2.0 2.905 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.906 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.908 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.908 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.908 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.908 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.908 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.908 * [taylor]: Taking taylor expansion of 1.0 in n 2.908 * [backup-simplify]: Simplify 1.0 into 1.0 2.908 * [taylor]: Taking taylor expansion of (log PI) in n 2.908 * [taylor]: Taking taylor expansion of PI in n 2.908 * [backup-simplify]: Simplify PI into PI 2.908 * [backup-simplify]: Simplify (log PI) into (log PI) 2.909 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.911 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.911 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.911 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.911 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.911 * [taylor]: Taking taylor expansion of 1.0 in n 2.911 * [backup-simplify]: Simplify 1.0 into 1.0 2.911 * [taylor]: Taking taylor expansion of (log n) in n 2.911 * [taylor]: Taking taylor expansion of n in n 2.911 * [backup-simplify]: Simplify 0 into 0 2.912 * [backup-simplify]: Simplify 1 into 1 2.912 * [backup-simplify]: Simplify (log 1) into 0 2.912 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.912 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.913 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.913 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.915 * [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) 2.916 * [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)) 2.917 * [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))) 2.919 * [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) 2.919 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.919 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.919 * [taylor]: Taking taylor expansion of 2.0 in n 2.919 * [backup-simplify]: Simplify 2.0 into 2.0 2.919 * [taylor]: Taking taylor expansion of (* n PI) in n 2.919 * [taylor]: Taking taylor expansion of n in n 2.919 * [backup-simplify]: Simplify 0 into 0 2.919 * [backup-simplify]: Simplify 1 into 1 2.919 * [taylor]: Taking taylor expansion of PI in n 2.919 * [backup-simplify]: Simplify PI into PI 2.920 * [backup-simplify]: Simplify (* 0 PI) into 0 2.920 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.921 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.923 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.924 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.926 * [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)) 2.927 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.930 * [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)) 2.932 * [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))) 2.935 * [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)))))) 2.949 * [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)))))))) 2.955 * [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)))))))) 2.962 * [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)))))))) 2.964 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.965 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.967 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.969 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.969 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.970 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.971 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.971 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.973 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.974 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.975 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.976 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.977 * [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 2.978 * [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 2.980 * [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 2.981 * [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 2.981 * [backup-simplify]: Simplify (- 0) into 0 2.981 * [backup-simplify]: Simplify 0 into 0 2.981 * [backup-simplify]: Simplify 0 into 0 2.982 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.982 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.984 * [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 2.984 * [backup-simplify]: Simplify (- 0) into 0 2.985 * [backup-simplify]: Simplify (+ 0 0) into 0 2.985 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.986 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.987 * [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))) 2.988 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.990 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.994 * [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)))))))) 3.000 * [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)))))))) 3.000 * [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 3.000 * [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 3.000 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 3.000 * [taylor]: Taking taylor expansion of +nan.0 in n 3.000 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.000 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 3.000 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 3.000 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 3.000 * [taylor]: Taking taylor expansion of 0.5 in n 3.000 * [backup-simplify]: Simplify 0.5 into 0.5 3.000 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 3.000 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 3.000 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.000 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.000 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.000 * [taylor]: Taking taylor expansion of 1.0 in n 3.001 * [backup-simplify]: Simplify 1.0 into 1.0 3.001 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.001 * [taylor]: Taking taylor expansion of 2.0 in n 3.001 * [backup-simplify]: Simplify 2.0 into 2.0 3.001 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.001 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.002 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.002 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 3.002 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.002 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.002 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.002 * [taylor]: Taking taylor expansion of 1.0 in n 3.002 * [backup-simplify]: Simplify 1.0 into 1.0 3.002 * [taylor]: Taking taylor expansion of (log n) in n 3.003 * [taylor]: Taking taylor expansion of n in n 3.003 * [backup-simplify]: Simplify 0 into 0 3.003 * [backup-simplify]: Simplify 1 into 1 3.003 * [backup-simplify]: Simplify (log 1) into 0 3.003 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.003 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.004 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.004 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.004 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.004 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.004 * [taylor]: Taking taylor expansion of 1.0 in n 3.004 * [backup-simplify]: Simplify 1.0 into 1.0 3.004 * [taylor]: Taking taylor expansion of (log PI) in n 3.004 * [taylor]: Taking taylor expansion of PI in n 3.004 * [backup-simplify]: Simplify PI into PI 3.004 * [backup-simplify]: Simplify (log PI) into (log PI) 3.005 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.007 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.008 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.009 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 3.010 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 3.012 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 3.013 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.013 * [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 3.013 * [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 3.013 * [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 3.013 * [taylor]: Taking taylor expansion of +nan.0 in n 3.013 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.013 * [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 3.013 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 3.013 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 3.013 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 3.013 * [taylor]: Taking taylor expansion of 0.5 in n 3.014 * [backup-simplify]: Simplify 0.5 into 0.5 3.014 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 3.014 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 3.014 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.014 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.014 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.014 * [taylor]: Taking taylor expansion of 1.0 in n 3.014 * [backup-simplify]: Simplify 1.0 into 1.0 3.014 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.014 * [taylor]: Taking taylor expansion of 2.0 in n 3.014 * [backup-simplify]: Simplify 2.0 into 2.0 3.014 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.015 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.017 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.017 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 3.017 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.017 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.017 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.017 * [taylor]: Taking taylor expansion of 1.0 in n 3.017 * [backup-simplify]: Simplify 1.0 into 1.0 3.017 * [taylor]: Taking taylor expansion of (log PI) in n 3.017 * [taylor]: Taking taylor expansion of PI in n 3.017 * [backup-simplify]: Simplify PI into PI 3.018 * [backup-simplify]: Simplify (log PI) into (log PI) 3.019 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.020 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.020 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.020 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.021 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.021 * [taylor]: Taking taylor expansion of 1.0 in n 3.021 * [backup-simplify]: Simplify 1.0 into 1.0 3.021 * [taylor]: Taking taylor expansion of (log n) in n 3.021 * [taylor]: Taking taylor expansion of n in n 3.021 * [backup-simplify]: Simplify 0 into 0 3.021 * [backup-simplify]: Simplify 1 into 1 3.021 * [backup-simplify]: Simplify (log 1) into 0 3.022 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.022 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.022 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.022 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.024 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 3.025 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 3.026 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 3.028 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.028 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.028 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.028 * [taylor]: Taking taylor expansion of 2.0 in n 3.028 * [backup-simplify]: Simplify 2.0 into 2.0 3.028 * [taylor]: Taking taylor expansion of (* n PI) in n 3.028 * [taylor]: Taking taylor expansion of n in n 3.028 * [backup-simplify]: Simplify 0 into 0 3.028 * [backup-simplify]: Simplify 1 into 1 3.028 * [taylor]: Taking taylor expansion of PI in n 3.028 * [backup-simplify]: Simplify PI into PI 3.029 * [backup-simplify]: Simplify (* 0 PI) into 0 3.029 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.030 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.032 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.033 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.033 * [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 3.033 * [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 3.033 * [taylor]: Taking taylor expansion of +nan.0 in n 3.033 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.033 * [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 3.033 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 3.033 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 3.033 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 3.033 * [taylor]: Taking taylor expansion of 0.5 in n 3.033 * [backup-simplify]: Simplify 0.5 into 0.5 3.033 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 3.034 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 3.034 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 3.034 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 3.034 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 3.034 * [taylor]: Taking taylor expansion of 1.0 in n 3.034 * [backup-simplify]: Simplify 1.0 into 1.0 3.034 * [taylor]: Taking taylor expansion of (log 2.0) in n 3.034 * [taylor]: Taking taylor expansion of 2.0 in n 3.034 * [backup-simplify]: Simplify 2.0 into 2.0 3.034 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 3.035 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 3.037 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 3.037 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 3.037 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 3.037 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 3.037 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 3.037 * [taylor]: Taking taylor expansion of 1.0 in n 3.037 * [backup-simplify]: Simplify 1.0 into 1.0 3.037 * [taylor]: Taking taylor expansion of (log PI) in n 3.037 * [taylor]: Taking taylor expansion of PI in n 3.037 * [backup-simplify]: Simplify PI into PI 3.037 * [backup-simplify]: Simplify (log PI) into (log PI) 3.038 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 3.040 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 3.040 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 3.040 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 3.040 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 3.040 * [taylor]: Taking taylor expansion of 1.0 in n 3.040 * [backup-simplify]: Simplify 1.0 into 1.0 3.040 * [taylor]: Taking taylor expansion of (log n) in n 3.040 * [taylor]: Taking taylor expansion of n in n 3.040 * [backup-simplify]: Simplify 0 into 0 3.040 * [backup-simplify]: Simplify 1 into 1 3.040 * [backup-simplify]: Simplify (log 1) into 0 3.041 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 3.041 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 3.041 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 3.042 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 3.043 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 3.044 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 3.045 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 3.047 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 3.047 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 3.047 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 3.047 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 3.047 * [taylor]: Taking taylor expansion of 2.0 in n 3.047 * [backup-simplify]: Simplify 2.0 into 2.0 3.047 * [taylor]: Taking taylor expansion of (* n PI) in n 3.047 * [taylor]: Taking taylor expansion of n in n 3.047 * [backup-simplify]: Simplify 0 into 0 3.047 * [backup-simplify]: Simplify 1 into 1 3.047 * [taylor]: Taking taylor expansion of PI in n 3.047 * [backup-simplify]: Simplify PI into PI 3.048 * [backup-simplify]: Simplify (* 0 PI) into 0 3.048 * [backup-simplify]: Simplify (* 2.0 0) into 0 3.049 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.051 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 3.052 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.053 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.055 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 3.057 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.059 * [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)) 3.062 * [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))) 3.063 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.064 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 3.065 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 3.067 * [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)) 3.068 * [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))) 3.074 * [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)))))))) 3.080 * [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)))))))))))) 3.089 * [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)))))))))))) 3.103 * [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)))))))))))))) 3.122 * [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)))))))))))))) 3.139 * [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)))))))))))))) 3.167 * [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)))))))))))))))))))))) 3.169 * [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)))))) 3.169 * [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 3.169 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 3.169 * [taylor]: Taking taylor expansion of 1.0 in n 3.169 * [backup-simplify]: Simplify 1.0 into 1.0 3.169 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 3.169 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.169 * [taylor]: Taking taylor expansion of k in n 3.169 * [backup-simplify]: Simplify k into k 3.169 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.169 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.169 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 3.169 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 3.169 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 3.169 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 3.169 * [taylor]: Taking taylor expansion of 0.5 in n 3.169 * [backup-simplify]: Simplify 0.5 into 0.5 3.170 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.170 * [taylor]: Taking taylor expansion of 1.0 in n 3.170 * [backup-simplify]: Simplify 1.0 into 1.0 3.170 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.170 * [taylor]: Taking taylor expansion of k in n 3.170 * [backup-simplify]: Simplify k into k 3.170 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.170 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.170 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.170 * [taylor]: Taking taylor expansion of 2.0 in n 3.170 * [backup-simplify]: Simplify 2.0 into 2.0 3.170 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.170 * [taylor]: Taking taylor expansion of PI in n 3.170 * [backup-simplify]: Simplify PI into PI 3.170 * [taylor]: Taking taylor expansion of n in n 3.170 * [backup-simplify]: Simplify 0 into 0 3.170 * [backup-simplify]: Simplify 1 into 1 3.171 * [backup-simplify]: Simplify (/ PI 1) into PI 3.171 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.172 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.172 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.173 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.173 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 3.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.175 * [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)))) 3.176 * [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))))) 3.176 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 3.176 * [taylor]: Taking taylor expansion of 1.0 in k 3.176 * [backup-simplify]: Simplify 1.0 into 1.0 3.176 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 3.176 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.176 * [taylor]: Taking taylor expansion of k in k 3.176 * [backup-simplify]: Simplify 0 into 0 3.176 * [backup-simplify]: Simplify 1 into 1 3.176 * [backup-simplify]: Simplify (sqrt 0) into 0 3.177 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.177 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.177 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.177 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.177 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.177 * [taylor]: Taking taylor expansion of 0.5 in k 3.177 * [backup-simplify]: Simplify 0.5 into 0.5 3.177 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.177 * [taylor]: Taking taylor expansion of 1.0 in k 3.177 * [backup-simplify]: Simplify 1.0 into 1.0 3.177 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.178 * [taylor]: Taking taylor expansion of k in k 3.178 * [backup-simplify]: Simplify 0 into 0 3.178 * [backup-simplify]: Simplify 1 into 1 3.178 * [backup-simplify]: Simplify (/ 1 1) into 1 3.178 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.178 * [taylor]: Taking taylor expansion of 2.0 in k 3.178 * [backup-simplify]: Simplify 2.0 into 2.0 3.178 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.178 * [taylor]: Taking taylor expansion of PI in k 3.178 * [backup-simplify]: Simplify PI into PI 3.178 * [taylor]: Taking taylor expansion of n in k 3.178 * [backup-simplify]: Simplify n into n 3.178 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.178 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.178 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.178 * [backup-simplify]: Simplify (- 1) into -1 3.179 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.179 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.179 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.179 * [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))))) 3.179 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 3.179 * [taylor]: Taking taylor expansion of 1.0 in k 3.179 * [backup-simplify]: Simplify 1.0 into 1.0 3.179 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 3.179 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.179 * [taylor]: Taking taylor expansion of k in k 3.179 * [backup-simplify]: Simplify 0 into 0 3.179 * [backup-simplify]: Simplify 1 into 1 3.180 * [backup-simplify]: Simplify (sqrt 0) into 0 3.180 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.180 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 3.180 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 3.180 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 3.180 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 3.180 * [taylor]: Taking taylor expansion of 0.5 in k 3.181 * [backup-simplify]: Simplify 0.5 into 0.5 3.181 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 3.181 * [taylor]: Taking taylor expansion of 1.0 in k 3.181 * [backup-simplify]: Simplify 1.0 into 1.0 3.181 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.181 * [taylor]: Taking taylor expansion of k in k 3.181 * [backup-simplify]: Simplify 0 into 0 3.181 * [backup-simplify]: Simplify 1 into 1 3.181 * [backup-simplify]: Simplify (/ 1 1) into 1 3.181 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 3.181 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 3.181 * [taylor]: Taking taylor expansion of 2.0 in k 3.181 * [backup-simplify]: Simplify 2.0 into 2.0 3.181 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.181 * [taylor]: Taking taylor expansion of PI in k 3.181 * [backup-simplify]: Simplify PI into PI 3.181 * [taylor]: Taking taylor expansion of n in k 3.181 * [backup-simplify]: Simplify n into n 3.181 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.181 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 3.181 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 3.181 * [backup-simplify]: Simplify (- 1) into -1 3.182 * [backup-simplify]: Simplify (+ 0 -1) into -1 3.182 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 3.182 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 3.182 * [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))))) 3.182 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 3.183 * [backup-simplify]: Simplify (* 1.0 0) into 0 3.183 * [taylor]: Taking taylor expansion of 0 in n 3.183 * [backup-simplify]: Simplify 0 into 0 3.183 * [backup-simplify]: Simplify 0 into 0 3.183 * [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))))))) 3.184 * [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))))))) 3.184 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.184 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.184 * [taylor]: Taking taylor expansion of +nan.0 in n 3.184 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.184 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.184 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.184 * [taylor]: Taking taylor expansion of 0.5 in n 3.184 * [backup-simplify]: Simplify 0.5 into 0.5 3.184 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.184 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.184 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.184 * [taylor]: Taking taylor expansion of 2.0 in n 3.184 * [backup-simplify]: Simplify 2.0 into 2.0 3.184 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.184 * [taylor]: Taking taylor expansion of PI in n 3.184 * [backup-simplify]: Simplify PI into PI 3.184 * [taylor]: Taking taylor expansion of n in n 3.184 * [backup-simplify]: Simplify 0 into 0 3.184 * [backup-simplify]: Simplify 1 into 1 3.184 * [backup-simplify]: Simplify (/ PI 1) into PI 3.185 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.185 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.185 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.185 * [taylor]: Taking taylor expansion of 1.0 in n 3.185 * [backup-simplify]: Simplify 1.0 into 1.0 3.185 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.185 * [taylor]: Taking taylor expansion of k in n 3.185 * [backup-simplify]: Simplify k into k 3.185 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.186 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.186 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.186 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.187 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.188 * [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)))) 3.189 * [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))))) 3.189 * [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)))))) 3.190 * [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))))))) 3.191 * [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))))))) 3.191 * [backup-simplify]: Simplify 0 into 0 3.193 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.194 * [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))))))) 3.194 * [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))))))) 3.194 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.194 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.194 * [taylor]: Taking taylor expansion of +nan.0 in n 3.194 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.194 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.194 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.194 * [taylor]: Taking taylor expansion of 0.5 in n 3.194 * [backup-simplify]: Simplify 0.5 into 0.5 3.194 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.194 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.194 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.194 * [taylor]: Taking taylor expansion of 2.0 in n 3.194 * [backup-simplify]: Simplify 2.0 into 2.0 3.194 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.194 * [taylor]: Taking taylor expansion of PI in n 3.194 * [backup-simplify]: Simplify PI into PI 3.194 * [taylor]: Taking taylor expansion of n in n 3.194 * [backup-simplify]: Simplify 0 into 0 3.195 * [backup-simplify]: Simplify 1 into 1 3.195 * [backup-simplify]: Simplify (/ PI 1) into PI 3.195 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.196 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.196 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.196 * [taylor]: Taking taylor expansion of 1.0 in n 3.196 * [backup-simplify]: Simplify 1.0 into 1.0 3.196 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.196 * [taylor]: Taking taylor expansion of k in n 3.196 * [backup-simplify]: Simplify k into k 3.196 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.197 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.197 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.197 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.202 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.202 * [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)))) 3.203 * [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))))) 3.204 * [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)))))) 3.205 * [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))))))) 3.206 * [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))))))) 3.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.207 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.207 * [backup-simplify]: Simplify (- 0) into 0 3.207 * [backup-simplify]: Simplify (+ 0 0) into 0 3.208 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.208 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 3.209 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 3.210 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 3.211 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 3.212 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.213 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 3.213 * [backup-simplify]: Simplify (- 0) into 0 3.213 * [backup-simplify]: Simplify 0 into 0 3.213 * [backup-simplify]: Simplify 0 into 0 3.217 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.218 * [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))))))) 3.219 * [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))))))) 3.220 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 3.220 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 3.220 * [taylor]: Taking taylor expansion of +nan.0 in n 3.220 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.220 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 3.220 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 3.220 * [taylor]: Taking taylor expansion of 0.5 in n 3.220 * [backup-simplify]: Simplify 0.5 into 0.5 3.220 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 3.220 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 3.220 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 3.220 * [taylor]: Taking taylor expansion of 2.0 in n 3.220 * [backup-simplify]: Simplify 2.0 into 2.0 3.220 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.220 * [taylor]: Taking taylor expansion of PI in n 3.220 * [backup-simplify]: Simplify PI into PI 3.220 * [taylor]: Taking taylor expansion of n in n 3.220 * [backup-simplify]: Simplify 0 into 0 3.220 * [backup-simplify]: Simplify 1 into 1 3.221 * [backup-simplify]: Simplify (/ PI 1) into PI 3.221 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 3.223 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 3.223 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 3.223 * [taylor]: Taking taylor expansion of 1.0 in n 3.223 * [backup-simplify]: Simplify 1.0 into 1.0 3.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.223 * [taylor]: Taking taylor expansion of k in n 3.223 * [backup-simplify]: Simplify k into k 3.223 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.224 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 3.225 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 3.225 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 3.226 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 3.227 * [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)))) 3.229 * [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))))) 3.230 * [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)))))) 3.231 * [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))))))) 3.233 * [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))))))) 3.238 * [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)))))))) 3.239 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 3.239 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 3.239 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 3.239 * [taylor]: Taking taylor expansion of 1.0 in n 3.239 * [backup-simplify]: Simplify 1.0 into 1.0 3.239 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 3.239 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 3.239 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 3.239 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 3.239 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 3.239 * [taylor]: Taking taylor expansion of 0.5 in n 3.239 * [backup-simplify]: Simplify 0.5 into 0.5 3.239 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.239 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.239 * [taylor]: Taking taylor expansion of k in n 3.239 * [backup-simplify]: Simplify k into k 3.239 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.239 * [taylor]: Taking taylor expansion of 1.0 in n 3.239 * [backup-simplify]: Simplify 1.0 into 1.0 3.239 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.239 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.239 * [taylor]: Taking taylor expansion of -2.0 in n 3.239 * [backup-simplify]: Simplify -2.0 into -2.0 3.239 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.239 * [taylor]: Taking taylor expansion of PI in n 3.239 * [backup-simplify]: Simplify PI into PI 3.239 * [taylor]: Taking taylor expansion of n in n 3.239 * [backup-simplify]: Simplify 0 into 0 3.239 * [backup-simplify]: Simplify 1 into 1 3.240 * [backup-simplify]: Simplify (/ PI 1) into PI 3.240 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.241 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.242 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.242 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 3.