45.094 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.159 * * * [progress]: [2/2] Setting up program. 0.167 * [progress]: [Phase 2 of 3] Improving. 0.167 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.167 * [simplify]: Sending expressions to egg_math: (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) 0.285 * * [progress]: iteration 1 / 4 0.285 * * * [progress]: picking best candidate 0.288 * * * * [pick]: Picked # 0.288 * * * [progress]: localizing error 0.306 * * * [progress]: generating rewritten candidates 0.306 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 0.340 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 0.359 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 0.376 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 0.438 * * * [progress]: generating series expansions 0.438 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 0.439 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 0.439 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 0.439 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.439 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.439 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.439 * [taylor]: Taking taylor expansion of 0.5 in k 0.439 * [backup-simplify]: Simplify 0.5 into 0.5 0.439 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.439 * [taylor]: Taking taylor expansion of 1.0 in k 0.439 * [backup-simplify]: Simplify 1.0 into 1.0 0.439 * [taylor]: Taking taylor expansion of k in k 0.439 * [backup-simplify]: Simplify 0 into 0 0.439 * [backup-simplify]: Simplify 1 into 1 0.439 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.439 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.439 * [taylor]: Taking taylor expansion of 2.0 in k 0.439 * [backup-simplify]: Simplify 2.0 into 2.0 0.439 * [taylor]: Taking taylor expansion of (* n PI) in k 0.439 * [taylor]: Taking taylor expansion of n in k 0.439 * [backup-simplify]: Simplify n into n 0.439 * [taylor]: Taking taylor expansion of PI in k 0.439 * [backup-simplify]: Simplify PI into PI 0.439 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.439 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.439 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.439 * [backup-simplify]: Simplify (- 0) into 0 0.440 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.440 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.440 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.440 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.440 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.440 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.440 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.440 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.440 * [taylor]: Taking taylor expansion of 0.5 in n 0.440 * [backup-simplify]: Simplify 0.5 into 0.5 0.440 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.440 * [taylor]: Taking taylor expansion of 1.0 in n 0.440 * [backup-simplify]: Simplify 1.0 into 1.0 0.441 * [taylor]: Taking taylor expansion of k in n 0.441 * [backup-simplify]: Simplify k into k 0.441 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.441 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.441 * [taylor]: Taking taylor expansion of 2.0 in n 0.441 * [backup-simplify]: Simplify 2.0 into 2.0 0.441 * [taylor]: Taking taylor expansion of (* n PI) in n 0.441 * [taylor]: Taking taylor expansion of n in n 0.441 * [backup-simplify]: Simplify 0 into 0 0.441 * [backup-simplify]: Simplify 1 into 1 0.441 * [taylor]: Taking taylor expansion of PI in n 0.441 * [backup-simplify]: Simplify PI into PI 0.441 * [backup-simplify]: Simplify (* 0 PI) into 0 0.441 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.442 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.443 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.444 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.444 * [backup-simplify]: Simplify (- k) into (- k) 0.444 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.444 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.445 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.446 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.447 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.447 * [taylor]: Taking taylor expansion of 0.5 in n 0.447 * [backup-simplify]: Simplify 0.5 into 0.5 0.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.447 * [taylor]: Taking taylor expansion of 1.0 in n 0.447 * [backup-simplify]: Simplify 1.0 into 1.0 0.447 * [taylor]: Taking taylor expansion of k in n 0.447 * [backup-simplify]: Simplify k into k 0.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.447 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.447 * [taylor]: Taking taylor expansion of 2.0 in n 0.447 * [backup-simplify]: Simplify 2.0 into 2.0 0.447 * [taylor]: Taking taylor expansion of (* n PI) in n 0.447 * [taylor]: Taking taylor expansion of n in n 0.447 * [backup-simplify]: Simplify 0 into 0 0.447 * [backup-simplify]: Simplify 1 into 1 0.447 * [taylor]: Taking taylor expansion of PI in n 0.447 * [backup-simplify]: Simplify PI into PI 0.447 * [backup-simplify]: Simplify (* 0 PI) into 0 0.448 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.448 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.449 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.450 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.450 * [backup-simplify]: Simplify (- k) into (- k) 0.450 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.450 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.451 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.452 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.453 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.453 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 0.453 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 0.453 * [taylor]: Taking taylor expansion of 0.5 in k 0.453 * [backup-simplify]: Simplify 0.5 into 0.5 0.453 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 0.453 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.453 * [taylor]: Taking taylor expansion of 1.0 in k 0.453 * [backup-simplify]: Simplify 1.0 into 1.0 0.453 * [taylor]: Taking taylor expansion of k in k 0.453 * [backup-simplify]: Simplify 0 into 0 0.453 * [backup-simplify]: Simplify 1 into 1 0.453 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 0.453 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.453 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.453 * [taylor]: Taking taylor expansion of 2.0 in k 0.454 * [backup-simplify]: Simplify 2.0 into 2.0 0.454 * [taylor]: Taking taylor expansion of PI in k 0.454 * [backup-simplify]: Simplify PI into PI 0.454 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.455 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.455 * [taylor]: Taking taylor expansion of (log n) in k 0.455 * [taylor]: Taking taylor expansion of n in k 0.455 * [backup-simplify]: Simplify