33.399 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.489 * * * [progress]: [2/2] Setting up program. 0.491 * [progress]: [Phase 2 of 3] Improving. 0.491 * [simplify]: Simplifying using # : (*.f64 (/.f64 1 (sqrt.f64 k)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) 0.532 * * [simplify]: iteration 0 : 5065 enodes (cost 14 ) 0.532 * [simplify]: Simplified to: (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) 0.539 * * [progress]: iteration 1 / 4 0.539 * * * [progress]: picking best candidate 0.543 * * * * [pick]: Picked # 0.543 * * * [progress]: localizing error 0.555 * * * [progress]: generating rewritten candidates 0.555 * * * * [progress]: [ 1 / 3 ] rewriting at (2) 0.562 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1) 0.568 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1) 0.584 * * * [progress]: generating series expansions 0.584 * * * * [progress]: [ 1 / 3 ] generating series at (2) 0.584 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in (n k) around 0 0.584 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in k 0.584 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.584 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.584 * [taylor]: Taking taylor expansion of k in k 0.584 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 0.584 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 0.584 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 0.584 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 0.584 * [taylor]: Taking taylor expansion of 1/2 in k 0.584 * [taylor]: Taking taylor expansion of (- 1 k) in k 0.584 * [taylor]: Taking taylor expansion of 1 in k 0.584 * [taylor]: Taking taylor expansion of k in k 0.584 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 0.584 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 0.584 * [taylor]: Taking taylor expansion of 2 in k 0.585 * [taylor]: Taking taylor expansion of (* n PI) in k 0.585 * [taylor]: Taking taylor expansion of n in k 0.585 * [taylor]: Taking taylor expansion of PI in k 0.585 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in n 0.585 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.585 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.585 * [taylor]: Taking taylor expansion of k in n 0.585 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 0.585 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 0.585 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 0.585 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 0.585 * [taylor]: Taking taylor expansion of 1/2 in n 0.585 * [taylor]: Taking taylor expansion of (- 1 k) in n 0.585 * [taylor]: Taking taylor expansion of 1 in n 0.585 * [taylor]: Taking taylor expansion of k in n 0.585 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 0.585 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.585 * [taylor]: Taking taylor expansion of 2 in n 0.585 * [taylor]: Taking taylor expansion of (* n PI) in n 0.585 * [taylor]: Taking taylor expansion of n in n 0.585 * [taylor]: Taking taylor expansion of PI in n 0.586 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))) in n 0.586 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.586 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.586 * [taylor]: Taking taylor expansion of k in n 0.586 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 0.586 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 0.586 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 0.586 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 0.586 * [taylor]: Taking taylor expansion of 1/2 in n 0.586 * [taylor]: Taking taylor expansion of (- 1 k) in n 0.586 * [taylor]: Taking taylor expansion of 1 in n 0.586 * [taylor]: Taking taylor expansion of k in n 0.586 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 0.586 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.586 * [taylor]: Taking taylor expansion of 2 in n 0.586 * [taylor]: Taking taylor expansion of (* n PI) in n 0.586 * [taylor]: Taking taylor expansion of n in n 0.586 * [taylor]: Taking taylor expansion of PI in n 0.587 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k))))) in k 0.587 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.587 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.587 * [taylor]: Taking taylor expansion of k in k 0.587 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) in k 0.587 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k))) in k 0.587 * [taylor]: Taking taylor expansion of 1/2 in k 0.587 * [taylor]: Taking taylor expansion of (* (+ (log (* 2 PI)) (log n)) (- 1 k)) in k 0.587 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 0.587 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.587 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.587 * [taylor]: Taking taylor expansion of 2 in k 0.587 * [taylor]: Taking taylor expansion of PI in k 0.587 * [taylor]: Taking taylor expansion of (log n) in k 0.587 * [taylor]: Taking taylor expansion of n in k 0.587 * [taylor]: Taking taylor expansion of (- 1 k) in k 0.587 * [taylor]: Taking taylor expansion of 1 in k 0.587 * [taylor]: Taking taylor expansion of k in k 0.588 * [taylor]: Taking taylor expansion of 0 in k 0.590 * [taylor]: Taking taylor expansion of 0 in k 0.594 * [taylor]: Taking taylor expansion of 0 in k 0.603 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in (n k) around 0 0.603 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in k 0.603 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.603 * [taylor]: Taking taylor expansion of k in k 0.603 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 0.603 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 0.603 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 0.603 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 0.603 * [taylor]: Taking taylor expansion of 1/2 in k 0.603 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 0.603 * [taylor]: Taking taylor expansion of 1 in k 0.603 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.603 * [taylor]: Taking taylor expansion of k in k 0.603 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 0.603 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 0.603 * [taylor]: Taking taylor expansion of 2 in k 0.603 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.603 * [taylor]: Taking taylor expansion of PI in k 0.603 * [taylor]: Taking taylor expansion of n in k 0.604 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in n 0.604 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.604 * [taylor]: Taking taylor expansion of k in n 0.604 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 0.604 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 0.604 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 0.604 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 0.604 * [taylor]: Taking taylor expansion of 1/2 in n 0.604 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 0.604 * [taylor]: Taking taylor expansion of 1 in n 0.604 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.604 * [taylor]: Taking taylor expansion of k in n 0.604 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 0.604 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.604 * [taylor]: Taking taylor expansion of 2 in n 0.604 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.604 * [taylor]: Taking taylor expansion of PI in n 0.604 * [taylor]: Taking taylor expansion of n in n 0.605 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))) in n 0.605 * [taylor]: Taking taylor expansion of (sqrt k) in n 0.605 * [taylor]: Taking taylor expansion of k in n 0.605 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 0.605 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 0.605 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 0.605 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 0.605 * [taylor]: Taking taylor expansion of 1/2 in n 0.605 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 0.605 * [taylor]: Taking taylor expansion of 1 in n 0.605 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.605 * [taylor]: Taking taylor expansion of k in n 0.605 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 0.605 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.605 * [taylor]: Taking taylor expansion of 2 in n 0.605 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.605 * [taylor]: Taking taylor expansion of PI in n 0.605 * [taylor]: Taking taylor expansion of n in n 0.605 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) in k 0.605 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.605 * [taylor]: Taking taylor expansion of k in k 0.606 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 0.606 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 0.606 * [taylor]: Taking taylor expansion of 1/2 in k 0.606 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 0.606 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 0.606 * [taylor]: Taking taylor expansion of 1 in k 0.606 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.606 * [taylor]: Taking taylor expansion of k in k 0.606 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.606 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.606 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.606 * [taylor]: Taking taylor expansion of 2 in k 0.606 * [taylor]: Taking taylor expansion of PI in k 0.606 * [taylor]: Taking taylor expansion of (log n) in k 0.606 * [taylor]: Taking taylor expansion of n in k 0.607 * [taylor]: Taking taylor expansion of 0 in k 0.608 * [taylor]: Taking taylor expansion of 0 in k 0.610 * [taylor]: Taking taylor expansion of 0 in k 0.612 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0 0.612 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k 0.612 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 0.612 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 0.612 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 0.612 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 0.612 * [taylor]: Taking taylor expansion of 1/2 in k 0.612 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 0.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.612 * [taylor]: Taking taylor expansion of k in k 0.612 * [taylor]: Taking taylor expansion of 1 in k 0.612 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 0.612 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 0.612 * [taylor]: Taking taylor expansion of -2 in k 0.612 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.612 * [taylor]: Taking taylor expansion of PI in k 0.612 * [taylor]: Taking taylor expansion of n in k 0.612 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.612 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.613 * [taylor]: Taking taylor expansion of -1 in k 0.613 * [taylor]: Taking taylor expansion of k in k 0.613 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 0.613 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 0.613 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 0.613 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 0.613 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 0.613 * [taylor]: Taking taylor expansion of 1/2 in n 0.613 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 0.613 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.613 * [taylor]: Taking taylor expansion of k in n 0.613 * [taylor]: Taking taylor expansion of 1 in n 0.613 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 0.613 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.613 * [taylor]: Taking taylor expansion of -2 in n 0.613 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.613 * [taylor]: Taking taylor expansion of PI in n 0.613 * [taylor]: Taking taylor expansion of n in n 0.613 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.613 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.613 * [taylor]: Taking taylor expansion of -1 in n 0.613 * [taylor]: Taking taylor expansion of k in n 0.614 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n 0.614 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 0.614 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 0.614 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 0.614 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 0.614 * [taylor]: Taking taylor expansion of 1/2 in n 0.614 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 0.614 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.614 * [taylor]: Taking taylor expansion of k in n 0.614 * [taylor]: Taking taylor expansion of 1 in n 0.614 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 0.614 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.614 * [taylor]: Taking taylor expansion of -2 in n 0.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.614 * [taylor]: Taking taylor expansion of PI in n 0.614 * [taylor]: Taking taylor expansion of n in n 0.614 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.614 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.614 * [taylor]: Taking taylor expansion of -1 in n 0.614 * [taylor]: Taking taylor expansion of k in n 0.615 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k 0.615 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 0.615 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 0.615 * [taylor]: Taking taylor expansion of 1/2 in k 0.615 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 0.615 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 0.615 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.615 * [taylor]: Taking taylor expansion of k in k 0.615 * [taylor]: Taking taylor expansion of 1 in k 0.615 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 0.615 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 0.615 * [taylor]: Taking taylor expansion of (* -2 PI) in k 0.615 * [taylor]: Taking taylor expansion of -2 in k 0.615 * [taylor]: Taking taylor expansion of PI in k 0.615 * [taylor]: Taking taylor expansion of (log n) in k 0.615 * [taylor]: Taking taylor expansion of n in k 0.615 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.615 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.615 * [taylor]: Taking taylor expansion of -1 in k 0.616 * [taylor]: Taking taylor expansion of k in k 0.617 * [taylor]: Taking taylor expansion of 0 in k 0.618 * [taylor]: Taking taylor expansion of 0 in k 0.620 * [taylor]: Taking taylor expansion of 0 in k 0.621 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1) 0.621 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 0.621 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.621 * [taylor]: Taking taylor expansion of 2 in n 0.621 * [taylor]: Taking taylor expansion of (* n PI) in n 0.621 * [taylor]: Taking taylor expansion of n in n 0.621 * [taylor]: Taking taylor expansion of PI in n 0.621 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.621 * [taylor]: Taking taylor expansion of 2 in n 0.621 * [taylor]: Taking taylor expansion of (* n PI) in n 0.621 * [taylor]: Taking taylor expansion of n in n 0.621 * [taylor]: Taking taylor expansion of PI in n 0.622 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 0.622 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.622 * [taylor]: Taking taylor expansion of 2 in n 0.622 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.622 * [taylor]: Taking taylor expansion of PI in n 0.622 * [taylor]: Taking taylor expansion of n in n 0.622 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.622 * [taylor]: Taking taylor expansion of 2 in n 0.622 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.622 * [taylor]: Taking taylor expansion of PI in n 0.623 * [taylor]: Taking taylor expansion of n in n 0.623 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 0.624 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.624 * [taylor]: Taking taylor expansion of -2 in n 0.624 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.624 * [taylor]: Taking taylor expansion of PI in n 0.624 * [taylor]: Taking taylor expansion of n in n 0.624 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.624 * [taylor]: Taking taylor expansion of -2 in n 0.624 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.624 * [taylor]: Taking taylor expansion of PI in n 0.624 * [taylor]: Taking taylor expansion of n in n 0.625 * * * * [progress]: [ 3 / 3 ] generating series at (2 1) 0.625 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0 0.625 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k 0.625 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k 0.625 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k 0.625 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k 0.625 * [taylor]: Taking taylor expansion of 1/2 in k 0.625 * [taylor]: Taking taylor expansion of (- 1 k) in k 0.625 * [taylor]: Taking taylor expansion of 1 in k 0.625 * [taylor]: Taking taylor expansion of k in k 0.625 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 0.625 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 0.625 * [taylor]: Taking taylor expansion of 2 in k 0.625 * [taylor]: Taking taylor expansion of (* n PI) in k 0.625 * [taylor]: Taking taylor expansion of n in k 0.625 * [taylor]: Taking taylor expansion of PI in k 0.625 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 0.625 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 0.625 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 0.625 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 0.625 * [taylor]: Taking taylor expansion of 1/2 in n 0.625 * [taylor]: Taking taylor expansion of (- 1 k) in n 0.625 * [taylor]: Taking taylor expansion of 1 in n 0.625 * [taylor]: Taking taylor expansion of k in n 0.625 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 0.625 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.625 * [taylor]: Taking taylor expansion of 2 in n 0.625 * [taylor]: Taking taylor expansion of (* n PI) in n 0.625 * [taylor]: Taking taylor expansion of n in n 0.625 * [taylor]: Taking taylor expansion of PI in n 0.626 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n 0.626 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n 0.626 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n 0.626 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n 0.626 * [taylor]: Taking taylor expansion of 1/2 in n 0.626 * [taylor]: Taking taylor expansion of (- 1 k) in n 0.626 * [taylor]: Taking taylor expansion of 1 in n 0.626 * [taylor]: Taking taylor expansion of k in n 0.626 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 0.626 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.626 * [taylor]: Taking taylor expansion of 2 in n 0.626 * [taylor]: Taking taylor expansion of (* n PI) in n 0.626 * [taylor]: Taking taylor expansion of n in n 0.626 * [taylor]: Taking taylor expansion of PI in n 0.626 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k)))) in k 0.626 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (log (* 2 PI)) (log n)) (- 1 k))) in k 0.627 * [taylor]: Taking taylor expansion of 1/2 in k 0.627 * [taylor]: Taking taylor expansion of (* (+ (log (* 2 PI)) (log n)) (- 1 k)) in k 0.627 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 0.627 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.627 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.627 * [taylor]: Taking taylor expansion of 2 in k 0.627 * [taylor]: Taking taylor expansion of PI in k 0.627 * [taylor]: Taking taylor expansion of (log n) in k 0.627 * [taylor]: Taking taylor expansion of n in k 0.627 * [taylor]: Taking taylor expansion of (- 1 k) in k 0.627 * [taylor]: Taking taylor expansion of 1 in k 0.627 * [taylor]: Taking taylor expansion of k in k 0.628 * [taylor]: Taking taylor expansion of 0 in k 0.632 * [taylor]: Taking taylor expansion of 0 in k 0.635 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0 0.635 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k 0.635 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k 0.635 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k 0.635 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k 0.635 * [taylor]: Taking taylor expansion of 1/2 in k 0.635 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 0.635 * [taylor]: Taking taylor expansion of 1 in k 0.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.635 * [taylor]: Taking taylor expansion of k in k 0.635 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 0.635 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 0.635 * [taylor]: Taking taylor expansion of 2 in k 0.635 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.635 * [taylor]: Taking taylor expansion of PI in k 0.635 * [taylor]: Taking taylor expansion of n in k 0.635 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 0.635 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 0.635 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 0.635 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 0.636 * [taylor]: Taking taylor expansion of 1/2 in n 0.636 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 0.636 * [taylor]: Taking taylor expansion of 1 in n 0.636 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.636 * [taylor]: Taking taylor expansion of k in n 0.636 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 0.636 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.636 * [taylor]: Taking taylor expansion of 2 in n 0.636 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.636 * [taylor]: Taking taylor expansion of PI in n 0.636 * [taylor]: Taking taylor expansion of n in n 0.636 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n 0.636 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n 0.636 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n 0.636 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n 0.636 * [taylor]: Taking taylor expansion of 1/2 in n 0.636 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n 0.636 * [taylor]: Taking taylor expansion of 1 in n 0.636 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.636 * [taylor]: Taking taylor expansion of k in n 0.636 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 0.636 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.636 * [taylor]: Taking taylor expansion of 2 in n 0.636 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.636 * [taylor]: Taking taylor expansion of PI in n 0.636 * [taylor]: Taking taylor expansion of n in n 0.637 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k 0.637 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k 0.637 * [taylor]: Taking taylor expansion of 1/2 in k 0.637 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k 0.637 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k 0.637 * [taylor]: Taking taylor expansion of 1 in k 0.637 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.637 * [taylor]: Taking taylor expansion of k in k 0.637 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.637 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.637 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.637 * [taylor]: Taking taylor expansion of 2 in k 0.637 * [taylor]: Taking taylor expansion of PI in k 0.637 * [taylor]: Taking taylor expansion of (log n) in k 0.637 * [taylor]: Taking taylor expansion of n in k 0.638 * [taylor]: Taking taylor expansion of 0 in k 0.639 * [taylor]: Taking taylor expansion of 0 in k 0.640 * [taylor]: Taking taylor expansion of 0 in k 0.641 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0 0.641 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k 0.641 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k 0.641 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k 0.641 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k 0.641 * [taylor]: Taking taylor expansion of 1/2 in k 0.641 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 0.641 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.641 * [taylor]: Taking taylor expansion of k in k 0.641 * [taylor]: Taking taylor expansion of 1 in k 0.641 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 0.641 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 0.641 * [taylor]: Taking taylor expansion of -2 in k 0.641 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.641 * [taylor]: Taking taylor expansion of PI in k 0.641 * [taylor]: Taking taylor expansion of n in k 0.641 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 0.641 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 0.641 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 0.641 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 0.641 * [taylor]: Taking taylor expansion of 1/2 in n 0.641 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 0.641 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.641 * [taylor]: Taking taylor expansion of k in n 0.641 * [taylor]: Taking taylor expansion of 1 in n 0.641 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 0.641 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.641 * [taylor]: Taking taylor expansion of -2 in n 0.641 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.641 * [taylor]: Taking taylor expansion of PI in n 0.641 * [taylor]: Taking taylor expansion of n in n 0.642 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n 0.642 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n 0.642 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n 0.642 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n 0.642 * [taylor]: Taking taylor expansion of 1/2 in n 0.642 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n 0.642 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.642 * [taylor]: Taking taylor expansion of k in n 0.642 * [taylor]: Taking taylor expansion of 1 in n 0.642 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 0.642 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.642 * [taylor]: Taking taylor expansion of -2 in n 0.642 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.642 * [taylor]: Taking taylor expansion of PI in n 0.642 * [taylor]: Taking taylor expansion of n in n 0.643 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k 0.643 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k 0.643 * [taylor]: Taking taylor expansion of 1/2 in k 0.643 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k 0.643 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k 0.643 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.643 * [taylor]: Taking taylor expansion of k in k 0.643 * [taylor]: Taking taylor expansion of 1 in k 0.643 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 0.643 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 0.643 * [taylor]: Taking taylor expansion of (* -2 PI) in k 0.643 * [taylor]: Taking taylor expansion of -2 in k 0.643 * [taylor]: Taking taylor expansion of PI in k 0.643 * [taylor]: Taking taylor expansion of (log n) in k 0.643 * [taylor]: Taking taylor expansion of n in k 0.644 * [taylor]: Taking taylor expansion of 0 in k 0.645 * [taylor]: Taking taylor expansion of 0 in k 0.646 * [taylor]: Taking taylor expansion of 0 in k 0.646 * * * [progress]: simplifying candidates 0.648 * [simplify]: Simplifying using # : (-.f64 (*.f64 (+.f64 (+.f64 (log.f64 2) (log.f64 PI.f64)) (log.f64 n)) (/.f64 (-.f64 1 k) 2)) (log.f64 (sqrt.f64 k))) (-.f64 (*.f64 (+.f64 (log.f64 (*.f64 2 PI.f64)) (log.f64 n)) (/.f64 (-.f64 1 k) 2)) (log.f64 (sqrt.f64 k))) (-.