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.244 * [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)))) 3.245 * [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))))) 3.246 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.246 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.246 * [taylor]: Taking taylor expansion of -1 in n 3.246 * [backup-simplify]: Simplify -1 into -1 3.246 * [taylor]: Taking taylor expansion of k in n 3.246 * [backup-simplify]: Simplify k into k 3.246 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.246 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.246 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.246 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.248 * [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))) 3.248 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.248 * [taylor]: Taking taylor expansion of 1.0 in k 3.248 * [backup-simplify]: Simplify 1.0 into 1.0 3.248 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.248 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.248 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.248 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.248 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.248 * [taylor]: Taking taylor expansion of 0.5 in k 3.248 * [backup-simplify]: Simplify 0.5 into 0.5 3.248 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.248 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.248 * [taylor]: Taking taylor expansion of k in k 3.248 * [backup-simplify]: Simplify 0 into 0 3.248 * [backup-simplify]: Simplify 1 into 1 3.249 * [backup-simplify]: Simplify (/ 1 1) into 1 3.249 * [taylor]: Taking taylor expansion of 1.0 in k 3.249 * [backup-simplify]: Simplify 1.0 into 1.0 3.249 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.249 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.249 * [taylor]: Taking taylor expansion of -2.0 in k 3.249 * [backup-simplify]: Simplify -2.0 into -2.0 3.249 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.249 * [taylor]: Taking taylor expansion of PI in k 3.249 * [backup-simplify]: Simplify PI into PI 3.249 * [taylor]: Taking taylor expansion of n in k 3.249 * [backup-simplify]: Simplify n into n 3.249 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.249 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.249 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.250 * [backup-simplify]: Simplify (+ 1 0) into 1 3.250 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.250 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.251 * [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)))))) 3.251 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.251 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.251 * [taylor]: Taking taylor expansion of -1 in k 3.251 * [backup-simplify]: Simplify -1 into -1 3.251 * [taylor]: Taking taylor expansion of k in k 3.251 * [backup-simplify]: Simplify 0 into 0 3.251 * [backup-simplify]: Simplify 1 into 1 3.251 * [backup-simplify]: Simplify (/ -1 1) into -1 3.252 * [backup-simplify]: Simplify (sqrt 0) into 0 3.253 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.253 * [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))))))) 3.254 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 3.254 * [taylor]: Taking taylor expansion of 1.0 in k 3.254 * [backup-simplify]: Simplify 1.0 into 1.0 3.254 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 3.254 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 3.254 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 3.254 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 3.254 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 3.254 * [taylor]: Taking taylor expansion of 0.5 in k 3.254 * [backup-simplify]: Simplify 0.5 into 0.5 3.254 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 3.254 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.254 * [taylor]: Taking taylor expansion of k in k 3.254 * [backup-simplify]: Simplify 0 into 0 3.254 * [backup-simplify]: Simplify 1 into 1 3.255 * [backup-simplify]: Simplify (/ 1 1) into 1 3.255 * [taylor]: Taking taylor expansion of 1.0 in k 3.255 * [backup-simplify]: Simplify 1.0 into 1.0 3.255 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 3.255 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 3.255 * [taylor]: Taking taylor expansion of -2.0 in k 3.255 * [backup-simplify]: Simplify -2.0 into -2.0 3.255 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.255 * [taylor]: Taking taylor expansion of PI in k 3.255 * [backup-simplify]: Simplify PI into PI 3.255 * [taylor]: Taking taylor expansion of n in k 3.255 * [backup-simplify]: Simplify n into n 3.255 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.255 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 3.255 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 3.256 * [backup-simplify]: Simplify (+ 1 0) into 1 3.256 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 3.256 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 3.257 * [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)))))) 3.257 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.257 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.257 * [taylor]: Taking taylor expansion of -1 in k 3.257 * [backup-simplify]: Simplify -1 into -1 3.257 * [taylor]: Taking taylor expansion of k in k 3.257 * [backup-simplify]: Simplify 0 into 0 3.257 * [backup-simplify]: Simplify 1 into 1 3.257 * [backup-simplify]: Simplify (/ -1 1) into -1 3.258 * [backup-simplify]: Simplify (sqrt 0) into 0 3.259 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.259 * [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))))))) 3.260 * [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))))))) 3.260 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.260 * [taylor]: Taking taylor expansion of +nan.0 in n 3.260 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.260 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.260 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.260 * [taylor]: Taking taylor expansion of 0.5 in n 3.260 * [backup-simplify]: Simplify 0.5 into 0.5 3.260 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.260 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.260 * [taylor]: Taking taylor expansion of k in n 3.260 * [backup-simplify]: Simplify k into k 3.260 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.260 * [taylor]: Taking taylor expansion of 1.0 in n 3.260 * [backup-simplify]: Simplify 1.0 into 1.0 3.260 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.260 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.260 * [taylor]: Taking taylor expansion of -2.0 in n 3.260 * [backup-simplify]: Simplify -2.0 into -2.0 3.261 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.261 * [taylor]: Taking taylor expansion of PI in n 3.261 * [backup-simplify]: Simplify PI into PI 3.261 * [taylor]: Taking taylor expansion of n in n 3.261 * [backup-simplify]: Simplify 0 into 0 3.261 * [backup-simplify]: Simplify 1 into 1 3.261 * [backup-simplify]: Simplify (/ PI 1) into PI 3.262 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.263 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.263 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.264 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.266 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.267 * [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)))) 3.268 * [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))))) 3.270 * [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)))))) 3.271 * [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)))))) 3.272 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 3.275 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.276 * [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)))))))) 3.277 * [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)))))))) 3.277 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 3.277 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.277 * [taylor]: Taking taylor expansion of +nan.0 in n 3.277 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.277 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.277 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.277 * [taylor]: Taking taylor expansion of 0.5 in n 3.277 * [backup-simplify]: Simplify 0.5 into 0.5 3.277 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.277 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.278 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.278 * [taylor]: Taking taylor expansion of k in n 3.278 * [backup-simplify]: Simplify k into k 3.278 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.278 * [taylor]: Taking taylor expansion of 1.0 in n 3.278 * [backup-simplify]: Simplify 1.0 into 1.0 3.278 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.278 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.278 * [taylor]: Taking taylor expansion of -2.0 in n 3.278 * [backup-simplify]: Simplify -2.0 into -2.0 3.278 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.278 * [taylor]: Taking taylor expansion of PI in n 3.278 * [backup-simplify]: Simplify PI into PI 3.278 * [taylor]: Taking taylor expansion of n in n 3.278 * [backup-simplify]: Simplify 0 into 0 3.278 * [backup-simplify]: Simplify 1 into 1 3.279 * [backup-simplify]: Simplify (/ PI 1) into PI 3.279 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.280 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.281 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.283 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.285 * [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)))) 3.286 * [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))))) 3.287 * [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)))))) 3.289 * [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))))))) 3.290 * [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))))))) 3.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.291 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 3.292 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 3.292 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.293 * [backup-simplify]: Simplify (+ 0 0) into 0 3.293 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.294 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 3.295 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 3.296 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.297 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 3.297 * [backup-simplify]: Simplify 0 into 0 3.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.300 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.301 * [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)))))))) 3.302 * [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)))))))) 3.302 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 3.302 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 3.302 * [taylor]: Taking taylor expansion of +nan.0 in n 3.302 * [backup-simplify]: Simplify +nan.0 into +nan.0 3.302 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 3.302 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 3.302 * [taylor]: Taking taylor expansion of 0.5 in n 3.302 * [backup-simplify]: Simplify 0.5 into 0.5 3.302 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 3.302 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 3.302 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.302 * [taylor]: Taking taylor expansion of k in n 3.302 * [backup-simplify]: Simplify k into k 3.302 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.302 * [taylor]: Taking taylor expansion of 1.0 in n 3.302 * [backup-simplify]: Simplify 1.0 into 1.0 3.302 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 3.302 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 3.302 * [taylor]: Taking taylor expansion of -2.0 in n 3.302 * [backup-simplify]: Simplify -2.0 into -2.0 3.302 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.302 * [taylor]: Taking taylor expansion of PI in n 3.302 * [backup-simplify]: Simplify PI into PI 3.302 * [taylor]: Taking taylor expansion of n in n 3.302 * [backup-simplify]: Simplify 0 into 0 3.302 * [backup-simplify]: Simplify 1 into 1 3.303 * [backup-simplify]: Simplify (/ PI 1) into PI 3.303 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 3.304 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 3.304 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 3.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 3.305 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 3.306 * [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)))) 3.307 * [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))))) 3.308 * [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)))))) 3.308 * [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))))))) 3.309 * [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))))))) 3.312 * [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)))))))))))) 3.312 * * * [progress]: simplifying candidates 3.315 * [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) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 5.220 * * * [progress]: adding candidates to table 6.306 * * [progress]: iteration 2 / 4 6.306 * * * [progress]: picking best candidate 6.327 * * * * [pick]: Picked # 6.327 * * * [progress]: localizing error 6.352 * * * [progress]: generating rewritten candidates 6.352 * * * * [progress]: [ 1 / 3 ] rewriting at (2 2 1) 6.403 * * * * [progress]: [ 2 / 3 ] rewriting at (2 2 1 1) 6.439 * * * * [progress]: [ 3 / 3 ] rewriting at (2 2) 6.475 * * * [progress]: generating series expansions 6.475 * * * * [progress]: [ 1 / 3 ] generating series at (2 2 1) 6.476 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 6.476 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 6.476 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.476 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.476 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.476 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.476 * [taylor]: Taking taylor expansion of 0.5 in k 6.476 * [backup-simplify]: Simplify 0.5 into 0.5 6.476 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.477 * [taylor]: Taking taylor expansion of 1.0 in k 6.477 * [backup-simplify]: Simplify 1.0 into 1.0 6.477 * [taylor]: Taking taylor expansion of k in k 6.477 * [backup-simplify]: Simplify 0 into 0 6.477 * [backup-simplify]: Simplify 1 into 1 6.477 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.477 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.477 * [taylor]: Taking taylor expansion of 2.0 in k 6.477 * [backup-simplify]: Simplify 2.0 into 2.0 6.477 * [taylor]: Taking taylor expansion of (* n PI) in k 6.477 * [taylor]: Taking taylor expansion of n in k 6.477 * [backup-simplify]: Simplify n into n 6.477 * [taylor]: Taking taylor expansion of PI in k 6.477 * [backup-simplify]: Simplify PI into PI 6.477 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.477 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.477 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.478 * [backup-simplify]: Simplify (- 0) into 0 6.478 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.478 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.479 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.479 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.479 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.479 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.479 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.479 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.479 * [taylor]: Taking taylor expansion of 0.5 in n 6.479 * [backup-simplify]: Simplify 0.5 into 0.5 6.479 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.479 * [taylor]: Taking taylor expansion of 1.0 in n 6.479 * [backup-simplify]: Simplify 1.0 into 1.0 6.479 * [taylor]: Taking taylor expansion of k in n 6.479 * [backup-simplify]: Simplify k into k 6.479 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.479 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.479 * [taylor]: Taking taylor expansion of 2.0 in n 6.479 * [backup-simplify]: Simplify 2.0 into 2.0 6.479 * [taylor]: Taking taylor expansion of (* n PI) in n 6.479 * [taylor]: Taking taylor expansion of n in n 6.479 * [backup-simplify]: Simplify 0 into 0 6.479 * [backup-simplify]: Simplify 1 into 1 6.479 * [taylor]: Taking taylor expansion of PI in n 6.479 * [backup-simplify]: Simplify PI into PI 6.480 * [backup-simplify]: Simplify (* 0 PI) into 0 6.480 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.482 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.483 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.484 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.484 * [backup-simplify]: Simplify (- k) into (- k) 6.484 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.485 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.486 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.487 * [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)))) 6.488 * [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))))) 6.488 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.488 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.488 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.488 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.488 * [taylor]: Taking taylor expansion of 0.5 in n 6.489 * [backup-simplify]: Simplify 0.5 into 0.5 6.489 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.489 * [taylor]: Taking taylor expansion of 1.0 in n 6.489 * [backup-simplify]: Simplify 1.0 into 1.0 6.489 * [taylor]: Taking taylor expansion of k in n 6.489 * [backup-simplify]: Simplify k into k 6.489 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.489 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.489 * [taylor]: Taking taylor expansion of 2.0 in n 6.489 * [backup-simplify]: Simplify 2.0 into 2.0 6.489 * [taylor]: Taking taylor expansion of (* n PI) in n 6.489 * [taylor]: Taking taylor expansion of n in n 6.489 * [backup-simplify]: Simplify 0 into 0 6.489 * [backup-simplify]: Simplify 1 into 1 6.489 * [taylor]: Taking taylor expansion of PI in n 6.489 * [backup-simplify]: Simplify PI into PI 6.489 * [backup-simplify]: Simplify (* 0 PI) into 0 6.490 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.491 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.493 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.494 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.494 * [backup-simplify]: Simplify (- k) into (- k) 6.494 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.494 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.496 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.497 * [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)))) 6.498 * [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))))) 6.498 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.498 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.498 * [taylor]: Taking taylor expansion of 0.5 in k 6.498 * [backup-simplify]: Simplify 0.5 into 0.5 6.498 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.498 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.498 * [taylor]: Taking taylor expansion of 1.0 in k 6.498 * [backup-simplify]: Simplify 1.0 into 1.0 6.498 * [taylor]: Taking taylor expansion of k in k 6.498 * [backup-simplify]: Simplify 0 into 0 6.498 * [backup-simplify]: Simplify 1 into 1 6.498 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.498 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.499 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.499 * [taylor]: Taking taylor expansion of 2.0 in k 6.499 * [backup-simplify]: Simplify 2.0 into 2.0 6.499 * [taylor]: Taking taylor expansion of PI in k 6.499 * [backup-simplify]: Simplify PI into PI 6.499 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.500 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.500 * [taylor]: Taking taylor expansion of (log n) in k 6.500 * [taylor]: Taking taylor expansion of n in k 6.500 * [backup-simplify]: Simplify n into n 6.500 * [backup-simplify]: Simplify (log n) into (log n) 6.501 * [backup-simplify]: Simplify (- 0) into 0 6.501 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.502 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.504 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.505 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.506 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.507 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.508 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.509 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.511 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.511 * [backup-simplify]: Simplify (- 0) into 0 6.512 * [backup-simplify]: Simplify (+ 0 0) into 0 6.512 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.514 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.521 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.523 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.523 * [taylor]: Taking taylor expansion of 0 in k 6.523 * [backup-simplify]: Simplify 0 into 0 6.523 * [backup-simplify]: Simplify 0 into 0 6.524 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.526 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.527 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.527 * [backup-simplify]: Simplify (+ 0 0) into 0 6.527 * [backup-simplify]: Simplify (- 1) into -1 6.528 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.529 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.531 * [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)))) 6.535 * [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)))))) 6.538 * [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)))))) 6.539 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.540 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.544 * [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 6.544 * [backup-simplify]: Simplify (- 0) into 0 6.545 * [backup-simplify]: Simplify (+ 0 0) into 0 6.545 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.547 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.549 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.551 * [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 6.551 * [taylor]: Taking taylor expansion of 0 in k 6.551 * [backup-simplify]: Simplify 0 into 0 6.551 * [backup-simplify]: Simplify 0 into 0 6.551 * [backup-simplify]: Simplify 0 into 0 6.552 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.556 * [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 6.558 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.559 * [backup-simplify]: Simplify (+ 0 0) into 0 6.559 * [backup-simplify]: Simplify (- 0) into 0 6.559 * [backup-simplify]: Simplify (+ 0 0) into 0 6.561 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.564 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.567 * [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)))))) 6.573 * [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)))))) 6.583 * [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)))))) 6.584 * [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)))) 6.584 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 6.584 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.584 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.584 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.584 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.584 * [taylor]: Taking taylor expansion of 0.5 in k 6.584 * [backup-simplify]: Simplify 0.5 into 0.5 6.584 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.585 * [taylor]: Taking taylor expansion of 1.0 in k 6.585 * [backup-simplify]: Simplify 1.0 into 1.0 6.585 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.585 * [taylor]: Taking taylor expansion of k in k 6.585 * [backup-simplify]: Simplify 0 into 0 6.585 * [backup-simplify]: Simplify 1 into 1 6.585 * [backup-simplify]: Simplify (/ 1 1) into 1 6.585 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.585 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.585 * [taylor]: Taking taylor expansion of 2.0 in k 6.585 * [backup-simplify]: Simplify 2.0 into 2.0 6.585 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.585 * [taylor]: Taking taylor expansion of PI in k 6.585 * [backup-simplify]: Simplify PI into PI 6.585 * [taylor]: Taking taylor expansion of n in k 6.585 * [backup-simplify]: Simplify n into n 6.585 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.586 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.586 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.586 * [backup-simplify]: Simplify (- 1) into -1 6.586 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.587 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.587 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.587 * [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))))) 6.587 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.587 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.587 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.587 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.587 * [taylor]: Taking taylor expansion of 0.5 in n 6.587 * [backup-simplify]: Simplify 0.5 into 0.5 6.587 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.587 * [taylor]: Taking taylor expansion of 1.0 in n 6.587 * [backup-simplify]: Simplify 1.0 into 1.0 6.588 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.588 * [taylor]: Taking taylor expansion of k in n 6.588 * [backup-simplify]: Simplify k into k 6.588 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.588 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.588 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.588 * [taylor]: Taking taylor expansion of 2.0 in n 6.588 * [backup-simplify]: Simplify 2.0 into 2.0 6.588 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.588 * [taylor]: Taking taylor expansion of PI in n 6.588 * [backup-simplify]: Simplify PI into PI 6.588 * [taylor]: Taking taylor expansion of n in n 6.588 * [backup-simplify]: Simplify 0 into 0 6.588 * [backup-simplify]: Simplify 1 into 1 6.588 * [backup-simplify]: Simplify (/ PI 1) into PI 6.589 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.590 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.590 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.590 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.590 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.592 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.593 * [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)))) 6.594 * [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))))) 6.594 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.594 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.594 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.594 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.594 * [taylor]: Taking taylor expansion of 0.5 in n 6.594 * [backup-simplify]: Simplify 0.5 into 0.5 6.594 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.595 * [taylor]: Taking taylor expansion of 1.0 in n 6.595 * [backup-simplify]: Simplify 1.0 into 1.0 6.595 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.595 * [taylor]: Taking taylor expansion of k in n 6.595 * [backup-simplify]: Simplify k into k 6.595 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.595 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.595 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.595 * [taylor]: Taking taylor expansion of 2.0 in n 6.595 * [backup-simplify]: Simplify 2.0 into 2.0 6.595 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.595 * [taylor]: Taking taylor expansion of PI in n 6.595 * [backup-simplify]: Simplify PI into PI 6.595 * [taylor]: Taking taylor expansion of n in n 6.595 * [backup-simplify]: Simplify 0 into 0 6.595 * [backup-simplify]: Simplify 1 into 1 6.596 * [backup-simplify]: Simplify (/ PI 1) into PI 6.596 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.597 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.597 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.597 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.597 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.600 * [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)))) 6.601 * [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))))) 6.602 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.602 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.602 * [taylor]: Taking taylor expansion of 0.5 in k 6.602 * [backup-simplify]: Simplify 0.5 into 0.5 6.602 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.602 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.602 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.602 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.602 * [taylor]: Taking taylor expansion of 2.0 in k 6.602 * [backup-simplify]: Simplify 2.0 into 2.0 6.602 * [taylor]: Taking taylor expansion of PI in k 6.602 * [backup-simplify]: Simplify PI into PI 6.602 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.603 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.604 * [taylor]: Taking taylor expansion of (log n) in k 6.604 * [taylor]: Taking taylor expansion of n in k 6.604 * [backup-simplify]: Simplify n into n 6.604 * [backup-simplify]: Simplify (log n) into (log n) 6.604 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.604 * [taylor]: Taking taylor expansion of 1.0 in k 6.604 * [backup-simplify]: Simplify 1.0 into 1.0 6.