n into n 0.455 * [backup-simplify]: Simplify (log n) into (log n) 0.455 * [backup-simplify]: Simplify (- 0) into 0 0.455 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.456 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 0.457 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 0.461 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 0.462 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.462 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0.463 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.465 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.465 * [backup-simplify]: Simplify (- 0) into 0 0.465 * [backup-simplify]: Simplify (+ 0 0) into 0 0.466 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 0.467 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.468 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 0.469 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.469 * [taylor]: Taking taylor expansion of 0 in k 0.469 * [backup-simplify]: Simplify 0 into 0 0.469 * [backup-simplify]: Simplify 0 into 0 0.470 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.471 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.471 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 0.472 * [backup-simplify]: Simplify (+ 0 0) into 0 0.472 * [backup-simplify]: Simplify (- 1) into -1 0.472 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.473 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 0.474 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 0.476 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.478 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0.479 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.482 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.482 * [backup-simplify]: Simplify (- 0) into 0 0.483 * [backup-simplify]: Simplify (+ 0 0) into 0 0.484 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 0.485 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.487 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.489 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.489 * [taylor]: Taking taylor expansion of 0 in k 0.490 * [backup-simplify]: Simplify 0 into 0 0.490 * [backup-simplify]: Simplify 0 into 0 0.490 * [backup-simplify]: Simplify 0 into 0 0.491 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.495 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.497 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 0.497 * [backup-simplify]: Simplify (+ 0 0) into 0 0.497 * [backup-simplify]: Simplify (- 0) into 0 0.498 * [backup-simplify]: Simplify (+ 0 0) into 0 0.499 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 0.500 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 0.503 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.506 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0.513 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 0.513 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 0.513 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 0.513 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 0.514 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 0.514 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 0.514 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 0.514 * [taylor]: Taking taylor expansion of 0.5 in k 0.514 * [backup-simplify]: Simplify 0.5 into 0.5 0.514 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.514 * [taylor]: Taking taylor expansion of 1.0 in k 0.514 * [backup-simplify]: Simplify 1.0 into 1.0 0.514 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.514 * [taylor]: Taking taylor expansion of k in k 0.514 * [backup-simplify]: Simplify 0 into 0 0.514 * [backup-simplify]: Simplify 1 into 1 0.514 * [backup-simplify]: Simplify (/ 1 1) into 1 0.514 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 0.514 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 0.514 * [taylor]: Taking taylor expansion of 2.0 in k 0.514 * [backup-simplify]: Simplify 2.0 into 2.0 0.514 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.514 * [taylor]: Taking taylor expansion of PI in k 0.514 * [backup-simplify]: Simplify PI into PI 0.514 * [taylor]: Taking taylor expansion of n in k 0.514 * [backup-simplify]: Simplify n into n 0.514 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.514 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 0.514 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 0.515 * [backup-simplify]: Simplify (- 1) into -1 0.515 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.515 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 0.515 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 0.515 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 0.515 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.515 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.515 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.515 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.515 * [taylor]: Taking taylor expansion of 0.5 in n 0.515 * [backup-simplify]: Simplify 0.5 into 0.5 0.516 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.516 * [taylor]: Taking taylor expansion of 1.0 in n 0.516 * [backup-simplify]: Simplify 1.0 into 1.0 0.516 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.516 * [taylor]: Taking taylor expansion of k in n 0.516 * [backup-simplify]: Simplify k into k 0.516 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.516 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.516 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.516 * [taylor]: Taking taylor expansion of 2.0 in n 0.516 * [backup-simplify]: Simplify 2.0 into 2.0 0.516 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.516 * [taylor]: Taking taylor expansion of PI in n 0.516 * [backup-simplify]: Simplify PI into PI 0.516 * [taylor]: Taking taylor expansion of n in n 0.516 * [backup-simplify]: Simplify 0 into 0 0.516 * [backup-simplify]: Simplify 1 into 1 0.516 * [backup-simplify]: Simplify (/ PI 1) into PI 0.516 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.517 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.517 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.517 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.517 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.518 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.519 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.520 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.520 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 0.520 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 0.520 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 0.520 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 0.520 * [taylor]: Taking taylor expansion of 0.5 in n 0.520 * [backup-simplify]: Simplify 0.5 into 0.5 0.520 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 0.520 * [taylor]: Taking taylor expansion of 1.0 in n 0.520 * [backup-simplify]: Simplify 1.0 into 1.0 0.520 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.520 * [taylor]: Taking taylor expansion of k in n 0.520 * [backup-simplify]: Simplify k into k 0.