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (log.f64 (sqrt.f64 k))) (-.f64 (*.f64 (log.f64 (*.f64 (*.f64 2 PI.f64) n)) (/.f64 (-.f64 1 k) 2)) (log.f64 (sqrt.f64 k))) (-.f64 (log.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (log.f64 (sqrt.f64 k))) (log.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (exp.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (/.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k))) (*.f64 (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (sqrt.f64 (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k))) (neg.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (neg.f64 (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 1)) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) 1) (/.f64 (pow.f64 n (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (cbrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 1)) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) 1) (/.f64 (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (cbrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 1)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) 1) (/.f64 (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (cbrt.f64 k))) (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 1 (sqrt.f64 1)) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 1 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 1)) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) 1) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (/.f64 (-.f64 1 k) 2) 2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 1)) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)) 1) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 (*.f64 2 PI.f64) n) (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (pow.f64 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(/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 k)) (/.f64 1 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (sqrt.f64 k))) (/.f64 1 (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (cbrt.f64 k))) (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) 1 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) 1 (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (sqrt.f64 k)) (/.f64 1 (sqrt.f64 k)) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (fabs.f64 (cbrt.f64 k))) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (sqrt.f64 (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) (/.f64 (sqrt.f64 k) (pow.f64 n (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 k) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (/.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4)))) (*.f64 (sqrt.f64 k) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (exp.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 8 (pow.f64 (*.f64 PI.f64 n) 3)) (*.f64 8 (pow.f64 (*.f64 PI.f64 n) 3)) (*.f64 (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 8 (pow.f64 (*.f64 PI.f64 n) 3)) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 (*.f64 2 PI.f64) (*.f64 (cbrt.f64 n) (cbrt.f64 n))) (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (*.f64 2 PI.f64) (*.f64 PI.f64 n) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 (-.f64 1 k) 2)) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 (-.f64 1 k) 2)) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 (-.f64 1 k) 2)) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 (-.f64 1 k) 2)) (/.f64 (-.f64 1 k) 2) (/.f64 (-.f64 1 k) 2) (/.f64 (-.f64 1 k) 2) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 (cbrt.f64 (/.f64 (-.f64 1 k) 2)) (cbrt.f64 (/.f64 (-.f64 1 k) 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (sqrt.f64 (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 k)) (cbrt.f64 (-.f64 1 k))) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (*.f64 (cbrt.f64 (-.f64 1 k)) (cbrt.f64 (-.f64 1 k))) (sqrt.f64 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 (cbrt.f64 (-.f64 1 k)) (cbrt.f64 (-.f64 1 k)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (sqrt.f64 (-.f64 1 k)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (sqrt.f64 (-.f64 1 k)) (sqrt.f64 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (sqrt.f64 (-.f64 1 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 1 (sqrt.f64 2))) (*.f64 n (*.f64 2 PI.f64)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (+.f64 1 (sqrt.f64 k)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (+.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (+.f64 1 (sqrt.f64 k)) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (+.f64 1 (sqrt.f64 k)) (sqrt.f64 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (+.f64 1 (sqrt.f64 k))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 1 (*.f64 (cbrt.f64 2) (cbrt.f64 2)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 1 (sqrt.f64 2))) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1 k)) (pow.f64 (*.f64 2 PI.f64) (/.f64 (-.f64 1 k) 2)) (pow.f64 n (/.f64 (-.f64 1 k) 2)) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 (-.f64 1 k) 2)) (exp.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2)) 3) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 (-.f64 1 k) 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (-.f64 1/4 (/.f64 k 4))) (-.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 NAN.f64 (pow.f64 (log.f64 n) 2))))) (+.f64 (*.f64 1/4 (*.f64 (*.f64 k k) (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (log.f64 n) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) NAN.f64))))) (+.f64 (*.f64 k (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 NAN.f64 3))) (+.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) NAN.f64) (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 NAN.f64 (pow.f64 (log.f64 (*.f64 2 PI.f64)) 2))))) (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 NAN.f64 5)))))))) (+.f64 (*.f64 1/2 (*.f64 (*.f64 k k) (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 NAN.f64 3))))) (*.f64 1/2 (+.f64 (*.f64 k (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) NAN.f64))) (+.f64 (*.f64 k (*.f64 (log.f64 n) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) NAN.f64))) (*.f64 (*.f64 k k) (*.f64 (log.f64 n) (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 NAN.f64 3))))))))) (+.f64 (/.f64 (*.f64 (pow.f64 NAN.f64 3) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (-.f64 1 k))) (*.f64 k k)) (+.f64 (/.f64 (*.f64 (pow.f64 NAN.f64 5) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (-.f64 1 k))) (pow.f64 k 3)) (/.f64 (*.f64 NAN.f64 (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (-.f64 1 k))) k))) (+.f64 (/.f64 (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))) (/.f64 k NAN.f64)) (/.f64 (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))) NAN.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (+.f64 (+.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 1/8 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 k k)) (+.f64 (pow.f64 (log.f64 (*.f64 2 PI.f64)) 2) (pow.f64 (log.f64 n) 2))))) (+.f64 (*.f64 1/4 (*.f64 (*.f64 k k) (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (log.f64 n) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))))) (*.f64 (*.f64 (*.f64 k (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (log.f64 (*.f64 n (*.f64 2 PI.f64)))) -1/2))) (pow.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (-.f64 1 k)) (sqrt.f64 (exp.f64 (*.f64 (-.f64 1 k) (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))) 0.685 * * * [progress]: adding candidates to table 0.788 * * [progress]: iteration 2 / 4 0.788 * * * [progress]: picking best candidate 0.805 * * * * [pick]: Picked # 0.805 * * * [progress]: localizing error 0.816 * * * [progress]: generating rewritten candidates 0.816 * * * * [progress]: [ 1 / 4 ] rewriting at (2) 0.833 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 0.838 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1) 0.844 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 0.862 * * * [progress]: generating series expansions 0.862 * * * * [progress]: [ 1 / 4 ] generating series at (2) 0.863 * [approximate]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in (n k) around 0 0.863 * [taylor]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in k 0.863 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in k 0.863 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.863 * [taylor]: Taking taylor expansion of 2 in k 0.863 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 0.863 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 0.863 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 0.863 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 0.863 * [taylor]: Taking taylor expansion of 1/2 in k 0.863 * [taylor]: Taking taylor expansion of k in k 0.863 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 0.863 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 0.863 * [taylor]: Taking taylor expansion of 2 in k 0.863 * [taylor]: Taking taylor expansion of (* n PI) in k 0.863 * [taylor]: Taking taylor expansion of n in k 0.863 * [taylor]: Taking taylor expansion of PI in k 0.864 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 0.864 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in k 0.864 * [taylor]: Taking taylor expansion of (* n PI) in k 0.864 * [taylor]: Taking taylor expansion of n in k 0.864 * [taylor]: Taking taylor expansion of PI in k 0.864 * [taylor]: Taking taylor expansion of k in k 0.864 * [taylor]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 0.864 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 0.864 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.864 * [taylor]: Taking taylor expansion of 2 in n 0.864 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 0.864 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 0.864 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 0.864 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 0.864 * [taylor]: Taking taylor expansion of 1/2 in n 0.864 * [taylor]: Taking taylor expansion of k in n 0.864 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 0.864 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.864 * [taylor]: Taking taylor expansion of 2 in n 0.864 * [taylor]: Taking taylor expansion of (* n PI) in n 0.864 * [taylor]: Taking taylor expansion of n in n 0.864 * [taylor]: Taking taylor expansion of PI in n 0.865 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 0.865 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in n 0.865 * [taylor]: Taking taylor expansion of (* n PI) in n 0.865 * [taylor]: Taking taylor expansion of n in n 0.865 * [taylor]: Taking taylor expansion of PI in n 0.865 * [taylor]: Taking taylor expansion of k in n 0.865 * [taylor]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 0.865 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 0.865 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.865 * [taylor]: Taking taylor expansion of 2 in n 0.865 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 0.865 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 0.865 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 0.865 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 0.865 * [taylor]: Taking taylor expansion of 1/2 in n 0.865 * [taylor]: Taking taylor expansion of k in n 0.865 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 0.865 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.865 * [taylor]: Taking taylor expansion of 2 in n 0.865 * [taylor]: Taking taylor expansion of (* n PI) in n 0.865 * [taylor]: Taking taylor expansion of n in n 0.865 * [taylor]: Taking taylor expansion of PI in n 0.865 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 0.865 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in n 0.865 * [taylor]: Taking taylor expansion of (* n PI) in n 0.866 * [taylor]: Taking taylor expansion of n in n 0.866 * [taylor]: Taking taylor expansion of PI in n 0.866 * [taylor]: Taking taylor expansion of k in n 0.866 * [taylor]: Taking taylor expansion of 0 in k 0.867 * [taylor]: Taking taylor expansion of (/ (* (sqrt 2) (* NAN PI)) (* k (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k 0.867 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* NAN PI)) in k 0.867 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.867 * [taylor]: Taking taylor expansion of 2 in k 0.867 * [taylor]: Taking taylor expansion of (* NAN PI) in k 0.867 * [taylor]: Taking taylor expansion of NAN in k 0.867 * [taylor]: Taking taylor expansion of PI in k 0.867 * [taylor]: Taking taylor expansion of (* k (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k 0.867 * [taylor]: Taking taylor expansion of k in k 0.867 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k 0.867 * [taylor]: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k 0.867 * [taylor]: Taking taylor expansion of 1/2 in k 0.867 * [taylor]: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k 0.867 * [taylor]: Taking taylor expansion of k in k 0.867 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 0.867 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.867 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.867 * [taylor]: Taking taylor expansion of 2 in k 0.867 * [taylor]: Taking taylor expansion of PI in k 0.867 * [taylor]: Taking taylor expansion of (log n) in k 0.867 * [taylor]: Taking taylor expansion of n in k 0.870 * [taylor]: Taking taylor expansion of (/ (* (sqrt 2) (* (pow NAN 3) (pow PI 2))) (* (pow k 2) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k 0.870 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 3) (pow PI 2))) in k 0.870 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.870 * [taylor]: Taking taylor expansion of 2 in k 0.870 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (pow PI 2)) in k 0.870 * [taylor]: Taking taylor expansion of (pow NAN 3) in k 0.870 * [taylor]: Taking taylor expansion of NAN in k 0.870 * [taylor]: Taking taylor expansion of (pow PI 2) in k 0.870 * [taylor]: Taking taylor expansion of PI in k 0.870 * [taylor]: Taking taylor expansion of (* (pow k 2) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k 0.870 * [taylor]: Taking taylor expansion of (pow k 2) in k 0.870 * [taylor]: Taking taylor expansion of k in k 0.870 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k 0.870 * [taylor]: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k 0.870 * [taylor]: Taking taylor expansion of 1/2 in k 0.870 * [taylor]: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k 0.870 * [taylor]: Taking taylor expansion of k in k 0.870 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 0.870 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.870 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.870 * [taylor]: Taking taylor expansion of 2 in k 0.870 * [taylor]: Taking taylor expansion of PI in k 0.870 * [taylor]: Taking taylor expansion of (log n) in k 0.870 * [taylor]: Taking taylor expansion of n in k 0.881 * [approximate]: Taking taylor expansion of (* (sqrt (/ (* PI k) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in (n k) around 0 0.881 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* PI k) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in k 0.881 * [taylor]: Taking taylor expansion of (sqrt (/ (* PI k) n)) in k 0.881 * [taylor]: Taking taylor expansion of (/ (* PI k) n) in k 0.881 * [taylor]: Taking taylor expansion of (* PI k) in k 0.881 * [taylor]: Taking taylor expansion of PI in k 0.881 * [taylor]: Taking taylor expansion of k in k 0.881 * [taylor]: Taking taylor expansion of n in k 0.881 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 0.881 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.881 * [taylor]: Taking taylor expansion of 2 in k 0.881 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 0.881 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 0.881 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 0.881 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 0.881 * [taylor]: Taking taylor expansion of 1/2 in k 0.881 * [taylor]: Taking taylor expansion of k in k 0.881 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 0.881 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 0.881 * [taylor]: Taking taylor expansion of 2 in k 0.881 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.882 * [taylor]: Taking taylor expansion of PI in k 0.882 * [taylor]: Taking taylor expansion of n in k 0.882 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* PI k) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 0.882 * [taylor]: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 0.882 * [taylor]: Taking taylor expansion of (/ (* PI k) n) in n 0.882 * [taylor]: Taking taylor expansion of (* PI k) in n 0.882 * [taylor]: Taking taylor expansion of PI in n 0.882 * [taylor]: Taking taylor expansion of k in n 0.882 * [taylor]: Taking taylor expansion of n in n 0.882 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 0.882 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.882 * [taylor]: Taking taylor expansion of 2 in n 0.882 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 0.882 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 0.882 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 0.882 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 0.882 * [taylor]: Taking taylor expansion of 1/2 in n 0.882 * [taylor]: Taking taylor expansion of k in n 0.882 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 0.882 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.882 * [taylor]: Taking taylor expansion of 2 in n 0.882 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.882 * [taylor]: Taking taylor expansion of PI in n 0.882 * [taylor]: Taking taylor expansion of n in n 0.883 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* PI k) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 0.883 * [taylor]: Taking taylor expansion of (sqrt (/ (* PI k) n)) in n 0.883 * [taylor]: Taking taylor expansion of (/ (* PI k) n) in n 0.883 * [taylor]: Taking taylor expansion of (* PI k) in n 0.883 * [taylor]: Taking taylor expansion of PI in n 0.883 * [taylor]: Taking taylor expansion of k in n 0.883 * [taylor]: Taking taylor expansion of n in n 0.883 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 0.883 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.883 * [taylor]: Taking taylor expansion of 2 in n 0.883 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 0.883 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 0.883 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 0.883 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 0.883 * [taylor]: Taking taylor expansion of 1/2 in n 0.883 * [taylor]: Taking taylor expansion of k in n 0.883 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 0.883 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.883 * [taylor]: Taking taylor expansion of 2 in n 0.883 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.883 * [taylor]: Taking taylor expansion of PI in n 0.883 * [taylor]: Taking taylor expansion of n in n 0.884 * [taylor]: Taking taylor expansion of 0 in k 0.885 * [taylor]: Taking taylor expansion of (/ (* k (* (sqrt 2) (* NAN PI))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 0.885 * [taylor]: Taking taylor expansion of (* k (* (sqrt 2) (* NAN PI))) in k 0.885 * [taylor]: Taking taylor expansion of k in k 0.885 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* NAN PI)) in k 0.885 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.885 * [taylor]: Taking taylor expansion of 2 in k 0.885 * [taylor]: Taking taylor expansion of (* NAN PI) in k 0.885 * [taylor]: Taking taylor expansion of NAN in k 0.885 * [taylor]: Taking taylor expansion of PI in k 0.885 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 0.885 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 0.885 * [taylor]: Taking taylor expansion of 1/2 in k 0.885 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 0.885 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.885 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.885 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.885 * [taylor]: Taking taylor expansion of 2 in k 0.885 * [taylor]: Taking taylor expansion of PI in k 0.885 * [taylor]: Taking taylor expansion of (log n) in k 0.885 * [taylor]: Taking taylor expansion of n in k 0.885 * [taylor]: Taking taylor expansion of k in k 0.888 * [taylor]: Taking taylor expansion of (/ (* (pow k 2) (* (sqrt 2) (* (pow NAN 3) (pow PI 2)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 0.888 * [taylor]: Taking taylor expansion of (* (pow k 2) (* (sqrt 2) (* (pow NAN 3) (pow PI 2)))) in k 0.888 * [taylor]: Taking taylor expansion of (pow k 2) in k 0.888 * [taylor]: Taking taylor expansion of k in k 0.888 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 3) (pow PI 2))) in k 0.888 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.888 * [taylor]: Taking taylor expansion of 2 in k 0.888 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (pow PI 2)) in k 0.888 * [taylor]: Taking taylor expansion of (pow NAN 3) in k 0.888 * [taylor]: Taking taylor expansion of NAN in k 0.888 * [taylor]: Taking taylor expansion of (pow PI 2) in k 0.888 * [taylor]: Taking taylor expansion of PI in k 0.888 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 0.888 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 0.888 * [taylor]: Taking taylor expansion of 1/2 in k 0.888 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 0.888 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.888 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.888 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.888 * [taylor]: Taking taylor expansion of 2 in k 0.888 * [taylor]: Taking taylor expansion of PI in k 0.888 * [taylor]: Taking taylor expansion of (log n) in k 0.888 * [taylor]: Taking taylor expansion of n in k 0.888 * [taylor]: Taking taylor expansion of k in k 0.892 * [taylor]: Taking taylor expansion of (/ (* (pow k 3) (* (sqrt 2) (* (pow NAN 5) (pow PI 3)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 0.892 * [taylor]: Taking taylor expansion of (* (pow k 3) (* (sqrt 2) (* (pow NAN 5) (pow PI 3)))) in k 0.892 * [taylor]: Taking taylor expansion of (pow k 3) in k 0.892 * [taylor]: Taking taylor expansion of k in k 0.892 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 5) (pow PI 3))) in k 0.892 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.892 * [taylor]: Taking taylor expansion of 2 in k 0.892 * [taylor]: Taking taylor expansion of (* (pow NAN 5) (pow PI 3)) in k 0.892 * [taylor]: Taking taylor expansion of (pow NAN 5) in k 0.892 * [taylor]: Taking taylor expansion of NAN in k 0.892 * [taylor]: Taking taylor expansion of (pow PI 3) in k 0.892 * [taylor]: Taking taylor expansion of PI in k 0.892 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 0.892 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 0.892 * [taylor]: Taking taylor expansion of 1/2 in k 0.893 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 0.893 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.893 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.893 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.893 * [taylor]: Taking taylor expansion of 2 in k 0.893 * [taylor]: Taking taylor expansion of PI in k 0.893 * [taylor]: Taking taylor expansion of (log n) in k 0.893 * [taylor]: Taking taylor expansion of n in k 0.893 * [taylor]: Taking taylor expansion of k in k 0.898 * [taylor]: Taking taylor expansion of (/ (* (pow k 4) (* (sqrt 2) (* (pow NAN 7) (pow PI 4)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 0.898 * [taylor]: Taking taylor expansion of (* (pow k 4) (* (sqrt 2) (* (pow NAN 7) (pow PI 4)))) in k 0.898 * [taylor]: Taking taylor expansion of (pow k 4) in k 0.898 * [taylor]: Taking taylor expansion of k in k 0.898 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 7) (pow PI 4))) in k 0.898 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.898 * [taylor]: Taking taylor expansion of 2 in k 0.898 * [taylor]: Taking taylor expansion of (* (pow NAN 7) (pow PI 4)) in k 0.898 * [taylor]: Taking taylor expansion of (pow NAN 7) in k 0.898 * [taylor]: Taking taylor expansion of NAN in k 0.898 * [taylor]: Taking taylor expansion of (pow PI 4) in k 0.898 * [taylor]: Taking taylor expansion of PI in k 0.898 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 0.899 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 0.899 * [taylor]: Taking taylor expansion of 1/2 in k 0.899 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 0.899 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.899 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.899 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.899 * [taylor]: Taking taylor expansion of 2 in k 0.899 * [taylor]: Taking taylor expansion of PI in k 0.899 * [taylor]: Taking taylor expansion of (log n) in k 0.899 * [taylor]: Taking taylor expansion of n in k 0.899 * [taylor]: Taking taylor expansion of k in k 0.906 * [taylor]: Taking taylor expansion of (/ (* (pow k 5) (* (sqrt 2) (* (pow NAN 9) (pow PI 5)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 0.906 * [taylor]: Taking taylor expansion of (* (pow k 5) (* (sqrt 2) (* (pow NAN 9) (pow PI 5)))) in k 0.906 * [taylor]: Taking taylor expansion of (pow k 5) in k 0.906 * [taylor]: Taking taylor expansion of k in k 0.906 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 9) (pow PI 5))) in k 0.906 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.906 * [taylor]: Taking taylor expansion of 2 in k 0.906 * [taylor]: Taking taylor expansion of (* (pow NAN 9) (pow PI 5)) in k 0.906 * [taylor]: Taking taylor expansion of (pow NAN 9) in k 0.906 * [taylor]: Taking taylor expansion of NAN in k 0.906 * [taylor]: Taking taylor expansion of (pow PI 5) in k 0.906 * [taylor]: Taking taylor expansion of PI in k 0.906 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 0.906 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 0.906 * [taylor]: Taking taylor expansion of 1/2 in k 0.906 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 0.906 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.906 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.906 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.906 * [taylor]: Taking taylor expansion of 2 in k 0.906 * [taylor]: Taking taylor expansion of PI in k 0.906 * [taylor]: Taking taylor expansion of (log n) in k 0.906 * [taylor]: Taking taylor expansion of n in k 0.907 * [taylor]: Taking taylor expansion of k in k 0.916 * [taylor]: Taking taylor expansion of (/ (* (pow k 6) (* (sqrt 2) (* (pow NAN 11) (pow PI 6)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 0.916 * [taylor]: Taking taylor expansion of (* (pow k 6) (* (sqrt 2) (* (pow NAN 11) (pow PI 6)))) in k 0.916 * [taylor]: Taking taylor expansion of (pow k 6) in k 0.916 * [taylor]: Taking taylor expansion of k in k 0.916 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 11) (pow PI 6))) in k 0.916 * [taylor]: Taking taylor expansion of (sqrt 2) in k 0.916 * [taylor]: Taking taylor expansion of 2 in k 0.916 * [taylor]: Taking taylor expansion of (* (pow NAN 11) (pow PI 6)) in k 0.916 * [taylor]: Taking taylor expansion of (pow NAN 11) in k 0.916 * [taylor]: Taking taylor expansion of NAN in k 0.916 * [taylor]: Taking taylor expansion of (pow PI 6) in k 0.916 * [taylor]: Taking taylor expansion of PI in k 0.916 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 0.916 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 0.916 * [taylor]: Taking taylor expansion of 1/2 in k 0.916 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 0.916 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 0.916 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 0.916 * [taylor]: Taking taylor expansion of (* 2 PI) in k 0.916 * [taylor]: Taking taylor expansion of 2 in k 0.916 * [taylor]: Taking taylor expansion of PI in k 0.916 * [taylor]: Taking taylor expansion of (log n) in k 0.916 * [taylor]: Taking taylor expansion of n in k 0.916 * [taylor]: Taking taylor expansion of k in k 0.920 * [approximate]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in (n k) around 0 0.920 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in k 0.920 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 0.920 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 0.920 * [taylor]: Taking taylor expansion of -2 in k 0.920 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.920 * [taylor]: Taking taylor expansion of PI in k 0.920 * [taylor]: Taking taylor expansion of n in k 0.920 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 0.920 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.920 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.920 * [taylor]: Taking taylor expansion of -1 in k 0.920 * [taylor]: Taking taylor expansion of k in k 0.920 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 0.920 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 0.920 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 0.920 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 0.920 * [taylor]: Taking taylor expansion of -1/2 in k 0.920 * [taylor]: Taking taylor expansion of k in k 0.921 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 0.921 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 0.921 * [taylor]: Taking taylor expansion of -2 in k 0.921 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.921 * [taylor]: Taking taylor expansion of PI in k 0.921 * [taylor]: Taking taylor expansion of n in k 0.921 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 0.921 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 0.921 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.921 * [taylor]: Taking taylor expansion of -2 in n 0.921 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.921 * [taylor]: Taking taylor expansion of PI in n 0.921 * [taylor]: Taking taylor expansion of n in n 0.921 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 0.921 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.921 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.921 * [taylor]: Taking taylor expansion of -1 in n 0.921 * [taylor]: Taking taylor expansion of k in n 0.922 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 0.922 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 0.922 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 0.922 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 0.922 * [taylor]: Taking taylor expansion of -1/2 in n 0.922 * [taylor]: Taking taylor expansion of k in n 0.922 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 0.922 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.922 * [taylor]: Taking taylor expansion of -2 in n 0.922 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.922 * [taylor]: Taking taylor expansion of PI in n 0.922 * [taylor]: Taking taylor expansion of n in n 0.922 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 0.922 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 0.922 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.922 * [taylor]: Taking taylor expansion of -2 in n 0.922 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.922 * [taylor]: Taking taylor expansion of PI in n 0.922 * [taylor]: Taking taylor expansion of n in n 0.923 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 0.923 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 0.923 * [taylor]: Taking taylor expansion of (/ -1 k) in n 0.923 * [taylor]: Taking taylor expansion of -1 in n 0.923 * [taylor]: Taking taylor expansion of k in n 0.923 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 0.923 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 0.923 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 0.923 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 0.923 * [taylor]: Taking taylor expansion of -1/2 in n 0.923 * [taylor]: Taking taylor expansion of k in n 0.923 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 0.923 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.923 * [taylor]: Taking taylor expansion of -2 in n 0.923 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.923 * [taylor]: Taking taylor expansion of PI in n 0.923 * [taylor]: Taking taylor expansion of n in n 0.924 * [taylor]: Taking taylor expansion of (/ (* NAN PI) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 0.924 * [taylor]: Taking taylor expansion of (* NAN PI) in k 0.924 * [taylor]: Taking taylor expansion of NAN in k 0.924 * [taylor]: Taking taylor expansion of PI in k 0.924 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 0.924 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.924 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.924 * [taylor]: Taking taylor expansion of -1 in k 0.924 * [taylor]: Taking taylor expansion of k in k 0.924 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 0.924 * [taylor]: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 0.924 * [taylor]: Taking taylor expansion of -1/2 in k 0.924 * [taylor]: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 0.924 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 0.924 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 0.924 * [taylor]: Taking taylor expansion of (* -2 PI) in k 0.924 * [taylor]: Taking taylor expansion of -2 in k 0.924 * [taylor]: Taking taylor expansion of PI in k 0.924 * [taylor]: Taking taylor expansion of (log n) in k 0.924 * [taylor]: Taking taylor expansion of n in k 0.924 * [taylor]: Taking taylor expansion of k in k 0.926 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 3) (pow PI 2)) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 0.926 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (pow PI 2)) in k 0.926 * [taylor]: Taking taylor expansion of (pow NAN 3) in k 0.926 * [taylor]: Taking taylor expansion of NAN in k 0.926 * [taylor]: Taking taylor expansion of (pow PI 2) in k 0.926 * [taylor]: Taking taylor expansion of PI in k 0.926 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 0.927 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.927 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.927 * [taylor]: Taking taylor expansion of -1 in k 0.927 * [taylor]: Taking taylor expansion of k in k 0.927 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 0.927 * [taylor]: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 0.927 * [taylor]: Taking taylor expansion of -1/2 in k 0.927 * [taylor]: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 0.927 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 0.927 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 0.927 * [taylor]: Taking taylor expansion of (* -2 PI) in k 0.927 * [taylor]: Taking taylor expansion of -2 in k 0.927 * [taylor]: Taking taylor expansion of PI in k 0.927 * [taylor]: Taking taylor expansion of (log n) in k 0.927 * [taylor]: Taking taylor expansion of n in k 0.927 * [taylor]: Taking taylor expansion of k in k 0.930 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 0.930 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 0.930 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.930 * [taylor]: Taking taylor expansion of 2 in n 0.930 * [taylor]: Taking taylor expansion of (* n PI) in n 0.930 * [taylor]: Taking taylor expansion of n in n 0.930 * [taylor]: Taking taylor expansion of PI in n 0.930 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.931 * [taylor]: Taking taylor expansion of 2 in n 0.931 * [taylor]: Taking taylor expansion of (* n PI) in n 0.931 * [taylor]: Taking taylor expansion of n in n 0.931 * [taylor]: Taking taylor expansion of PI in n 0.932 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 0.932 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.932 * [taylor]: Taking taylor expansion of 2 in n 0.932 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.932 * [taylor]: Taking taylor expansion of PI in n 0.932 * [taylor]: Taking taylor expansion of n in n 0.932 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.932 * [taylor]: Taking taylor expansion of 2 in n 0.932 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.932 * [taylor]: Taking taylor expansion of PI in n 0.932 * [taylor]: Taking taylor expansion of n in n 0.933 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 0.933 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.933 * [taylor]: Taking taylor expansion of -2 in n 0.933 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.933 * [taylor]: Taking taylor expansion of PI in n 0.933 * [taylor]: Taking taylor expansion of n in n 0.933 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.933 * [taylor]: Taking taylor expansion of -2 in n 0.933 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.933 * [taylor]: Taking taylor expansion of PI in n 0.933 * [taylor]: Taking taylor expansion of n in n 0.934 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1) 0.934 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 0.934 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.934 * [taylor]: Taking taylor expansion of 2 in n 0.934 * [taylor]: Taking taylor expansion of (* n PI) in n 0.934 * [taylor]: Taking taylor expansion of n in n 0.934 * [taylor]: Taking taylor expansion of PI in n 0.934 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 0.934 * [taylor]: Taking taylor expansion of 2 in n 0.934 * [taylor]: Taking taylor expansion of (* n PI) in n 0.934 * [taylor]: Taking taylor expansion of n in n 0.934 * [taylor]: Taking taylor expansion of PI in n 0.935 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 0.935 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.936 * [taylor]: Taking taylor expansion of 2 in n 0.936 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.936 * [taylor]: Taking taylor expansion of PI in n 0.936 * [taylor]: Taking taylor expansion of n in n 0.936 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 0.936 * [taylor]: Taking taylor expansion of 2 in n 0.936 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.936 * [taylor]: Taking taylor expansion of PI in n 0.936 * [taylor]: Taking taylor expansion of n in n 0.937 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 0.937 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.937 * [taylor]: Taking taylor expansion of -2 in n 0.937 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.937 * [taylor]: Taking taylor expansion of PI in n 0.937 * [taylor]: Taking taylor expansion of n in n 0.937 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.937 * [taylor]: Taking taylor expansion of -2 in n 0.937 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.937 * [taylor]: Taking taylor expansion of PI in n 0.937 * [taylor]: Taking taylor expansion of n in n 0.938 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 0.938 * [approximate]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in (n) around 0 0.938 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 0.938 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.938 * [taylor]: Taking taylor expansion of 2 in n 0.938 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 0.938 * [taylor]: Taking taylor expansion of (* n PI) in n 0.938 * [taylor]: Taking taylor expansion of n in n 0.938 * [taylor]: Taking taylor expansion of PI in n 0.938 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 0.938 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.938 * [taylor]: Taking taylor expansion of 2 in n 0.938 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 0.938 * [taylor]: Taking taylor expansion of (* n PI) in n 0.938 * [taylor]: Taking taylor expansion of n in n 0.938 * [taylor]: Taking taylor expansion of PI in n 0.941 * [approximate]: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in (n) around 0 0.941 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 0.941 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.941 * [taylor]: Taking taylor expansion of 2 in n 0.941 * [taylor]: Taking taylor expansion of (sqrt (/ PI n)) in n 0.941 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.941 * [taylor]: Taking taylor expansion of PI in n 0.941 * [taylor]: Taking taylor expansion of n in n 0.941 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (/ PI n))) in n 0.941 * [taylor]: Taking taylor expansion of (sqrt 2) in n 0.941 * [taylor]: Taking taylor expansion of 2 in n 0.941 * [taylor]: Taking taylor expansion of (sqrt (/ PI n)) in n 0.941 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.941 * [taylor]: Taking taylor expansion of PI in n 0.941 * [taylor]: Taking taylor expansion of n in n 0.944 * [approximate]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in (n) around 0 0.944 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 0.944 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.944 * [taylor]: Taking taylor expansion of -2 in n 0.944 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.944 * [taylor]: Taking taylor expansion of PI in n 0.944 * [taylor]: Taking taylor expansion of n in n 0.944 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 0.944 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 0.944 * [taylor]: Taking taylor expansion of -2 in n 0.944 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.944 * [taylor]: Taking taylor expansion of PI in n 0.944 * [taylor]: Taking taylor expansion of n in n 0.945 * * * [progress]: simplifying candidates 0.950 * [simplify]: Simplifying using # : (-.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (+.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k))) (-.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k))) (-.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k))) (-.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k))) (-.f64 (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (log.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (log.f64 (sqrt.f64 k))) (-.f64 (log.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (log.f64 (sqrt.f64 k))) (log.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (exp.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (/.f64 (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k))) (/.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k))) (*.f64 (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)))) (cbrt.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (*.f64 (*.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k)) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (sqrt.f64 (/.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (neg.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (neg.f64 (sqrt.f64 k)) (/.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (cbrt.f64 (sqrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (sqrt.f64 (*.f64 (cbrt.f64 k) (cbrt.f64 k)))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (sqrt.f64 (cbrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (sqrt.f64 (sqrt.f64 k))) (/.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 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PI.f64))) (*.f64 8 (pow.f64 (*.f64 n PI.f64) 3)) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 n 2) (*.f64 (*.f64 2 PI.f64) (cbrt.f64 n)) (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (exp.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 8 (pow.f64 (*.f64 n PI.f64) 3)) (*.f64 8 (pow.f64 (*.f64 n PI.f64) 3)) (*.f64 (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 8 (pow.f64 (*.f64 n PI.f64) 3)) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 n 2) (*.f64 (*.f64 2 PI.f64) (cbrt.f64 n)) (*.f64 (*.f64 2 PI.f64) (sqrt.f64 n)) (*.f64 n (*.f64 2 PI.f64)) (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (exp.