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.604 * [taylor]: Taking taylor expansion of k in k 6.604 * [backup-simplify]: Simplify 0 into 0 6.604 * [backup-simplify]: Simplify 1 into 1 6.604 * [backup-simplify]: Simplify (/ 1 1) into 1 6.604 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.605 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.606 * [backup-simplify]: Simplify (- 1) into -1 6.606 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.607 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.608 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.610 * [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))))) 6.611 * [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))))) 6.612 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.613 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.614 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.615 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.615 * [backup-simplify]: Simplify (- 0) into 0 6.616 * [backup-simplify]: Simplify (+ 0 0) into 0 6.616 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.619 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.621 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.621 * [taylor]: Taking taylor expansion of 0 in k 6.621 * [backup-simplify]: Simplify 0 into 0 6.621 * [backup-simplify]: Simplify 0 into 0 6.621 * [backup-simplify]: Simplify 0 into 0 6.622 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.623 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.626 * [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 6.627 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.627 * [backup-simplify]: Simplify (- 0) into 0 6.627 * [backup-simplify]: Simplify (+ 0 0) into 0 6.628 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.631 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.634 * [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 6.634 * [taylor]: Taking taylor expansion of 0 in k 6.634 * [backup-simplify]: Simplify 0 into 0 6.634 * [backup-simplify]: Simplify 0 into 0 6.634 * [backup-simplify]: Simplify 0 into 0 6.634 * [backup-simplify]: Simplify 0 into 0 6.635 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.636 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.643 * [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 6.643 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.643 * [backup-simplify]: Simplify (- 0) into 0 6.644 * [backup-simplify]: Simplify (+ 0 0) into 0 6.645 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.648 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.651 * [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 6.651 * [taylor]: Taking taylor expansion of 0 in k 6.651 * [backup-simplify]: Simplify 0 into 0 6.652 * [backup-simplify]: Simplify 0 into 0 6.653 * [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)))) 6.654 * [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))) 6.654 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.654 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.654 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.654 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.654 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.654 * [taylor]: Taking taylor expansion of 0.5 in k 6.654 * [backup-simplify]: Simplify 0.5 into 0.5 6.654 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.654 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.654 * [taylor]: Taking taylor expansion of k in k 6.654 * [backup-simplify]: Simplify 0 into 0 6.654 * [backup-simplify]: Simplify 1 into 1 6.655 * [backup-simplify]: Simplify (/ 1 1) into 1 6.655 * [taylor]: Taking taylor expansion of 1.0 in k 6.655 * [backup-simplify]: Simplify 1.0 into 1.0 6.655 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.655 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.655 * [taylor]: Taking taylor expansion of -2.0 in k 6.655 * [backup-simplify]: Simplify -2.0 into -2.0 6.655 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.655 * [taylor]: Taking taylor expansion of PI in k 6.655 * [backup-simplify]: Simplify PI into PI 6.655 * [taylor]: Taking taylor expansion of n in k 6.655 * [backup-simplify]: Simplify n into n 6.655 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.655 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.655 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.656 * [backup-simplify]: Simplify (+ 1 0) into 1 6.656 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.656 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.657 * [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)))))) 6.657 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.657 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.657 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.657 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.657 * [taylor]: Taking taylor expansion of 0.5 in n 6.657 * [backup-simplify]: Simplify 0.5 into 0.5 6.657 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.657 * [taylor]: Taking taylor expansion of k in n 6.657 * [backup-simplify]: Simplify k into k 6.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.657 * [taylor]: Taking taylor expansion of 1.0 in n 6.657 * [backup-simplify]: Simplify 1.0 into 1.0 6.657 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.657 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.657 * [taylor]: Taking taylor expansion of -2.0 in n 6.657 * [backup-simplify]: Simplify -2.0 into -2.0 6.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.657 * [taylor]: Taking taylor expansion of PI in n 6.657 * [backup-simplify]: Simplify PI into PI 6.657 * [taylor]: Taking taylor expansion of n in n 6.657 * [backup-simplify]: Simplify 0 into 0 6.657 * [backup-simplify]: Simplify 1 into 1 6.658 * [backup-simplify]: Simplify (/ PI 1) into PI 6.658 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.660 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.660 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.660 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.662 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.663 * [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)))) 6.664 * [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))))) 6.664 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.664 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.664 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.664 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.664 * [taylor]: Taking taylor expansion of 0.5 in n 6.664 * [backup-simplify]: Simplify 0.5 into 0.5 6.664 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.665 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.665 * [taylor]: Taking taylor expansion of k in n 6.665 * [backup-simplify]: Simplify k into k 6.665 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.665 * [taylor]: Taking taylor expansion of 1.0 in n 6.665 * [backup-simplify]: Simplify 1.0 into 1.0 6.665 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.665 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.665 * [taylor]: Taking taylor expansion of -2.0 in n 6.665 * [backup-simplify]: Simplify -2.0 into -2.0 6.665 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.665 * [taylor]: Taking taylor expansion of PI in n 6.665 * [backup-simplify]: Simplify PI into PI 6.665 * [taylor]: Taking taylor expansion of n in n 6.665 * [backup-simplify]: Simplify 0 into 0 6.665 * [backup-simplify]: Simplify 1 into 1 6.666 * [backup-simplify]: Simplify (/ PI 1) into PI 6.666 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.667 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.668 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.668 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.669 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.678 * [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)))) 6.680 * [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))))) 6.680 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.680 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.680 * [taylor]: Taking taylor expansion of 0.5 in k 6.680 * [backup-simplify]: Simplify 0.5 into 0.5 6.680 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.680 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.680 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.680 * [taylor]: Taking taylor expansion of k in k 6.680 * [backup-simplify]: Simplify 0 into 0 6.680 * [backup-simplify]: Simplify 1 into 1 6.681 * [backup-simplify]: Simplify (/ 1 1) into 1 6.681 * [taylor]: Taking taylor expansion of 1.0 in k 6.681 * [backup-simplify]: Simplify 1.0 into 1.0 6.681 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.681 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.681 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.681 * [taylor]: Taking taylor expansion of -2.0 in k 6.681 * [backup-simplify]: Simplify -2.0 into -2.0 6.681 * [taylor]: Taking taylor expansion of PI in k 6.681 * [backup-simplify]: Simplify PI into PI 6.681 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.683 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.683 * [taylor]: Taking taylor expansion of (log n) in k 6.683 * [taylor]: Taking taylor expansion of n in k 6.683 * [backup-simplify]: Simplify n into n 6.683 * [backup-simplify]: Simplify (log n) into (log n) 6.683 * [backup-simplify]: Simplify (+ 1 0) into 1 6.683 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.684 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.685 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.687 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.688 * [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))))) 6.689 * [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))))) 6.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.691 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.692 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.692 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.692 * [backup-simplify]: Simplify (+ 0 0) into 0 6.692 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.693 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.694 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.696 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.696 * [taylor]: Taking taylor expansion of 0 in k 6.696 * [backup-simplify]: Simplify 0 into 0 6.696 * [backup-simplify]: Simplify 0 into 0 6.696 * [backup-simplify]: Simplify 0 into 0 6.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.697 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.699 * [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 6.699 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.699 * [backup-simplify]: Simplify (+ 0 0) into 0 6.700 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.702 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.703 * [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 6.703 * [taylor]: Taking taylor expansion of 0 in k 6.703 * [backup-simplify]: Simplify 0 into 0 6.703 * [backup-simplify]: Simplify 0 into 0 6.703 * [backup-simplify]: Simplify 0 into 0 6.703 * [backup-simplify]: Simplify 0 into 0 6.704 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.704 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.708 * [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 6.708 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.708 * [backup-simplify]: Simplify (+ 0 0) into 0 6.709 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.710 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.711 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.712 * [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 6.712 * [taylor]: Taking taylor expansion of 0 in k 6.712 * [backup-simplify]: Simplify 0 into 0 6.712 * [backup-simplify]: Simplify 0 into 0 6.713 * [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)))))) 6.713 * * * * [progress]: [ 2 / 3 ] generating series at (2 2 1 1) 6.714 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.714 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.714 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.714 * [taylor]: Taking taylor expansion of 2.0 in n 6.714 * [backup-simplify]: Simplify 2.0 into 2.0 6.714 * [taylor]: Taking taylor expansion of (* n PI) in n 6.714 * [taylor]: Taking taylor expansion of n in n 6.714 * [backup-simplify]: Simplify 0 into 0 6.714 * [backup-simplify]: Simplify 1 into 1 6.714 * [taylor]: Taking taylor expansion of PI in n 6.714 * [backup-simplify]: Simplify PI into PI 6.714 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.714 * [taylor]: Taking taylor expansion of 2.0 in n 6.714 * [backup-simplify]: Simplify 2.0 into 2.0 6.714 * [taylor]: Taking taylor expansion of (* n PI) in n 6.714 * [taylor]: Taking taylor expansion of n in n 6.714 * [backup-simplify]: Simplify 0 into 0 6.714 * [backup-simplify]: Simplify 1 into 1 6.714 * [taylor]: Taking taylor expansion of PI in n 6.714 * [backup-simplify]: Simplify PI into PI 6.714 * [backup-simplify]: Simplify (* 0 PI) into 0 6.715 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.715 * [backup-simplify]: Simplify 0 into 0 6.716 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.717 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.717 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.718 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.718 * [backup-simplify]: Simplify 0 into 0 6.719 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.720 * [backup-simplify]: Simplify 0 into 0 6.722 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.723 * [backup-simplify]: Simplify 0 into 0 6.725 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.726 * [backup-simplify]: Simplify 0 into 0 6.728 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.730 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.730 * [backup-simplify]: Simplify 0 into 0 6.732 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.734 * [backup-simplify]: Simplify 0 into 0 6.734 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.735 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.735 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.735 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.735 * [taylor]: Taking taylor expansion of 2.0 in n 6.735 * [backup-simplify]: Simplify 2.0 into 2.0 6.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.735 * [taylor]: Taking taylor expansion of PI in n 6.735 * [backup-simplify]: Simplify PI into PI 6.735 * [taylor]: Taking taylor expansion of n in n 6.735 * [backup-simplify]: Simplify 0 into 0 6.735 * [backup-simplify]: Simplify 1 into 1 6.735 * [backup-simplify]: Simplify (/ PI 1) into PI 6.735 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.735 * [taylor]: Taking taylor expansion of 2.0 in n 6.735 * [backup-simplify]: Simplify 2.0 into 2.0 6.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.735 * [taylor]: Taking taylor expansion of PI in n 6.735 * [backup-simplify]: Simplify PI into PI 6.735 * [taylor]: Taking taylor expansion of n in n 6.735 * [backup-simplify]: Simplify 0 into 0 6.735 * [backup-simplify]: Simplify 1 into 1 6.736 * [backup-simplify]: Simplify (/ PI 1) into PI 6.736 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.736 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.737 * [backup-simplify]: Simplify 0 into 0 6.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.738 * [backup-simplify]: Simplify 0 into 0 6.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.740 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.740 * [backup-simplify]: Simplify 0 into 0 6.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.741 * [backup-simplify]: Simplify 0 into 0 6.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.743 * [backup-simplify]: Simplify 0 into 0 6.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.744 * [backup-simplify]: Simplify 0 into 0 6.745 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.745 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.745 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.745 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.745 * [taylor]: Taking taylor expansion of -2.0 in n 6.745 * [backup-simplify]: Simplify -2.0 into -2.0 6.745 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.745 * [taylor]: Taking taylor expansion of PI in n 6.745 * [backup-simplify]: Simplify PI into PI 6.745 * [taylor]: Taking taylor expansion of n in n 6.745 * [backup-simplify]: Simplify 0 into 0 6.745 * [backup-simplify]: Simplify 1 into 1 6.745 * [backup-simplify]: Simplify (/ PI 1) into PI 6.745 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.745 * [taylor]: Taking taylor expansion of -2.0 in n 6.745 * [backup-simplify]: Simplify -2.0 into -2.0 6.745 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.745 * [taylor]: Taking taylor expansion of PI in n 6.746 * [backup-simplify]: Simplify PI into PI 6.746 * [taylor]: Taking taylor expansion of n in n 6.746 * [backup-simplify]: Simplify 0 into 0 6.746 * [backup-simplify]: Simplify 1 into 1 6.746 * [backup-simplify]: Simplify (/ PI 1) into PI 6.746 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.747 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.747 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.747 * [backup-simplify]: Simplify 0 into 0 6.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.749 * [backup-simplify]: Simplify 0 into 0 6.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.750 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.750 * [backup-simplify]: Simplify 0 into 0 6.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.751 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.751 * [backup-simplify]: Simplify 0 into 0 6.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.753 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.753 * [backup-simplify]: Simplify 0 into 0 6.754 * [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 6.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.754 * [backup-simplify]: Simplify 0 into 0 6.755 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.755 * * * * [progress]: [ 3 / 3 ] generating series at (2 2) 6.755 * [backup-simplify]: Simplify (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) into (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) 6.755 * [approximate]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in (n k) around 0 6.755 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 6.755 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.756 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.756 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.756 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.756 * [taylor]: Taking taylor expansion of 0.5 in k 6.756 * [backup-simplify]: Simplify 0.5 into 0.5 6.756 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.756 * [taylor]: Taking taylor expansion of 1.0 in k 6.756 * [backup-simplify]: Simplify 1.0 into 1.0 6.756 * [taylor]: Taking taylor expansion of k in k 6.756 * [backup-simplify]: Simplify 0 into 0 6.756 * [backup-simplify]: Simplify 1 into 1 6.756 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.756 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.756 * [taylor]: Taking taylor expansion of 2.0 in k 6.756 * [backup-simplify]: Simplify 2.0 into 2.0 6.756 * [taylor]: Taking taylor expansion of (* n PI) in k 6.756 * [taylor]: Taking taylor expansion of n in k 6.756 * [backup-simplify]: Simplify n into n 6.756 * [taylor]: Taking taylor expansion of PI in k 6.756 * [backup-simplify]: Simplify PI into PI 6.756 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.756 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.756 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.756 * [backup-simplify]: Simplify (- 0) into 0 6.756 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.757 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.757 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.757 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.757 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.757 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.757 * [taylor]: Taking taylor expansion of k in k 6.757 * [backup-simplify]: Simplify 0 into 0 6.757 * [backup-simplify]: Simplify 1 into 1 6.757 * [backup-simplify]: Simplify (/ 1 1) into 1 6.758 * [backup-simplify]: Simplify (sqrt 0) into 0 6.758 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.758 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 6.758 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.758 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.758 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.759 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.759 * [taylor]: Taking taylor expansion of 0.5 in n 6.759 * [backup-simplify]: Simplify 0.5 into 0.5 6.759 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.759 * [taylor]: Taking taylor expansion of 1.0 in n 6.759 * [backup-simplify]: Simplify 1.0 into 1.0 6.759 * [taylor]: Taking taylor expansion of k in n 6.759 * [backup-simplify]: Simplify k into k 6.759 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.759 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.759 * [taylor]: Taking taylor expansion of 2.0 in n 6.759 * [backup-simplify]: Simplify 2.0 into 2.0 6.759 * [taylor]: Taking taylor expansion of (* n PI) in n 6.759 * [taylor]: Taking taylor expansion of n in n 6.759 * [backup-simplify]: Simplify 0 into 0 6.759 * [backup-simplify]: Simplify 1 into 1 6.759 * [taylor]: Taking taylor expansion of PI in n 6.759 * [backup-simplify]: Simplify PI into PI 6.759 * [backup-simplify]: Simplify (* 0 PI) into 0 6.759 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.760 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.761 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.762 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.762 * [backup-simplify]: Simplify (- k) into (- k) 6.762 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.762 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.763 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.764 * [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)))) 6.764 * [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))))) 6.764 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.764 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.764 * [taylor]: Taking taylor expansion of k in n 6.764 * [backup-simplify]: Simplify k into k 6.764 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.764 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.764 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.765 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.765 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 6.765 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.765 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.765 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.765 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.765 * [taylor]: Taking taylor expansion of 0.5 in n 6.765 * [backup-simplify]: Simplify 0.5 into 0.5 6.765 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.765 * [taylor]: Taking taylor expansion of 1.0 in n 6.765 * [backup-simplify]: Simplify 1.0 into 1.0 6.765 * [taylor]: Taking taylor expansion of k in n 6.765 * [backup-simplify]: Simplify k into k 6.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.765 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.765 * [taylor]: Taking taylor expansion of 2.0 in n 6.765 * [backup-simplify]: Simplify 2.0 into 2.0 6.765 * [taylor]: Taking taylor expansion of (* n PI) in n 6.765 * [taylor]: Taking taylor expansion of n in n 6.765 * [backup-simplify]: Simplify 0 into 0 6.765 * [backup-simplify]: Simplify 1 into 1 6.765 * [taylor]: Taking taylor expansion of PI in n 6.765 * [backup-simplify]: Simplify PI into PI 6.765 * [backup-simplify]: Simplify (* 0 PI) into 0 6.765 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.767 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.768 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.769 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.769 * [backup-simplify]: Simplify (- k) into (- k) 6.770 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.770 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.771 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.772 * [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)))) 6.773 * [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))))) 6.774 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.774 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.774 * [taylor]: Taking taylor expansion of k in n 6.774 * [backup-simplify]: Simplify k into k 6.774 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.774 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.774 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.774 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.775 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 6.775 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k 6.776 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.776 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.776 * [taylor]: Taking taylor expansion of k in k 6.776 * [backup-simplify]: Simplify 0 into 0 6.776 * [backup-simplify]: Simplify 1 into 1 6.776 * [backup-simplify]: Simplify (/ 1 1) into 1 6.776 * [backup-simplify]: Simplify (sqrt 0) into 0 6.778 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.778 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.778 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.778 * [taylor]: Taking taylor expansion of 0.5 in k 6.778 * [backup-simplify]: Simplify 0.5 into 0.5 6.778 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.778 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.778 * [taylor]: Taking taylor expansion of 1.0 in k 6.778 * [backup-simplify]: Simplify 1.0 into 1.0 6.778 * [taylor]: Taking taylor expansion of k in k 6.778 * [backup-simplify]: Simplify 0 into 0 6.778 * [backup-simplify]: Simplify 1 into 1 6.778 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.778 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.778 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.778 * [taylor]: Taking taylor expansion of 2.0 in k 6.778 * [backup-simplify]: Simplify 2.0 into 2.0 6.778 * [taylor]: Taking taylor expansion of PI in k 6.778 * [backup-simplify]: Simplify PI into PI 6.779 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.780 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.780 * [taylor]: Taking taylor expansion of (log n) in k 6.780 * [taylor]: Taking taylor expansion of n in k 6.780 * [backup-simplify]: Simplify n into n 6.780 * [backup-simplify]: Simplify (log n) into (log n) 6.781 * [backup-simplify]: Simplify (- 0) into 0 6.781 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.782 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.783 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.792 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.793 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.794 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0 6.794 * [backup-simplify]: Simplify 0 into 0 6.795 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.797 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.797 * [backup-simplify]: Simplify (- 0) into 0 6.797 * [backup-simplify]: Simplify (+ 0 0) into 0 6.797 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.798 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.799 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.800 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.801 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 6.801 * [taylor]: Taking taylor expansion of 0 in k 6.801 * [backup-simplify]: Simplify 0 into 0 6.801 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.802 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.803 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.803 * [backup-simplify]: Simplify (+ 0 0) into 0 6.803 * [backup-simplify]: Simplify (- 1) into -1 6.804 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.805 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.806 * [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)))) 6.808 * [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)))))) 6.810 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.811 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.811 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.812 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 6.812 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.813 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.815 * [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 6.815 * [backup-simplify]: Simplify (- 0) into 0 6.815 * [backup-simplify]: Simplify (+ 0 0) into 0 6.816 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.817 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.818 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.820 * [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 6.822 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 6.822 * [taylor]: Taking taylor expansion of 0 in k 6.822 * [backup-simplify]: Simplify 0 into 0 6.822 * [backup-simplify]: Simplify 0 into 0 6.823 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.826 * [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 6.828 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.829 * [backup-simplify]: Simplify (+ 0 0) into 0 6.829 * [backup-simplify]: Simplify (- 0) into 0 6.829 * [backup-simplify]: Simplify (+ 0 0) into 0 6.831 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.834 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.837 * [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)))))) 6.838 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.841 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.851 * [backup-simplify]: Simplify (+ (* 0 (* (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))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 6.855 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 6.856 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.857 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 6.858 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.859 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.864 * [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 6.864 * [backup-simplify]: Simplify (- 0) into 0 6.864 * [backup-simplify]: Simplify (+ 0 0) into 0 6.865 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 6.866 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.867 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.869 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.870 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 6.870 * [taylor]: Taking taylor expansion of 0 in k 6.870 * [backup-simplify]: Simplify 0 into 0 6.870 * [backup-simplify]: Simplify 0 into 0 6.870 * [backup-simplify]: Simplify 0 into 0 6.871 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.874 * [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 6.876 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0 6.876 * [backup-simplify]: Simplify (+ 0 0) into 0 6.876 * [backup-simplify]: Simplify (- 0) into 0 6.877 * [backup-simplify]: Simplify (+ 0 0) into 0 6.878 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.880 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0 6.884 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3))))))) 6.884 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.886 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.910 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))) (+ (* +nan.0 (* (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))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))) 6.924 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) 6.945 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))))))))) 6.946 * [backup-simplify]: Simplify (/ (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) 6.946 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in (n k) around 0 6.946 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 6.946 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.946 * [taylor]: Taking taylor expansion of k in k 6.946 * [backup-simplify]: Simplify 0 into 0 6.946 * [backup-simplify]: Simplify 1 into 1 6.947 * [backup-simplify]: Simplify (sqrt 0) into 0 6.948 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.948 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.948 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.948 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.948 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.948 * [taylor]: Taking taylor expansion of 0.5 in k 6.948 * [backup-simplify]: Simplify 0.5 into 0.5 6.948 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.948 * [taylor]: Taking taylor expansion of 1.0 in k 6.948 * [backup-simplify]: Simplify 1.0 into 1.0 6.948 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.948 * [taylor]: Taking taylor expansion of k in k 6.948 * [backup-simplify]: Simplify 0 into 0 6.948 * [backup-simplify]: Simplify 1 into 1 6.949 * [backup-simplify]: Simplify (/ 1 1) into 1 6.949 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.949 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.949 * [taylor]: Taking taylor expansion of 2.0 in k 6.949 * [backup-simplify]: Simplify 2.0 into 2.0 6.949 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.949 * [taylor]: Taking taylor expansion of PI in k 6.949 * [backup-simplify]: Simplify PI into PI 6.949 * [taylor]: Taking taylor expansion of n in k 6.949 * [backup-simplify]: Simplify n into n 6.949 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.949 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.949 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.950 * [backup-simplify]: Simplify (- 1) into -1 6.950 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.951 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.951 