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.520 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 0.520 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.520 * [taylor]: Taking taylor expansion of 2.0 in n 0.520 * [backup-simplify]: Simplify 2.0 into 2.0 0.520 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.520 * [taylor]: Taking taylor expansion of PI in n 0.520 * [backup-simplify]: Simplify PI into PI 0.520 * [taylor]: Taking taylor expansion of n in n 0.520 * [backup-simplify]: Simplify 0 into 0 0.520 * [backup-simplify]: Simplify 1 into 1 0.521 * [backup-simplify]: Simplify (/ PI 1) into PI 0.521 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.521 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.522 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 0.522 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 0.522 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 0.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.523 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 0.524 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.524 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 0.524 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 0.524 * [taylor]: Taking taylor expansion of 0.5 in k 0.524 * [backup-simplify]: Simplify 0.5 into 0.5 0.524 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 0.524 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 0.524 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 0.524 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 0.524 * [taylor]: Taking taylor expansion of 2.0 in k 0.524 * [backup-simplify]: Simplify 2.0 into 2.0 0.524 * [taylor]: Taking taylor expansion of PI in k 0.524 * [backup-simplify]: Simplify PI into PI 0.525 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.525 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.525 * [taylor]: Taking taylor expansion of (log n) in k 0.525 * [taylor]: Taking taylor expansion of n in k 0.525 * [backup-simplify]: Simplify n into n 0.526 * [backup-simplify]: Simplify (log n) into (log n) 0.526 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 0.526 * [taylor]: Taking taylor expansion of 1.0 in k 0.526 * [backup-simplify]: Simplify 1.0 into 1.0 0.526 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.526 * [taylor]: Taking taylor expansion of k in k 0.526 * [backup-simplify]: Simplify 0 into 0 0.526 * [backup-simplify]: Simplify 1 into 1 0.526 * [backup-simplify]: Simplify (/ 1 1) into 1 0.526 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.527 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 0.527 * [backup-simplify]: Simplify (- 1) into -1 0.527 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.528 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 0.528 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 0.529 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.530 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0.531 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.531 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.532 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 0.532 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.533 * [backup-simplify]: Simplify (- 0) into 0 0.533 * [backup-simplify]: Simplify (+ 0 0) into 0 0.533 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 0.535 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.536 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 0.538 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.538 * [taylor]: Taking taylor expansion of 0 in k 0.538 * [backup-simplify]: Simplify 0 into 0 0.538 * [backup-simplify]: Simplify 0 into 0 0.538 * [backup-simplify]: Simplify 0 into 0 0.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.541 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.545 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 0.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.546 * [backup-simplify]: Simplify (- 0) into 0 0.546 * [backup-simplify]: Simplify (+ 0 0) into 0 0.547 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 0.549 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.550 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 0.553 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.553 * [taylor]: Taking taylor expansion of 0 in k 0.553 * [backup-simplify]: Simplify 0 into 0 0.553 * [backup-simplify]: Simplify 0 into 0 0.553 * [backup-simplify]: Simplify 0 into 0 0.553 * [backup-simplify]: Simplify 0 into 0 0.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.562 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 0.562 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.563 * [backup-simplify]: Simplify (- 0) into 0 0.563 * [backup-simplify]: Simplify (+ 0 0) into 0 0.564 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 0.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 0.568 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 0.571 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.571 * [taylor]: Taking taylor expansion of 0 in k 0.571 * [backup-simplify]: Simplify 0 into 0 0.571 * [backup-simplify]: Simplify 0 into 0 0.573 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 0.573 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 0.573 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 0.574 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 0.574 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 0.574 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 0.574 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 0.574 * [taylor]: Taking taylor expansion of 0.5 in k 0.574 * [backup-simplify]: Simplify 0.5 into 0.5 0.574 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.574 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.574 * [taylor]: Taking taylor expansion of k in k 0.574 * [backup-simplify]: Simplify 0 into 0 0.574 * [backup-simplify]: Simplify 1 into 1 0.574 * [backup-simplify]: Simplify (/ 1 1) into 1 0.574 * [taylor]: Taking taylor expansion of 1.0 in k 0.574 * [backup-simplify]: Simplify 1.0 into 1.0 0.574 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 0.574 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 0.574 * [taylor]: Taking taylor expansion of -2.0 in k 0.575 * [backup-simplify]: Simplify -2.0 into -2.0 0.575 * [taylor]: Taking taylor expansion of (/ PI n) in k 0.575 * [taylor]: Taking taylor expansion of PI in k 0.575 * [backup-simplify]: Simplify PI into PI 0.575 * [taylor]: Taking taylor expansion of n in k 0.575 * [backup-simplify]: Simplify n into n 0.575 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 0.575 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 0.575 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 0.575 * [backup-simplify]: Simplify (+ 1 0) into 1 0.580 