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (cbrt.f64 (sqrt.f64 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(+.f64 (/.f64 (*.f64 (pow.f64 PI.f64 3) (*.f64 (sqrt.f64 2) (pow.f64 NAN.f64 5))) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) k)) (*.f64 (*.f64 n n) (pow.f64 k 3)))) (/.f64 (*.f64 (sqrt.f64 2) (*.f64 PI.f64 NAN.f64)) (*.f64 k (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) k)))))) (-.f64 (*.f64 (+.f64 (/.f64 (*.f64 NAN.f64 NAN.f64) k) 1) (/.f64 PI.f64 (sqrt.f64 (exp.f64 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))))) (/.f64 (*.f64 PI.f64 (*.f64 PI.f64 (*.f64 NAN.f64 NAN.f64))) (*.f64 n (sqrt.f64 (exp.f64 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n))))))))) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 (pow.f64 n 3) (*.f64 (pow.f64 PI.f64 3) (pow.f64 NAN.f64 5)))) (+.f64 (*.f64 NAN.f64 (*.f64 (sqrt.f64 2) (*.f64 n PI.f64))) (*.f64 (pow.f64 NAN.f64 3) (*.f64 (sqrt.f64 2) (*.f64 (*.f64 n n) (*.f64 PI.f64 PI.f64)))))) (+.f64 (*.f64 (/.f64 (pow.f64 NAN.f64 5) (*.f64 n n)) (*.f64 (pow.f64 PI.f64 3) (sqrt.f64 2))) (+.f64 (*.f64 (sqrt.f64 2) (*.f64 PI.f64 NAN.f64)) (/.f64 (*.f64 (*.f64 PI.f64 PI.f64) (*.f64 (sqrt.f64 2) (pow.f64 NAN.f64 3))) n))) (+.f64 (*.f64 (/.f64 (pow.f64 NAN.f64 5) (*.f64 n n)) (pow.f64 PI.f64 3)) (-.f64 (*.f64 PI.f64 NAN.f64) (/.f64 (*.f64 (*.f64 PI.f64 PI.f64) (pow.f64 NAN.f64 3)) n))) 1.029 * * * [progress]: adding candidates to table 1.273 * * [progress]: iteration 3 / 4 1.273 * * * [progress]: picking best candidate 1.290 * * * * [pick]: Picked # 1.290 * * * [progress]: localizing error 1.303 * * * [progress]: generating rewritten candidates 1.303 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 2 1) 1.308 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1 1) 1.316 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2) 1.331 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.479 * * * [progress]: generating series expansions 1.479 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 2 1) 1.480 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1.480 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.480 * [taylor]: Taking taylor expansion of 2 in n 1.480 * [taylor]: Taking taylor expansion of (* n PI) in n 1.480 * [taylor]: Taking taylor expansion of n in n 1.480 * [taylor]: Taking taylor expansion of PI in n 1.480 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.480 * [taylor]: Taking taylor expansion of 2 in n 1.480 * [taylor]: Taking taylor expansion of (* n PI) in n 1.480 * [taylor]: Taking taylor expansion of n in n 1.480 * [taylor]: Taking taylor expansion of PI in n 1.481 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1.481 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.481 * [taylor]: Taking taylor expansion of 2 in n 1.481 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.481 * [taylor]: Taking taylor expansion of PI in n 1.481 * [taylor]: Taking taylor expansion of n in n 1.481 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.481 * [taylor]: Taking taylor expansion of 2 in n 1.481 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.481 * [taylor]: Taking taylor expansion of PI in n 1.481 * [taylor]: Taking taylor expansion of n in n 1.490 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1.490 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.490 * [taylor]: Taking taylor expansion of -2 in n 1.490 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.490 * [taylor]: Taking taylor expansion of PI in n 1.490 * [taylor]: Taking taylor expansion of n in n 1.490 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.490 * [taylor]: Taking taylor expansion of -2 in n 1.490 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.490 * [taylor]: Taking taylor expansion of PI in n 1.490 * [taylor]: Taking taylor expansion of n in n 1.491 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1 1) 1.491 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 1.491 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.491 * [taylor]: Taking taylor expansion of 2 in n 1.491 * [taylor]: Taking taylor expansion of (* n PI) in n 1.491 * [taylor]: Taking taylor expansion of n in n 1.491 * [taylor]: Taking taylor expansion of PI in n 1.491 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.491 * [taylor]: Taking taylor expansion of 2 in n 1.491 * [taylor]: Taking taylor expansion of (* n PI) in n 1.491 * [taylor]: Taking taylor expansion of n in n 1.491 * [taylor]: Taking taylor expansion of PI in n 1.492 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 1.492 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.492 * [taylor]: Taking taylor expansion of 2 in n 1.492 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.492 * [taylor]: Taking taylor expansion of PI in n 1.492 * [taylor]: Taking taylor expansion of n in n 1.492 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.492 * [taylor]: Taking taylor expansion of 2 in n 1.492 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.492 * [taylor]: Taking taylor expansion of PI in n 1.492 * [taylor]: Taking taylor expansion of n in n 1.493 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 1.493 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.493 * [taylor]: Taking taylor expansion of -2 in n 1.493 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.493 * [taylor]: Taking taylor expansion of PI in n 1.493 * [taylor]: Taking taylor expansion of n in n 1.493 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.493 * [taylor]: Taking taylor expansion of -2 in n 1.493 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.494 * [taylor]: Taking taylor expansion of PI in n 1.494 * [taylor]: Taking taylor expansion of n in n 1.494 * * * * [progress]: [ 3 / 4 ] generating series at (2 2) 1.495 * [approximate]: Taking taylor expansion of (* (sqrt (/ k (* PI n))) (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2))) in (k n) around 0 1.495 * [taylor]: Taking taylor expansion of (* (sqrt (/ k (* PI n))) (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2))) in n 1.495 * [taylor]: Taking taylor expansion of (sqrt (/ k (* PI n))) in n 1.495 * [taylor]: Taking taylor expansion of (/ k (* PI n)) in n 1.495 * [taylor]: Taking taylor expansion of k in n 1.495 * [taylor]: Taking taylor expansion of (* PI n) in n 1.495 * [taylor]: Taking taylor expansion of PI in n 1.495 * [taylor]: Taking taylor expansion of n in n 1.495 * [taylor]: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in n 1.495 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1.495 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1.495 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1.495 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.495 * [taylor]: Taking taylor expansion of 1/2 in n 1.495 * [taylor]: Taking taylor expansion of k in n 1.495 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.495 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.495 * [taylor]: Taking taylor expansion of 2 in n 1.495 * [taylor]: Taking taylor expansion of (* n PI) in n 1.495 * [taylor]: Taking taylor expansion of n in n 1.495 * [taylor]: Taking taylor expansion of PI in n 1.496 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.496 * [taylor]: Taking taylor expansion of 2 in n 1.496 * [taylor]: Taking taylor expansion of (* (sqrt (/ k (* PI n))) (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2))) in k 1.496 * [taylor]: Taking taylor expansion of (sqrt (/ k (* PI n))) in k 1.496 * [taylor]: Taking taylor expansion of (/ k (* PI n)) in k 1.496 * [taylor]: Taking taylor expansion of k in k 1.496 * [taylor]: Taking taylor expansion of (* PI n) in k 1.496 * [taylor]: Taking taylor expansion of PI in k 1.496 * [taylor]: Taking taylor expansion of n in k 1.496 * [taylor]: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1.496 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1.496 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1.496 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1.496 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.496 * [taylor]: Taking taylor expansion of 1/2 in k 1.496 * [taylor]: Taking taylor expansion of k in k 1.496 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.496 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.496 * [taylor]: Taking taylor expansion of 2 in k 1.496 * [taylor]: Taking taylor expansion of (* n PI) in k 1.496 * [taylor]: Taking taylor expansion of n in k 1.496 * [taylor]: Taking taylor expansion of PI in k 1.497 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.497 * [taylor]: Taking taylor expansion of 2 in k 1.497 * [taylor]: Taking taylor expansion of (* (sqrt (/ k (* PI n))) (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2))) in k 1.497 * [taylor]: Taking taylor expansion of (sqrt (/ k (* PI n))) in k 1.497 * [taylor]: Taking taylor expansion of (/ k (* PI n)) in k 1.497 * [taylor]: Taking taylor expansion of k in k 1.497 * [taylor]: Taking taylor expansion of (* PI n) in k 1.497 * [taylor]: Taking taylor expansion of PI in k 1.497 * [taylor]: Taking taylor expansion of n in k 1.497 * [taylor]: Taking taylor expansion of (/ (pow (* 2 (* n PI)) (* 1/2 k)) (sqrt 2)) in k 1.497 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1.497 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1.497 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1.497 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.497 * [taylor]: Taking taylor expansion of 1/2 in k 1.497 * [taylor]: Taking taylor expansion of k in k 1.497 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.497 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.497 * [taylor]: Taking taylor expansion of 2 in k 1.497 * [taylor]: Taking taylor expansion of (* n PI) in k 1.497 * [taylor]: Taking taylor expansion of n in k 1.497 * [taylor]: Taking taylor expansion of PI in k 1.497 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.498 * [taylor]: Taking taylor expansion of 2 in k 1.498 * [taylor]: Taking taylor expansion of 0 in n 1.498 * [taylor]: Taking taylor expansion of (/ NAN (* PI (* n (sqrt 2)))) in n 1.498 * [taylor]: Taking taylor expansion of NAN in n 1.498 * [taylor]: Taking taylor expansion of (* PI (* n (sqrt 2))) in n 1.498 * [taylor]: Taking taylor expansion of PI in n 1.498 * [taylor]: Taking taylor expansion of (* n (sqrt 2)) in n 1.498 * [taylor]: Taking taylor expansion of n in n 1.498 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.498 * [taylor]: Taking taylor expansion of 2 in n 1.500 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ (* (log (* 2 (* n PI))) NAN) (* (sqrt 2) (* n PI)))) (/ (pow NAN 3) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1.500 * [taylor]: Taking taylor expansion of (* 1/2 (/ (* (log (* 2 (* n PI))) NAN) (* (sqrt 2) (* n PI)))) in n 1.501 * [taylor]: Taking taylor expansion of 1/2 in n 1.501 * [taylor]: Taking taylor expansion of (/ (* (log (* 2 (* n PI))) NAN) (* (sqrt 2) (* n PI))) in n 1.501 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) NAN) in n 1.501 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.501 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.501 * [taylor]: Taking taylor expansion of 2 in n 1.501 * [taylor]: Taking taylor expansion of (* n PI) in n 1.501 * [taylor]: Taking taylor expansion of n in n 1.501 * [taylor]: Taking taylor expansion of PI in n 1.501 * [taylor]: Taking taylor expansion of NAN in n 1.501 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1.501 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.501 * [taylor]: Taking taylor expansion of 2 in n 1.501 * [taylor]: Taking taylor expansion of (* n PI) in n 1.501 * [taylor]: Taking taylor expansion of n in n 1.501 * [taylor]: Taking taylor expansion of PI in n 1.501 * [taylor]: Taking taylor expansion of (/ (pow NAN 3) (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1.501 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.501 * [taylor]: Taking taylor expansion of NAN in n 1.501 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1.501 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.501 * [taylor]: Taking taylor expansion of 2 in n 1.501 * [taylor]: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1.501 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.501 * [taylor]: Taking taylor expansion of n in n 1.501 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.501 * [taylor]: Taking taylor expansion of PI in n 1.507 * [taylor]: Taking taylor expansion of (+ (* 1/8 (/ (* (pow (log (* 2 (* n PI))) 2) NAN) (* (sqrt 2) (* n PI)))) (+ (* 1/2 (/ (* (log (* 2 (* n PI))) (pow NAN 3)) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (/ (pow NAN 5) (* (pow PI 3) (* (pow n 3) (sqrt 2)))))) in n 1.507 * [taylor]: Taking taylor expansion of (* 1/8 (/ (* (pow (log (* 2 (* n PI))) 2) NAN) (* (sqrt 2) (* n PI)))) in n 1.507 * [taylor]: Taking taylor expansion of 1/8 in n 1.507 * [taylor]: Taking taylor expansion of (/ (* (pow (log (* 2 (* n PI))) 2) NAN) (* (sqrt 2) (* n PI))) in n 1.507 * [taylor]: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) NAN) in n 1.507 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1.507 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.507 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.507 * [taylor]: Taking taylor expansion of 2 in n 1.507 * [taylor]: Taking taylor expansion of (* n PI) in n 1.507 * [taylor]: Taking taylor expansion of n in n 1.507 * [taylor]: Taking taylor expansion of PI in n 1.507 * [taylor]: Taking taylor expansion of NAN in n 1.507 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1.507 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.507 * [taylor]: Taking taylor expansion of 2 in n 1.507 * [taylor]: Taking taylor expansion of (* n PI) in n 1.507 * [taylor]: Taking taylor expansion of n in n 1.507 * [taylor]: Taking taylor expansion of PI in n 1.508 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ (* (log (* 2 (* n PI))) (pow NAN 3)) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) (/ (pow NAN 5) (* (pow PI 3) (* (pow n 3) (sqrt 2))))) in n 1.508 * [taylor]: Taking taylor expansion of (* 1/2 (/ (* (log (* 2 (* n PI))) (pow NAN 3)) (* (sqrt 2) (* (pow n 2) (pow PI 2))))) in n 1.508 * [taylor]: Taking taylor expansion of 1/2 in n 1.508 * [taylor]: Taking taylor expansion of (/ (* (log (* 2 (* n PI))) (pow NAN 3)) (* (sqrt 2) (* (pow n 2) (pow PI 2)))) in n 1.508 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow NAN 3)) in n 1.508 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.508 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.508 * [taylor]: Taking taylor expansion of 2 in n 1.508 * [taylor]: Taking taylor expansion of (* n PI) in n 1.508 * [taylor]: Taking taylor expansion of n in n 1.508 * [taylor]: Taking taylor expansion of PI in n 1.508 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.508 * [taylor]: Taking taylor expansion of NAN in n 1.508 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow n 2) (pow PI 2))) in n 1.508 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.508 * [taylor]: Taking taylor expansion of 2 in n 1.508 * [taylor]: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1.508 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.508 * [taylor]: Taking taylor expansion of n in n 1.508 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.508 * [taylor]: Taking taylor expansion of PI in n 1.509 * [taylor]: Taking taylor expansion of (/ (pow NAN 5) (* (pow PI 3) (* (pow n 3) (sqrt 2)))) in n 1.509 * [taylor]: Taking taylor expansion of (pow NAN 5) in n 1.509 * [taylor]: Taking taylor expansion of NAN in n 1.509 * [taylor]: Taking taylor expansion of (* (pow PI 3) (* (pow n 3) (sqrt 2))) in n 1.509 * [taylor]: Taking taylor expansion of (pow PI 3) in n 1.509 * [taylor]: Taking taylor expansion of PI in n 1.509 * [taylor]: Taking taylor expansion of (* (pow n 3) (sqrt 2)) in n 1.509 * [taylor]: Taking taylor expansion of (pow n 3) in n 1.509 * [taylor]: Taking taylor expansion of n in n 1.509 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.509 * [taylor]: Taking taylor expansion of 2 in n 1.516 * [approximate]: Taking taylor expansion of (* (sqrt (/ n (* k PI))) (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2))) in (k n) around 0 1.516 * [taylor]: Taking taylor expansion of (* (sqrt (/ n (* k PI))) (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2))) in n 1.516 * [taylor]: Taking taylor expansion of (sqrt (/ n (* k PI))) in n 1.516 * [taylor]: Taking taylor expansion of (/ n (* k PI)) in n 1.516 * [taylor]: Taking taylor expansion of n in n 1.516 * [taylor]: Taking taylor expansion of (* k PI) in n 1.516 * [taylor]: Taking taylor expansion of k in n 1.516 * [taylor]: Taking taylor expansion of PI in n 1.516 * [taylor]: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in n 1.516 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1.516 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1.516 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1.516 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 1.516 * [taylor]: Taking taylor expansion of 1/2 in n 1.516 * [taylor]: Taking taylor expansion of k in n 1.516 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.516 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.516 * [taylor]: Taking taylor expansion of 2 in n 1.516 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.516 * [taylor]: Taking taylor expansion of PI in n 1.516 * [taylor]: Taking taylor expansion of n in n 1.517 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.517 * [taylor]: Taking taylor expansion of 2 in n 1.517 * [taylor]: Taking taylor expansion of (* (sqrt (/ n (* k PI))) (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2))) in k 1.517 * [taylor]: Taking taylor expansion of (sqrt (/ n (* k PI))) in k 1.517 * [taylor]: Taking taylor expansion of (/ n (* k PI)) in k 1.517 * [taylor]: Taking taylor expansion of n in k 1.517 * [taylor]: Taking taylor expansion of (* k PI) in k 1.517 * [taylor]: Taking taylor expansion of k in k 1.517 * [taylor]: Taking taylor expansion of PI in k 1.517 * [taylor]: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1.517 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1.517 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1.517 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1.517 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 1.517 * [taylor]: Taking taylor expansion of 1/2 in k 1.517 * [taylor]: Taking taylor expansion of k in k 1.517 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.517 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.517 * [taylor]: Taking taylor expansion of 2 in k 1.517 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.517 * [taylor]: Taking taylor expansion of PI in k 1.517 * [taylor]: Taking taylor expansion of n in k 1.518 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.518 * [taylor]: Taking taylor expansion of 2 in k 1.518 * [taylor]: Taking taylor expansion of (* (sqrt (/ n (* k PI))) (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2))) in k 1.518 * [taylor]: Taking taylor expansion of (sqrt (/ n (* k PI))) in k 1.518 * [taylor]: Taking taylor expansion of (/ n (* k PI)) in k 1.518 * [taylor]: Taking taylor expansion of n in k 1.518 * [taylor]: Taking taylor expansion of (* k PI) in k 1.518 * [taylor]: Taking taylor expansion of k in k 1.518 * [taylor]: Taking taylor expansion of PI in k 1.518 * [taylor]: Taking taylor expansion of (/ (pow (* 2 (/ PI n)) (/ 1/2 k)) (sqrt 2)) in k 1.518 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1.518 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1.518 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1.518 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 1.518 * [taylor]: Taking taylor expansion of 1/2 in k 1.518 * [taylor]: Taking taylor expansion of k in k 1.518 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.518 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.518 * [taylor]: Taking taylor expansion of 2 in k 1.518 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.518 * [taylor]: Taking taylor expansion of PI in k 1.518 * [taylor]: Taking taylor expansion of n in k 1.518 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.518 * [taylor]: Taking taylor expansion of 2 in k 1.519 * [taylor]: Taking taylor expansion of 0 in n 1.519 * [taylor]: Taking taylor expansion of (/ (* NAN (* n (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (* PI (sqrt 2))) in n 1.519 * [taylor]: Taking taylor expansion of (* NAN (* n (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.519 * [taylor]: Taking taylor expansion of NAN in n 1.519 * [taylor]: Taking taylor expansion of (* n (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.519 * [taylor]: Taking taylor expansion of n in n 1.519 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.519 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.519 * [taylor]: Taking taylor expansion of 1/2 in n 1.519 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.519 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.519 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.519 * [taylor]: Taking taylor expansion of 2 in n 1.519 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.519 * [taylor]: Taking taylor expansion of PI in n 1.519 * [taylor]: Taking taylor expansion of n in n 1.519 * [taylor]: Taking taylor expansion of k in n 1.520 * [taylor]: Taking taylor expansion of (* PI (sqrt 2)) in n 1.520 * [taylor]: Taking taylor expansion of PI in n 1.520 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.520 * [taylor]: Taking taylor expansion of 2 in n 1.522 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 3) (* (pow n 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (* (sqrt 2) (pow PI 2))) in n 1.522 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (* (pow n 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.522 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.522 * [taylor]: Taking taylor expansion of NAN in n 1.522 * [taylor]: Taking taylor expansion of (* (pow n 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.522 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.522 * [taylor]: Taking taylor expansion of n in n 1.522 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.522 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.522 * [taylor]: Taking taylor expansion of 1/2 in n 1.522 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.522 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.522 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.522 * [taylor]: Taking taylor expansion of 2 in n 1.522 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.522 * [taylor]: Taking taylor expansion of PI in n 1.522 * [taylor]: Taking taylor expansion of n in n 1.522 * [taylor]: Taking taylor expansion of k in n 1.523 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in n 1.523 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.523 * [taylor]: Taking taylor expansion of 2 in n 1.523 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.523 * [taylor]: Taking taylor expansion of PI in n 1.525 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 5) (* (pow n 3) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (* (pow PI 3) (sqrt 2))) in n 1.525 * [taylor]: Taking taylor expansion of (* (pow NAN 5) (* (pow n 3) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.525 * [taylor]: Taking taylor expansion of (pow NAN 5) in n 1.525 * [taylor]: Taking taylor expansion of NAN in n 1.525 * [taylor]: Taking taylor expansion of (* (pow n 3) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.525 * [taylor]: Taking taylor expansion of (pow n 3) in n 1.525 * [taylor]: Taking taylor expansion of n in n 1.525 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.525 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.525 * [taylor]: Taking taylor expansion of 1/2 in n 1.525 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.525 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.525 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.525 * [taylor]: Taking taylor expansion of 2 in n 1.525 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.525 * [taylor]: Taking taylor expansion of PI in n 1.525 * [taylor]: Taking taylor expansion of n in n 1.526 * [taylor]: Taking taylor expansion of k in n 1.526 * [taylor]: Taking taylor expansion of (* (pow PI 3) (sqrt 2)) in n 1.526 * [taylor]: Taking taylor expansion of (pow PI 3) in n 1.526 * [taylor]: Taking taylor expansion of PI in n 1.526 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.526 * [taylor]: Taking taylor expansion of 2 in n 1.530 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 7) (* (pow n 4) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (* (sqrt 2) (pow PI 4))) in n 1.530 * [taylor]: Taking taylor expansion of (* (pow NAN 7) (* (pow n 4) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.530 * [taylor]: Taking taylor expansion of (pow NAN 7) in n 1.530 * [taylor]: Taking taylor expansion of NAN in n 1.530 * [taylor]: Taking taylor expansion of (* (pow n 4) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.530 * [taylor]: Taking taylor expansion of (pow n 4) in n 1.530 * [taylor]: Taking taylor expansion of n in n 1.530 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.530 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.530 * [taylor]: Taking taylor expansion of 1/2 in n 1.530 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.530 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.530 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.530 * [taylor]: Taking taylor expansion of 2 in n 1.530 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.530 * [taylor]: Taking taylor expansion of PI in n 1.531 * [taylor]: Taking taylor expansion of n in n 1.531 * [taylor]: Taking taylor expansion of k in n 1.531 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow PI 4)) in n 1.531 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.531 * [taylor]: Taking taylor expansion of 2 in n 1.531 * [taylor]: Taking taylor expansion of (pow PI 4) in n 1.531 * [taylor]: Taking taylor expansion of PI in n 1.536 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 9) (* (pow n 5) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (* (pow PI 5) (sqrt 2))) in n 1.536 * [taylor]: Taking taylor expansion of (* (pow NAN 9) (* (pow n 5) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.536 * [taylor]: Taking taylor expansion of (pow NAN 9) in n 1.536 * [taylor]: Taking taylor expansion of NAN in n 1.537 * [taylor]: Taking taylor expansion of (* (pow n 5) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.537 * [taylor]: Taking taylor expansion of (pow n 5) in n 1.537 * [taylor]: Taking taylor expansion of n in n 1.537 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.537 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.537 * [taylor]: Taking taylor expansion of 1/2 in n 1.537 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.537 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.537 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.537 * [taylor]: Taking taylor expansion of 2 in n 1.537 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.537 * [taylor]: Taking taylor expansion of PI in n 1.537 * [taylor]: Taking taylor expansion of n in n 1.537 * [taylor]: Taking taylor expansion of k in n 1.537 * [taylor]: Taking