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.951 * [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))))) 6.951 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.951 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.951 * [taylor]: Taking taylor expansion of k in n 6.951 * [backup-simplify]: Simplify k into k 6.951 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.951 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.951 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.951 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.951 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.951 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.951 * [taylor]: Taking taylor expansion of 0.5 in n 6.951 * [backup-simplify]: Simplify 0.5 into 0.5 6.951 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.951 * [taylor]: Taking taylor expansion of 1.0 in n 6.951 * [backup-simplify]: Simplify 1.0 into 1.0 6.951 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.951 * [taylor]: Taking taylor expansion of k in n 6.951 * [backup-simplify]: Simplify k into k 6.951 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.951 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.951 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.951 * [taylor]: Taking taylor expansion of 2.0 in n 6.951 * [backup-simplify]: Simplify 2.0 into 2.0 6.951 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.951 * [taylor]: Taking taylor expansion of PI in n 6.951 * [backup-simplify]: Simplify PI into PI 6.951 * [taylor]: Taking taylor expansion of n in n 6.951 * [backup-simplify]: Simplify 0 into 0 6.951 * [backup-simplify]: Simplify 1 into 1 6.952 * [backup-simplify]: Simplify (/ PI 1) into PI 6.952 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.953 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.953 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.953 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.953 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.954 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.954 * [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)))) 6.955 * [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))))) 6.955 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.955 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.955 * [taylor]: Taking taylor expansion of k in n 6.955 * [backup-simplify]: Simplify k into k 6.955 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.955 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.955 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.955 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.955 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.955 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.955 * [taylor]: Taking taylor expansion of 0.5 in n 6.955 * [backup-simplify]: Simplify 0.5 into 0.5 6.955 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.955 * [taylor]: Taking taylor expansion of 1.0 in n 6.955 * [backup-simplify]: Simplify 1.0 into 1.0 6.955 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.956 * [taylor]: Taking taylor expansion of k in n 6.956 * [backup-simplify]: Simplify k into k 6.956 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.956 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.956 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.956 * [taylor]: Taking taylor expansion of 2.0 in n 6.956 * [backup-simplify]: Simplify 2.0 into 2.0 6.956 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.956 * [taylor]: Taking taylor expansion of PI in n 6.956 * [backup-simplify]: Simplify PI into PI 6.956 * [taylor]: Taking taylor expansion of n in n 6.956 * [backup-simplify]: Simplify 0 into 0 6.956 * [backup-simplify]: Simplify 1 into 1 6.956 * [backup-simplify]: Simplify (/ PI 1) into PI 6.956 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.957 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.957 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.957 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.957 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.958 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.959 * [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)))) 6.959 * [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))))) 6.960 * [backup-simplify]: Simplify (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 6.960 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k 6.960 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.960 * [taylor]: Taking taylor expansion of k in k 6.960 * [backup-simplify]: Simplify 0 into 0 6.960 * [backup-simplify]: Simplify 1 into 1 6.961 * [backup-simplify]: Simplify (sqrt 0) into 0 6.961 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.962 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.962 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.962 * [taylor]: Taking taylor expansion of 0.5 in k 6.962 * [backup-simplify]: Simplify 0.5 into 0.5 6.962 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.962 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.962 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.962 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.962 * [taylor]: Taking taylor expansion of 2.0 in k 6.962 * [backup-simplify]: Simplify 2.0 into 2.0 6.962 * [taylor]: Taking taylor expansion of PI in k 6.962 * [backup-simplify]: Simplify PI into PI 6.962 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.963 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.963 * [taylor]: Taking taylor expansion of (log n) in k 6.963 * [taylor]: Taking taylor expansion of n in k 6.963 * [backup-simplify]: Simplify n into n 6.963 * [backup-simplify]: Simplify (log n) into (log n) 6.963 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.963 * [taylor]: Taking taylor expansion of 1.0 in k 6.963 * [backup-simplify]: Simplify 1.0 into 1.0 6.963 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.963 * [taylor]: Taking taylor expansion of k in k 6.963 * [backup-simplify]: Simplify 0 into 0 6.963 * [backup-simplify]: Simplify 1 into 1 6.963 * [backup-simplify]: Simplify (/ 1 1) into 1 6.963 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.964 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.964 * [backup-simplify]: Simplify (- 1) into -1 6.964 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.965 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.966 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.966 * [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))))) 6.967 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0 6.967 * [backup-simplify]: Simplify 0 into 0 6.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.968 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.969 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.969 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.970 * [backup-simplify]: Simplify (- 0) into 0 6.970 * [backup-simplify]: Simplify (+ 0 0) into 0 6.970 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.971 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.972 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.973 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.974 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 6.974 * [taylor]: Taking taylor expansion of 0 in k 6.974 * [backup-simplify]: Simplify 0 into 0 6.974 * [backup-simplify]: Simplify 0 into 0 6.975 * [backup-simplify]: Simplify (+ (* 0 0) (* +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))))))) 6.976 * [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))))))) 6.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.977 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.980 * [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 6.980 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.981 * [backup-simplify]: Simplify (- 0) into 0 6.981 * [backup-simplify]: Simplify (+ 0 0) into 0 6.982 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.985 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.987 * [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 6.988 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 6.989 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.989 * [taylor]: Taking taylor expansion of 0 in k 6.989 * [backup-simplify]: Simplify 0 into 0 6.989 * [backup-simplify]: Simplify 0 into 0 6.989 * [backup-simplify]: Simplify 0 into 0 6.993 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.995 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +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))))))) 6.996 * [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))))))) 6.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.998 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 7.004 * [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 7.005 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.005 * [backup-simplify]: Simplify (- 0) into 0 7.006 * [backup-simplify]: Simplify (+ 0 0) into 0 7.007 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 7.008 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 7.010 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 7.013 * [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 7.014 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 7.016 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 7.016 * [taylor]: Taking taylor expansion of 0 in k 7.016 * [backup-simplify]: Simplify 0 into 0 7.016 * [backup-simplify]: Simplify 0 into 0 7.016 * [backup-simplify]: Simplify 0 into 0 7.016 * [backup-simplify]: Simplify 0 into 0 7.020 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.022 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +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))))))) 7.024 * [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))))))) 7.029 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) 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)))))))) 7.037 * [backup-simplify]: Simplify (/ (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) 7.037 * [approximate]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in (n k) around 0 7.037 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 7.037 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 7.037 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 7.037 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 7.037 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 7.037 * [taylor]: Taking taylor expansion of 0.5 in k 7.038 * [backup-simplify]: Simplify 0.5 into 0.5 7.038 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.038 * [taylor]: Taking taylor expansion of k in k 7.038 * [backup-simplify]: Simplify 0 into 0 7.038 * [backup-simplify]: Simplify 1 into 1 7.038 * [backup-simplify]: Simplify (/ 1 1) into 1 7.038 * [taylor]: Taking taylor expansion of 1.0 in k 7.038 * [backup-simplify]: Simplify 1.0 into 1.0 7.038 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 7.038 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 7.038 * [taylor]: Taking taylor expansion of -2.0 in k 7.038 * [backup-simplify]: Simplify -2.0 into -2.0 7.038 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.038 * [taylor]: Taking taylor expansion of PI in k 7.039 * [backup-simplify]: Simplify PI into PI 7.039 * [taylor]: Taking taylor expansion of n in k 7.039 * [backup-simplify]: Simplify n into n 7.039 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.039 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 7.039 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 7.039 * [backup-simplify]: Simplify (+ 1 0) into 1 7.040 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 7.040 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 7.040 * [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)))))) 7.040 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.040 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.040 * [taylor]: Taking taylor expansion of -1 in k 7.040 * [backup-simplify]: Simplify -1 into -1 7.040 * [taylor]: Taking taylor expansion of k in k 7.040 * [backup-simplify]: Simplify 0 into 0 7.040 * [backup-simplify]: Simplify 1 into 1 7.041 * [backup-simplify]: Simplify (/ -1 1) into -1 7.041 * [backup-simplify]: Simplify (sqrt 0) into 0 7.043 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.043 * [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))))))) 7.043 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 7.043 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.043 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.043 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.043 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.043 * [taylor]: Taking taylor expansion of 0.5 in n 7.043 * [backup-simplify]: Simplify 0.5 into 0.5 7.043 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.043 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.043 * [taylor]: Taking taylor expansion of k in n 7.043 * [backup-simplify]: Simplify k into k 7.043 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.043 * [taylor]: Taking taylor expansion of 1.0 in n 7.043 * [backup-simplify]: Simplify 1.0 into 1.0 7.043 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.043 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.043 * [taylor]: Taking taylor expansion of -2.0 in n 7.043 * [backup-simplify]: Simplify -2.0 into -2.0 7.044 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.044 * [taylor]: Taking taylor expansion of PI in n 7.044 * [backup-simplify]: Simplify PI into PI 7.044 * [taylor]: Taking taylor expansion of n in n 7.044 * [backup-simplify]: Simplify 0 into 0 7.044 * [backup-simplify]: Simplify 1 into 1 7.044 * [backup-simplify]: Simplify (/ PI 1) into PI 7.045 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.046 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.046 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.046 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.047 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.049 * [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)))) 7.050 * [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))))) 7.050 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 7.050 * [taylor]: Taking taylor expansion of (/ -1 k) in n 7.050 * [taylor]: Taking taylor expansion of -1 in n 7.050 * [backup-simplify]: Simplify -1 into -1 7.050 * [taylor]: Taking taylor expansion of k in n 7.050 * [backup-simplify]: Simplify k into k 7.050 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 7.050 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 7.050 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 7.050 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 7.052 * [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))) 7.052 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 7.052 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.052 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.052 * [taylor]: Taking taylor expansion of 0.5 in n 7.052 * [backup-simplify]: Simplify 0.5 into 0.5 7.052 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.052 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.052 * [taylor]: Taking taylor expansion of k in n 7.052 * [backup-simplify]: Simplify k into k 7.052 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.052 * [taylor]: Taking taylor expansion of 1.0 in n 7.052 * [backup-simplify]: Simplify 1.0 into 1.0 7.052 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.052 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.052 * [taylor]: Taking taylor expansion of -2.0 in n 7.052 * [backup-simplify]: Simplify -2.0 into -2.0 7.052 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.052 * [taylor]: Taking taylor expansion of PI in n 7.052 * [backup-simplify]: Simplify PI into PI 7.052 * [taylor]: Taking taylor expansion of n in n 7.052 * [backup-simplify]: Simplify 0 into 0 7.053 * [backup-simplify]: Simplify 1 into 1 7.053 * [backup-simplify]: Simplify (/ PI 1) into PI 7.053 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.054 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.055 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.055 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.057 * [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)))) 7.059 * [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))))) 7.059 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 7.059 * [taylor]: Taking taylor expansion of (/ -1 k) in n 7.059 * [taylor]: Taking taylor expansion of -1 in n 7.059 * [backup-simplify]: Simplify -1 into -1 7.059 * [taylor]: Taking taylor expansion of k in n 7.059 * [backup-simplify]: Simplify k into k 7.059 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 7.059 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 7.059 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 7.059 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 7.061 * [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))) 7.061 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k 7.061 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 7.061 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 7.061 * [taylor]: Taking taylor expansion of 0.5 in k 7.061 * [backup-simplify]: Simplify 0.5 into 0.5 7.061 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 7.061 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.061 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.061 * [taylor]: Taking taylor expansion of k in k 7.061 * [backup-simplify]: Simplify 0 into 0 7.061 * [backup-simplify]: Simplify 1 into 1 7.061 * [backup-simplify]: Simplify (/ 1 1) into 1 7.061 * [taylor]: Taking taylor expansion of 1.0 in k 7.061 * [backup-simplify]: Simplify 1.0 into 1.0 7.061 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 7.062 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 7.062 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 7.062 * [taylor]: Taking taylor expansion of -2.0 in k 7.062 * [backup-simplify]: Simplify -2.0 into -2.0 7.062 * [taylor]: Taking taylor expansion of PI in k 7.062 * [backup-simplify]: Simplify PI into PI 7.062 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.063 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.063 * [taylor]: Taking taylor expansion of (log n) in k 7.063 * [taylor]: Taking taylor expansion of n in k 7.063 * [backup-simplify]: Simplify n into n 7.063 * [backup-simplify]: Simplify (log n) into (log n) 7.063 * [backup-simplify]: Simplify (+ 1 0) into 1 7.063 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.064 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 7.065 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 7.065 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 7.066 * [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))))) 7.066 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.066 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.066 * [taylor]: Taking taylor expansion of -1 in k 7.066 * [backup-simplify]: Simplify -1 into -1 7.066 * [taylor]: Taking taylor expansion of k in k 7.066 * [backup-simplify]: Simplify 0 into 0 7.066 * [backup-simplify]: Simplify 1 into 1 7.066 * [backup-simplify]: Simplify (/ -1 1) into -1 7.067 * [backup-simplify]: Simplify (sqrt 0) into 0 7.067 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.068 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 7.069 * [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)))))) 7.069 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.070 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 7.071 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 7.071 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.071 * [backup-simplify]: Simplify (+ 0 0) into 0 7.072 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 7.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.073 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 7.074 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.075 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 7.075 * [taylor]: Taking taylor expansion of 0 in k 7.075 * [backup-simplify]: Simplify 0 into 0 7.075 * [backup-simplify]: Simplify 0 into 0 7.076 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 7.078 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.079 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 7.080 * [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))))))) 7.080 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.081 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.083 * [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 7.083 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.083 * [backup-simplify]: Simplify (+ 0 0) into 0 7.084 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 7.084 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.085 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 7.087 * [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 7.087 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.087 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 7.089 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 7.089 * [taylor]: Taking taylor expansion of 0 in k 7.089 * [backup-simplify]: Simplify 0 into 0 7.089 * [backup-simplify]: Simplify 0 into 0 7.089 * [backup-simplify]: Simplify 0 into 0 7.089 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.092 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.096 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 7.097 * [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))))))) 7.102 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +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)))))))))))) 7.102 * * * [progress]: simplifying candidates 7.106 * [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 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (log (sqrt k))) (- (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (log (sqrt k))) (- (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (log (sqrt k))) (- (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (log (sqrt k))) (- (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (log (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (exp (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (/ (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (cbrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)))) (cbrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (* (* (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (sqrt k)) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow n (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow n (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ (pow n (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt 1)) (/ (pow n (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ (pow n (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) 1) (/ (pow n (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (sqrt k))) (/ (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (/ (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt 1)) (/ (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) 1) (/ (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (sqrt k))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1)) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1) (/ (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ 1 1) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (cbrt k))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt 1)) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 1) (/ (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt 1)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1) (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 8.433 * * * [progress]: adding candidates to table 9.012 * * [progress]: iteration 3 / 4 9.012 * * * [progress]: picking best candidate 9.034 * * * * [pick]: Picked # 9.034 * * * [progress]: localizing error 9.056 * * * [progress]: generating rewritten candidates 9.056 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 9.122 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 9.161 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 9.168 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1) 9.215 * * * [progress]: generating series expansions 9.216 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 9.216 * [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))) 9.216 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.216 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.216 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.216 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.216 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.217 * [taylor]: Taking taylor expansion of 0.25 in k 9.217 * [backup-simplify]: Simplify 0.25 into 0.25 9.217 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.217 * [taylor]: Taking taylor expansion of 1.0 in k 9.217 * [backup-simplify]: Simplify 1.0 into 1.0 9.217 * [taylor]: Taking taylor expansion of k in k 9.217 * [backup-simplify]: Simplify 0 into 0 9.217 * [backup-simplify]: Simplify 1 into 1 9.217 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.217 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.217 * [taylor]: Taking taylor expansion of 2.0 in k 9.217 * [backup-simplify]: Simplify 2.0 into 2.0 9.217 * [taylor]: Taking taylor expansion of (* n PI) in k 9.217 * [taylor]: Taking taylor expansion of n in k 9.217 * [backup-simplify]: Simplify n into n 9.217 * [taylor]: Taking taylor expansion of PI in k 9.217 * [backup-simplify]: Simplify PI into PI 9.217 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.217 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.217 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.217 * [backup-simplify]: Simplify (- 0) into 0 9.217 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.218 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.218 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.218 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.218 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.218 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.218 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.218 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.218 * [taylor]: Taking taylor expansion of 0.25 in n 9.218 * [backup-simplify]: Simplify 0.25 into 0.25 9.218 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.218 * [taylor]: Taking taylor expansion of 1.0 in n 9.218 * [backup-simplify]: Simplify 1.0 into 1.0 9.218 * [taylor]: Taking taylor expansion of k in n 9.218 * [backup-simplify]: Simplify k into k 9.218 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.218 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.218 * [taylor]: Taking taylor expansion of 2.0 in n 9.218 * [backup-simplify]: Simplify 2.0 into 2.0 9.218 * [taylor]: Taking taylor expansion of (* n PI) in n 9.218 * [taylor]: Taking taylor expansion of n in n 9.218 * [backup-simplify]: Simplify 0 into 0 9.218 * [backup-simplify]: Simplify 1 into 1 9.218 * [taylor]: Taking taylor expansion of PI in n 9.218 * [backup-simplify]: Simplify PI into PI 9.219 * [backup-simplify]: Simplify (* 0 PI) into 0 9.219 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.220 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.221 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.221 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.221 * [backup-simplify]: Simplify (- k) into (- k) 9.222 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.222 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.222 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.223 * [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)))) 9.224 * [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))))) 9.