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 0.580 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 0.580 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0.580 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.580 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.580 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.580 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.581 * [taylor]: Taking taylor expansion of 0.5 in n 0.581 * [backup-simplify]: Simplify 0.5 into 0.5 0.581 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.581 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.581 * [taylor]: Taking taylor expansion of k in n 0.581 * [backup-simplify]: Simplify k into k 0.581 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.581 * [taylor]: Taking taylor expansion of 1.0 in n 0.581 * [backup-simplify]: Simplify 1.0 into 1.0 0.581 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.581 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.581 * [taylor]: Taking taylor expansion of -2.0 in n 0.581 * [backup-simplify]: Simplify -2.0 into -2.0 0.581 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.581 * [taylor]: Taking taylor expansion of PI in n 0.581 * [backup-simplify]: Simplify PI into PI 0.581 * [taylor]: Taking taylor expansion of n in n 0.581 * [backup-simplify]: Simplify 0 into 0 0.581 * [backup-simplify]: Simplify 1 into 1 0.582 * [backup-simplify]: Simplify (/ PI 1) into PI 0.582 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.584 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.584 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.584 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.587 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.588 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.588 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 0.588 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 0.588 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 0.588 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 0.588 * [taylor]: Taking taylor expansion of 0.5 in n 0.588 * [backup-simplify]: Simplify 0.5 into 0.5 0.588 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 0.588 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.588 * [taylor]: Taking taylor expansion of k in n 0.588 * [backup-simplify]: Simplify k into k 0.588 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.588 * [taylor]: Taking taylor expansion of 1.0 in n 0.588 * [backup-simplify]: Simplify 1.0 into 1.0 0.588 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 0.588 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.588 * [taylor]: Taking taylor expansion of -2.0 in n 0.588 * [backup-simplify]: Simplify -2.0 into -2.0 0.589 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.589 * [taylor]: Taking taylor expansion of PI in n 0.589 * [backup-simplify]: Simplify PI into PI 0.589 * [taylor]: Taking taylor expansion of n in n 0.589 * [backup-simplify]: Simplify 0 into 0 0.589 * [backup-simplify]: Simplify 1 into 1 0.589 * [backup-simplify]: Simplify (/ PI 1) into PI 0.590 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.591 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.591 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 0.591 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 0.592 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.593 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 0.595 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.595 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 0.595 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 0.595 * [taylor]: Taking taylor expansion of 0.5 in k 0.595 * [backup-simplify]: Simplify 0.5 into 0.5 0.595 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 0.595 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 0.595 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.595 * [taylor]: Taking taylor expansion of k in k 0.595 * [backup-simplify]: Simplify 0 into 0 0.595 * [backup-simplify]: Simplify 1 into 1 0.595 * [backup-simplify]: Simplify (/ 1 1) into 1 0.595 * [taylor]: Taking taylor expansion of 1.0 in k 0.596 * [backup-simplify]: Simplify 1.0 into 1.0 0.596 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 0.596 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 0.596 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 0.596 * [taylor]: Taking taylor expansion of -2.0 in k 0.596 * [backup-simplify]: Simplify -2.0 into -2.0 0.596 * [taylor]: Taking taylor expansion of PI in k 0.596 * [backup-simplify]: Simplify PI into PI 0.596 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.598 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 0.598 * [taylor]: Taking taylor expansion of (log n) in k 0.598 * [taylor]: Taking taylor expansion of n in k 0.598 * [backup-simplify]: Simplify n into n 0.598 * [backup-simplify]: Simplify (log n) into (log n) 0.598 * [backup-simplify]: Simplify (+ 1 0) into 1 0.598 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 0.599 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 0.601 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 0.602 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 0.603 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.604 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.606 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.608 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 0.608 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.609 * [backup-simplify]: Simplify (+ 0 0) into 0 0.609 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 0.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.611 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 0.612 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 0.612 * [taylor]: Taking taylor expansion of 0 in k 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.612 * [backup-simplify]: Simplify 0 into 0 0.613 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.613 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.615 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 0.616 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.616 * [backup-simplify]: Simplify (+ 0 0) into 0 0.616 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 0.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.618 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 0.620 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 0.620 * [taylor]: Taking taylor expansion of 0 in k 0.620 * [backup-simplify]: Simplify 0 into 0 0.620 * [backup-simplify]: Simplify 0 into 0 0.620 * [backup-simplify]: Simplify 0 into 0 0.620 * [backup-simplify]: Simplify 0 into 0 0.