taylor expansion of (* (pow PI 5) (sqrt 2)) in n 1.537 * [taylor]: Taking taylor expansion of (pow PI 5) in n 1.537 * [taylor]: Taking taylor expansion of PI in n 1.537 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.537 * [taylor]: Taking taylor expansion of 2 in n 1.545 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 11) (* (pow n 6) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) (* (sqrt 2) (pow PI 6))) in n 1.545 * [taylor]: Taking taylor expansion of (* (pow NAN 11) (* (pow n 6) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.545 * [taylor]: Taking taylor expansion of (pow NAN 11) in n 1.545 * [taylor]: Taking taylor expansion of NAN in n 1.545 * [taylor]: Taking taylor expansion of (* (pow n 6) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.545 * [taylor]: Taking taylor expansion of (pow n 6) in n 1.545 * [taylor]: Taking taylor expansion of n in n 1.545 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.545 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.545 * [taylor]: Taking taylor expansion of 1/2 in n 1.545 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.545 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.545 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.545 * [taylor]: Taking taylor expansion of 2 in n 1.545 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.545 * [taylor]: Taking taylor expansion of PI in n 1.545 * [taylor]: Taking taylor expansion of n in n 1.545 * [taylor]: Taking taylor expansion of k in n 1.546 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow PI 6)) in n 1.546 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.546 * [taylor]: Taking taylor expansion of 2 in n 1.546 * [taylor]: Taking taylor expansion of (pow PI 6) in n 1.546 * [taylor]: Taking taylor expansion of PI in n 1.549 * [approximate]: Taking taylor expansion of (/ (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) (sqrt (* -2 (/ PI n)))) in (k n) around 0 1.549 * [taylor]: Taking taylor expansion of (/ (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) (sqrt (* -2 (/ PI n)))) in n 1.549 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 1.549 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 1.549 * [taylor]: Taking taylor expansion of (/ -1 k) in n 1.549 * [taylor]: Taking taylor expansion of -1 in n 1.549 * [taylor]: Taking taylor expansion of k in n 1.549 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1.549 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1.549 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1.549 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 1.549 * [taylor]: Taking taylor expansion of -1/2 in n 1.549 * [taylor]: Taking taylor expansion of k in n 1.549 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.549 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.549 * [taylor]: Taking taylor expansion of -2 in n 1.549 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.549 * [taylor]: Taking taylor expansion of PI in n 1.549 * [taylor]: Taking taylor expansion of n in n 1.549 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1.550 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.550 * [taylor]: Taking taylor expansion of -2 in n 1.550 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.550 * [taylor]: Taking taylor expansion of PI in n 1.550 * [taylor]: Taking taylor expansion of n in n 1.550 * [taylor]: Taking taylor expansion of (/ (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) (sqrt (* -2 (/ PI n)))) in k 1.550 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 1.550 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.550 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.550 * [taylor]: Taking taylor expansion of -1 in k 1.550 * [taylor]: Taking taylor expansion of k in k 1.550 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1.550 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1.550 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1.550 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 1.550 * [taylor]: Taking taylor expansion of -1/2 in k 1.550 * [taylor]: Taking taylor expansion of k in k 1.550 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.550 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.550 * [taylor]: Taking taylor expansion of -2 in k 1.550 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.550 * [taylor]: Taking taylor expansion of PI in k 1.550 * [taylor]: Taking taylor expansion of n in k 1.551 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1.551 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.551 * [taylor]: Taking taylor expansion of -2 in k 1.551 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.551 * [taylor]: Taking taylor expansion of PI in k 1.551 * [taylor]: Taking taylor expansion of n in k 1.551 * [taylor]: Taking taylor expansion of (/ (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) (sqrt (* -2 (/ PI n)))) in k 1.551 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 1.551 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.551 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.551 * [taylor]: Taking taylor expansion of -1 in k 1.551 * [taylor]: Taking taylor expansion of k in k 1.551 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1.551 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1.551 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1.552 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 1.552 * [taylor]: Taking taylor expansion of -1/2 in k 1.552 * [taylor]: Taking taylor expansion of k in k 1.552 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.552 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.552 * [taylor]: Taking taylor expansion of -2 in k 1.552 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.552 * [taylor]: Taking taylor expansion of PI in k 1.552 * [taylor]: Taking taylor expansion of n in k 1.552 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1.552 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.552 * [taylor]: Taking taylor expansion of -2 in k 1.552 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.552 * [taylor]: Taking taylor expansion of PI in k 1.552 * [taylor]: Taking taylor expansion of n in k 1.553 * [taylor]: Taking taylor expansion of (/ (* NAN (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) (sqrt (* -2 (/ PI n)))) in n 1.553 * [taylor]: Taking taylor expansion of (* NAN (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1.553 * [taylor]: Taking taylor expansion of NAN in n 1.553 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1.553 * [taylor]: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1.553 * [taylor]: Taking taylor expansion of -1/2 in n 1.553 * [taylor]: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1.553 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.553 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.553 * [taylor]: Taking taylor expansion of -2 in n 1.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.553 * [taylor]: Taking taylor expansion of PI in n 1.553 * [taylor]: Taking taylor expansion of n in n 1.553 * [taylor]: Taking taylor expansion of k in n 1.553 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1.553 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.553 * [taylor]: Taking taylor expansion of -2 in n 1.553 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.553 * [taylor]: Taking taylor expansion of PI in n 1.553 * [taylor]: Taking taylor expansion of n in n 1.554 * [taylor]: Taking taylor expansion of (/ (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (pow NAN 3)) (sqrt (* -2 (/ PI n)))) in n 1.554 * [taylor]: Taking taylor expansion of (* (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) (pow NAN 3)) in n 1.554 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1.555 * [taylor]: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1.555 * [taylor]: Taking taylor expansion of -1/2 in n 1.555 * [taylor]: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1.555 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.555 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.555 * [taylor]: Taking taylor expansion of -2 in n 1.555 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.555 * [taylor]: Taking taylor expansion of PI in n 1.555 * [taylor]: Taking taylor expansion of n in n 1.555 * [taylor]: Taking taylor expansion of k in n 1.555 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.555 * [taylor]: Taking taylor expansion of NAN in n 1.555 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1.555 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.555 * [taylor]: Taking taylor expansion of -2 in n 1.555 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.555 * [taylor]: Taking taylor expansion of PI in n 1.555 * [taylor]: Taking taylor expansion of n in n 1.558 * * * * [progress]: [ 4 / 4 ] generating series at (2) 1.558 * [approximate]: Taking taylor expansion of (* (sqrt (/ (* n PI) k)) (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k)))) in (k n) around 0 1.558 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* n PI) k)) (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k)))) in n 1.558 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 1.559 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in n 1.559 * [taylor]: Taking taylor expansion of (* n PI) in n 1.559 * [taylor]: Taking taylor expansion of n in n 1.559 * [taylor]: Taking taylor expansion of PI in n 1.559 * [taylor]: Taking taylor expansion of k in n 1.559 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 1.559 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.559 * [taylor]: Taking taylor expansion of 2 in n 1.559 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 1.559 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 1.559 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 1.559 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 1.559 * [taylor]: Taking taylor expansion of 1/2 in n 1.559 * [taylor]: Taking taylor expansion of k in n 1.559 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.559 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.559 * [taylor]: Taking taylor expansion of 2 in n 1.559 * [taylor]: Taking taylor expansion of (* n PI) in n 1.559 * [taylor]: Taking taylor expansion of n in n 1.559 * [taylor]: Taking taylor expansion of PI in n 1.559 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* n PI) k)) (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k)))) in k 1.559 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1.559 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in k 1.559 * [taylor]: Taking taylor expansion of (* n PI) in k 1.560 * [taylor]: Taking taylor expansion of n in k 1.560 * [taylor]: Taking taylor expansion of PI in k 1.560 * [taylor]: Taking taylor expansion of k in k 1.560 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in k 1.560 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.560 * [taylor]: Taking taylor expansion of 2 in k 1.560 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1.560 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1.560 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1.560 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.560 * [taylor]: Taking taylor expansion of 1/2 in k 1.560 * [taylor]: Taking taylor expansion of k in k 1.560 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.560 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.560 * [taylor]: Taking taylor expansion of 2 in k 1.560 * [taylor]: Taking taylor expansion of (* n PI) in k 1.560 * [taylor]: Taking taylor expansion of n in k 1.560 * [taylor]: Taking taylor expansion of PI in k 1.560 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* n PI) k)) (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k)))) in k 1.560 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 1.560 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in k 1.560 * [taylor]: Taking taylor expansion of (* n PI) in k 1.560 * [taylor]: Taking taylor expansion of n in k 1.560 * [taylor]: Taking taylor expansion of PI in k 1.560 * [taylor]: Taking taylor expansion of k in k 1.561 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in k 1.561 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.561 * [taylor]: Taking taylor expansion of 2 in k 1.561 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 1.561 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 1.561 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 1.561 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 1.561 * [taylor]: Taking taylor expansion of 1/2 in k 1.561 * [taylor]: Taking taylor expansion of k in k 1.561 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 1.561 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 1.561 * [taylor]: Taking taylor expansion of 2 in k 1.561 * [taylor]: Taking taylor expansion of (* n PI) in k 1.561 * [taylor]: Taking taylor expansion of n in k 1.561 * [taylor]: Taking taylor expansion of PI in k 1.561 * [taylor]: Taking taylor expansion of 0 in n 1.562 * [taylor]: Taking taylor expansion of (* NAN (* (sqrt 2) (* n PI))) in n 1.562 * [taylor]: Taking taylor expansion of NAN in n 1.562 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1.562 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.562 * [taylor]: Taking taylor expansion of 2 in n 1.562 * [taylor]: Taking taylor expansion of (* n PI) in n 1.562 * [taylor]: Taking taylor expansion of n in n 1.562 * [taylor]: Taking taylor expansion of PI in n 1.564 * [taylor]: Taking taylor expansion of (- (* (pow PI 2) (* (pow NAN 3) (* (pow n 2) (sqrt 2)))) (* 1/2 (* NAN (* (log (* 2 (* n PI))) (* (sqrt 2) (* n PI)))))) in n 1.564 * [taylor]: Taking taylor expansion of (* (pow PI 2) (* (pow NAN 3) (* (pow n 2) (sqrt 2)))) in n 1.564 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.564 * [taylor]: Taking taylor expansion of PI in n 1.564 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (* (pow n 2) (sqrt 2))) in n 1.564 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.564 * [taylor]: Taking taylor expansion of NAN in n 1.564 * [taylor]: Taking taylor expansion of (* (pow n 2) (sqrt 2)) in n 1.564 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.564 * [taylor]: Taking taylor expansion of n in n 1.564 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.564 * [taylor]: Taking taylor expansion of 2 in n 1.564 * [taylor]: Taking taylor expansion of (* 1/2 (* NAN (* (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))))) in n 1.564 * [taylor]: Taking taylor expansion of 1/2 in n 1.564 * [taylor]: Taking taylor expansion of (* NAN (* (log (* 2 (* n PI))) (* (sqrt 2) (* n PI)))) in n 1.564 * [taylor]: Taking taylor expansion of NAN in n 1.564 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (* (sqrt 2) (* n PI))) in n 1.564 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.565 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.565 * [taylor]: Taking taylor expansion of 2 in n 1.565 * [taylor]: Taking taylor expansion of (* n PI) in n 1.565 * [taylor]: Taking taylor expansion of n in n 1.565 * [taylor]: Taking taylor expansion of PI in n 1.565 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1.565 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.565 * [taylor]: Taking taylor expansion of 2 in n 1.565 * [taylor]: Taking taylor expansion of (* n PI) in n 1.565 * [taylor]: Taking taylor expansion of n in n 1.565 * [taylor]: Taking taylor expansion of PI in n 1.569 * [taylor]: Taking taylor expansion of (- (+ (* 1/8 (* NAN (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))))) (* (sqrt 2) (* (pow NAN 5) (* (pow n 3) (pow PI 3))))) (* 1/2 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow NAN 3) (* (pow n 2) (pow PI 2))))))) in n 1.569 * [taylor]: Taking taylor expansion of (+ (* 1/8 (* NAN (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))))) (* (sqrt 2) (* (pow NAN 5) (* (pow n 3) (pow PI 3))))) in n 1.569 * [taylor]: Taking taylor expansion of (* 1/8 (* NAN (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))))) in n 1.569 * [taylor]: Taking taylor expansion of 1/8 in n 1.569 * [taylor]: Taking taylor expansion of (* NAN (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI)))) in n 1.569 * [taylor]: Taking taylor expansion of NAN in n 1.569 * [taylor]: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) (* (sqrt 2) (* n PI))) in n 1.569 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1.569 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.569 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.569 * [taylor]: Taking taylor expansion of 2 in n 1.569 * [taylor]: Taking taylor expansion of (* n PI) in n 1.569 * [taylor]: Taking taylor expansion of n in n 1.569 * [taylor]: Taking taylor expansion of PI in n 1.570 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1.570 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.570 * [taylor]: Taking taylor expansion of 2 in n 1.570 * [taylor]: Taking taylor expansion of (* n PI) in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 5) (* (pow n 3) (pow PI 3)))) in n 1.570 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.570 * [taylor]: Taking taylor expansion of 2 in n 1.570 * [taylor]: Taking taylor expansion of (* (pow NAN 5) (* (pow n 3) (pow PI 3))) in n 1.570 * [taylor]: Taking taylor expansion of (pow NAN 5) in n 1.570 * [taylor]: Taking taylor expansion of NAN in n 1.570 * [taylor]: Taking taylor expansion of (* (pow n 3) (pow PI 3)) in n 1.570 * [taylor]: Taking taylor expansion of (pow n 3) in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [taylor]: Taking taylor expansion of (pow PI 3) in n 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [taylor]: Taking taylor expansion of (* 1/2 (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow NAN 3) (* (pow n 2) (pow PI 2)))))) in n 1.570 * [taylor]: Taking taylor expansion of 1/2 in n 1.570 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (* (pow NAN 3) (* (pow n 2) (pow PI 2))))) in n 1.570 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.570 * [taylor]: Taking taylor expansion of 2 in n 1.570 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (* (pow NAN 3) (* (pow n 2) (pow PI 2)))) in n 1.570 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.570 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.570 * [taylor]: Taking taylor expansion of 2 in n 1.570 * [taylor]: Taking taylor expansion of (* n PI) in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (* (pow n 2) (pow PI 2))) in n 1.570 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.570 * [taylor]: Taking taylor expansion of NAN in n 1.570 * [taylor]: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1.570 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.571 * [taylor]: Taking taylor expansion of PI in n 1.579 * [taylor]: Taking taylor expansion of (- (+ (* 1/8 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow NAN 3) (* (pow n 2) (pow PI 2)))))) (* (pow NAN 7) (* (sqrt 2) (* (pow n 4) (pow PI 4))))) (+ (* 1/2 (* (pow PI 3) (* (log (* 2 (* n PI))) (* (pow NAN 5) (* (pow n 3) (sqrt 2)))))) (* 1/48 (* NAN (* (pow (log (* 2 (* n PI))) 3) (* (sqrt 2) (* n PI))))))) in n 1.579 * [taylor]: Taking taylor expansion of (+ (* 1/8 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow NAN 3) (* (pow n 2) (pow PI 2)))))) (* (pow NAN 7) (* (sqrt 2) (* (pow n 4) (pow PI 4))))) in n 1.579 * [taylor]: Taking taylor expansion of (* 1/8 (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow NAN 3) (* (pow n 2) (pow PI 2)))))) in n 1.579 * [taylor]: Taking taylor expansion of 1/8 in n 1.579 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow (log (* 2 (* n PI))) 2) (* (pow NAN 3) (* (pow n 2) (pow PI 2))))) in n 1.579 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.579 * [taylor]: Taking taylor expansion of 2 in n 1.579 * [taylor]: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 2) (* (pow NAN 3) (* (pow n 2) (pow PI 2)))) in n 1.579 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 1.580 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.580 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.580 * [taylor]: Taking taylor expansion of 2 in n 1.580 * [taylor]: Taking taylor expansion of (* n PI) in n 1.580 * [taylor]: Taking taylor expansion of n in n 1.580 * [taylor]: Taking taylor expansion of PI in n 1.580 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (* (pow n 2) (pow PI 2))) in n 1.580 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.580 * [taylor]: Taking taylor expansion of NAN in n 1.580 * [taylor]: Taking taylor expansion of (* (pow n 2) (pow PI 2)) in n 1.580 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.580 * [taylor]: Taking taylor expansion of n in n 1.580 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.580 * [taylor]: Taking taylor expansion of PI in n 1.580 * [taylor]: Taking taylor expansion of (* (pow NAN 7) (* (sqrt 2) (* (pow n 4) (pow PI 4)))) in n 1.580 * [taylor]: Taking taylor expansion of (pow NAN 7) in n 1.580 * [taylor]: Taking taylor expansion of NAN in n 1.580 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow n 4) (pow PI 4))) in n 1.580 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.580 * [taylor]: Taking taylor expansion of 2 in n 1.580 * [taylor]: Taking taylor expansion of (* (pow n 4) (pow PI 4)) in n 1.580 * [taylor]: Taking taylor expansion of (pow n 4) in n 1.580 * [taylor]: Taking taylor expansion of n in n 1.580 * [taylor]: Taking taylor expansion of (pow PI 4) in n 1.580 * [taylor]: Taking taylor expansion of PI in n 1.580 * [taylor]: Taking taylor expansion of (+ (* 1/2 (* (pow PI 3) (* (log (* 2 (* n PI))) (* (pow NAN 5) (* (pow n 3) (sqrt 2)))))) (* 1/48 (* NAN (* (pow (log (* 2 (* n PI))) 3) (* (sqrt 2) (* n PI)))))) in n 1.580 * [taylor]: Taking taylor expansion of (* 1/2 (* (pow PI 3) (* (log (* 2 (* n PI))) (* (pow NAN 5) (* (pow n 3) (sqrt 2)))))) in n 1.580 * [taylor]: Taking taylor expansion of 1/2 in n 1.580 * [taylor]: Taking taylor expansion of (* (pow PI 3) (* (log (* 2 (* n PI))) (* (pow NAN 5) (* (pow n 3) (sqrt 2))))) in n 1.580 * [taylor]: Taking taylor expansion of (pow PI 3) in n 1.580 * [taylor]: Taking taylor expansion of PI in n 1.580 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (* (pow NAN 5) (* (pow n 3) (sqrt 2)))) in n 1.580 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.580 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.580 * [taylor]: Taking taylor expansion of 2 in n 1.580 * [taylor]: Taking taylor expansion of (* n PI) in n 1.580 * [taylor]: Taking taylor expansion of n in n 1.580 * [taylor]: Taking taylor expansion of PI in n 1.580 * [taylor]: Taking taylor expansion of (* (pow NAN 5) (* (pow n 3) (sqrt 2))) in n 1.581 * [taylor]: Taking taylor expansion of (pow NAN 5) in n 1.581 * [taylor]: Taking taylor expansion of NAN in n 1.581 * [taylor]: Taking taylor expansion of (* (pow n 3) (sqrt 2)) in n 1.581 * [taylor]: Taking taylor expansion of (pow n 3) in n 1.581 * [taylor]: Taking taylor expansion of n in n 1.581 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.581 * [taylor]: Taking taylor expansion of 2 in n 1.581 * [taylor]: Taking taylor expansion of (* 1/48 (* NAN (* (pow (log (* 2 (* n PI))) 3) (* (sqrt 2) (* n PI))))) in n 1.581 * [taylor]: Taking taylor expansion of 1/48 in n 1.581 * [taylor]: Taking taylor expansion of (* NAN (* (pow (log (* 2 (* n PI))) 3) (* (sqrt 2) (* n PI)))) in n 1.581 * [taylor]: Taking taylor expansion of NAN in n 1.581 * [taylor]: Taking taylor expansion of (* (pow (log (* 2 (* n PI))) 3) (* (sqrt 2) (* n PI))) in n 1.581 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 3) in n 1.581 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 1.581 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 1.581 * [taylor]: Taking taylor expansion of 2 in n 1.581 * [taylor]: Taking taylor expansion of (* n PI) in n 1.581 * [taylor]: Taking taylor expansion of n in n 1.581 * [taylor]: Taking taylor expansion of PI in n 1.581 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* n PI)) in n 1.581 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.581 * [taylor]: Taking taylor expansion of 2 in n 1.581 * [taylor]: Taking taylor expansion of (* n PI) in n 1.581 * [taylor]: Taking taylor expansion of n in n 1.581 * [taylor]: Taking taylor expansion of PI in n 1.591 * [approximate]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in (k n) around 0 1.591 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 1.591 * [taylor]: Taking taylor expansion