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.224 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.224 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.224 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.224 * [taylor]: Taking taylor expansion of 0.25 in n 9.224 * [backup-simplify]: Simplify 0.25 into 0.25 9.224 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.224 * [taylor]: Taking taylor expansion of 1.0 in n 9.224 * [backup-simplify]: Simplify 1.0 into 1.0 9.224 * [taylor]: Taking taylor expansion of k in n 9.224 * [backup-simplify]: Simplify k into k 9.224 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.224 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.224 * [taylor]: Taking taylor expansion of 2.0 in n 9.224 * [backup-simplify]: Simplify 2.0 into 2.0 9.224 * [taylor]: Taking taylor expansion of (* n PI) in n 9.224 * [taylor]: Taking taylor expansion of n in n 9.224 * [backup-simplify]: Simplify 0 into 0 9.224 * [backup-simplify]: Simplify 1 into 1 9.224 * [taylor]: Taking taylor expansion of PI in n 9.224 * [backup-simplify]: Simplify PI into PI 9.225 * [backup-simplify]: Simplify (* 0 PI) into 0 9.225 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.226 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.227 * [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)) 9.229 * [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)))) 9.230 * [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))))) 9.230 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.230 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.230 * [taylor]: Taking taylor expansion of 0.25 in k 9.230 * [backup-simplify]: Simplify 0.25 into 0.25 9.230 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.230 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.230 * [taylor]: Taking taylor expansion of 1.0 in k 9.230 * [backup-simplify]: Simplify 1.0 into 1.0 9.230 * [taylor]: Taking taylor expansion of k in k 9.230 * [backup-simplify]: Simplify 0 into 0 9.230 * [backup-simplify]: Simplify 1 into 1 9.230 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.230 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.230 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.230 * [taylor]: Taking taylor expansion of 2.0 in k 9.230 * [backup-simplify]: Simplify 2.0 into 2.0 9.230 * [taylor]: Taking taylor expansion of PI in k 9.230 * [backup-simplify]: Simplify PI into PI 9.231 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.231 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.231 * [taylor]: Taking taylor expansion of (log n) in k 9.231 * [taylor]: Taking taylor expansion of n in k 9.231 * [backup-simplify]: Simplify n into n 9.231 * [backup-simplify]: Simplify (log n) into (log n) 9.232 * [backup-simplify]: Simplify (- 0) into 0 9.232 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.232 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.233 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.234 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.234 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.235 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.236 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.236 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.237 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.238 * [backup-simplify]: Simplify (- 0) into 0 9.238 * [backup-simplify]: Simplify (+ 0 0) into 0 9.238 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.240 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.241 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.243 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.243 * [taylor]: Taking taylor expansion of 0 in k 9.243 * [backup-simplify]: Simplify 0 into 0 9.243 * [backup-simplify]: Simplify 0 into 0 9.244 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.246 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.247 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.247 * [backup-simplify]: Simplify (+ 0 0) into 0 9.247 * [backup-simplify]: Simplify (- 1) into -1 9.248 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.249 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.251 * [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)))) 9.255 * [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)))))) 9.257 * [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)))))) 9.257 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.258 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.260 * [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 9.260 * [backup-simplify]: Simplify (- 0) into 0 9.261 * [backup-simplify]: Simplify (+ 0 0) into 0 9.261 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.262 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.263 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.265 * [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 9.265 * [taylor]: Taking taylor expansion of 0 in k 9.265 * [backup-simplify]: Simplify 0 into 0 9.265 * [backup-simplify]: Simplify 0 into 0 9.265 * [backup-simplify]: Simplify 0 into 0 9.266 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.268 * [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 9.269 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.269 * [backup-simplify]: Simplify (+ 0 0) into 0 9.270 * [backup-simplify]: Simplify (- 0) into 0 9.270 * [backup-simplify]: Simplify (+ 0 0) into 0 9.271 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.273 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.276 * [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))))) 9.279 * [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))))) 9.285 * [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)))))) 9.286 * [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)))) 9.286 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.286 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.286 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.286 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.286 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.286 * [taylor]: Taking taylor expansion of 0.25 in k 9.286 * [backup-simplify]: Simplify 0.25 into 0.25 9.286 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.286 * [taylor]: Taking taylor expansion of 1.0 in k 9.286 * [backup-simplify]: Simplify 1.0 into 1.0 9.286 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.286 * [taylor]: Taking taylor expansion of k in k 9.286 * [backup-simplify]: Simplify 0 into 0 9.286 * [backup-simplify]: Simplify 1 into 1 9.287 * [backup-simplify]: Simplify (/ 1 1) into 1 9.287 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.287 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.287 * [taylor]: Taking taylor expansion of 2.0 in k 9.287 * [backup-simplify]: Simplify 2.0 into 2.0 9.287 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.287 * [taylor]: Taking taylor expansion of PI in k 9.287 * [backup-simplify]: Simplify PI into PI 9.287 * [taylor]: Taking taylor expansion of n in k 9.287 * [backup-simplify]: Simplify n into n 9.287 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.287 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.287 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.287 * [backup-simplify]: Simplify (- 1) into -1 9.288 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.288 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.288 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.288 * [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))))) 9.288 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.288 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.288 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.288 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.288 * [taylor]: Taking taylor expansion of 0.25 in n 9.288 * [backup-simplify]: Simplify 0.25 into 0.25 9.288 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.288 * [taylor]: Taking taylor expansion of 1.0 in n 9.288 * [backup-simplify]: Simplify 1.0 into 1.0 9.288 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.288 * [taylor]: Taking taylor expansion of k in n 9.288 * [backup-simplify]: Simplify k into k 9.288 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.289 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.289 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.289 * [taylor]: Taking taylor expansion of 2.0 in n 9.289 * [backup-simplify]: Simplify 2.0 into 2.0 9.289 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.289 * [taylor]: Taking taylor expansion of PI in n 9.289 * [backup-simplify]: Simplify PI into PI 9.289 * [taylor]: Taking taylor expansion of n in n 9.289 * [backup-simplify]: Simplify 0 into 0 9.289 * [backup-simplify]: Simplify 1 into 1 9.289 * [backup-simplify]: Simplify (/ PI 1) into PI 9.290 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.291 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.291 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.291 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.291 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.292 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.294 * [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)))) 9.304 * [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))))) 9.304 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.304 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.304 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.304 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.304 * [taylor]: Taking taylor expansion of 0.25 in n 9.304 * [backup-simplify]: Simplify 0.25 into 0.25 9.304 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.304 * [taylor]: Taking taylor expansion of 1.0 in n 9.304 * [backup-simplify]: Simplify 1.0 into 1.0 9.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.304 * [taylor]: Taking taylor expansion of k in n 9.304 * [backup-simplify]: Simplify k into k 9.304 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.304 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.304 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.304 * [taylor]: Taking taylor expansion of 2.0 in n 9.304 * [backup-simplify]: Simplify 2.0 into 2.0 9.304 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.304 * [taylor]: Taking taylor expansion of PI in n 9.304 * [backup-simplify]: Simplify PI into PI 9.304 * [taylor]: Taking taylor expansion of n in n 9.304 * [backup-simplify]: Simplify 0 into 0 9.304 * [backup-simplify]: Simplify 1 into 1 9.305 * [backup-simplify]: Simplify (/ PI 1) into PI 9.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.306 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.306 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.306 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.308 * [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)))) 9.308 * [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))))) 9.309 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.309 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.309 * [taylor]: Taking taylor expansion of 0.25 in k 9.309 * [backup-simplify]: Simplify 0.25 into 0.25 9.309 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.309 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.309 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.309 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.309 * [taylor]: Taking taylor expansion of 2.0 in k 9.309 * [backup-simplify]: Simplify 2.0 into 2.0 9.309 * [taylor]: Taking taylor expansion of PI in k 9.309 * [backup-simplify]: Simplify PI into PI 9.309 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.310 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.310 * [taylor]: Taking taylor expansion of (log n) in k 9.310 * [taylor]: Taking taylor expansion of n in k 9.310 * [backup-simplify]: Simplify n into n 9.310 * [backup-simplify]: Simplify (log n) into (log n) 9.310 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.310 * [taylor]: Taking taylor expansion of 1.0 in k 9.310 * [backup-simplify]: Simplify 1.0 into 1.0 9.310 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.310 * [taylor]: Taking taylor expansion of k in k 9.310 * [backup-simplify]: Simplify 0 into 0 9.310 * [backup-simplify]: Simplify 1 into 1 9.310 * [backup-simplify]: Simplify (/ 1 1) into 1 9.310 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.311 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.311 * [backup-simplify]: Simplify (- 1) into -1 9.312 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.312 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.313 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.314 * [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))))) 9.314 * [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))))) 9.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.316 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.317 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.317 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.317 * [backup-simplify]: Simplify (- 0) into 0 9.317 * [backup-simplify]: Simplify (+ 0 0) into 0 9.317 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.319 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.320 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.320 * [taylor]: Taking taylor expansion of 0 in k 9.320 * [backup-simplify]: Simplify 0 into 0 9.320 * [backup-simplify]: Simplify 0 into 0 9.320 * [backup-simplify]: Simplify 0 into 0 9.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.322 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.324 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.324 * [backup-simplify]: Simplify (- 0) into 0 9.324 * [backup-simplify]: Simplify (+ 0 0) into 0 9.325 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.327 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.329 * [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 9.329 * [taylor]: Taking taylor expansion of 0 in k 9.330 * [backup-simplify]: Simplify 0 into 0 9.330 * [backup-simplify]: Simplify 0 into 0 9.330 * [backup-simplify]: Simplify 0 into 0 9.330 * [backup-simplify]: Simplify 0 into 0 9.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.339 * [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 9.339 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.340 * [backup-simplify]: Simplify (- 0) into 0 9.340 * [backup-simplify]: Simplify (+ 0 0) into 0 9.341 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.343 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.345 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.348 * [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 9.348 * [taylor]: Taking taylor expansion of 0 in k 9.348 * [backup-simplify]: Simplify 0 into 0 9.348 * [backup-simplify]: Simplify 0 into 0 9.350 * [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)))) 9.351 * [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))) 9.351 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.351 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.351 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.351 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.351 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.351 * [taylor]: Taking taylor expansion of 0.25 in k 9.351 * [backup-simplify]: Simplify 0.25 into 0.25 9.351 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.351 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.351 * [taylor]: Taking taylor expansion of k in k 9.351 * [backup-simplify]: Simplify 0 into 0 9.351 * [backup-simplify]: Simplify 1 into 1 9.352 * [backup-simplify]: Simplify (/ 1 1) into 1 9.352 * [taylor]: Taking taylor expansion of 1.0 in k 9.352 * [backup-simplify]: Simplify 1.0 into 1.0 9.352 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.352 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.352 * [taylor]: Taking taylor expansion of -2.0 in k 9.352 * [backup-simplify]: Simplify -2.0 into -2.0 9.352 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.352 * [taylor]: Taking taylor expansion of PI in k 9.352 * [backup-simplify]: Simplify PI into PI 9.352 * [taylor]: Taking taylor expansion of n in k 9.352 * [backup-simplify]: Simplify n into n 9.352 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.352 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.352 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.353 * [backup-simplify]: Simplify (+ 1 0) into 1 9.353 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.353 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.354 * [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)))))) 9.354 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.354 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.354 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.354 * [taylor]: Taking taylor expansion of 0.25 in n 9.354 * [backup-simplify]: Simplify 0.25 into 0.25 9.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.354 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.354 * [taylor]: Taking taylor expansion of k in n 9.354 * [backup-simplify]: Simplify k into k 9.354 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.354 * [taylor]: Taking taylor expansion of 1.0 in n 9.354 * [backup-simplify]: Simplify 1.0 into 1.0 9.354 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.354 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.354 * [taylor]: Taking taylor expansion of -2.0 in n 9.354 * [backup-simplify]: Simplify -2.0 into -2.0 9.354 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.354 * [taylor]: Taking taylor expansion of PI in n 9.354 * [backup-simplify]: Simplify PI into PI 9.354 * [taylor]: Taking taylor expansion of n in n 9.354 * [backup-simplify]: Simplify 0 into 0 9.354 * [backup-simplify]: Simplify 1 into 1 9.355 * [backup-simplify]: Simplify (/ PI 1) into PI 9.355 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.356 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.356 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.356 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.358 * [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)))) 9.358 * [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))))) 9.358 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.358 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.359 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.359 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.360 * [taylor]: Taking taylor expansion of 0.25 in n 9.360 * [backup-simplify]: Simplify 0.25 into 0.25 9.360 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.360 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.360 * [taylor]: Taking taylor expansion of k in n 9.360 * [backup-simplify]: Simplify k into k 9.360 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.360 * [taylor]: Taking taylor expansion of 1.0 in n 9.360 * [backup-simplify]: Simplify 1.0 into 1.0 9.360 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.360 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.360 * [taylor]: Taking taylor expansion of -2.0 in n 9.360 * [backup-simplify]: Simplify -2.0 into -2.0 9.360 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.360 * [taylor]: Taking taylor expansion of PI in n 9.360 * [backup-simplify]: Simplify PI into PI 9.360 * [taylor]: Taking taylor expansion of n in n 9.360 * [backup-simplify]: Simplify 0 into 0 9.360 * [backup-simplify]: Simplify 1 into 1 9.360 * [backup-simplify]: Simplify (/ PI 1) into PI 9.360 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.361 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.361 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.361 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.362 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.363 * [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)))) 9.364 * [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))))) 9.364 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.364 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.364 * [taylor]: Taking taylor expansion of 0.25 in k 9.364 * [backup-simplify]: Simplify 0.25 into 0.25 9.364 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.364 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.364 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.364 * [taylor]: Taking taylor expansion of k in k 9.364 * [backup-simplify]: Simplify 0 into 0 9.364 * [backup-simplify]: Simplify 1 into 1 9.364 * [backup-simplify]: Simplify (/ 1 1) into 1 9.364 * [taylor]: Taking taylor expansion of 1.0 in k 9.365 * [backup-simplify]: Simplify 1.0 into 1.0 9.365 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.365 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.365 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.365 * [taylor]: Taking taylor expansion of -2.0 in k 9.365 * [backup-simplify]: Simplify -2.0 into -2.0 9.365 * [taylor]: Taking taylor expansion of PI in k 9.365 * [backup-simplify]: Simplify PI 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 * [taylor]: Taking taylor expansion of (log n) in k 9.366 * [taylor]: Taking taylor expansion of n in k 9.366 * [backup-simplify]: Simplify n into n 9.366 * [backup-simplify]: Simplify (log n) into (log n) 9.366 * [backup-simplify]: Simplify (+ 1 0) into 1 9.366 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.367 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.367 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.368 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (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))))) 9.370 * [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))))) 9.370 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.371 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.372 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.372 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.372 * [backup-simplify]: Simplify (+ 0 0) into 0 9.372 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 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)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.376 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.376 * [taylor]: Taking taylor expansion of 0 in k 9.376 * [backup-simplify]: Simplify 0 into 0 9.376 * [backup-simplify]: Simplify 0 into 0 9.376 * [backup-simplify]: Simplify 0 into 0 9.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.378 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.382 * [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 9.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.383 * [backup-simplify]: Simplify (+ 0 0) into 0 9.384 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.385 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.387 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.390 * [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 9.390 * [taylor]: Taking taylor expansion of 0 in k 9.390 * [backup-simplify]: Simplify 0 into 0 9.390 * [backup-simplify]: Simplify 0 into 0 9.390 * [backup-simplify]: Simplify 0 into 0 9.390 * [backup-simplify]: Simplify 0 into 0 9.391 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.392 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.399 * [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 9.399 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 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 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)) 9.405 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.408 * [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 9.408 * [taylor]: Taking taylor expansion of 0 in k 9.408 * [backup-simplify]: Simplify 0 into 0 9.408 * [backup-simplify]: Simplify 0 into 0 9.409 * [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)))))) 9.409 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 9.410 * [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))) 9.410 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.410 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.410 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.410 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.410 * [taylor]: Taking taylor expansion of 0.25 in k 9.410 * [backup-simplify]: Simplify 0.25 into 0.25 9.410 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.410 * [taylor]: Taking taylor expansion of 1.0 in k 9.410 * [backup-simplify]: Simplify 1.0 into 1.0 9.410 * [taylor]: Taking taylor expansion of k in k 9.410 * [backup-simplify]: Simplify 0 into 0 9.411 * [backup-simplify]: Simplify 1 into 1 9.411 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.411 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.411 * [taylor]: Taking taylor expansion of 2.0 in k 9.411 * [backup-simplify]: Simplify 2.0 into 2.0 9.411 * [taylor]: Taking taylor expansion of (* n PI) in k 9.411 * [taylor]: Taking taylor expansion of n in k 9.411 * [backup-simplify]: Simplify n into n 9.411 * [taylor]: Taking taylor expansion of PI in k 9.411 * [backup-simplify]: Simplify PI into PI 9.411 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.411 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.411 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.411 * [backup-simplify]: Simplify (- 0) into 0 9.411 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.412 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.412 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.412 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.412 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.412 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.412 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.412 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.412 * [taylor]: Taking taylor expansion of 0.25 in n 9.412 * [backup-simplify]: Simplify 0.25 into 0.25 9.412 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.412 * [taylor]: Taking taylor expansion of 1.0 in n 9.412 * [backup-simplify]: Simplify 1.0 into 1.0 9.412 * [taylor]: Taking taylor expansion of k in n 9.412 * [backup-simplify]: Simplify k into k 9.412 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.412 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.412 * [taylor]: Taking taylor expansion of 2.0 in n 9.412 * [backup-simplify]: Simplify 2.0 into 2.0 9.412 * [taylor]: Taking taylor expansion of (* n PI) in n 9.412 * [taylor]: Taking taylor expansion of n in n 9.412 * [backup-simplify]: Simplify 0 into 0 9.412 * [backup-simplify]: Simplify 1 into 1 9.412 * [taylor]: Taking taylor expansion of PI in n 9.412 * [backup-simplify]: Simplify PI into PI 9.412 * [backup-simplify]: Simplify (* 0 PI) into 0 9.413 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.414 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.415 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.415 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.415 * [backup-simplify]: Simplify (- k) into (- k) 9.415 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.416 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.416 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.417 * [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)))) 9.418 * [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))))) 9.418 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.418 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.418 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.418 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.418 * [taylor]: Taking taylor expansion of 0.25 in n 9.418 * [backup-simplify]: Simplify 0.25 into 0.25 9.418 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.418 * [taylor]: Taking taylor expansion of 1.0 in n 9.418 * [backup-simplify]: Simplify 1.0 into 1.0 9.418 * [taylor]: Taking taylor expansion of k in n 9.418 * [backup-simplify]: Simplify k into k 9.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.418 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.418 * [taylor]: Taking taylor expansion of 2.0 in n 9.418 * [backup-simplify]: Simplify 2.0 into 2.0 9.418 * [taylor]: Taking taylor expansion of (* n PI) in n 9.418 * [taylor]: Taking taylor expansion of n in n 9.418 * [backup-simplify]: Simplify 0 into 0 9.418 * [backup-simplify]: Simplify 1 into 1 9.418 * [taylor]: Taking taylor expansion of PI in n 9.418 * [backup-simplify]: Simplify PI into PI 9.418 * [backup-simplify]: Simplify (* 0 PI) into 0 9.419 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.420 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.421 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.421 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.421 * [backup-simplify]: Simplify (- k) into (- k) 9.421 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.421 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.422 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.423 * [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)))) 9.430 * [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))))) 9.430 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.430 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.430 * [taylor]: Taking taylor expansion of 0.25 in k 9.430 * [backup-simplify]: Simplify 0.25 into 0.25 9.430 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.430 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.430 * [taylor]: Taking taylor expansion of 1.0 in k 9.430 * [backup-simplify]: Simplify 1.0 into 1.0 9.430 * [taylor]: Taking taylor expansion of k in k 9.430 * [backup-simplify]: Simplify 0 into 0 9.430 * [backup-simplify]: Simplify 1 into 1 9.430 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.430 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.430 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.430 * [taylor]: Taking taylor expansion of 2.0 in k 9.430 * [backup-simplify]: Simplify 2.0 into 2.0 9.430 * [taylor]: Taking taylor expansion of PI in k 9.430 * [backup-simplify]: Simplify PI into PI 9.430 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.432 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.432 * [taylor]: Taking taylor expansion of (log n) in k 9.432 * [taylor]: Taking taylor expansion of n in k 9.432 * [backup-simplify]: Simplify n into n 9.432 * [backup-simplify]: Simplify (log n) into (log n) 9.432 * [backup-simplify]: Simplify (- 0) into 0 9.433 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.434 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.435 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.436 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.437 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.438 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.439 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.440 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.442 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.443 * [backup-simplify]: Simplify (- 0) into 0 9.443 * [backup-simplify]: Simplify (+ 0 0) into 0 9.443 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.446 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.448 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.448 * [taylor]: Taking taylor expansion of 0 in k 9.448 * [backup-simplify]: Simplify 0 into 0 9.448 * [backup-simplify]: Simplify 0 into 0 9.449 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.451 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.452 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.452 * [backup-simplify]: Simplify (+ 0 0) into 0 9.453 * [backup-simplify]: Simplify (- 1) into -1 9.453 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.455 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.456 * [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)))) 9.459 * [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)))))) 9.461 * [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)))))) 9.462 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.463 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.465 * [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 9.465 * [backup-simplify]: Simplify (- 0) into 0 9.466 * [backup-simplify]: Simplify (+ 0 0) into 0 9.466 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.467 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.468 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.470 * [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 9.470 * [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 9.470 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.472 * [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 9.473 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.474 * [backup-simplify]: Simplify (+ 0 0) into 0 9.474 * [backup-simplify]: Simplify (- 0) into 0 9.474 * [backup-simplify]: Simplify (+ 0 0) into 0 9.475 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.477 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.479 * [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))))) 9.483 * [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))))) 9.489 * [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)))))) 9.489 * [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)))) 9.489 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.489 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.489 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.489 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.489 * [taylor]: Taking taylor expansion of 0.25 in k 9.490 * [backup-simplify]: Simplify 0.25 into 0.25 9.490 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.490 * [taylor]: Taking taylor expansion of 1.0 in k 9.490 * [backup-simplify]: Simplify 1.0 into 1.0 9.490 * [taylor]: Taking taylor expansion of (/ 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 (log (* 2.0 (/ PI n))) in k 9.490 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.490 * [taylor]: Taking taylor expansion of 2.0 in k 9.490 * [backup-simplify]: Simplify 2.0 into 2.0 9.490 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.490 * [taylor]: Taking taylor expansion of PI in k 9.490 * [backup-simplify]: Simplify PI into PI 9.490 * [taylor]: Taking taylor expansion of n in k 9.490 * [backup-simplify]: Simplify n into n 9.490 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.490 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.490 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.490 * [backup-simplify]: Simplify (- 1) into -1 9.491 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.491 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.492 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.492 * [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))))) 9.492 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.492 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.492 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.492 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.492 * [taylor]: Taking taylor expansion of 0.25 in n 9.492 * [backup-simplify]: Simplify 0.25 into 0.25 9.492 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.492 * [taylor]: Taking taylor expansion of 1.0 in n 9.492 * [backup-simplify]: Simplify 1.0 into 1.0 9.492 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.492 * [taylor]: Taking taylor expansion of k in n 9.492 * [backup-simplify]: Simplify k into k 9.492 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.492 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.492 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.492 * [taylor]: Taking taylor expansion of 2.0 in n 9.492 * [backup-simplify]: Simplify 2.0 into 2.0 9.492 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.492 * [taylor]: Taking taylor expansion of PI in n 9.492 * [backup-simplify]: Simplify PI into PI 9.492 * [taylor]: Taking taylor expansion of n in n 9.492 * [backup-simplify]: Simplify 0 into 0 9.493 * [backup-simplify]: Simplify 1 into 1 9.493 * [backup-simplify]: Simplify (/ PI 1) into PI 9.494 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.495 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.495 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.495 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.495 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.496 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.498 * [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)))) 9.499 * [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))))) 9.499 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.499 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.499 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.499 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.499 * [taylor]: Taking taylor expansion of 0.25 in n 9.499 * [backup-simplify]: Simplify 0.25 into 0.25 9.499 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.500 * [taylor]: Taking taylor expansion of 1.0 in n 9.500 * [backup-simplify]: Simplify 1.0 into 1.0 9.500 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.500 * [taylor]: Taking taylor expansion of k in n 9.500 * [backup-simplify]: Simplify k into k 9.500 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.500 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.500 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.500 * [taylor]: Taking taylor expansion of 2.0 in n 9.500 * [backup-simplify]: Simplify 2.0 into 2.0 9.500 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.500 * [taylor]: Taking taylor expansion of PI in n 9.500 * [backup-simplify]: Simplify PI into PI 9.500 * [taylor]: Taking taylor expansion of n in n 9.500 * [backup-simplify]: Simplify 0 into 0 9.500 * [backup-simplify]: Simplify 1 into 1 9.501 * [backup-simplify]: Simplify (/ PI 1) into PI 9.501 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.502 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.502 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.502 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.502 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.505 * [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)))) 9.507 * [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))))) 9.507 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.507 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.507 * [taylor]: Taking taylor expansion of 0.25 in k 9.507 * [backup-simplify]: Simplify 0.25 into 0.25 9.507 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.507 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.507 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.507 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.507 * [taylor]: Taking taylor expansion of 2.0 in k 9.507 * [backup-simplify]: Simplify 2.0 into 2.0 9.507 * [taylor]: Taking taylor expansion of PI in k 9.507 * [backup-simplify]: Simplify PI into PI 9.508 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.509 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.509 * [taylor]: Taking taylor expansion of (log n) in k 9.509 * [taylor]: Taking taylor expansion of n in k 9.509 * [backup-simplify]: Simplify n into n 9.509 * [backup-simplify]: Simplify (log n) into (log n) 9.509 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.509 * [taylor]: Taking taylor expansion of 1.0 in k 9.509 * [backup-simplify]: Simplify 1.0 into 1.0 9.