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.621 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.625 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 0.625 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 0.625 * [backup-simplify]: Simplify (+ 0 0) into 0 0.626 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 0.627 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 0.628 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 0.630 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 0.630 * [taylor]: Taking taylor expansion of 0 in k 0.630 * [backup-simplify]: Simplify 0 into 0 0.630 * [backup-simplify]: Simplify 0 into 0 0.631 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 0.631 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 0.631 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.631 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 0.631 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.631 * [taylor]: Taking taylor expansion of 2.0 in n 0.631 * [backup-simplify]: Simplify 2.0 into 2.0 0.631 * [taylor]: Taking taylor expansion of (* n PI) in n 0.631 * [taylor]: Taking taylor expansion of n in n 0.631 * [backup-simplify]: Simplify 0 into 0 0.631 * [backup-simplify]: Simplify 1 into 1 0.631 * [taylor]: Taking taylor expansion of PI in n 0.631 * [backup-simplify]: Simplify PI into PI 0.631 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.631 * [taylor]: Taking taylor expansion of 2.0 in n 0.631 * [backup-simplify]: Simplify 2.0 into 2.0 0.631 * [taylor]: Taking taylor expansion of (* n PI) in n 0.631 * [taylor]: Taking taylor expansion of n in n 0.631 * [backup-simplify]: Simplify 0 into 0 0.631 * [backup-simplify]: Simplify 1 into 1 0.631 * [taylor]: Taking taylor expansion of PI in n 0.631 * [backup-simplify]: Simplify PI into PI 0.632 * [backup-simplify]: Simplify (* 0 PI) into 0 0.632 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.632 * [backup-simplify]: Simplify 0 into 0 0.633 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.634 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.634 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.635 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 0.635 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 0.635 * [backup-simplify]: Simplify 0 into 0 0.636 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 0.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 0.637 * [backup-simplify]: Simplify 0 into 0 0.638 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.639 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 0.639 * [backup-simplify]: Simplify 0 into 0 0.641 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.642 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 0.642 * [backup-simplify]: Simplify 0 into 0 0.644 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 0.647 * [backup-simplify]: Simplify 0 into 0 0.649 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 0.651 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 0.651 * [backup-simplify]: Simplify 0 into 0 0.651 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 0.652 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 0.652 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 0.652 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.652 * [taylor]: Taking taylor expansion of 2.0 in n 0.652 * [backup-simplify]: Simplify 2.0 into 2.0 0.652 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.652 * [taylor]: Taking taylor expansion of PI in n 0.652 * [backup-simplify]: Simplify PI into PI 0.652 * [taylor]: Taking taylor expansion of n in n 0.652 * [backup-simplify]: Simplify 0 into 0 0.652 * [backup-simplify]: Simplify 1 into 1 0.653 * [backup-simplify]: Simplify (/ PI 1) into PI 0.653 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 0.653 * [taylor]: Taking taylor expansion of 2.0 in n 0.653 * [backup-simplify]: Simplify 2.0 into 2.0 0.653 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.653 * [taylor]: Taking taylor expansion of PI in n 0.653 * [backup-simplify]: Simplify PI into PI 0.653 * [taylor]: Taking taylor expansion of n in n 0.653 * [backup-simplify]: Simplify 0 into 0 0.653 * [backup-simplify]: Simplify 1 into 1 0.654 * [backup-simplify]: Simplify (/ PI 1) into PI 0.654 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.655 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 0.656 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.656 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 0.656 * [backup-simplify]: Simplify 0 into 0 0.658 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.659 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.659 * [backup-simplify]: Simplify 0 into 0 0.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.661 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.661 * [backup-simplify]: Simplify 0 into 0 0.662 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.664 * [backup-simplify]: Simplify 0 into 0 0.665 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.666 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.666 * [backup-simplify]: Simplify 0 into 0 0.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.669 * [backup-simplify]: Simplify 0 into 0 0.670 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 0.670 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 0.670 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 0.670 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.670 * [taylor]: Taking taylor expansion of -2.0 in n 0.671 * [backup-simplify]: Simplify -2.0 into -2.0 0.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.671 * [taylor]: Taking taylor expansion of PI in n 0.671 * [backup-simplify]: Simplify PI into PI 0.671 * [taylor]: Taking taylor expansion of n in n 0.671 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify 1 into 1 0.671 * [backup-simplify]: Simplify (/ PI 1) into PI 0.671 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 0.671 * [taylor]: Taking taylor expansion of -2.0 in n 0.671 * [backup-simplify]: Simplify -2.0 into -2.0 0.671 * [taylor]: Taking taylor expansion of (/ PI n) in n 0.671 * [taylor]: Taking taylor expansion of PI in n 0.671 * [backup-simplify]: Simplify PI into PI 0.671 * [taylor]: Taking taylor expansion of n in n 0.671 * [backup-simplify]: Simplify 0 into 0 0.671 * [backup-simplify]: Simplify 1 into 1 0.672 * [backup-simplify]: Simplify (/ PI 1) into PI 0.673 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.673 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 0.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 0.675 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 0.675 * [backup-simplify]: Simplify 0 into 0 0.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.677 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 0.677 * [backup-simplify]: Simplify 0 into 0 0.678 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.679 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.679 * [backup-simplify]: Simplify 0 into 0 0.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.682 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 0.682 * [backup-simplify]: Simplify 0 into 0 0.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.683 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 0.683 * [backup-simplify]: Simplify 0 into 0 0.