of (sqrt (/ (* k PI) n)) in n 1.591 * [taylor]: Taking taylor expansion of (/ (* k PI) n) in n 1.591 * [taylor]: Taking taylor expansion of (* k PI) in n 1.591 * [taylor]: Taking taylor expansion of k in n 1.591 * [taylor]: Taking taylor expansion of PI in n 1.591 * [taylor]: Taking taylor expansion of n in n 1.591 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 1.591 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.591 * [taylor]: Taking taylor expansion of 2 in n 1.591 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 1.591 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 1.591 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 1.591 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 1.591 * [taylor]: Taking taylor expansion of 1/2 in n 1.591 * [taylor]: Taking taylor expansion of k in n 1.591 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.591 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.591 * [taylor]: Taking taylor expansion of 2 in n 1.591 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.591 * [taylor]: Taking taylor expansion of PI in n 1.591 * [taylor]: Taking taylor expansion of n in n 1.592 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in k 1.592 * [taylor]: Taking taylor expansion of (sqrt (/ (* k PI) n)) in k 1.592 * [taylor]: Taking taylor expansion of (/ (* k PI) n) in k 1.592 * [taylor]: Taking taylor expansion of (* k PI) in k 1.592 * [taylor]: Taking taylor expansion of k in k 1.592 * [taylor]: Taking taylor expansion of PI in k 1.592 * [taylor]: Taking taylor expansion of n in k 1.592 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 1.592 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.592 * [taylor]: Taking taylor expansion of 2 in k 1.592 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1.592 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1.592 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1.592 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 1.592 * [taylor]: Taking taylor expansion of 1/2 in k 1.592 * [taylor]: Taking taylor expansion of k in k 1.592 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.592 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.592 * [taylor]: Taking taylor expansion of 2 in k 1.592 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.592 * [taylor]: Taking taylor expansion of PI in k 1.592 * [taylor]: Taking taylor expansion of n in k 1.592 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in k 1.592 * [taylor]: Taking taylor expansion of (sqrt (/ (* k PI) n)) in k 1.592 * [taylor]: Taking taylor expansion of (/ (* k PI) n) in k 1.592 * [taylor]: Taking taylor expansion of (* k PI) in k 1.592 * [taylor]: Taking taylor expansion of k in k 1.592 * [taylor]: Taking taylor expansion of PI in k 1.592 * [taylor]: Taking taylor expansion of n in k 1.593 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 1.593 * [taylor]: Taking taylor expansion of (sqrt 2) in k 1.593 * [taylor]: Taking taylor expansion of 2 in k 1.593 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 1.593 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 1.593 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 1.593 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 1.593 * [taylor]: Taking taylor expansion of 1/2 in k 1.593 * [taylor]: Taking taylor expansion of k in k 1.593 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 1.593 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 1.593 * [taylor]: Taking taylor expansion of 2 in k 1.593 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.593 * [taylor]: Taking taylor expansion of PI in k 1.593 * [taylor]: Taking taylor expansion of n in k 1.593 * [taylor]: Taking taylor expansion of 0 in n 1.594 * [taylor]: Taking taylor expansion of (/ (* PI (* NAN (sqrt 2))) (* n (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.594 * [taylor]: Taking taylor expansion of (* PI (* NAN (sqrt 2))) in n 1.594 * [taylor]: Taking taylor expansion of PI in n 1.594 * [taylor]: Taking taylor expansion of (* NAN (sqrt 2)) in n 1.594 * [taylor]: Taking taylor expansion of NAN in n 1.594 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.594 * [taylor]: Taking taylor expansion of 2 in n 1.594 * [taylor]: Taking taylor expansion of (* n (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.594 * [taylor]: Taking taylor expansion of n in n 1.594 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.594 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.594 * [taylor]: Taking taylor expansion of 1/2 in n 1.594 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.594 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.594 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.594 * [taylor]: Taking taylor expansion of 2 in n 1.594 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.594 * [taylor]: Taking taylor expansion of PI in n 1.594 * [taylor]: Taking taylor expansion of n in n 1.594 * [taylor]: Taking taylor expansion of k in n 1.597 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 3) (* (sqrt 2) (pow PI 2))) (* (pow n 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.597 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (* (sqrt 2) (pow PI 2))) in n 1.597 * [taylor]: Taking taylor expansion of (pow NAN 3) in n 1.597 * [taylor]: Taking taylor expansion of NAN in n 1.597 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow PI 2)) in n 1.597 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.597 * [taylor]: Taking taylor expansion of 2 in n 1.597 * [taylor]: Taking taylor expansion of (pow PI 2) in n 1.597 * [taylor]: Taking taylor expansion of PI in n 1.597 * [taylor]: Taking taylor expansion of (* (pow n 2) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.597 * [taylor]: Taking taylor expansion of (pow n 2) in n 1.597 * [taylor]: Taking taylor expansion of n in n 1.597 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.597 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.597 * [taylor]: Taking taylor expansion of 1/2 in n 1.597 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.597 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.597 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.597 * [taylor]: Taking taylor expansion of 2 in n 1.597 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.597 * [taylor]: Taking taylor expansion of PI in n 1.597 * [taylor]: Taking taylor expansion of n in n 1.598 * [taylor]: Taking taylor expansion of k in n 1.603 * [taylor]: Taking taylor expansion of (/ (* (sqrt 2) (* (pow NAN 5) (pow PI 3))) (* (pow n 3) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))))) in n 1.603 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 5) (pow PI 3))) in n 1.603 * [taylor]: Taking taylor expansion of (sqrt 2) in n 1.603 * [taylor]: Taking taylor expansion of 2 in n 1.603 * [taylor]: Taking taylor expansion of (* (pow NAN 5) (pow PI 3)) in n 1.603 * [taylor]: Taking taylor expansion of (pow NAN 5) in n 1.603 * [taylor]: Taking taylor expansion of NAN in n 1.603 * [taylor]: Taking taylor expansion of (pow PI 3) in n 1.603 * [taylor]: Taking taylor expansion of PI in n 1.603 * [taylor]: Taking taylor expansion of (* (pow n 3) (exp (* 1/2 (/ (log (* 2 (/ PI n))) k)))) in n 1.603 * [taylor]: Taking taylor expansion of (pow n 3) in n 1.603 * [taylor]: Taking taylor expansion of n in n 1.603 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (log (* 2 (/ PI n))) k))) in n 1.603 * [taylor]: Taking taylor expansion of (* 1/2 (/ (log (* 2 (/ PI n))) k)) in n 1.603 * [taylor]: Taking taylor expansion of 1/2 in n 1.603 * [taylor]: Taking taylor expansion of (/ (log (* 2 (/ PI n))) k) in n 1.603 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 1.603 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 1.603 * [taylor]: Taking taylor expansion of 2 in n 1.603 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.603 * [taylor]: Taking taylor expansion of PI in n 1.603 * [taylor]: Taking taylor expansion of n in n 1.603 * [taylor]: Taking taylor expansion of k in n 1.610 * [approximate]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in (k n) around 0 1.610 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 1.610 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1.610 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.610 * [taylor]: Taking taylor expansion of -2 in n 1.610 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.610 * [taylor]: Taking taylor expansion of PI in n 1.610 * [taylor]: Taking taylor expansion of n in n 1.610 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 1.610 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 1.610 * [taylor]: Taking taylor expansion of (/ -1 k) in n 1.610 * [taylor]: Taking taylor expansion of -1 in n 1.610 * [taylor]: Taking taylor expansion of k in n 1.610 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 1.610 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 1.610 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 1.610 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 1.610 * [taylor]: Taking taylor expansion of -1/2 in n 1.610 * [taylor]: Taking taylor expansion of k in n 1.610 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.611 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.611 * [taylor]: Taking taylor expansion of -2 in n 1.611 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.611 * [taylor]: Taking taylor expansion of PI in n 1.611 * [taylor]: Taking taylor expansion of n in n 1.611 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in k 1.611 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1.611 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.611 * [taylor]: Taking taylor expansion of -2 in k 1.611 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.611 * [taylor]: Taking taylor expansion of PI in k 1.611 * [taylor]: Taking taylor expansion of n in k 1.611 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 1.611 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.611 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.611 * [taylor]: Taking taylor expansion of -1 in k 1.612 * [taylor]: Taking taylor expansion of k in k 1.612 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1.612 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1.612 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1.612 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 1.612 * [taylor]: Taking taylor expansion of -1/2 in k 1.612 * [taylor]: Taking taylor expansion of k in k 1.612 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.612 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.612 * [taylor]: Taking taylor expansion of -2 in k 1.612 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.612 * [taylor]: Taking taylor expansion of PI in k 1.612 * [taylor]: Taking taylor expansion of n in k 1.612 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in k 1.612 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 1.612 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.613 * [taylor]: Taking taylor expansion of -2 in k 1.613 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.613 * [taylor]: Taking taylor expansion of PI in k 1.613 * [taylor]: Taking taylor expansion of n in k 1.613 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 1.613 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.613 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.613 * [taylor]: Taking taylor expansion of -1 in k 1.613 * [taylor]: Taking taylor expansion of k in k 1.613 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 1.613 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 1.613 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 1.613 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 1.613 * [taylor]: Taking taylor expansion of -1/2 in k 1.613 * [taylor]: Taking taylor expansion of k in k 1.613 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 1.613 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 1.613 * [taylor]: Taking taylor expansion of -2 in k 1.613 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.613 * [taylor]: Taking taylor expansion of PI in k 1.613 * [taylor]: Taking taylor expansion of n in k 1.614 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* NAN (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) in n 1.614 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1.614 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.614 * [taylor]: Taking taylor expansion of -2 in n 1.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.614 * [taylor]: Taking taylor expansion of PI in n 1.614 * [taylor]: Taking taylor expansion of n in n 1.614 * [taylor]: Taking taylor expansion of (* NAN (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1.614 * [taylor]: Taking taylor expansion of NAN in n 1.614 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1.614 * [taylor]: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1.614 * [taylor]: Taking taylor expansion of -1/2 in n 1.614 * [taylor]: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1.614 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.614 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.614 * [taylor]: Taking taylor expansion of -2 in n 1.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.614 * [taylor]: Taking taylor expansion of PI in n 1.614 * [taylor]: Taking taylor expansion of n in n 1.614 * [taylor]: Taking taylor expansion of k in n 1.616 * [taylor]: Taking taylor expansion of (neg (/ (* NAN (sqrt (* -2 (/ PI n)))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))))) in n 1.616 * [taylor]: Taking taylor expansion of (/ (* NAN (sqrt (* -2 (/ PI n)))) (exp (* -1/2 (/ (log (* -2 (/ PI n))) k)))) in n 1.616 * [taylor]: Taking taylor expansion of (* NAN (sqrt (* -2 (/ PI n)))) in n 1.616 * [taylor]: Taking taylor expansion of NAN in n 1.616 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 1.616 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.616 * [taylor]: Taking taylor expansion of -2 in n 1.616 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.616 * [taylor]: Taking taylor expansion of PI in n 1.616 * [taylor]: Taking taylor expansion of n in n 1.616 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (log (* -2 (/ PI n))) k))) in n 1.616 * [taylor]: Taking taylor expansion of (* -1/2 (/ (log (* -2 (/ PI n))) k)) in n 1.616 * [taylor]: Taking taylor expansion of -1/2 in n 1.616 * [taylor]: Taking taylor expansion of (/ (log (* -2 (/ PI n))) k) in n 1.616 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 1.616 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 1.616 * [taylor]: Taking taylor expansion of -2 in n 1.616 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.616 * [taylor]: Taking taylor expansion of PI in n 1.616 * [taylor]: Taking taylor expansion of n in n 1.616 * [taylor]: Taking taylor expansion of k in n 1.620 * * * [progress]: simplifying candidates 1.637 * [simplify]: Simplifying using # : (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (+.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 PI.f64))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (exp.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 (*.f64 (*.f64 n n) n) (*.f64 (*.f64 (*.f64 2 2) 2) (*.f64 (*.f64 PI.f64 PI.f64) PI.f64))) (*.f64 (*.f64 (*.f64 n n) n) (*.f64 (*.f64 (*.f64 2 PI.f64) (*.f64 2 PI.f64)) (*.f64 2 PI.f64))) (*.f64 (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 (*.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64))) (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 n 2) (*.f64 (cbrt.f64 n) (*.f64 2 PI.f64)) (*.f64 (sqrt.f64 n) (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (+.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 PI.f64))) (+.f64 (log.f64 n) (log.f64 (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (exp.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 (*.f64 (*.f64 n n) n) (*.f64 (*.f64 (*.f64 2 2) 2) (*.f64 (*.f64 PI.f64 PI.f64) PI.f64))) (*.f64 (*.f64 (*.f64 n n) n) (*.f64 (*.f64 (*.f64 2 PI.f64) (*.f64 2 PI.f64)) (*.f64 2 PI.f64))) (*.f64 (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 (*.f64 (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64))) (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 n 2) (*.f64 (cbrt.f64 n) (*.f64 2 PI.f64)) (*.f64 (sqrt.f64 n) (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (-.f64 (log.f64 (sqrt.f64 k)) (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (+.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 PI.f64))) (/.f64 k 2)))) (-.f64 (log.f64 (sqrt.f64 k)) (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 PI.f64))) (/.f64 k 2)))) (-.f64 (log.f64 (sqrt.f64 k)) (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 k 2)))) (-.f64 (log.f64 (sqrt.f64 k)) (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 k 2)))) (-.f64 (log.f64 (sqrt.f64 k)) (-.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (log.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (-.f64 (log.f64 (sqrt.f64 k)) (log.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (log.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (exp.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k)) (/.f64 (*.f64 (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (*.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (*.f64 (*.f64 (sqrt.f64 k) (sqrt.f64 k)) (sqrt.f64 k)) (*.f64 (*.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))))) (cbrt.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (*.f64 (*.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (neg.f64 (sqrt.f64 k)) (neg.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 (sqrt.f64 k))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (pow.f64 n (/.f64 k 2)))) (/.f64 (cbrt.f64 (sqrt.f64 k)) (/.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (pow.f64 (*.f64 2 PI.f64) (/.f64 k 2)))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 k)) (cbrt.f64 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(sqrt.f64 2) (*.f64 n PI.f64)))) (+.f64 (*.f64 1/4 (/.f64 (*.f64 NAN.f64 (*.f64 (pow.f64 k 3) (*.f64 (log.f64 (*.f64 2 PI.f64)) (log.f64 n)))) (*.f64 PI.f64 (*.f64 (sqrt.f64 2) n)))) (*.f64 1/2 (/.f64 (*.f64 (pow.f64 k 2) (*.f64 (log.f64 (*.f64 2 PI.f64)) NAN.f64)) (*.f64 n (*.f64 (sqrt.f64 2) PI.f64))))))))) (+.f64 (/.f64 (*.f64 (pow.f64 NAN.f64 3) (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 2 PI.f64)) (log.f64 (/.f64 1 n))))))) (*.f64 k (*.f64 (pow.f64 n 2) (*.f64 (sqrt.f64 2) (pow.f64 PI.f64 2))))) (+.f64 (/.f64 (*.f64 (pow.f64 NAN.f64 5) (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 2 PI.f64)) (log.f64 (/.f64 1 n))))))) (*.f64 (pow.f64 k 2) (*.f64 (pow.f64 n 3) (*.f64 (sqrt.f64 2) (pow.f64 PI.f64 3))))) (/.f64 (*.f64 NAN.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 2 PI.f64)) (log.f64 (/.f64 1 n))))))) (*.f64 (sqrt.f64 2) (*.f64 n PI.f64))))) (-.f64 (+.f64 (/.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 -2 PI.f64)) (log.f64 (/.f64 -1 n)))))) PI.f64) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 -2 PI.f64)) (log.f64 (/.f64 -1 n)))))) (pow.f64 NAN.f64 2)) n)) (/.f64 (*.f64 (pow.f64 NAN.f64 2) (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 -2 PI.f64)) (log.f64 (/.f64 -1 n))))))) (*.f64 k PI.f64))) (-.f64 (+.f64 (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (*.f64 n (*.f64 (pow.f64 (log.f64 (*.f64 2 PI.f64)) 2) (*.f64 NAN.f64 PI.f64)))))) (+.f64 (*.f64 PI.f64 (*.f64 NAN.f64 (*.f64 n (sqrt.f64 2)))) (+.f64 (*.f64 1/4 (*.f64 NAN.f64 (*.f64 PI.f64 (*.f64 (pow.f64 k 2) (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (sqrt.f64 2) (*.f64 n (log.f64 n)))))))) (*.f64 1/8 (*.f64 (pow.f64 k 2) (*.f64 (sqrt.f64 2) (*.f64 n (*.f64 PI.f64 (*.f64 NAN.f64 (pow.f64 (log.f64 n) 2)))))))))) (+.f64 (*.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (sqrt.f64 2) (*.f64 NAN.f64 (*.f64 PI.f64 n)))))) (*.f64 1/2 (*.f64 k (*.f64 NAN.f64 (*.f64 (sqrt.f64 2) (*.f64 n (*.f64 (log.f64 n) PI.f64)))))))) (/.f64 (*.f64 NAN.f64 (*.f64 n (*.f64 (sqrt.f64 2) PI.f64))) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 2 PI.f64)) (log.f64 (/.f64 1 n)))))) k)) (-.f64 (+.f64 (/.f64 (*.f64 (pow.f64 NAN.f64 2) PI.f64) (*.f64 k (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 -2 PI.f64)) (log.f64 (/.f64 -1 n)))))))) (/.f64 PI.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 -2 PI.f64)) (log.f64 (/.f64 -1 n)))))))) (/.f64 (*.f64 (pow.f64 NAN.f64 2) (pow.f64 PI.f64 2)) (*.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 -2 PI.f64)) (log.f64 (/.f64 -1 n)))))) n))) 1.709 * * [simplify]: iteration 0 : 5578 enodes (cost 30219 ) 1.806 * [simplify]: Simplified to: (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (log.f64 (*.f64 n (*.f64 2 PI.f64))) (exp.f64 (*.f64 n (*.f64 2 PI.f64))) (*.f64 (pow.f64 n 3) (*.f64 8 (pow.f64 PI.f64 3))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) 3) (*.f64 (cbrt.f64 (*.f64 n (*.f64 2 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1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))))) (/.f64 1 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 k)) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4)))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 n) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 n))) (/.f64 1 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 n)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4)))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (pow.f64 n (/.f64 k 2))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))))) (/.f64 1 (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))))) (/.f64 1 (*.f64 (/.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4)))) (/.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 k)) (pow.f64 n (/.f64 k 2)))) (/.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 k)) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))))) (/.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 k)) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (/.f64 1 (*.f64 (sqrt.f64 (sqrt.f64 k)) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4)))) (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (*.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 k))) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (cbrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (sqrt.f64 (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (pow.f64 n (/.f64 k 2))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (cbrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4))) (/.f64 (sqrt.f64 n) (pow.f64 n (/.f64 k 2))) (/.f64 (sqrt.f64 n) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (sqrt.f64 n) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (sqrt.f64 n) (/.f64 (sqrt.f64 n) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (pow.f64 n (/.f64 k 2))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (/.f64 (sqrt.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4))) (/.f64 1 (pow.f64 n (/.f64 k 2))) (/.f64 1 (*.f64 (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (cbrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 1 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) 1 (/.f64 1 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 4))) 1 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) 1 (/.f64 1 (sqrt.f64 k)) (*.f64 (/.f64 1 (sqrt.f64 k)) (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (/.f64 (sqrt.f64 k) (*.f64 (cbrt.f64 1) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 (sqrt.f64 k) (/.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2)))) (/.f64 1 (sqrt.f64 k)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (+.f64 (*.f64 1/2 (/.f64 (*.f64 (*.f64 k k) (*.f64 (log.f64 n) NAN.f64)) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2)))) (+.f64 (*.f64 1/8 (/.f64 (*.f64 (pow.f64 k 3) (*.f64 NAN.f64 (pow.f64 (log.f64 n) 2))) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2)))) (+.f64 (/.f64 (*.f64 k NAN.f64) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2))) (+.f64 (*.f64 1/8 (/.f64 (*.f64 (pow.f64 k 3) (*.f64 NAN.f64 (pow.f64 (log.f64 (*.f64 2 PI.f64)) 2))) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2)))) (+.f64 (*.f64 1/4 (/.f64 (*.f64 NAN.f64 (*.f64 (pow.f64 k 3) (*.f64 (log.f64 n) (log.f64 (*.f64 2 PI.f64))))) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2)))) (*.f64 1/2 (/.f64 (*.f64 (*.f64 k k) (*.f64 (log.f64 (*.f64 2 PI.f64)) NAN.f64)) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2))))))))) (+.f64 (/.f64 (*.f64 (pow.f64 NAN.f64 3) (exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) k)))) (*.f64 k (*.f64 (*.f64 n n) (*.f64 PI.f64 (*.f64 PI.f64 (sqrt.f64 2)))))) (+.