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.509 * [taylor]: Taking taylor expansion of k in k 9.509 * [backup-simplify]: Simplify 0 into 0 9.509 * [backup-simplify]: Simplify 1 into 1 9.509 * [backup-simplify]: Simplify (/ 1 1) into 1 9.510 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.511 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.511 * [backup-simplify]: Simplify (- 1) into -1 9.512 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.513 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.514 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.515 * [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))))) 9.517 * [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))))) 9.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.519 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.520 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.521 * [backup-simplify]: Simplify (- 0) into 0 9.521 * [backup-simplify]: Simplify (+ 0 0) into 0 9.522 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.524 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.525 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.525 * [taylor]: Taking taylor expansion of 0 in k 9.525 * [backup-simplify]: Simplify 0 into 0 9.525 * [backup-simplify]: Simplify 0 into 0 9.525 * [backup-simplify]: Simplify 0 into 0 9.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.526 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.528 * [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 9.528 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.529 * [backup-simplify]: Simplify (- 0) into 0 9.529 * [backup-simplify]: Simplify (+ 0 0) into 0 9.529 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.531 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.533 * [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 9.533 * [taylor]: Taking taylor expansion of 0 in k 9.533 * [backup-simplify]: Simplify 0 into 0 9.533 * [backup-simplify]: Simplify 0 into 0 9.533 * [backup-simplify]: Simplify 0 into 0 9.533 * [backup-simplify]: Simplify 0 into 0 9.534 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.534 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.538 * [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 9.538 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.538 * [backup-simplify]: Simplify (- 0) into 0 9.538 * [backup-simplify]: Simplify (+ 0 0) into 0 9.539 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.541 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.550 * [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 9.550 * [taylor]: Taking taylor expansion of 0 in k 9.550 * [backup-simplify]: Simplify 0 into 0 9.550 * [backup-simplify]: Simplify 0 into 0 9.551 * [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)))) 9.551 * [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))) 9.551 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.551 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.551 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.551 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.551 * [taylor]: Taking taylor expansion of 0.25 in k 9.551 * [backup-simplify]: Simplify 0.25 into 0.25 9.551 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.551 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.551 * [taylor]: Taking taylor expansion of k in k 9.551 * [backup-simplify]: Simplify 0 into 0 9.551 * [backup-simplify]: Simplify 1 into 1 9.552 * [backup-simplify]: Simplify (/ 1 1) into 1 9.552 * [taylor]: Taking taylor expansion of 1.0 in k 9.552 * [backup-simplify]: Simplify 1.0 into 1.0 9.552 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.552 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.552 * [taylor]: Taking taylor expansion of -2.0 in k 9.552 * [backup-simplify]: Simplify -2.0 into -2.0 9.552 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.552 * [taylor]: Taking taylor expansion of PI in k 9.552 * [backup-simplify]: Simplify PI into PI 9.552 * [taylor]: Taking taylor expansion of n in k 9.552 * [backup-simplify]: Simplify n into n 9.552 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.552 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.552 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.552 * [backup-simplify]: Simplify (+ 1 0) into 1 9.553 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.553 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.553 * [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)))))) 9.553 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.553 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.553 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.553 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.553 * [taylor]: Taking taylor expansion of 0.25 in n 9.553 * [backup-simplify]: Simplify 0.25 into 0.25 9.553 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.553 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.553 * [taylor]: Taking taylor expansion of k in n 9.553 * [backup-simplify]: Simplify k into k 9.553 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.553 * [taylor]: Taking taylor expansion of 1.0 in n 9.553 * [backup-simplify]: Simplify 1.0 into 1.0 9.553 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.553 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.553 * [taylor]: Taking taylor expansion of -2.0 in n 9.553 * [backup-simplify]: Simplify -2.0 into -2.0 9.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.553 * [taylor]: Taking taylor expansion of PI in n 9.553 * [backup-simplify]: Simplify PI into PI 9.553 * [taylor]: Taking taylor expansion of n in n 9.553 * [backup-simplify]: Simplify 0 into 0 9.553 * [backup-simplify]: Simplify 1 into 1 9.554 * [backup-simplify]: Simplify (/ PI 1) into PI 9.554 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.555 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.555 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.555 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.556 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.558 * [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)))) 9.559 * [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))))) 9.559 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.559 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.559 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.559 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.559 * [taylor]: Taking taylor expansion of 0.25 in n 9.559 * [backup-simplify]: Simplify 0.25 into 0.25 9.559 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.559 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.559 * [taylor]: Taking taylor expansion of k in n 9.559 * [backup-simplify]: Simplify k into k 9.559 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.559 * [taylor]: Taking taylor expansion of 1.0 in n 9.559 * [backup-simplify]: Simplify 1.0 into 1.0 9.559 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.560 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.560 * [taylor]: Taking taylor expansion of -2.0 in n 9.560 * [backup-simplify]: Simplify -2.0 into -2.0 9.560 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.560 * [taylor]: Taking taylor expansion of PI in n 9.560 * [backup-simplify]: Simplify PI into PI 9.560 * [taylor]: Taking taylor expansion of n in n 9.560 * [backup-simplify]: Simplify 0 into 0 9.560 * [backup-simplify]: Simplify 1 into 1 9.560 * [backup-simplify]: Simplify (/ PI 1) into PI 9.561 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.562 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.562 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.562 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.563 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.565 * [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)))) 9.566 * [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))))) 9.566 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.566 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.566 * [taylor]: Taking taylor expansion of 0.25 in k 9.567 * [backup-simplify]: Simplify 0.25 into 0.25 9.567 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.567 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.567 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.567 * [taylor]: Taking taylor expansion of k in k 9.567 * [backup-simplify]: Simplify 0 into 0 9.567 * [backup-simplify]: Simplify 1 into 1 9.567 * [backup-simplify]: Simplify (/ 1 1) into 1 9.567 * [taylor]: Taking taylor expansion of 1.0 in k 9.567 * [backup-simplify]: Simplify 1.0 into 1.0 9.567 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.567 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.567 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.567 * [taylor]: Taking taylor expansion of -2.0 in k 9.567 * [backup-simplify]: Simplify -2.0 into -2.0 9.567 * [taylor]: Taking taylor expansion of PI in k 9.567 * [backup-simplify]: Simplify PI into PI 9.568 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.569 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.569 * [taylor]: Taking taylor expansion of (log n) in k 9.569 * [taylor]: Taking taylor expansion of n in k 9.569 * [backup-simplify]: Simplify n into n 9.569 * [backup-simplify]: Simplify (log n) into (log n) 9.570 * [backup-simplify]: Simplify (+ 1 0) into 1 9.570 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.571 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.572 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.573 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.575 * [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))))) 9.576 * [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))))) 9.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.578 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.580 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.580 * [backup-simplify]: Simplify (+ 0 0) into 0 9.581 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.583 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.584 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.584 * [taylor]: Taking taylor expansion of 0 in k 9.584 * [backup-simplify]: Simplify 0 into 0 9.584 * [backup-simplify]: Simplify 0 into 0 9.585 * [backup-simplify]: Simplify 0 into 0 9.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.586 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.588 * [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 9.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.588 * [backup-simplify]: Simplify (+ 0 0) into 0 9.589 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.591 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.592 * [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 9.592 * [taylor]: Taking taylor expansion of 0 in k 9.592 * [backup-simplify]: Simplify 0 into 0 9.592 * [backup-simplify]: Simplify 0 into 0 9.592 * [backup-simplify]: Simplify 0 into 0 9.592 * [backup-simplify]: Simplify 0 into 0 9.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.594 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.597 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 9.597 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.598 * [backup-simplify]: Simplify (+ 0 0) into 0 9.598 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.600 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.602 * [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 9.602 * [taylor]: Taking taylor expansion of 0 in k 9.602 * [backup-simplify]: Simplify 0 into 0 9.602 * [backup-simplify]: Simplify 0 into 0 9.603 * [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)))))) 9.603 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 9.603 * [backup-simplify]: Simplify (/ 1.0 (sqrt 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 k in k 9.603 * [backup-simplify]: Simplify 0 into 0 9.603 * [backup-simplify]: Simplify 1 into 1 9.604 * [backup-simplify]: Simplify (/ 1 1) into 1 9.604 * [backup-simplify]: Simplify (sqrt 0) into 0 9.605 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 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 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 9.607 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.607 * [backup-simplify]: Simplify 0 into 0 9.607 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.608 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.608 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 9.610 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.611 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.611 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.612 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.614 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.617 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.617 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.618 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 9.618 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 9.619 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 9.619 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.619 * [taylor]: Taking taylor expansion of 1.0 in k 9.619 * [backup-simplify]: Simplify 1.0 into 1.0 9.619 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.619 * [taylor]: Taking taylor expansion of k in k 9.619 * [backup-simplify]: Simplify 0 into 0 9.619 * [backup-simplify]: Simplify 1 into 1 9.619 * [backup-simplify]: Simplify (sqrt 0) into 0 9.621 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.621 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 9.621 * [taylor]: Taking taylor expansion of 1.0 in k 9.621 * [backup-simplify]: Simplify 1.0 into 1.0 9.621 * [taylor]: Taking taylor expansion of (sqrt k) in k 9.621 * [taylor]: Taking taylor expansion of k in k 9.621 * [backup-simplify]: Simplify 0 into 0 9.621 * [backup-simplify]: Simplify 1 into 1 9.621 * [backup-simplify]: Simplify (sqrt 0) into 0 9.622 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 9.623 * [backup-simplify]: Simplify (* 1.0 0) into 0 9.623 * [backup-simplify]: Simplify 0 into 0 9.624 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 9.625 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.628 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.629 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 9.630 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.633 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.636 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 9.636 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.638 * [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)))))))) 9.638 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 9.638 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 9.638 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.638 * [taylor]: Taking taylor expansion of 1.0 in k 9.638 * [backup-simplify]: Simplify 1.0 into 1.0 9.638 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.638 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.638 * [taylor]: Taking taylor expansion of -1 in k 9.638 * [backup-simplify]: Simplify -1 into -1 9.638 * [taylor]: Taking taylor expansion of k in k 9.638 * [backup-simplify]: Simplify 0 into 0 9.638 * [backup-simplify]: Simplify 1 into 1 9.639 * [backup-simplify]: Simplify (/ -1 1) into -1 9.639 * [backup-simplify]: Simplify (sqrt 0) into 0 9.640 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.641 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.641 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 9.641 * [taylor]: Taking taylor expansion of 1.0 in k 9.641 * [backup-simplify]: Simplify 1.0 into 1.0 9.641 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 9.641 * [taylor]: Taking taylor expansion of (/ -1 k) in k 9.641 * [taylor]: Taking taylor expansion of -1 in k 9.641 * [backup-simplify]: Simplify -1 into -1 9.641 * [taylor]: Taking taylor expansion of k in k 9.641 * [backup-simplify]: Simplify 0 into 0 9.641 * [backup-simplify]: Simplify 1 into 1 9.641 * [backup-simplify]: Simplify (/ -1 1) into -1 9.642 * [backup-simplify]: Simplify (sqrt 0) into 0 9.643 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 9.644 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 9.644 * [backup-simplify]: Simplify +nan.0 into +nan.0 9.645 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 9.649 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 9.651 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 9.652 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.653 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.656 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 9.660 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 9.660 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 9.661 * [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))))) 9.662 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1) 9.662 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.662 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 9.662 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.662 * [taylor]: Taking taylor expansion of 2.0 in n 9.662 * [backup-simplify]: Simplify 2.0 into 2.0 9.662 * [taylor]: Taking taylor expansion of (* n PI) in n 9.662 * [taylor]: Taking taylor expansion of n in n 9.662 * [backup-simplify]: Simplify 0 into 0 9.662 * [backup-simplify]: Simplify 1 into 1 9.662 * [taylor]: Taking taylor expansion of PI in n 9.662 * [backup-simplify]: Simplify PI into PI 9.662 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.662 * [taylor]: Taking taylor expansion of 2.0 in n 9.662 * [backup-simplify]: Simplify 2.0 into 2.0 9.662 * [taylor]: Taking taylor expansion of (* n PI) in n 9.662 * [taylor]: Taking taylor expansion of n in n 9.663 * [backup-simplify]: Simplify 0 into 0 9.663 * [backup-simplify]: Simplify 1 into 1 9.663 * [taylor]: Taking taylor expansion of PI in n 9.663 * [backup-simplify]: Simplify PI into PI 9.663 * [backup-simplify]: Simplify (* 0 PI) into 0 9.663 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.663 * [backup-simplify]: Simplify 0 into 0 9.665 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.667 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.667 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.668 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.669 * [backup-simplify]: Simplify 0 into 0 9.678 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.679 * [backup-simplify]: Simplify 0 into 0 9.681 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.682 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 9.682 * [backup-simplify]: Simplify 0 into 0 9.683 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.685 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 9.685 * [backup-simplify]: Simplify 0 into 0 9.686 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 9.688 * [backup-simplify]: Simplify 0 into 0 9.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 9.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 9.691 * [backup-simplify]: Simplify 0 into 0 9.692 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 9.692 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 9.693 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 9.693 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.693 * [taylor]: Taking taylor expansion of 2.0 in n 9.693 * [backup-simplify]: Simplify 2.0 into 2.0 9.693 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.693 * [taylor]: Taking taylor expansion of PI in n 9.693 * [backup-simplify]: Simplify PI into PI 9.693 * [taylor]: Taking taylor expansion of n in n 9.693 * [backup-simplify]: Simplify 0 into 0 9.693 * [backup-simplify]: Simplify 1 into 1 9.693 * [backup-simplify]: Simplify (/ PI 1) into PI 9.693 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.693 * [taylor]: Taking taylor expansion of 2.0 in n 9.693 * [backup-simplify]: Simplify 2.0 into 2.0 9.693 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.693 * [taylor]: Taking taylor expansion of PI in n 9.693 * [backup-simplify]: Simplify PI into PI 9.693 * [taylor]: Taking taylor expansion of n in n 9.693 * [backup-simplify]: Simplify 0 into 0 9.693 * [backup-simplify]: Simplify 1 into 1 9.694 * [backup-simplify]: Simplify (/ PI 1) into PI 9.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.696 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.697 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.697 * [backup-simplify]: Simplify 0 into 0 9.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.698 * [backup-simplify]: Simplify 0 into 0 9.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.700 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.700 * [backup-simplify]: Simplify 0 into 0 9.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.703 * [backup-simplify]: Simplify 0 into 0 9.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.705 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.705 * [backup-simplify]: Simplify 0 into 0 9.706 * [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 9.707 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.707 * [backup-simplify]: Simplify 0 into 0 9.708 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 9.708 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 9.708 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 9.709 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.709 * [taylor]: Taking taylor expansion of -2.0 in n 9.709 * [backup-simplify]: Simplify -2.0 into -2.0 9.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.709 * [taylor]: Taking taylor expansion of PI in n 9.709 * [backup-simplify]: Simplify PI into PI 9.709 * [taylor]: Taking taylor expansion of n in n 9.709 * [backup-simplify]: Simplify 0 into 0 9.709 * [backup-simplify]: Simplify 1 into 1 9.709 * [backup-simplify]: Simplify (/ PI 1) into PI 9.709 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.709 * [taylor]: Taking taylor expansion of -2.0 in n 9.709 * [backup-simplify]: Simplify -2.0 into -2.0 9.709 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.709 * [taylor]: Taking taylor expansion of PI in n 9.709 * [backup-simplify]: Simplify PI into PI 9.709 * [taylor]: Taking taylor expansion of n in n 9.709 * [backup-simplify]: Simplify 0 into 0 9.709 * [backup-simplify]: Simplify 1 into 1 9.710 * [backup-simplify]: Simplify (/ PI 1) into PI 9.710 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.711 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.712 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.712 * [backup-simplify]: Simplify 0 into 0 9.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.714 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.714 * [backup-simplify]: Simplify 0 into 0 9.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.717 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.717 * [backup-simplify]: Simplify 0 into 0 9.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.719 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 9.719 * [backup-simplify]: Simplify 0 into 0 9.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.722 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 9.722 * [backup-simplify]: Simplify 0 into 0 9.723 * [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 9.725 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 9.725 * [backup-simplify]: Simplify 0 into 0 9.725 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 9.726 * * * [progress]: simplifying candidates 9.732 * [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) 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(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 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 11.199 * * * [progress]: adding candidates to table 12.524 * * [progress]: iteration 4 / 4 12.524 * * * [progress]: picking best candidate 12.553 * * * * [pick]: Picked # 12.553 * * * [progress]: localizing error 12.595 * * * [progress]: generating rewritten candidates 12.595 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2) 12.649 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 12.707 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 2 1) 12.726 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1) 12.757 * * * [progress]: generating series expansions 12.757 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2) 12.758 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 12.758 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.758 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.758 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.758 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.758 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.758 * [taylor]: Taking taylor expansion of 0.25 in k 12.759 * [backup-simplify]: Simplify 0.25 into 0.25 12.759 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.759 * [taylor]: Taking taylor expansion of 1.0 in k 12.759 * [backup-simplify]: Simplify 1.0 into 1.0 12.759 * [taylor]: Taking taylor expansion of k in k 12.759 * [backup-simplify]: Simplify 0 into 0 12.759 * [backup-simplify]: Simplify 1 into 1 12.759 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.759 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.759 * [taylor]: Taking taylor expansion of 2.0 in k 12.759 * [backup-simplify]: Simplify 2.0 into 2.0 12.759 * [taylor]: Taking taylor expansion of (* n PI) in k 12.759 * [taylor]: Taking taylor expansion of n in k 12.759 * [backup-simplify]: Simplify n into n 12.759 * [taylor]: Taking taylor expansion of PI in k 12.759 * [backup-simplify]: Simplify PI into PI 12.759 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.759 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.759 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.760 * [backup-simplify]: Simplify (- 0) into 0 12.760 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.761 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.761 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.761 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.761 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.761 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.761 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.761 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.761 * [taylor]: Taking taylor expansion of 0.25 in n 12.761 * [backup-simplify]: Simplify 0.25 into 0.25 12.761 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.761 * [taylor]: Taking taylor expansion of 1.0 in n 12.762 * [backup-simplify]: Simplify 1.0 into 1.0 12.762 * [taylor]: Taking taylor expansion of k in n 12.762 * [backup-simplify]: Simplify k into k 12.762 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.762 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.762 * [taylor]: Taking taylor expansion of 2.0 in n 12.762 * [backup-simplify]: Simplify 2.0 into 2.0 12.762 * [taylor]: Taking taylor expansion of (* n PI) in n 12.762 * [taylor]: Taking taylor expansion of n in n 12.762 * [backup-simplify]: Simplify 0 into 0 12.762 * [backup-simplify]: Simplify 1 into 1 12.762 * [taylor]: Taking taylor expansion of PI in n 12.762 * [backup-simplify]: Simplify PI into PI 12.762 * [backup-simplify]: Simplify (* 0 PI) into 0 12.763 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.765 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.766 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.768 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.768 * [backup-simplify]: Simplify (- k) into (- k) 12.768 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.768 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.769 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.771 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.772 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.772 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.772 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.772 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.772 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.772 * [taylor]: Taking taylor expansion of 0.25 in n 12.772 * [backup-simplify]: Simplify 0.25 into 0.25 12.772 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.772 * [taylor]: Taking taylor expansion of 1.0 in n 12.772 * [backup-simplify]: Simplify 1.0 into 1.0 12.772 * [taylor]: Taking taylor expansion of k in n 12.773 * [backup-simplify]: Simplify k into k 12.773 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.773 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.773 * [taylor]: Taking taylor expansion of 2.0 in n 12.773 * [backup-simplify]: Simplify 2.0 into 2.0 12.773 * [taylor]: Taking taylor expansion of (* n PI) in n 12.773 * [taylor]: Taking taylor expansion of n in n 12.773 * [backup-simplify]: Simplify 0 into 0 12.773 * [backup-simplify]: Simplify 1 into 1 12.773 * [taylor]: Taking taylor expansion of PI in n 12.773 * [backup-simplify]: Simplify PI into PI 12.773 * [backup-simplify]: Simplify (* 0 PI) into 0 12.774 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.775 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.777 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.778 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.778 * [backup-simplify]: Simplify (- k) into (- k) 12.778 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.778 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.786 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.787 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.788 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.788 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.788 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.788 * [taylor]: Taking taylor expansion of 0.25 in k 12.788 * [backup-simplify]: Simplify 0.25 into 0.25 12.788 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.788 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.788 * [taylor]: Taking taylor expansion of 1.0 in k 12.788 * [backup-simplify]: Simplify 1.0 into 1.0 12.788 * [taylor]: Taking taylor expansion of k in k 12.788 * [backup-simplify]: Simplify 0 into 0 12.788 * [backup-simplify]: Simplify 1 into 1 12.788 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.788 