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.685 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 0.685 * [backup-simplify]: Simplify 0 into 0 0.685 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 0.685 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 0.685 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 0.685 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 0.685 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.685 * [taylor]: Taking taylor expansion of 1.0 in k 0.685 * [backup-simplify]: Simplify 1.0 into 1.0 0.686 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.686 * [taylor]: Taking taylor expansion of k in k 0.686 * [backup-simplify]: Simplify 0 into 0 0.686 * [backup-simplify]: Simplify 1 into 1 0.686 * [backup-simplify]: Simplify (/ 1 1) into 1 0.686 * [backup-simplify]: Simplify (sqrt 0) into 0 0.687 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.687 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 0.687 * [taylor]: Taking taylor expansion of 1.0 in k 0.687 * [backup-simplify]: Simplify 1.0 into 1.0 0.687 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.687 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.687 * [taylor]: Taking taylor expansion of k in k 0.687 * [backup-simplify]: Simplify 0 into 0 0.687 * [backup-simplify]: Simplify 1 into 1 0.687 * [backup-simplify]: Simplify (/ 1 1) into 1 0.688 * [backup-simplify]: Simplify (sqrt 0) into 0 0.688 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.689 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.689 * [backup-simplify]: Simplify 0 into 0 0.690 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.690 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.690 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.692 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.694 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.694 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.694 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.697 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.698 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.698 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.699 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 0.699 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 0.699 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 0.699 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.699 * [taylor]: Taking taylor expansion of 1.0 in k 0.699 * [backup-simplify]: Simplify 1.0 into 1.0 0.699 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.699 * [taylor]: Taking taylor expansion of k in k 0.699 * [backup-simplify]: Simplify 0 into 0 0.700 * [backup-simplify]: Simplify 1 into 1 0.700 * [backup-simplify]: Simplify (sqrt 0) into 0 0.704 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.704 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 0.704 * [taylor]: Taking taylor expansion of 1.0 in k 0.704 * [backup-simplify]: Simplify 1.0 into 1.0 0.704 * [taylor]: Taking taylor expansion of (sqrt k) in k 0.704 * [taylor]: Taking taylor expansion of k in k 0.704 * [backup-simplify]: Simplify 0 into 0 0.704 * [backup-simplify]: Simplify 1 into 1 0.704 * [backup-simplify]: Simplify (sqrt 0) into 0 0.705 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.705 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.705 * [backup-simplify]: Simplify 0 into 0 0.706 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 0.706 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.708 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.709 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 0.710 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.712 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.713 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 0.713 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.714 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 0.715 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 0.715 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 0.715 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.715 * [taylor]: Taking taylor expansion of 1.0 in k 0.715 * [backup-simplify]: Simplify 1.0 into 1.0 0.715 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.715 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.715 * [taylor]: Taking taylor expansion of -1 in k 0.715 * [backup-simplify]: Simplify -1 into -1 0.715 * [taylor]: Taking taylor expansion of k in k 0.715 * [backup-simplify]: Simplify 0 into 0 0.715 * [backup-simplify]: Simplify 1 into 1 0.715 * [backup-simplify]: Simplify (/ -1 1) into -1 0.715 * [backup-simplify]: Simplify (sqrt 0) into 0 0.716 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.716 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.716 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 0.716 * [taylor]: Taking taylor expansion of 1.0 in k 0.716 * [backup-simplify]: Simplify 1.0 into 1.0 0.716 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 0.716 * [taylor]: Taking taylor expansion of (/ -1 k) in k 0.717 * [taylor]: Taking taylor expansion of -1 in k 0.717 * [backup-simplify]: Simplify -1 into -1 0.717 * [taylor]: Taking taylor expansion of k in k 0.717 * [backup-simplify]: Simplify 0 into 0 0.717 * [backup-simplify]: Simplify 1 into 1 0.717 * [backup-simplify]: Simplify (/ -1 1) into -1 0.717 * [backup-simplify]: Simplify (sqrt 0) into 0 0.718 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 0.718 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 0.718 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 0.720 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.722 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 0.722 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.725 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.728 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 0.728 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 0.729 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 0.729 * * * * [progress]: [ 4 / 4 ] generating series at (2) 0.729 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 0.729 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 0.729 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 0.729 * [taylor]: Taking taylor expansion of 1.0 in n 0.729 * [backup-simplify]: Simplify 1.0 into 1.0 0.729 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 0.729 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 0.729 * [taylor]: Taking taylor expansion of (/ 1 k) in n 0.729 * [taylor]: Taking taylor expansion of k in n 0.729 * [backup-simplify]: Simplify k into k 0.729 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 0.729 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 0.730 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 0.730 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 0.730 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 0.