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) k))) (pow.f64 NAN.f64 5)) (*.f64 (*.f64 k k) (*.f64 (pow.f64 n 3) (*.f64 (pow.f64 PI.f64 3) (sqrt.f64 2))))) (/.f64 (*.f64 NAN.f64 (exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) k)))) (*.f64 (*.f64 n PI.f64) (sqrt.f64 2))))) (-.f64 (+.f64 (/.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))) PI.f64) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))) (*.f64 NAN.f64 NAN.f64)) n)) (/.f64 (*.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))) (*.f64 NAN.f64 NAN.f64)) (*.f64 PI.f64 k))) (-.f64 (+.f64 (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (*.f64 n (*.f64 PI.f64 (*.f64 NAN.f64 (pow.f64 (log.f64 (*.f64 2 PI.f64)) 2))))))) (+.f64 (*.f64 PI.f64 (*.f64 NAN.f64 (*.f64 n (sqrt.f64 2)))) (+.f64 (*.f64 1/4 (*.f64 NAN.f64 (*.f64 PI.f64 (*.f64 (*.f64 k k) (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (log.f64 n) (*.f64 n (sqrt.f64 2)))))))) (*.f64 1/8 (*.f64 (*.f64 k k) (*.f64 (sqrt.f64 2) (*.f64 n (*.f64 PI.f64 (*.f64 NAN.f64 (pow.f64 (log.f64 n) 2)))))))))) (*.f64 (*.f64 1/2 k) (+.f64 (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 PI.f64 (*.f64 NAN.f64 (*.f64 n (sqrt.f64 2))))) (*.f64 NAN.f64 (*.f64 (sqrt.f64 2) (*.f64 n (*.f64 PI.f64 (log.f64 n)))))))) (/.f64 (*.f64 PI.f64 (*.f64 NAN.f64 (*.f64 n (sqrt.f64 2)))) (*.f64 k (exp.f64 (*.f64 1/2 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) k))))) (-.f64 (*.f64 (+.f64 (/.f64 (*.f64 NAN.f64 NAN.f64) k) 1) (/.f64 PI.f64 (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))))) (/.f64 (*.f64 PI.f64 (*.f64 PI.f64 (*.f64 NAN.f64 NAN.f64))) (*.f64 n (exp.f64 (*.f64 1/2 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n))))))))) 1.816 * * * [progress]: adding candidates to table 3.230 * * [progress]: iteration 4 / 4 3.230 * * * [progress]: picking best candidate 3.246 * * * * [pick]: Picked # 3.246 * * * [progress]: localizing error 3.261 * * * [progress]: generating rewritten candidates 3.261 * * * * [progress]: [ 1 / 4 ] rewriting at (2) 3.301 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1 2 1) 3.307 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1) 3.312 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 3.353 * * * [progress]: generating series expansions 3.353 * * * * [progress]: [ 1 / 4 ] generating series at (2) 3.354 * [approximate]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in (n k) around 0 3.354 * [taylor]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in k 3.354 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in k 3.354 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.354 * [taylor]: Taking taylor expansion of 2 in k 3.354 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 3.354 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 3.354 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 3.354 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 3.354 * [taylor]: Taking taylor expansion of 1/2 in k 3.354 * [taylor]: Taking taylor expansion of k in k 3.354 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 3.354 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 3.354 * [taylor]: Taking taylor expansion of 2 in k 3.354 * [taylor]: Taking taylor expansion of (* n PI) in k 3.354 * [taylor]: Taking taylor expansion of n in k 3.354 * [taylor]: Taking taylor expansion of PI in k 3.354 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in k 3.354 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in k 3.354 * [taylor]: Taking taylor expansion of (* n PI) in k 3.354 * [taylor]: Taking taylor expansion of n in k 3.354 * [taylor]: Taking taylor expansion of PI in k 3.354 * [taylor]: Taking taylor expansion of k in k 3.355 * [taylor]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 3.355 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 3.355 * [taylor]: Taking taylor expansion of (sqrt 2) in n 3.355 * [taylor]: Taking taylor expansion of 2 in n 3.355 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 3.355 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 3.355 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 3.355 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.355 * [taylor]: Taking taylor expansion of 1/2 in n 3.355 * [taylor]: Taking taylor expansion of k in n 3.355 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.355 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.355 * [taylor]: Taking taylor expansion of 2 in n 3.355 * [taylor]: Taking taylor expansion of (* n PI) in n 3.355 * [taylor]: Taking taylor expansion of n in n 3.355 * [taylor]: Taking taylor expansion of PI in n 3.355 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 3.355 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in n 3.355 * [taylor]: Taking taylor expansion of (* n PI) in n 3.355 * [taylor]: Taking taylor expansion of n in n 3.355 * [taylor]: Taking taylor expansion of PI in n 3.355 * [taylor]: Taking taylor expansion of k in n 3.356 * [taylor]: Taking taylor expansion of (* (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ (* n PI) k))) in n 3.356 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (* n PI)) (* 1/2 k))) in n 3.356 * [taylor]: Taking taylor expansion of (sqrt 2) in n 3.356 * [taylor]: Taking taylor expansion of 2 in n 3.356 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 3.356 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 3.356 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 3.356 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.356 * [taylor]: Taking taylor expansion of 1/2 in n 3.356 * [taylor]: Taking taylor expansion of k in n 3.356 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.356 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.356 * [taylor]: Taking taylor expansion of 2 in n 3.356 * [taylor]: Taking taylor expansion of (* n PI) in n 3.356 * [taylor]: Taking taylor expansion of n in n 3.356 * [taylor]: Taking taylor expansion of PI in n 3.356 * [taylor]: Taking taylor expansion of (sqrt (/ (* n PI) k)) in n 3.356 * [taylor]: Taking taylor expansion of (/ (* n PI) k) in n 3.356 * [taylor]: Taking taylor expansion of (* n PI) in n 3.356 * [taylor]: Taking taylor expansion of n in n 3.356 * [taylor]: Taking taylor expansion of PI in n 3.356 * [taylor]: Taking taylor expansion of k in n 3.357 * [taylor]: Taking taylor expansion of 0 in k 3.358 * [taylor]: Taking taylor expansion of (/ (* (sqrt 2) (* NAN PI)) (* k (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k 3.358 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* NAN PI)) in k 3.358 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.358 * [taylor]: Taking taylor expansion of 2 in k 3.358 * [taylor]: Taking taylor expansion of (* NAN PI) in k 3.358 * [taylor]: Taking taylor expansion of NAN in k 3.358 * [taylor]: Taking taylor expansion of PI in k 3.358 * [taylor]: Taking taylor expansion of (* k (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k 3.358 * [taylor]: Taking taylor expansion of k in k 3.358 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k 3.358 * [taylor]: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k 3.358 * [taylor]: Taking taylor expansion of 1/2 in k 3.358 * [taylor]: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k 3.358 * [taylor]: Taking taylor expansion of k in k 3.358 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 3.358 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.358 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.358 * [taylor]: Taking taylor expansion of 2 in k 3.358 * [taylor]: Taking taylor expansion of PI in k 3.358 * [taylor]: Taking taylor expansion of (log n) in k 3.358 * [taylor]: Taking taylor expansion of n in k 3.361 * [taylor]: Taking taylor expansion of (/ (* (sqrt 2) (* (pow NAN 3) (pow PI 2))) (* (pow k 2) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k 3.361 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 3) (pow PI 2))) in k 3.361 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.361 * [taylor]: Taking taylor expansion of 2 in k 3.361 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (pow PI 2)) in k 3.361 * [taylor]: Taking taylor expansion of (pow NAN 3) in k 3.361 * [taylor]: Taking taylor expansion of NAN in k 3.361 * [taylor]: Taking taylor expansion of (pow PI 2) in k 3.361 * [taylor]: Taking taylor expansion of PI in k 3.361 * [taylor]: Taking taylor expansion of (* (pow k 2) (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k 3.361 * [taylor]: Taking taylor expansion of (pow k 2) in k 3.361 * [taylor]: Taking taylor expansion of k in k 3.361 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k 3.361 * [taylor]: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k 3.361 * [taylor]: Taking taylor expansion of 1/2 in k 3.361 * [taylor]: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k 3.361 * [taylor]: Taking taylor expansion of k in k 3.361 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 3.361 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.361 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.361 * [taylor]: Taking taylor expansion of 2 in k 3.361 * [taylor]: Taking taylor expansion of PI in k 3.361 * [taylor]: Taking taylor expansion of (log n) in k 3.361 * [taylor]: Taking taylor expansion of n in k 3.369 * [approximate]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in (n k) around 0 3.369 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in k 3.369 * [taylor]: Taking taylor expansion of (sqrt (/ (* k PI) n)) in k 3.369 * [taylor]: Taking taylor expansion of (/ (* k PI) n) in k 3.369 * [taylor]: Taking taylor expansion of (* k PI) in k 3.369 * [taylor]: Taking taylor expansion of k in k 3.369 * [taylor]: Taking taylor expansion of PI in k 3.369 * [taylor]: Taking taylor expansion of n in k 3.369 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 3.369 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.369 * [taylor]: Taking taylor expansion of 2 in k 3.369 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 3.369 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 3.369 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 3.369 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 3.369 * [taylor]: Taking taylor expansion of 1/2 in k 3.369 * [taylor]: Taking taylor expansion of k in k 3.369 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 3.370 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 3.370 * [taylor]: Taking taylor expansion of 2 in k 3.370 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.370 * [taylor]: Taking taylor expansion of PI in k 3.370 * [taylor]: Taking taylor expansion of n in k 3.370 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 3.370 * [taylor]: Taking taylor expansion of (sqrt (/ (* k PI) n)) in n 3.370 * [taylor]: Taking taylor expansion of (/ (* k PI) n) in n 3.370 * [taylor]: Taking taylor expansion of (* k PI) in n 3.370 * [taylor]: Taking taylor expansion of k in n 3.370 * [taylor]: Taking taylor expansion of PI in n 3.370 * [taylor]: Taking taylor expansion of n in n 3.370 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 3.370 * [taylor]: Taking taylor expansion of (sqrt 2) in n 3.370 * [taylor]: Taking taylor expansion of 2 in n 3.371 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 3.371 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 3.371 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 3.371 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 3.371 * [taylor]: Taking taylor expansion of 1/2 in n 3.371 * [taylor]: Taking taylor expansion of k in n 3.371 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.371 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.371 * [taylor]: Taking taylor expansion of 2 in n 3.371 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.371 * [taylor]: Taking taylor expansion of PI in n 3.371 * [taylor]: Taking taylor expansion of n in n 3.371 * [taylor]: Taking taylor expansion of (* (sqrt (/ (* k PI) n)) (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 3.371 * [taylor]: Taking taylor expansion of (sqrt (/ (* k PI) n)) in n 3.372 * [taylor]: Taking taylor expansion of (/ (* k PI) n) in n 3.372 * [taylor]: Taking taylor expansion of (* k PI) in n 3.372 * [taylor]: Taking taylor expansion of k in n 3.372 * [taylor]: Taking taylor expansion of PI in n 3.372 * [taylor]: Taking taylor expansion of n in n 3.372 * [taylor]: Taking taylor expansion of (/ (sqrt 2) (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 3.372 * [taylor]: Taking taylor expansion of (sqrt 2) in n 3.372 * [taylor]: Taking taylor expansion of 2 in n 3.372 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 3.372 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 3.372 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 3.372 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 3.372 * [taylor]: Taking taylor expansion of 1/2 in n 3.372 * [taylor]: Taking taylor expansion of k in n 3.372 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.372 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.372 * [taylor]: Taking taylor expansion of 2 in n 3.372 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.372 * [taylor]: Taking taylor expansion of PI in n 3.372 * [taylor]: Taking taylor expansion of n in n 3.373 * [taylor]: Taking taylor expansion of 0 in k 3.375 * [taylor]: Taking taylor expansion of (/ (* k (* (sqrt 2) (* NAN PI))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.375 * [taylor]: Taking taylor expansion of (* k (* (sqrt 2) (* NAN PI))) in k 3.375 * [taylor]: Taking taylor expansion of k in k 3.375 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* NAN PI)) in k 3.375 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.375 * [taylor]: Taking taylor expansion of 2 in k 3.375 * [taylor]: Taking taylor expansion of (* NAN PI) in k 3.375 * [taylor]: Taking taylor expansion of NAN in k 3.375 * [taylor]: Taking taylor expansion of PI in k 3.375 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.375 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.375 * [taylor]: Taking taylor expansion of 1/2 in k 3.375 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.375 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.375 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.375 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.375 * [taylor]: Taking taylor expansion of 2 in k 3.375 * [taylor]: Taking taylor expansion of PI in k 3.375 * [taylor]: Taking taylor expansion of (log n) in k 3.375 * [taylor]: Taking taylor expansion of n in k 3.375 * [taylor]: Taking taylor expansion of k in k 3.378 * [taylor]: Taking taylor expansion of (/ (* (pow k 2) (* (sqrt 2) (* (pow NAN 3) (pow PI 2)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.378 * [taylor]: Taking taylor expansion of (* (pow k 2) (* (sqrt 2) (* (pow NAN 3) (pow PI 2)))) in k 3.378 * [taylor]: Taking taylor expansion of (pow k 2) in k 3.378 * [taylor]: Taking taylor expansion of k in k 3.378 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 3) (pow PI 2))) in k 3.378 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.378 * [taylor]: Taking taylor expansion of 2 in k 3.379 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (pow PI 2)) in k 3.379 * [taylor]: Taking taylor expansion of (pow NAN 3) in k 3.379 * [taylor]: Taking taylor expansion of NAN in k 3.379 * [taylor]: Taking taylor expansion of (pow PI 2) in k 3.379 * [taylor]: Taking taylor expansion of PI in k 3.379 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.379 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.379 * [taylor]: Taking taylor expansion of 1/2 in k 3.379 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.379 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.379 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.379 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.379 * [taylor]: Taking taylor expansion of 2 in k 3.379 * [taylor]: Taking taylor expansion of PI in k 3.379 * [taylor]: Taking taylor expansion of (log n) in k 3.379 * [taylor]: Taking taylor expansion of n in k 3.379 * [taylor]: Taking taylor expansion of k in k 3.383 * [taylor]: Taking taylor expansion of (/ (* (pow k 3) (* (sqrt 2) (* (pow NAN 5) (pow PI 3)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.383 * [taylor]: Taking taylor expansion of (* (pow k 3) (* (sqrt 2) (* (pow NAN 5) (pow PI 3)))) in k 3.383 * [taylor]: Taking taylor expansion of (pow k 3) in k 3.383 * [taylor]: Taking taylor expansion of k in k 3.383 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 5) (pow PI 3))) in k 3.383 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.383 * [taylor]: Taking taylor expansion of 2 in k 3.383 * [taylor]: Taking taylor expansion of (* (pow NAN 5) (pow PI 3)) in k 3.383 * [taylor]: Taking taylor expansion of (pow NAN 5) in k 3.383 * [taylor]: Taking taylor expansion of NAN in k 3.383 * [taylor]: Taking taylor expansion of (pow PI 3) in k 3.383 * [taylor]: Taking taylor expansion of PI in k 3.383 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.383 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.383 * [taylor]: Taking taylor expansion of 1/2 in k 3.383 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.383 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.383 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.383 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.383 * [taylor]: Taking taylor expansion of 2 in k 3.383 * [taylor]: Taking taylor expansion of PI in k 3.383 * [taylor]: Taking taylor expansion of (log n) in k 3.383 * [taylor]: Taking taylor expansion of n in k 3.383 * [taylor]: Taking taylor expansion of k in k 3.389 * [taylor]: Taking taylor expansion of (/ (* (pow k 4) (* (sqrt 2) (* (pow NAN 7) (pow PI 4)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.389 * [taylor]: Taking taylor expansion of (* (pow k 4) (* (sqrt 2) (* (pow NAN 7) (pow PI 4)))) in k 3.389 * [taylor]: Taking taylor expansion of (pow k 4) in k 3.389 * [taylor]: Taking taylor expansion of k in k 3.389 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 7) (pow PI 4))) in k 3.389 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.389 * [taylor]: Taking taylor expansion of 2 in k 3.389 * [taylor]: Taking taylor expansion of (* (pow NAN 7) (pow PI 4)) in k 3.389 * [taylor]: Taking taylor expansion of (pow NAN 7) in k 3.389 * [taylor]: Taking taylor expansion of NAN in k 3.389 * [taylor]: Taking taylor expansion of (pow PI 4) in k 3.389 * [taylor]: Taking taylor expansion of PI in k 3.389 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.389 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.389 * [taylor]: Taking taylor expansion of 1/2 in k 3.389 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.389 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.389 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.389 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.389 * [taylor]: Taking taylor expansion of 2 in k 3.389 * [taylor]: Taking taylor expansion of PI in k 3.389 * [taylor]: Taking taylor expansion of (log n) in k 3.389 * [taylor]: Taking taylor expansion of n in k 3.389 * [taylor]: Taking taylor expansion of k in k 3.397 * [taylor]: Taking taylor expansion of (/ (* (pow k 5) (* (sqrt 2) (* (pow NAN 9) (pow PI 5)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.397 * [taylor]: Taking taylor expansion of (* (pow k 5) (* (sqrt 2) (* (pow NAN 9) (pow PI 5)))) in k 3.397 * [taylor]: Taking taylor expansion of (pow k 5) in k 3.397 * [taylor]: Taking taylor expansion of k in k 3.397 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 9) (pow PI 5))) in k 3.397 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.397 * [taylor]: Taking taylor expansion of 2 in k 3.397 * [taylor]: Taking taylor expansion of (* (pow NAN 9) (pow PI 5)) in k 3.397 * [taylor]: Taking taylor expansion of (pow NAN 9) in k 3.397 * [taylor]: Taking taylor expansion of NAN in k 3.397 * [taylor]: Taking taylor expansion of (pow PI 5) in k 3.397 * [taylor]: Taking taylor expansion of PI in k 3.397 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.397 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.397 * [taylor]: Taking taylor expansion of 1/2 in k 3.397 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.397 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.397 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.397 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.397 * [taylor]: Taking taylor expansion of 2 in k 3.397 * [taylor]: Taking taylor expansion of PI in k 3.397 * [taylor]: Taking taylor expansion of (log n) in k 3.397 * [taylor]: Taking taylor expansion of n in k 3.397 * [taylor]: Taking taylor expansion of k in k 3.406 * [taylor]: Taking taylor expansion of (/ (* (pow k 6) (* (sqrt 2) (* (pow NAN 11) (pow PI 6)))) (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.406 * [taylor]: Taking taylor expansion of (* (pow k 6) (* (sqrt 2) (* (pow NAN 11) (pow PI 6)))) in k 3.406 * [taylor]: Taking taylor expansion of (pow k 6) in k 3.406 * [taylor]: Taking taylor expansion of k in k 3.406 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (pow NAN 11) (pow PI 6))) in k 3.406 * [taylor]: Taking taylor expansion of (sqrt 2) in k 3.406 * [taylor]: Taking taylor expansion of 2 in k 3.407 * [taylor]: Taking taylor expansion of (* (pow NAN 11) (pow PI 6)) in k 3.407 * [taylor]: Taking taylor expansion of (pow NAN 11) in k 3.407 * [taylor]: Taking taylor expansion of NAN in k 3.407 * [taylor]: Taking taylor expansion of (pow PI 6) in k 3.407 * [taylor]: Taking taylor expansion of PI in k 3.407 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.407 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.407 * [taylor]: Taking taylor expansion of 1/2 in k 3.407 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.407 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.407 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.407 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.407 * [taylor]: Taking taylor expansion of 2 in k 3.407 * [taylor]: Taking taylor expansion of PI in k 3.407 * [taylor]: Taking taylor expansion of (log n) in k 3.407 * [taylor]: Taking taylor expansion of n in k 3.407 * [taylor]: Taking taylor expansion of k in k 3.410 * [approximate]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in (n k) around 0 3.410 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in k 3.410 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in k 3.410 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 3.410 * [taylor]: Taking taylor expansion of -2 in k 3.410 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.410 * [taylor]: Taking taylor expansion of PI in k 3.410 * [taylor]: Taking taylor expansion of n in k 3.410 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 3.410 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.410 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.410 * [taylor]: Taking taylor expansion of -1 in k 3.410 * [taylor]: Taking taylor expansion of k in k 3.411 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 3.411 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 3.411 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 3.411 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 3.411 * [taylor]: Taking taylor expansion of -1/2 in k 3.411 * [taylor]: Taking taylor expansion of k in k 3.411 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 3.411 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 3.411 * [taylor]: Taking taylor expansion of -2 in k 3.411 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.411 * [taylor]: Taking taylor expansion of PI in k 3.411 * [taylor]: Taking taylor expansion of n in k 3.411 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 3.411 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 3.412 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.412 * [taylor]: Taking taylor expansion of -2 in n 3.412 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.412 * [taylor]: Taking taylor expansion of PI in n 3.412 * [taylor]: Taking taylor expansion of n in n 3.412 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 3.412 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.412 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.412 * [taylor]: Taking taylor expansion of -1 in n 3.412 * [taylor]: Taking taylor expansion of k in n 3.412 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 3.412 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 3.412 