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.788 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.788 * [taylor]: Taking taylor expansion of 2.0 in k 12.788 * [backup-simplify]: Simplify 2.0 into 2.0 12.788 * [taylor]: Taking taylor expansion of PI in k 12.788 * [backup-simplify]: Simplify PI into PI 12.788 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.789 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.789 * [taylor]: Taking taylor expansion of (log n) in k 12.789 * [taylor]: Taking taylor expansion of n in k 12.789 * [backup-simplify]: Simplify n into n 12.789 * [backup-simplify]: Simplify (log n) into (log n) 12.790 * [backup-simplify]: Simplify (- 0) into 0 12.790 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.791 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.792 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.793 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.794 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.795 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.796 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.797 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.798 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.798 * [backup-simplify]: Simplify (- 0) into 0 12.799 * [backup-simplify]: Simplify (+ 0 0) into 0 12.799 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.800 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.801 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.802 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.802 * [taylor]: Taking taylor expansion of 0 in k 12.802 * [backup-simplify]: Simplify 0 into 0 12.802 * [backup-simplify]: Simplify 0 into 0 12.803 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.805 * [backup-simplify]: Simplify (+ 0 0) into 0 12.805 * [backup-simplify]: Simplify (- 1) into -1 12.805 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.806 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.807 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 12.810 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.812 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 12.813 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.814 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.817 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.817 * [backup-simplify]: Simplify (- 0) into 0 12.817 * [backup-simplify]: Simplify (+ 0 0) into 0 12.818 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.819 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.821 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.822 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.822 * [taylor]: Taking taylor expansion of 0 in k 12.822 * [backup-simplify]: Simplify 0 into 0 12.822 * [backup-simplify]: Simplify 0 into 0 12.822 * [backup-simplify]: Simplify 0 into 0 12.823 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.827 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.830 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.830 * [backup-simplify]: Simplify (+ 0 0) into 0 12.831 * [backup-simplify]: Simplify (- 0) into 0 12.831 * [backup-simplify]: Simplify (+ 0 0) into 0 12.833 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.835 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.838 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 12.841 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 12.847 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.848 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 12.848 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 12.848 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 12.848 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.848 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.848 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 12.848 * [taylor]: Taking taylor expansion of 0.25 in k 12.848 * [backup-simplify]: Simplify 0.25 into 0.25 12.848 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.848 * [taylor]: Taking taylor expansion of 1.0 in k 12.848 * [backup-simplify]: Simplify 1.0 into 1.0 12.848 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.848 * [taylor]: Taking taylor expansion of k in k 12.848 * [backup-simplify]: Simplify 0 into 0 12.848 * [backup-simplify]: Simplify 1 into 1 12.848 * [backup-simplify]: Simplify (/ 1 1) into 1 12.848 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.848 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.848 * [taylor]: Taking taylor expansion of 2.0 in k 12.848 * [backup-simplify]: Simplify 2.0 into 2.0 12.848 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.848 * [taylor]: Taking taylor expansion of PI in k 12.848 * [backup-simplify]: Simplify PI into PI 12.848 * [taylor]: Taking taylor expansion of n in k 12.848 * [backup-simplify]: Simplify n into n 12.849 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.849 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.849 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.849 * [backup-simplify]: Simplify (- 1) into -1 12.849 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.849 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 12.850 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 12.850 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.850 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.850 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.850 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.850 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.850 * [taylor]: Taking taylor expansion of 0.25 in n 12.850 * [backup-simplify]: Simplify 0.25 into 0.25 12.850 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.850 * [taylor]: Taking taylor expansion of 1.0 in n 12.850 * [backup-simplify]: Simplify 1.0 into 1.0 12.850 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.850 * [taylor]: Taking taylor expansion of k in n 12.850 * [backup-simplify]: Simplify k into k 12.850 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.850 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.850 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.850 * [taylor]: Taking taylor expansion of 2.0 in n 12.850 * [backup-simplify]: Simplify 2.0 into 2.0 12.850 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.850 * [taylor]: Taking taylor expansion of PI in n 12.850 * [backup-simplify]: Simplify PI into PI 12.850 * [taylor]: Taking taylor expansion of n in n 12.850 * [backup-simplify]: Simplify 0 into 0 12.850 * [backup-simplify]: Simplify 1 into 1 12.851 * [backup-simplify]: Simplify (/ PI 1) into PI 12.851 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.851 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.852 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.852 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.852 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.853 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.854 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.854 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.854 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 12.854 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.854 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.854 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 12.855 * [taylor]: Taking taylor expansion of 0.25 in n 12.855 * [backup-simplify]: Simplify 0.25 into 0.25 12.855 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.855 * [taylor]: Taking taylor expansion of 1.0 in n 12.855 * [backup-simplify]: Simplify 1.0 into 1.0 12.855 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.855 * [taylor]: Taking taylor expansion of k in n 12.855 * [backup-simplify]: Simplify k into k 12.855 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.855 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.855 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.855 * [taylor]: Taking taylor expansion of 2.0 in n 12.855 * [backup-simplify]: Simplify 2.0 into 2.0 12.855 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.855 * [taylor]: Taking taylor expansion of PI in n 12.855 * [backup-simplify]: Simplify PI into PI 12.855 * [taylor]: Taking taylor expansion of n in n 12.855 * [backup-simplify]: Simplify 0 into 0 12.855 * [backup-simplify]: Simplify 1 into 1 12.855 * [backup-simplify]: Simplify (/ PI 1) into PI 12.856 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.856 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.856 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.856 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.857 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 12.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.858 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.859 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.859 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.859 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.859 * [taylor]: Taking taylor expansion of 0.25 in k 12.859 * [backup-simplify]: Simplify 0.25 into 0.25 12.859 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.859 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.859 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.859 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.859 * [taylor]: Taking taylor expansion of 2.0 in k 12.859 * [backup-simplify]: Simplify 2.0 into 2.0 12.859 * [taylor]: Taking taylor expansion of PI in k 12.859 * [backup-simplify]: Simplify PI into PI 12.860 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.860 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.860 * [taylor]: Taking taylor expansion of (log n) in k 12.860 * [taylor]: Taking taylor expansion of n in k 12.860 * [backup-simplify]: Simplify n into n 12.860 * [backup-simplify]: Simplify (log n) into (log n) 12.860 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.860 * [taylor]: Taking taylor expansion of 1.0 in k 12.860 * [backup-simplify]: Simplify 1.0 into 1.0 12.860 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.860 * [taylor]: Taking taylor expansion of k in k 12.860 * [backup-simplify]: Simplify 0 into 0 12.860 * [backup-simplify]: Simplify 1 into 1 12.861 * [backup-simplify]: Simplify (/ 1 1) into 1 12.861 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.861 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.862 * [backup-simplify]: Simplify (- 1) into -1 12.862 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.862 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.863 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 12.864 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.865 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.865 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.866 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.867 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.868 * [backup-simplify]: Simplify (- 0) into 0 12.868 * [backup-simplify]: Simplify (+ 0 0) into 0 12.868 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.871 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.873 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.873 * [taylor]: Taking taylor expansion of 0 in k 12.873 * [backup-simplify]: Simplify 0 into 0 12.873 * [backup-simplify]: Simplify 0 into 0 12.874 * [backup-simplify]: Simplify 0 into 0 12.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.876 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.879 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.880 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.880 * [backup-simplify]: Simplify (- 0) into 0 12.880 * [backup-simplify]: Simplify (+ 0 0) into 0 12.881 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.883 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.885 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.887 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.887 * [taylor]: Taking taylor expansion of 0 in k 12.887 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify 0 into 0 12.888 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.890 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.896 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.896 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.897 * [backup-simplify]: Simplify (- 0) into 0 12.897 * [backup-simplify]: Simplify (+ 0 0) into 0 12.899 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.900 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.911 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.914 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.914 * [taylor]: Taking taylor expansion of 0 in k 12.914 * [backup-simplify]: Simplify 0 into 0 12.914 * [backup-simplify]: Simplify 0 into 0 12.915 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.916 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 12.916 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 12.916 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 12.916 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.916 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.916 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 12.916 * [taylor]: Taking taylor expansion of 0.25 in k 12.916 * [backup-simplify]: Simplify 0.25 into 0.25 12.916 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.917 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.917 * [taylor]: Taking taylor expansion of k in k 12.917 * [backup-simplify]: Simplify 0 into 0 12.917 * [backup-simplify]: Simplify 1 into 1 12.917 * [backup-simplify]: Simplify (/ 1 1) into 1 12.917 * [taylor]: Taking taylor expansion of 1.0 in k 12.917 * [backup-simplify]: Simplify 1.0 into 1.0 12.917 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.917 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.917 * [taylor]: Taking taylor expansion of -2.0 in k 12.917 * [backup-simplify]: Simplify -2.0 into -2.0 12.917 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.917 * [taylor]: Taking taylor expansion of PI in k 12.917 * [backup-simplify]: Simplify PI into PI 12.917 * [taylor]: Taking taylor expansion of n in k 12.917 * [backup-simplify]: Simplify n into n 12.917 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.918 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.918 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.918 * [backup-simplify]: Simplify (+ 1 0) into 1 12.919 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 12.919 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 12.919 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.919 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.919 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.919 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.919 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.919 * [taylor]: Taking taylor expansion of 0.25 in n 12.919 * [backup-simplify]: Simplify 0.25 into 0.25 12.919 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.919 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.919 * [taylor]: Taking taylor expansion of k in n 12.919 * [backup-simplify]: Simplify k into k 12.919 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.919 * [taylor]: Taking taylor expansion of 1.0 in n 12.919 * [backup-simplify]: Simplify 1.0 into 1.0 12.919 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.919 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.919 * [taylor]: Taking taylor expansion of -2.0 in n 12.919 * [backup-simplify]: Simplify -2.0 into -2.0 12.919 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.919 * [taylor]: Taking taylor expansion of PI in n 12.919 * [backup-simplify]: Simplify PI into PI 12.919 * [taylor]: Taking taylor expansion of n in n 12.919 * [backup-simplify]: Simplify 0 into 0 12.919 * [backup-simplify]: Simplify 1 into 1 12.920 * [backup-simplify]: Simplify (/ PI 1) into PI 12.920 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.920 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.921 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.921 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.921 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.922 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.923 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.923 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 12.923 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.923 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.923 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 12.923 * [taylor]: Taking taylor expansion of 0.25 in n 12.923 * [backup-simplify]: Simplify 0.25 into 0.25 12.923 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.923 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.923 * [taylor]: Taking taylor expansion of k in n 12.923 * [backup-simplify]: Simplify k into k 12.923 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.923 * [taylor]: Taking taylor expansion of 1.0 in n 12.923 * [backup-simplify]: Simplify 1.0 into 1.0 12.923 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.923 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.923 * [taylor]: Taking taylor expansion of -2.0 in n 12.923 * [backup-simplify]: Simplify -2.0 into -2.0 12.923 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.923 * [taylor]: Taking taylor expansion of PI in n 12.923 * [backup-simplify]: Simplify PI into PI 12.923 * [taylor]: Taking taylor expansion of n in n 12.923 * [backup-simplify]: Simplify 0 into 0 12.923 * [backup-simplify]: Simplify 1 into 1 12.924 * [backup-simplify]: Simplify (/ PI 1) into PI 12.924 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.925 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.925 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.925 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 12.926 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.926 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.927 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.927 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.927 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.927 * [taylor]: Taking taylor expansion of 0.25 in k 12.927 * [backup-simplify]: Simplify 0.25 into 0.25 12.927 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.927 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.927 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.927 * [taylor]: Taking taylor expansion of k in k 12.927 * [backup-simplify]: Simplify 0 into 0 12.927 * [backup-simplify]: Simplify 1 into 1 12.928 * [backup-simplify]: Simplify (/ 1 1) into 1 12.928 * [taylor]: Taking taylor expansion of 1.0 in k 12.928 * [backup-simplify]: Simplify 1.0 into 1.0 12.928 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.928 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.928 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.928 * [taylor]: Taking taylor expansion of -2.0 in k 12.928 * [backup-simplify]: Simplify -2.0 into -2.0 12.928 * [taylor]: Taking taylor expansion of PI in k 12.928 * [backup-simplify]: Simplify PI into PI 12.928 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.929 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.929 * [taylor]: Taking taylor expansion of (log n) in k 12.929 * [taylor]: Taking taylor expansion of n in k 12.929 * [backup-simplify]: Simplify n into n 12.929 * [backup-simplify]: Simplify (log n) into (log n) 12.929 * [backup-simplify]: Simplify (+ 1 0) into 1 12.929 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.930 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.931 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.931 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 12.932 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.933 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.933 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.934 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.935 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.935 * [backup-simplify]: Simplify (+ 0 0) into 0 12.935 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.937 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.938 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.938 * [taylor]: Taking taylor expansion of 0 in k 12.938 * [backup-simplify]: Simplify 0 into 0 12.938 * [backup-simplify]: Simplify 0 into 0 12.938 * [backup-simplify]: Simplify 0 into 0 12.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.940 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.941 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.942 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.942 * [backup-simplify]: Simplify (+ 0 0) into 0 12.942 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.943 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.944 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.946 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.946 * [taylor]: Taking taylor expansion of 0 in k 12.946 * [backup-simplify]: Simplify 0 into 0 12.946 * [backup-simplify]: Simplify 0 into 0 12.946 * [backup-simplify]: Simplify 0 into 0 12.946 * [backup-simplify]: Simplify 0 into 0 12.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.948 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.954 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.954 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.954 * [backup-simplify]: Simplify (+ 0 0) into 0 12.956 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.957 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.959 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.962 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.962 * [taylor]: Taking taylor expansion of 0 in k 12.962 * [backup-simplify]: Simplify 0 into 0 12.962 * [backup-simplify]: Simplify 0 into 0 12.963 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.964 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 12.964 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 12.964 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 12.964 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 12.964 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.965 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.965 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 12.965 * [taylor]: Taking taylor expansion of 0.25 in k 12.965 * [backup-simplify]: Simplify 0.25 into 0.25 12.965 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.965 * [taylor]: Taking taylor expansion of 1.0 in k 12.965 * [backup-simplify]: Simplify 1.0 into 1.0 12.965 * [taylor]: Taking taylor expansion of k in k 12.965 * [backup-simplify]: Simplify 0 into 0 12.965 * [backup-simplify]: Simplify 1 into 1 12.965 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.965 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.965 * [taylor]: Taking taylor expansion of 2.0 in k 12.965 * [backup-simplify]: Simplify 2.0 into 2.0 12.965 * [taylor]: Taking taylor expansion of (* n PI) in k 12.965 * [taylor]: Taking taylor expansion of n in k 12.965 * [backup-simplify]: Simplify n into n 12.965 * [taylor]: Taking taylor expansion of PI in k 12.965 * [backup-simplify]: Simplify PI into PI 12.965 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.965 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.966 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.966 * [backup-simplify]: Simplify (- 0) into 0 12.966 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.967 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 12.967 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 12.967 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 12.967 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.967 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.967 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.967 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.967 * [taylor]: Taking taylor expansion of 0.25 in n 12.967 * [backup-simplify]: Simplify 0.25 into 0.25 12.967 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.968 * [taylor]: Taking taylor expansion of 1.0 in n 12.968 * [backup-simplify]: Simplify 1.0 into 1.0 12.968 * [taylor]: Taking taylor expansion of k in n 12.968 * [backup-simplify]: Simplify k into k 12.968 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.968 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.968 * [taylor]: Taking taylor expansion of 2.0 in n 12.968 * [backup-simplify]: Simplify 2.0 into 2.0 12.968 * [taylor]: Taking taylor expansion of (* n PI) in n 12.968 * [taylor]: Taking taylor expansion of n in n 12.968 * [backup-simplify]: Simplify 0 into 0 12.968 * [backup-simplify]: Simplify 1 into 1 12.968 * [taylor]: Taking taylor expansion of PI in n 12.968 * [backup-simplify]: Simplify PI into PI 12.968 * [backup-simplify]: Simplify (* 0 PI) into 0 12.969 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.970 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.971 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.972 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.972 * [backup-simplify]: Simplify (- k) into (- k) 12.972 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.972 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.973 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.974 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.975 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.975 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 12.975 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.975 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.975 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 12.975 * [taylor]: Taking taylor expansion of 0.25 in n 12.975 * [backup-simplify]: Simplify 0.25 into 0.25 12.975 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.975 * [taylor]: Taking taylor expansion of 1.0 in n 12.975 * [backup-simplify]: Simplify 1.0 into 1.0 12.975 * [taylor]: Taking taylor expansion of k in n 12.975 * [backup-simplify]: Simplify k into k 12.975 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.975 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.975 * [taylor]: Taking taylor expansion of 2.0 in n 12.975 * [backup-simplify]: Simplify 2.0 into 2.0 12.975 * [taylor]: Taking taylor expansion of (* n PI) in n 12.975 * [taylor]: Taking taylor expansion of n in n 12.975 * [backup-simplify]: Simplify 0 into 0 12.975 * [backup-simplify]: Simplify 1 into 1 12.975 * [taylor]: Taking taylor expansion of PI in n 12.975 * [backup-simplify]: Simplify PI into PI 12.975 * [backup-simplify]: Simplify (* 0 PI) into 0 12.976 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.976 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.977 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.978 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.978 * [backup-simplify]: Simplify (- k) into (- k) 12.978 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.978 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 12.979 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.980 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.980 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.981 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.981 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.981 * [taylor]: Taking taylor expansion of 0.25 in k 12.981 * [backup-simplify]: Simplify 0.25 into 0.25 12.981 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.981 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.981 * [taylor]: Taking taylor expansion of 1.0 in k 12.981 * [backup-simplify]: Simplify 1.0 into 1.0 12.981 * [taylor]: Taking taylor expansion of k in k 12.981 * [backup-simplify]: Simplify 0 into 0 12.981 * [backup-simplify]: Simplify 1 into 1 12.981 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.981 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.981 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.981 * [taylor]: Taking taylor expansion of 2.0 in k 12.981 * [backup-simplify]: Simplify 2.0 into 2.0 12.981 * [taylor]: Taking taylor expansion of PI in k 12.981 * [backup-simplify]: Simplify PI into PI 12.981 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.982 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.982 * [taylor]: Taking taylor expansion of (log n) in k 12.982 * [taylor]: Taking taylor expansion of n in k 12.982 * [backup-simplify]: Simplify n into n 12.982 * [backup-simplify]: Simplify (log n) into (log n) 12.982 * [backup-simplify]: Simplify (- 0) into 0 12.982 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.983 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.984 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.984 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 12.985 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.986 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 12.986 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.987 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.988 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.988 * [backup-simplify]: Simplify (- 0) into 0 12.989 * [backup-simplify]: Simplify (+ 0 0) into 0 12.989 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 12.990 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.991 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.992 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.992 * [taylor]: Taking taylor expansion of 0 in k 12.992 * [backup-simplify]: Simplify 0 into 0 12.992 * [backup-simplify]: Simplify 0 into 0 12.992 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.993 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.994 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.994 * [backup-simplify]: Simplify (+ 0 0) into 0 12.994 * [backup-simplify]: Simplify (- 1) into -1 12.994 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.995 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.997 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 12.999 * [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)))))) 13.001 * [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)))))) 13.001 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.002 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.006 * [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 13.007 * [backup-simplify]: Simplify (- 0) into 0 13.007 * [backup-simplify]: Simplify (+ 0 0) into 0 13.008 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.010 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.011 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.014 * [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 13.014 * [taylor]: Taking taylor expansion of 0 in k 13.014 * [backup-simplify]: Simplify 0 into 0 13.014 * [backup-simplify]: Simplify 0 into 0 13.014 * [backup-simplify]: Simplify 0 into 0 13.015 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.027 * [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 13.029 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.030 * [backup-simplify]: Simplify (+ 0 0) into 0 13.030 * [backup-simplify]: Simplify (- 0) into 0 13.030 * [backup-simplify]: Simplify (+ 0 0) into 0 13.032 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.035 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.039 * [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))))) 13.045 * [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))))) 13.055 * [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)))))) 13.056 * [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)))) 13.056 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 13.056 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 13.056 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.056 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.056 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 13.056 * [taylor]: Taking taylor expansion of 0.25 in k 13.056 * [backup-simplify]: Simplify 0.25 into 0.25 13.056 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.056 * [taylor]: Taking taylor expansion of 1.0 in k 13.056 * [backup-simplify]: Simplify 1.0 into 1.0 13.056 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.056 * [taylor]: Taking taylor expansion of k in k 13.056 * [backup-simplify]: Simplify 0 into 0 13.056 * [backup-simplify]: Simplify 1 into 1 13.057 * [backup-simplify]: Simplify (/ 1 1) into 1 13.057 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.057 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.057 * [taylor]: Taking taylor expansion of 2.0 in k 13.057 * [backup-simplify]: Simplify 2.0 into 2.0 13.057 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.057 * [taylor]: Taking taylor expansion of PI in k 13.057 * [backup-simplify]: Simplify PI into PI 13.057 * [taylor]: Taking taylor expansion of n in k 13.057 * [backup-simplify]: Simplify n into n 13.057 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.057 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.057 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.057 * [backup-simplify]: Simplify (- 1) into -1 13.058 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.058 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 13.058 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 13.059 * [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))))) 13.059 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.059 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.059 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.059 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.059 * [taylor]: Taking taylor expansion of 0.25 in n 13.059 * [backup-simplify]: Simplify 0.25 into 0.25 13.059 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.059 * [taylor]: Taking taylor expansion of 1.0 in n 13.059 * [backup-simplify]: Simplify 1.0 into 1.0 13.059 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.059 * [taylor]: Taking taylor expansion of k in n 13.059 * [backup-simplify]: Simplify k into k 13.059 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.059 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.059 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.059 * [taylor]: Taking taylor expansion of 2.0 in n 13.059 * [backup-simplify]: Simplify 2.0 into 2.0 13.059 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.059 * [taylor]: Taking taylor expansion of PI in n 13.059 * [backup-simplify]: Simplify PI into PI 13.059 * [taylor]: Taking taylor expansion of n in n 13.059 * [backup-simplify]: Simplify 0 into 0 13.059 * [backup-simplify]: Simplify 1 into 1 13.060 * [backup-simplify]: Simplify (/ PI 1) into PI 13.060 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.061 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.062 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.062 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.062 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.063 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.065 * [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)))) 13.066 * [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))))) 13.066 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.066 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.066 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.066 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.066 * [taylor]: Taking taylor expansion of 0.25 in n 13.066 * [backup-simplify]: Simplify 0.25 into 0.25 13.066 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.066 * [taylor]: Taking taylor expansion of 1.0 in n 13.066 * [backup-simplify]: Simplify 1.0 into 1.0 13.066 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.067 * [taylor]: Taking taylor expansion of k in n 13.067 * [backup-simplify]: Simplify k into k 13.067 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.067 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.067 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.067 * [taylor]: Taking taylor expansion of 2.0 in n 13.067 * [backup-simplify]: Simplify 2.0 into 2.0 13.067 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.067 * [taylor]: Taking taylor expansion of PI in n 13.067 * [backup-simplify]: Simplify PI into PI 13.067 * [taylor]: Taking taylor expansion of n in n 13.067 * [backup-simplify]: Simplify 0 into 0 13.067 * [backup-simplify]: Simplify 1 into 1 13.067 * [backup-simplify]: Simplify (/ PI 1) into PI 13.068 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.069 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.069 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.069 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.069 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.071 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.072 * [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)))) 13.073 * [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))))) 13.073 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.073 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.073 * [taylor]: Taking taylor expansion of 0.25 in k 13.073 * [backup-simplify]: Simplify 0.25 into 0.25 13.073 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.073 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.074 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.074 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.074 * [taylor]: Taking taylor expansion of 2.0 in k 13.074 * [backup-simplify]: Simplify 2.0 into 2.0 13.074 * [taylor]: Taking taylor expansion of PI in k 13.074 * [backup-simplify]: Simplify PI into PI 13.074 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.075 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.075 * [taylor]: Taking taylor expansion of (log n) in k 13.075 * [taylor]: Taking taylor expansion of n in k 13.075 * [backup-simplify]: Simplify n into n 13.075 * [backup-simplify]: Simplify (log n) into (log n) 13.075 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.075 * [taylor]: Taking taylor expansion of 1.0 in k 13.075 * [backup-simplify]: Simplify 1.0 into 1.0 13.076 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.076 * [taylor]: Taking taylor expansion of k in k 13.076 * [backup-simplify]: Simplify 0 into 0 13.076 * [backup-simplify]: Simplify 1 into 1 13.076 * [backup-simplify]: Simplify (/ 1 1) into 1 13.076 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.077 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.077 * [backup-simplify]: Simplify (- 1) into -1 13.078 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.079 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.080 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 13.081 * [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))))) 13.083 * [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))))) 13.084 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.084 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.086 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.087 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.087 * [backup-simplify]: Simplify (- 0) into 0 13.087 * [backup-simplify]: Simplify (+ 0 0) into 0 13.088 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.089 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.090 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.092 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.092 * [taylor]: Taking taylor expansion of 0 in k 13.092 * [backup-simplify]: Simplify 0 into 0 13.092 * [backup-simplify]: Simplify 0 into 0 13.092 * [backup-simplify]: Simplify 0 into 0 13.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.093 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.095 * [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 13.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.095 * [backup-simplify]: Simplify (- 0) into 0 13.095 * [backup-simplify]: Simplify (+ 0 0) into 0 13.096 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.097 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.098 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.099 * [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 13.099 * [taylor]: Taking taylor expansion of 0 in k 13.099 * [backup-simplify]: Simplify 0 into 0 13.099 * [backup-simplify]: Simplify 0 into 0 13.099 * [backup-simplify]: Simplify 0 into 0 13.099 * [backup-simplify]: Simplify 0 into 0 13.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.101 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.104 * [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 13.104 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.104 * [backup-simplify]: Simplify (- 0) into 0 13.105 * [backup-simplify]: Simplify (+ 0 0) into 0 13.105 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.106 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.108 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.109 * [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 13.109 * [taylor]: Taking taylor expansion of 0 in k 13.109 * [backup-simplify]: Simplify 0 into 0 13.109 * [backup-simplify]: Simplify 0 into 0 13.110 * [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)))) 13.111 * [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))) 13.111 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 13.111 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 13.111 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.111 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.111 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 13.111 * [taylor]: Taking taylor expansion of 0.25 in k 13.111 * [backup-simplify]: Simplify 0.25 into 0.25 13.111 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.111 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.111 * [taylor]: Taking taylor expansion of k in k 13.111 * [backup-simplify]: Simplify 0 into 0 13.111 * [backup-simplify]: Simplify 1 into 1 13.111 * [backup-simplify]: Simplify (/ 1 1) into 1 13.111 * [taylor]: Taking taylor expansion of 1.0 in k 13.111 * [backup-simplify]: Simplify 1.0 into 1.0 13.111 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.111 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.111 * [taylor]: Taking taylor expansion of -2.0 in k 13.111 * [backup-simplify]: Simplify -2.0 into -2.0 13.111 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.111 * [taylor]: Taking taylor expansion of PI in k 13.111 * [backup-simplify]: Simplify PI into PI 13.111 * [taylor]: Taking taylor expansion of n in k 13.111 * [backup-simplify]: Simplify n into n 13.111 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.111 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.111 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.112 * [backup-simplify]: Simplify (+ 1 0) into 1 13.112 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 13.112 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 13.112 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 13.112 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.112 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.112 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.112 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.112 * [taylor]: Taking taylor expansion of 0.25 in n 13.112 * [backup-simplify]: Simplify 0.25 into 0.25 13.112 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.112 * [taylor]: Taking taylor expansion of k in n 13.112 * [backup-simplify]: Simplify k into k 13.112 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.112 * [taylor]: Taking taylor expansion of 1.0 in n 13.112 * [backup-simplify]: Simplify 1.0 into 1.0 13.112 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.113 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.113 * [taylor]: Taking taylor expansion of -2.0 in n 13.113 * [backup-simplify]: Simplify -2.0 into -2.0 13.113 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.113 * [taylor]: Taking taylor expansion of PI in n 13.113 * [backup-simplify]: Simplify PI into PI 13.113 * [taylor]: Taking taylor expansion of n in n 13.113 * [backup-simplify]: Simplify 0 into 0 13.113 * [backup-simplify]: Simplify 1 into 1 13.113 * [backup-simplify]: Simplify (/ PI 1) into PI 13.113 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.114 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.114 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.114 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.115 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.117 * [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)))) 13.118 * [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))))) 13.118 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.118 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.118 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.118 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.118 * [taylor]: Taking taylor expansion of 0.25 in n 13.118 * [backup-simplify]: Simplify 0.25 into 0.25 13.118 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.118 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.118 * [taylor]: Taking taylor expansion of k in n 13.119 * [backup-simplify]: Simplify k into k 13.119 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.119 * [taylor]: Taking taylor expansion of 1.0 in n 13.119 * [backup-simplify]: Simplify 1.0 into 1.0 13.119 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.119 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.119 * [taylor]: Taking taylor expansion of -2.0 in n 13.119 * [backup-simplify]: Simplify -2.0 into -2.0 13.119 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.119 * [taylor]: Taking taylor expansion of PI in n 13.119 * [backup-simplify]: Simplify PI into PI 13.119 * [taylor]: Taking taylor expansion of n in n 13.119 * [backup-simplify]: Simplify 0 into 0 13.119 * [backup-simplify]: Simplify 1 into 1 13.119 * [backup-simplify]: Simplify (/ PI 1) into PI 13.120 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.121 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.121 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.121 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.124 * [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)))) 13.125 * [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))))) 13.125 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.125 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.125 * [taylor]: Taking taylor expansion of 0.25 in k 13.126 * [backup-simplify]: Simplify 0.25 into 0.25 13.126 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.126 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.126 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.126 * [taylor]: Taking taylor expansion of k in k 13.126 * [backup-simplify]: Simplify 0 into 0 13.126 * [backup-simplify]: Simplify 1 into 1 13.126 * [backup-simplify]: Simplify (/ 1 1) into 1 13.126 * [taylor]: Taking taylor expansion of 1.0 in k 13.126 * [backup-simplify]: Simplify 1.0 into 1.0 13.126 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.126 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.126 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.126 * [taylor]: Taking taylor expansion of -2.0 in k 13.126 * [backup-simplify]: Simplify -2.0 into -2.0 13.126 * [taylor]: Taking taylor expansion of PI in k 13.126 * [backup-simplify]: Simplify PI into PI 13.127 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.128 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.128 * [taylor]: Taking taylor expansion of (log n) in k 13.128 * [taylor]: Taking taylor expansion of n in k 13.128 * [backup-simplify]: Simplify n into n 13.128 * [backup-simplify]: Simplify (log n) into (log n) 13.129 * [backup-simplify]: Simplify (+ 1 0) into 1 13.129 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.130 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.131 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.132 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 13.134 * [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))))) 13.135 * [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))))) 13.136 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.137 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.139 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.139 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.139 * [backup-simplify]: Simplify (+ 0 0) into 0 13.140 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.142 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.143 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.145 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.145 * [taylor]: Taking taylor expansion of 0 in k 13.145 * [backup-simplify]: Simplify 0 into 0 13.145 * [backup-simplify]: Simplify 0 into 0 13.145 * [backup-simplify]: Simplify 0 into 0 13.146 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.147 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.150 * [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 13.151 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.151 * [backup-simplify]: Simplify (+ 0 0) into 0 13.152 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.155 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.158 * [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 13.158 * [taylor]: Taking taylor expansion of 0 in k 13.158 * [backup-simplify]: Simplify 0 into 0 13.158 * [backup-simplify]: Simplify 0 into 0 13.158 * [backup-simplify]: Simplify 0 into 0 13.158 * [backup-simplify]: Simplify 0 into 0 13.159 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.169 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.176 * [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 13.177 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.178 * [backup-simplify]: Simplify (+ 0 0) into 0 13.180 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.183 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.185 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.189 * [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 13.189 * [taylor]: Taking taylor expansion of 0 in k 13.189 * [backup-simplify]: Simplify 0 into 0 13.189 * [backup-simplify]: Simplify 0 into 0 13.191 * [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)))))) 13.191 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 2 1) 13.192 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 13.192 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 13.192 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.192 * [taylor]: Taking taylor expansion of 2.0 in n 13.192 * [backup-simplify]: Simplify 2.0 into 2.0 13.192 * [taylor]: Taking taylor expansion of (* n PI) in n 13.192 * [taylor]: Taking taylor expansion of n in n 13.192 * [backup-simplify]: Simplify 0 into 0 13.192 * [backup-simplify]: Simplify 1 into 1 13.192 * [taylor]: Taking taylor expansion of PI in n 13.192 * [backup-simplify]: Simplify PI into PI 13.192 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.192 * [taylor]: Taking taylor expansion of 2.0 in n 13.192 * [backup-simplify]: Simplify 2.0 into 2.0 13.193 * [taylor]: Taking taylor expansion of (* n PI) in n 13.193 * [taylor]: Taking taylor expansion of n in n 13.193 * [backup-simplify]: Simplify 0 into 0 13.193 * [backup-simplify]: Simplify 1 into 1 13.193 * [taylor]: Taking taylor expansion of PI in n 13.193 * [backup-simplify]: Simplify PI into PI 13.194 * [backup-simplify]: Simplify (* 0 PI) into 0 13.194 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.194 * [backup-simplify]: Simplify 0 into 0 13.196 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.198 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.199 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.200 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.201 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.201 * [backup-simplify]: Simplify 0 into 0 13.202 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.204 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.204 * [backup-simplify]: Simplify 0 into 0 13.205 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.206 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.206 * [backup-simplify]: Simplify 0 into 0 13.208 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.210 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.210 * [backup-simplify]: Simplify 0 into 0 13.212 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.213 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.213 * [backup-simplify]: Simplify 0 into 0 13.215 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.217 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.217 * [backup-simplify]: Simplify 0 into 0 13.218 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 13.219 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 13.219 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 13.219 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.219 * [taylor]: Taking taylor expansion of 2.0 in n 13.219 * [backup-simplify]: Simplify 2.0 into 2.0 13.219 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.219 * [taylor]: Taking taylor expansion of PI in n 13.219 * [backup-simplify]: Simplify PI into PI 13.219 * [taylor]: Taking taylor expansion of n in n 13.219 * [backup-simplify]: Simplify 0 into 0 13.219 * [backup-simplify]: Simplify 1 into 1 13.219 * [backup-simplify]: Simplify (/ PI 1) into PI 13.219 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.219 * [taylor]: Taking taylor expansion of 2.0 in n 13.220 * [backup-simplify]: Simplify 2.0 into 2.0 13.220 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.220 * [taylor]: Taking taylor expansion of PI in n 13.220 * [backup-simplify]: Simplify PI into PI 13.220 * [taylor]: Taking taylor expansion of n in n 13.220 * [backup-simplify]: Simplify 0 into 0 13.220 * [backup-simplify]: Simplify 1 into 1 13.220 * [backup-simplify]: Simplify (/ PI 1) into PI 13.221 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.221 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.223 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.223 * [backup-simplify]: Simplify 0 into 0 13.224 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.225 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.225 * [backup-simplify]: Simplify 0 into 0 13.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.228 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.228 * [backup-simplify]: Simplify 0 into 0 13.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.230 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.230 * [backup-simplify]: Simplify 0 into 0 13.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.233 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.233 * [backup-simplify]: Simplify 0 into 0 13.234 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.236 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.236 * [backup-simplify]: Simplify 0 into 0 13.237 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 13.238 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 13.238 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 13.238 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.238 * [taylor]: Taking taylor expansion of -2.0 in n 13.238 * [backup-simplify]: Simplify -2.0 into -2.0 13.238 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.238 * [taylor]: Taking taylor expansion of PI in n 13.238 * [backup-simplify]: Simplify PI into PI 13.238 * [taylor]: Taking taylor expansion of n in n 13.238 * [backup-simplify]: Simplify 0 into 0 13.238 * [backup-simplify]: Simplify 1 into 1 13.238 * [backup-simplify]: Simplify (/ PI 1) into PI 13.238 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.238 * [taylor]: Taking taylor expansion of -2.0 in n 13.238 * [backup-simplify]: Simplify -2.0 into -2.0 13.238 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.239 * [taylor]: Taking taylor expansion of PI in n 13.239 * [backup-simplify]: Simplify PI into PI 13.239 * [taylor]: Taking taylor expansion of n in n 13.239 * [backup-simplify]: Simplify 0 into 0 13.239 * [backup-simplify]: Simplify 1 into 1 13.239 * [backup-simplify]: Simplify (/ PI 1) into PI 13.240 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.240 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.242 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.242 * [backup-simplify]: Simplify 0 into 0 13.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.244 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.244 * [backup-simplify]: Simplify 0 into 0 13.245 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.246 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.246 * [backup-simplify]: Simplify 0 into 0 13.247 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.249 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.249 * [backup-simplify]: Simplify 0 into 0 13.250 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.252 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.252 * [backup-simplify]: Simplify 0 into 0 13.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.254 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.255 * [backup-simplify]: Simplify 0 into 0 13.255 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 13.255 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1) 13.256 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 13.256 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 13.256 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.256 * [taylor]: Taking taylor expansion of 2.0 in n 13.256 * [backup-simplify]: Simplify 2.0 into 2.0 13.256 * [taylor]: Taking taylor expansion of (* n PI) in n 13.256 * [taylor]: Taking taylor expansion of n in n 13.256 * [backup-simplify]: Simplify 0 into 0 13.256 * [backup-simplify]: Simplify 1 into 1 13.256 * [taylor]: Taking taylor expansion of PI in n 13.256 * [backup-simplify]: Simplify PI into PI 13.256 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.256 * [taylor]: Taking taylor expansion of 2.0 in n 13.256 * [backup-simplify]: Simplify 2.0 into 2.0 13.256 * [taylor]: Taking taylor expansion of (* n PI) in n 13.256 * [taylor]: Taking taylor expansion of n in n 13.256 * [backup-simplify]: Simplify 0 into 0 13.256 * [backup-simplify]: Simplify 1 into 1 13.256 * [taylor]: Taking taylor expansion of PI in n 13.256 * [backup-simplify]: Simplify PI into PI 13.257 * [backup-simplify]: Simplify (* 0 PI) into 0 13.257 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.257 * [backup-simplify]: Simplify 0 into 0 13.259 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.261 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.261 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.262 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.263 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.263 * [backup-simplify]: Simplify 0 into 0 13.264 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.266 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.266 * [backup-simplify]: Simplify 0 into 0 13.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.268 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 13.268 * [backup-simplify]: Simplify 0 into 0 13.270 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.272 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 13.272 * [backup-simplify]: Simplify 0 into 0 13.273 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.275 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 13.275 * [backup-simplify]: Simplify 0 into 0 13.276 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 13.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 13.277 * [backup-simplify]: Simplify 0 into 0 13.277 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 13.278 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 13.278 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 13.278 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.278 * [taylor]: Taking taylor expansion of 2.0 in n 13.278 * [backup-simplify]: Simplify 2.0 into 2.0 13.278 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.278 * [taylor]: Taking taylor expansion of PI in n 13.278 * [backup-simplify]: Simplify PI into PI 13.278 * [taylor]: Taking taylor expansion of n in n 13.278 * [backup-simplify]: Simplify 0 into 0 13.278 * [backup-simplify]: Simplify 1 into 1 13.278 * [backup-simplify]: Simplify (/ PI 1) into PI 13.278 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.278 * [taylor]: Taking taylor expansion of 2.0 in n 13.278 * [backup-simplify]: Simplify 2.0 into 2.0 13.278 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.278 * [taylor]: Taking taylor expansion of PI in n 13.278 * [backup-simplify]: Simplify PI into PI 13.278 * [taylor]: Taking taylor expansion of n in n 13.278 * [backup-simplify]: Simplify 0 into 0 13.279 * [backup-simplify]: Simplify 1 into 1 13.279 * [backup-simplify]: Simplify (/ PI 1) into PI 13.279 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.279 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.280 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.280 * [backup-simplify]: Simplify 0 into 0 13.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.282 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.282 * [backup-simplify]: Simplify 0 into 0 13.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.283 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.283 * [backup-simplify]: Simplify 0 into 0 13.284 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.284 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.284 * [backup-simplify]: Simplify 0 into 0 13.285 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.286 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.286 * [backup-simplify]: Simplify 0 into 0 13.287 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.288 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.288 * [backup-simplify]: Simplify 0 into 0 13.288 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 13.289 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 13.289 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 13.289 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.289 * [taylor]: Taking taylor expansion of -2.0 in n 13.289 * [backup-simplify]: Simplify -2.0 into -2.0 13.289 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.289 * [taylor]: Taking taylor expansion of PI in n 13.289 * [backup-simplify]: Simplify PI into PI 13.289 * [taylor]: Taking taylor expansion of n in n 13.289 * [backup-simplify]: Simplify 0 into 0 13.289 * [backup-simplify]: Simplify 1 into 1 13.289 * [backup-simplify]: Simplify (/ PI 1) into PI 13.289 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.289 * [taylor]: Taking taylor expansion of -2.0 in n 13.289 * [backup-simplify]: Simplify -2.0 into -2.0 13.289 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.289 * [taylor]: Taking taylor expansion of PI in n 13.289 * [backup-simplify]: Simplify PI into PI 13.289 * [taylor]: Taking taylor expansion of n in n 13.289 * [backup-simplify]: Simplify 0 into 0 13.289 * [backup-simplify]: Simplify 1 into 1 13.289 * [backup-simplify]: Simplify (/ PI 1) into PI 13.290 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.290 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.291 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.291 * [backup-simplify]: Simplify 0 into 0 13.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.292 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.292 * [backup-simplify]: Simplify 0 into 0 13.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.294 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.294 * [backup-simplify]: Simplify 0 into 0 13.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.295 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 13.295 * [backup-simplify]: Simplify 0 into 0 13.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.297 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 13.297 * [backup-simplify]: Simplify 0 into 0 13.297 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.298 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 13.298 * [backup-simplify]: Simplify 0 into 0 13.299 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 13.299 * * * [progress]: simplifying candidates 13.302 * [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) 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)) (* (* 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) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 14.514 * * * [progress]: adding candidates to table 15.618 * [progress]: [Phase 3 of 3] Extracting. 15.618 * * [regime]: Finding splitpoints for: (# # # # # # # #) 15.622 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 15.622 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 15.672 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 15.740 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 15.777 * * * [regime]: Found split indices: #