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 0.730 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 0.730 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 0.730 * [taylor]: Taking taylor expansion of 0.5 in n 0.730 * [backup-simplify]: Simplify 0.5 into 0.5 0.730 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 0.730 * [taylor]: Taking taylor expansion of 1.0 in n 0.730 * [backup-simplify]: Simplify 1.0 into 1.0 0.730 * [taylor]: Taking taylor expansion of k in n 0.730 * [backup-simplify]: Simplify k into k 0.730 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.730 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.730 * [taylor]: Taking taylor expansion of 2.0 in n 0.730 * [backup-simplify]: Simplify 2.0 into 2.0 0.730 * [taylor]: Taking taylor expansion of (* n PI) in n 0.730 * [taylor]: Taking taylor expansion of n in n 0.730 * [backup-simplify]: Simplify 0 into 0 0.730 * [backup-simplify]: Simplify 1 into 1 0.730 * [taylor]: Taking taylor expansion of PI in n 0.730 * [backup-simplify]: Simplify PI into PI 0.730 * [backup-simplify]: Simplify (* 0 PI) into 0 0.731 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.731 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.732 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.733 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.733 * [backup-simplify]: Simplify (- k) into (- k) 0.733 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 0.733 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 0.734 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.735 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 0.736 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0.736 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.736 * [taylor]: Taking taylor expansion of 1.0 in k 0.736 * [backup-simplify]: Simplify 1.0 into 1.0 0.736 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.736 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.736 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.736 * [taylor]: Taking taylor expansion of k in k 0.736 * [backup-simplify]: Simplify 0 into 0 0.736 * [backup-simplify]: Simplify 1 into 1 0.736 * [backup-simplify]: Simplify (/ 1 1) into 1 0.736 * [backup-simplify]: Simplify (sqrt 0) into 0 0.737 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.737 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.737 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.737 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.737 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.737 * [taylor]: Taking taylor expansion of 0.5 in k 0.737 * [backup-simplify]: Simplify 0.5 into 0.5 0.737 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.737 * [taylor]: Taking taylor expansion of 1.0 in k 0.738 * [backup-simplify]: Simplify 1.0 into 1.0 0.738 * [taylor]: Taking taylor expansion of k in k 0.738 * [backup-simplify]: Simplify 0 into 0 0.738 * [backup-simplify]: Simplify 1 into 1 0.738 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.738 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.738 * [taylor]: Taking taylor expansion of 2.0 in k 0.738 * [backup-simplify]: Simplify 2.0 into 2.0 0.738 * [taylor]: Taking taylor expansion of (* n PI) in k 0.738 * [taylor]: Taking taylor expansion of n in k 0.738 * [backup-simplify]: Simplify n into n 0.738 * [taylor]: Taking taylor expansion of PI in k 0.738 * [backup-simplify]: Simplify PI into PI 0.738 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.738 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.738 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.738 * [backup-simplify]: Simplify (- 0) into 0 0.738 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.739 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.739 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.739 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.739 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 0.739 * [taylor]: Taking taylor expansion of 1.0 in k 0.739 * [backup-simplify]: Simplify 1.0 into 1.0 0.739 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 0.739 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 0.739 * [taylor]: Taking taylor expansion of (/ 1 k) in k 0.739 * [taylor]: Taking taylor expansion of k in k 0.739 * [backup-simplify]: Simplify 0 into 0 0.739 * [backup-simplify]: Simplify 1 into 1 0.739 * [backup-simplify]: Simplify (/ 1 1) into 1 0.739 * [backup-simplify]: Simplify (sqrt 0) into 0 0.740 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 0.740 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 0.740 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 0.740 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 0.740 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 0.740 * [taylor]: Taking taylor expansion of 0.5 in k 0.740 * [backup-simplify]: Simplify 0.5 into 0.5 0.740 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 0.740 * [taylor]: Taking taylor expansion of 1.0 in k 0.740 * [backup-simplify]: Simplify 1.0 into 1.0 0.740 * [taylor]: Taking taylor expansion of k in k 0.740 * [backup-simplify]: Simplify 0 into 0 0.740 * [backup-simplify]: Simplify 1 into 1 0.740 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 0.740 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 0.741 * [taylor]: Taking taylor expansion of 2.0 in k 0.741 * [backup-simplify]: Simplify 2.0 into 2.0 0.741 * [taylor]: Taking taylor expansion of (* n PI) in k 0.741 * [taylor]: Taking taylor expansion of n in k 0.741 * [backup-simplify]: Simplify n into n 0.741 * [taylor]: Taking taylor expansion of PI in k 0.741 * [backup-simplify]: Simplify PI into PI 0.741 * [backup-simplify]: Simplify (* n PI) into (* n PI) 0.741 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 0.741 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 0.741 * [backup-simplify]: Simplify (- 0) into 0 0.741 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 0.742 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 0.742 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 0.742 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 0.742 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 0.743 * [backup-simplify]: Simplify (* 1.0 0) into 0 0.743 * [taylor]: Taking taylor expansion of 0 in n 0.743 * [backup-simplify]: Simplify 0 into 0 0.743 * [backup-simplify]: Simplify 0 into 0 0.743 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 0.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 0.