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 3.412 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 3.412 * [taylor]: Taking taylor expansion of -1/2 in n 3.412 * [taylor]: Taking taylor expansion of k in n 3.412 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.412 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.412 * [taylor]: Taking taylor expansion of -2 in n 3.412 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.412 * [taylor]: Taking taylor expansion of PI in n 3.412 * [taylor]: Taking taylor expansion of n in n 3.413 * [taylor]: Taking taylor expansion of (/ (sqrt (* -2 (/ PI n))) (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 3.413 * [taylor]: Taking taylor expansion of (sqrt (* -2 (/ PI n))) in n 3.413 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.413 * [taylor]: Taking taylor expansion of -2 in n 3.413 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.413 * [taylor]: Taking taylor expansion of PI in n 3.413 * [taylor]: Taking taylor expansion of n in n 3.413 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 3.413 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.413 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.413 * [taylor]: Taking taylor expansion of -1 in n 3.413 * [taylor]: Taking taylor expansion of k in n 3.413 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 3.413 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 3.413 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 3.413 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 3.413 * [taylor]: Taking taylor expansion of -1/2 in n 3.413 * [taylor]: Taking taylor expansion of k in n 3.413 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.413 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.413 * [taylor]: Taking taylor expansion of -2 in n 3.413 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.413 * [taylor]: Taking taylor expansion of PI in n 3.413 * [taylor]: Taking taylor expansion of n in n 3.414 * [taylor]: Taking taylor expansion of (/ (* NAN PI) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 3.414 * [taylor]: Taking taylor expansion of (* NAN PI) in k 3.414 * [taylor]: Taking taylor expansion of NAN in k 3.414 * [taylor]: Taking taylor expansion of PI in k 3.414 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 3.414 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.414 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.414 * [taylor]: Taking taylor expansion of -1 in k 3.414 * [taylor]: Taking taylor expansion of k in k 3.414 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 3.414 * [taylor]: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 3.414 * [taylor]: Taking taylor expansion of -1/2 in k 3.414 * [taylor]: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 3.414 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 3.414 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 3.414 * [taylor]: Taking taylor expansion of (* -2 PI) in k 3.414 * [taylor]: Taking taylor expansion of -2 in k 3.414 * [taylor]: Taking taylor expansion of PI in k 3.414 * [taylor]: Taking taylor expansion of (log n) in k 3.414 * [taylor]: Taking taylor expansion of n in k 3.414 * [taylor]: Taking taylor expansion of k in k 3.417 * [taylor]: Taking taylor expansion of (/ (* (pow NAN 3) (pow PI 2)) (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 3.417 * [taylor]: Taking taylor expansion of (* (pow NAN 3) (pow PI 2)) in k 3.417 * [taylor]: Taking taylor expansion of (pow NAN 3) in k 3.417 * [taylor]: Taking taylor expansion of NAN in k 3.417 * [taylor]: Taking taylor expansion of (pow PI 2) in k 3.417 * [taylor]: Taking taylor expansion of PI in k 3.417 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 3.417 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.417 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.417 * [taylor]: Taking taylor expansion of -1 in k 3.417 * [taylor]: Taking taylor expansion of k in k 3.417 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 3.417 * [taylor]: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 3.417 * [taylor]: Taking taylor expansion of -1/2 in k 3.417 * [taylor]: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 3.417 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 3.417 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 3.417 * [taylor]: Taking taylor expansion of (* -2 PI) in k 3.417 * [taylor]: Taking taylor expansion of -2 in k 3.417 * [taylor]: Taking taylor expansion of PI in k 3.417 * [taylor]: Taking taylor expansion of (log n) in k 3.417 * [taylor]: Taking taylor expansion of n in k 3.417 * [taylor]: Taking taylor expansion of k in k 3.420 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1 2 1) 3.420 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 3.420 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.420 * [taylor]: Taking taylor expansion of 2 in n 3.420 * [taylor]: Taking taylor expansion of (* n PI) in n 3.420 * [taylor]: Taking taylor expansion of n in n 3.420 * [taylor]: Taking taylor expansion of PI in n 3.420 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.420 * [taylor]: Taking taylor expansion of 2 in n 3.420 * [taylor]: Taking taylor expansion of (* n PI) in n 3.420 * [taylor]: Taking taylor expansion of n in n 3.420 * [taylor]: Taking taylor expansion of PI in n 3.422 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 3.422 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.422 * [taylor]: Taking taylor expansion of 2 in n 3.422 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.422 * [taylor]: Taking taylor expansion of PI in n 3.422 * [taylor]: Taking taylor expansion of n in n 3.422 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.422 * [taylor]: Taking taylor expansion of 2 in n 3.422 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.422 * [taylor]: Taking taylor expansion of PI in n 3.422 * [taylor]: Taking taylor expansion of n in n 3.423 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 3.423 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.423 * [taylor]: Taking taylor expansion of -2 in n 3.423 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.423 * [taylor]: Taking taylor expansion of PI in n 3.423 * [taylor]: Taking taylor expansion of n in n 3.423 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.423 * [taylor]: Taking taylor expansion of -2 in n 3.423 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.423 * [taylor]: Taking taylor expansion of PI in n 3.423 * [taylor]: Taking taylor expansion of n in n 3.424 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1) 3.424 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 3.424 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.424 * [taylor]: Taking taylor expansion of 2 in n 3.424 * [taylor]: Taking taylor expansion of (* n PI) in n 3.424 * [taylor]: Taking taylor expansion of n in n 3.424 * [taylor]: Taking taylor expansion of PI in n 3.424 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.424 * [taylor]: Taking taylor expansion of 2 in n 3.424 * [taylor]: Taking taylor expansion of (* n PI) in n 3.424 * [taylor]: Taking taylor expansion of n in n 3.424 * [taylor]: Taking taylor expansion of PI in n 3.425 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 3.425 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.425 * [taylor]: Taking taylor expansion of 2 in n 3.425 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.425 * [taylor]: Taking taylor expansion of PI in n 3.425 * [taylor]: Taking taylor expansion of n in n 3.425 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.425 * [taylor]: Taking taylor expansion of 2 in n 3.425 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.425 * [taylor]: Taking taylor expansion of PI in n 3.425 * [taylor]: Taking taylor expansion of n in n 3.426 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 3.426 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.426 * [taylor]: Taking taylor expansion of -2 in n 3.426 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.426 * [taylor]: Taking taylor expansion of PI in n 3.426 * [taylor]: Taking taylor expansion of n in n 3.426 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.426 * [taylor]: Taking taylor expansion of -2 in n 3.426 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.426 * [taylor]: Taking taylor expansion of PI in n 3.426 * [taylor]: Taking taylor expansion of n in n 3.427 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 3.428 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ 1 k))) in (n k) around 0 3.428 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ 1 k))) in k 3.428 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) in k 3.428 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in k 3.428 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in k 3.428 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in k 3.428 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 3.428 * [taylor]: Taking taylor expansion of 1/2 in k 3.428 * [taylor]: Taking taylor expansion of k in k 3.428 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 3.428 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 3.428 * [taylor]: Taking taylor expansion of 2 in k 3.428 * [taylor]: Taking taylor expansion of (* n PI) in k 3.428 * [taylor]: Taking taylor expansion of n in k 3.428 * [taylor]: Taking taylor expansion of PI in k 3.428 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.428 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.428 * [taylor]: Taking taylor expansion of k in k 3.428 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ 1 k))) in n 3.428 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) in n 3.428 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 3.428 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 3.428 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 3.428 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.428 * [taylor]: Taking taylor expansion of 1/2 in n 3.429 * [taylor]: Taking taylor expansion of k in n 3.429 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.429 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.429 * [taylor]: Taking taylor expansion of 2 in n 3.429 * [taylor]: Taking taylor expansion of (* n PI) in n 3.429 * [taylor]: Taking taylor expansion of n in n 3.429 * [taylor]: Taking taylor expansion of PI in n 3.429 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.429 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.429 * [taylor]: Taking taylor expansion of k in n 3.429 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) (sqrt (/ 1 k))) in n 3.429 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (* 1/2 k))) in n 3.429 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 k)) in n 3.429 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 k) (log (* 2 (* n PI))))) in n 3.429 * [taylor]: Taking taylor expansion of (* (* 1/2 k) (log (* 2 (* n PI)))) in n 3.429 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.429 * [taylor]: Taking taylor expansion of 1/2 in n 3.429 * [taylor]: Taking taylor expansion of k in n 3.429 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.429 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.429 * [taylor]: Taking taylor expansion of 2 in n 3.429 * [taylor]: Taking taylor expansion of (* n PI) in n 3.429 * [taylor]: Taking taylor expansion of n in n 3.429 * [taylor]: Taking taylor expansion of PI in n 3.430 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.430 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.430 * [taylor]: Taking taylor expansion of k in n 3.430 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))))) in k 3.430 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.430 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.430 * [taylor]: Taking taylor expansion of k in k 3.430 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n)))))) in k 3.430 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* k (+ (log (* 2 PI)) (log n))))) in k 3.430 * [taylor]: Taking taylor expansion of (* 1/2 (* k (+ (log (* 2 PI)) (log n)))) in k 3.430 * [taylor]: Taking taylor expansion of 1/2 in k 3.430 * [taylor]: Taking taylor expansion of (* k (+ (log (* 2 PI)) (log n))) in k 3.430 * [taylor]: Taking taylor expansion of k in k 3.430 * [taylor]: Taking taylor expansion of (+ (log (* 2 PI)) (log n)) in k 3.430 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.430 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.431 * [taylor]: Taking taylor expansion of 2 in k 3.431 * [taylor]: Taking taylor expansion of PI in k 3.431 * [taylor]: Taking taylor expansion of (log n) in k 3.431 * [taylor]: Taking taylor expansion of n in k 3.432 * [taylor]: Taking taylor expansion of 0 in k 3.437 * [taylor]: Taking taylor expansion of 0 in k 3.441 * [taylor]: Taking taylor expansion of 0 in k 3.449 * [approximate]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k)))) in (n k) around 0 3.449 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k)))) in k 3.449 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.449 * [taylor]: Taking taylor expansion of k in k 3.450 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k))) in k 3.450 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in k 3.450 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in k 3.450 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in k 3.450 * [taylor]: Taking taylor expansion of (/ 1/2 k) in k 3.450 * [taylor]: Taking taylor expansion of 1/2 in k 3.450 * [taylor]: Taking taylor expansion of k in k 3.450 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 3.450 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 3.450 * [taylor]: Taking taylor expansion of 2 in k 3.450 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.450 * [taylor]: Taking taylor expansion of PI in k 3.450 * [taylor]: Taking taylor expansion of n in k 3.450 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 3.450 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.450 * [taylor]: Taking taylor expansion of k in n 3.450 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 3.450 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 3.450 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 3.450 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 3.450 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 3.450 * [taylor]: Taking taylor expansion of 1/2 in n 3.450 * [taylor]: Taking taylor expansion of k in n 3.450 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.450 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.450 * [taylor]: Taking taylor expansion of 2 in n 3.450 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.450 * [taylor]: Taking taylor expansion of PI in n 3.451 * [taylor]: Taking taylor expansion of n in n 3.451 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k)))) in n 3.451 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.451 * [taylor]: Taking taylor expansion of k in n 3.451 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (/ 1/2 k))) in n 3.451 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (/ 1/2 k)) in n 3.451 * [taylor]: Taking taylor expansion of (exp (* (/ 1/2 k) (log (* 2 (/ PI n))))) in n 3.451 * [taylor]: Taking taylor expansion of (* (/ 1/2 k) (log (* 2 (/ PI n)))) in n 3.451 * [taylor]: Taking taylor expansion of (/ 1/2 k) in n 3.451 * [taylor]: Taking taylor expansion of 1/2 in n 3.451 * [taylor]: Taking taylor expansion of k in n 3.451 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.451 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.451 * [taylor]: Taking taylor expansion of 2 in n 3.451 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.451 * [taylor]: Taking taylor expansion of PI in n 3.451 * [taylor]: Taking taylor expansion of n in n 3.452 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))))) in k 3.452 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.452 * [taylor]: Taking taylor expansion of k in k 3.452 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)))) in k 3.452 * [taylor]: Taking taylor expansion of (exp (* 1/2 (/ (- (log (* 2 PI)) (log n)) k))) in k 3.452 * [taylor]: Taking taylor expansion of (* 1/2 (/ (- (log (* 2 PI)) (log n)) k)) in k 3.452 * [taylor]: Taking taylor expansion of 1/2 in k 3.452 * [taylor]: Taking taylor expansion of (/ (- (log (* 2 PI)) (log n)) k) in k 3.452 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.452 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.452 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.452 * [taylor]: Taking taylor expansion of 2 in k 3.452 * [taylor]: Taking taylor expansion of PI in k 3.452 * [taylor]: Taking taylor expansion of (log n) in k 3.452 * [taylor]: Taking taylor expansion of n in k 3.452 * [taylor]: Taking taylor expansion of k in k 3.453 * [taylor]: Taking taylor expansion of 0 in k 3.455 * [taylor]: Taking taylor expansion of 0 in k 3.457 * [taylor]: Taking taylor expansion of 0 in k 3.459 * [approximate]: Taking taylor expansion of (/ 1 (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in (n k) around 0 3.459 * [taylor]: Taking taylor expansion of (/ 1 (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in k 3.459 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in k 3.459 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.459 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.459 * [taylor]: Taking taylor expansion of -1 in k 3.459 * [taylor]: Taking taylor expansion of k in k 3.459 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in k 3.459 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in k 3.460 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in k 3.460 * [taylor]: Taking taylor expansion of (/ -1/2 k) in k 3.460 * [taylor]: Taking taylor expansion of -1/2 in k 3.460 * [taylor]: Taking taylor expansion of k in k 3.460 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 3.460 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 3.460 * [taylor]: Taking taylor expansion of -2 in k 3.460 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.460 * [taylor]: Taking taylor expansion of PI in k 3.460 * [taylor]: Taking taylor expansion of n in k 3.460 * [taylor]: Taking taylor expansion of (/ 1 (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 3.460 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 3.460 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.460 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.460 * [taylor]: Taking taylor expansion of -1 in n 3.460 * [taylor]: Taking taylor expansion of k in n 3.460 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 3.460 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 3.460 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 3.460 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 3.460 * [taylor]: Taking taylor expansion of -1/2 in n 3.461 * [taylor]: Taking taylor expansion of k in n 3.461 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.461 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.461 * [taylor]: Taking taylor expansion of -2 in n 3.461 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.461 * [taylor]: Taking taylor expansion of PI in n 3.461 * [taylor]: Taking taylor expansion of n in n 3.461 * [taylor]: Taking taylor expansion of (/ 1 (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k)))) in n 3.461 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (/ -1/2 k))) in n 3.461 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.461 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.461 * [taylor]: Taking taylor expansion of -1 in n 3.461 * [taylor]: Taking taylor expansion of k in n 3.461 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (/ -1/2 k)) in n 3.461 * [taylor]: Taking taylor expansion of (exp (* (/ -1/2 k) (log (* -2 (/ PI n))))) in n 3.461 * [taylor]: Taking taylor expansion of (* (/ -1/2 k) (log (* -2 (/ PI n)))) in n 3.461 * [taylor]: Taking taylor expansion of (/ -1/2 k) in n 3.461 * [taylor]: Taking taylor expansion of -1/2 in n 3.461 * [taylor]: Taking taylor expansion of k in n 3.462 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.462 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.462 * [taylor]: Taking taylor expansion of -2 in n 3.462 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.462 * [taylor]: Taking taylor expansion of PI in n 3.462 * [taylor]: Taking taylor expansion of n in n 3.462 * [taylor]: Taking taylor expansion of (/ 1 (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))))) in k 3.462 * [taylor]: Taking taylor expansion of (* (sqrt (/ -1 k)) (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)))) in k 3.462 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.462 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.462 * [taylor]: Taking taylor expansion of -1 in k 3.462 * [taylor]: Taking taylor expansion of k in k 3.462 * [taylor]: Taking taylor expansion of (exp (* -1/2 (/ (- (log (* -2 PI)) (log n)) k))) in k 3.462 * [taylor]: Taking taylor expansion of (* -1/2 (/ (- (log (* -2 PI)) (log n)) k)) in k 3.462 * [taylor]: Taking taylor expansion of -1/2 in k 3.462 * [taylor]: Taking taylor expansion of (/ (- (log (* -2 PI)) (log n)) k) in k 3.462 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 3.462 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 3.462 * [taylor]: Taking taylor expansion of (* -2 PI) in k 3.462 * [taylor]: Taking taylor expansion of -2 in k 3.462 * [taylor]: Taking taylor expansion of PI in k 3.463 * [taylor]: Taking taylor expansion of (log n) in k 3.463 * [taylor]: Taking taylor expansion of n in k 3.463 * [taylor]: Taking taylor expansion of k in k 3.464 * [taylor]: Taking taylor expansion of 0 in k 3.466 * [taylor]: Taking taylor expansion of 0 in k 3.469 * [taylor]: Taking taylor expansion of 0 in k 3.470 * * * [progress]: simplifying candidates 3.476 * [simplify]: Simplifying using # : (*.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 (/.f64 1 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) (/.f64 k 2))) (sqrt.f64 k))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (-.f64 (neg.f64 (*.f64 (+.f64 (log.f64 n) (+.f64 (log.f64 2) (log.f64 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (-.f64 (neg.f64 (*.f64 (+.f64 (log.f64 n) (log.f64 (*.f64 2 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (-.f64 (neg.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (-.f64 (neg.f64 (*.f64 (log.f64 (*.f64 n (*.f64 2 PI.f64))) (/.f64 k 2))) (log.f64 (sqrt.f64 k)))) (+.f64 (log.f64 (sqrt.f64 (*.f64 n (*.f64 2 PI.f64)))) (-.f64 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(/.f64 (*.f64 NAN.f64 NAN.f64) k) 1) (/.f64 PI.f64 (sqrt.f64 (exp.f64 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))))) (/.f64 (*.f64 PI.f64 (*.f64 PI.f64 (*.f64 NAN.f64 NAN.f64))) (*.f64 n (sqrt.f64 (exp.f64 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n))))))))) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (*.f64 n (*.f64 2 PI.f64)) (-.f64 (+.f64 NAN.f64 (+.f64 (*.f64 k (pow.f64 NAN.f64 3)) (+.f64 (*.f64 1/4 (*.f64 (*.f64 k k) (*.f64 (log.f64 (*.f64 2 PI.f64)) (*.f64 (log.f64 n) NAN.f64)))) (+.f64 (*.f64 (*.f64 k k) (pow.f64 NAN.f64 5)) (*.f64 (*.f64 (*.f64 k k) 1/8) (+.f64 (*.f64 NAN.f64 (pow.f64 (log.f64 n) 2)) (*.f64 NAN.f64 (pow.f64 (log.f64 (*.f64 2 PI.f64)) 2)))))))) (+.f64 (*.f64 1/2 (*.f64 k (*.f64 (log.f64 n) NAN.f64))) (+.f64 (*.f64 1/2 (*.f64 k (*.f64 (log.f64 (*.f64 2 PI.f64)) NAN.f64))) (*.f64 (*.f64 1/2 (*.f64 k k)) (+.f64 (*.f64 (log.f64 (*.f64 2 PI.f64)) (pow.f64 NAN.f64 3)) (*.f64 (log.f64 n) (pow.f64 NAN.f64 3))))))) (+.f64 (/.f64 (pow.f64 NAN.f64 3) (*.f64 (*.f64 k k) (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) k)))) (+.f64 (/.f64 (pow.f64 NAN.f64 5) (*.f64 (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) k)) (pow.f64 k 3))) (/.f64 NAN.f64 (*.f64 k (sqrt.f64 (pow.f64 (*.f64 n (*.f64 2 PI.f64)) k)))))) (+.f64 (/.f64 1 (*.f64 NAN.f64 (sqrt.f64 (exp.f64 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n)))))))) (/.f64 NAN.f64 (*.f64 k (sqrt.f64 (exp.f64 (*.f64 k (-.f64 (log.f64 (*.f64 PI.f64 -2)) (log.f64 (/.f64 -1 n))))))))) 3.580 * * * [progress]: adding candidates to table 3.871 * [progress]: [Phase 3 of 3] Extracting. 3.872 * * [regime]: Finding splitpoints for: (# # # # # # # # # #) 3.875 * * * [regime-changes]: Trying 2 branch expressions: (n k) 3.875 * * * * [regimes]: Trying to branch on n from (# # # # # # # # # #) 3.916 * * * * [regimes]: Trying to branch on k from (# # # # # # # # # #) 3.958 * * * [regime]: Found split indices: #