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 0.745 * [backup-simplify]: Simplify (- 1) into -1 0.746 * [backup-simplify]: Simplify (+ 0 -1) into -1 0.748 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 0.749 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 0.749 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.751 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 0.753 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.753 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 0.753 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.753 * [taylor]: Taking taylor expansion of +nan.0 in n 0.753 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.753 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.753 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.753 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.753 * [taylor]: Taking taylor expansion of 0.5 in n 0.753 * [backup-simplify]: Simplify 0.5 into 0.5 0.753 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.754 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.754 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.754 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.754 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.754 * [taylor]: Taking taylor expansion of 1.0 in n 0.754 * [backup-simplify]: Simplify 1.0 into 1.0 0.754 * [taylor]: Taking taylor expansion of (log PI) in n 0.754 * [taylor]: Taking taylor expansion of PI in n 0.754 * [backup-simplify]: Simplify PI into PI 0.754 * [backup-simplify]: Simplify (log PI) into (log PI) 0.755 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.757 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.757 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.757 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.757 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.757 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.757 * [taylor]: Taking taylor expansion of 1.0 in n 0.757 * [backup-simplify]: Simplify 1.0 into 1.0 0.757 * [taylor]: Taking taylor expansion of (log n) in n 0.757 * [taylor]: Taking taylor expansion of n in n 0.757 * [backup-simplify]: Simplify 0 into 0 0.757 * [backup-simplify]: Simplify 1 into 1 0.758 * [backup-simplify]: Simplify (log 1) into 0 0.758 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.759 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.759 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.759 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.759 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.759 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.759 * [taylor]: Taking taylor expansion of 1.0 in n 0.759 * [backup-simplify]: Simplify 1.0 into 1.0 0.759 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.759 * [taylor]: Taking taylor expansion of 2.0 in n 0.759 * [backup-simplify]: Simplify 2.0 into 2.0 0.759 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.760 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.762 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.763 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 0.764 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 0.765 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 0.767 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 0.768 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.770 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.771 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 0.773 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.773 * [backup-simplify]: Simplify 0 into 0 0.774 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 0.775 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 0.777 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 0.777 * [backup-simplify]: Simplify (- 0) into 0 0.777 * [backup-simplify]: Simplify (+ 0 0) into 0 0.779 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 0.780 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 0.781 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.782 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 0.785 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 0.789 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 0.794 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 0.794 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 0.794 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 0.795 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 0.795 * [taylor]: Taking taylor expansion of +nan.0 in n 0.795 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.795 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 0.795 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 0.795 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 0.795 * [taylor]: Taking taylor expansion of 0.5 in n 0.795 * [backup-simplify]: Simplify 0.5 into 0.5 0.795 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 0.795 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 0.795 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.795 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.795 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.795 * [taylor]: Taking taylor expansion of 1.0 in n 0.795 * [backup-simplify]: Simplify 1.0 into 1.0 0.795 * [taylor]: Taking taylor expansion of (log PI) in n 0.795 * [taylor]: Taking taylor expansion of PI in n 0.795 * [backup-simplify]: Simplify PI into PI 0.796 * [backup-simplify]: Simplify (log PI) into (log PI) 0.797 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.798 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.798 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 0.798 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.798 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.798 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.798 * [taylor]: Taking taylor expansion of 1.0 in n 0.798 * [backup-simplify]: Simplify 1.0 into 1.0 0.798 * [taylor]: Taking taylor expansion of (log n) in n 0.799 * [taylor]: Taking taylor expansion of n in n 0.799 * [backup-simplify]: Simplify 0 into 0 0.799 * [backup-simplify]: Simplify 1 into 1 0.799 * [backup-simplify]: Simplify (log 1) into 0 0.799 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.800 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.800 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.800 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.800 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.800 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.800 * [taylor]: Taking taylor expansion of 1.0 in n 0.800 * [backup-simplify]: Simplify 1.0 into 1.0 0.800 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.800 * [taylor]: Taking taylor expansion of 2.0 in n 0.800 * [backup-simplify]: Simplify 2.0 into 2.0 0.800 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.801 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.802 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.803 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 0.803 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 0.804 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 0.805 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 0.806 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.806 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 0.806 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.806 * [taylor]: Taking taylor expansion of +nan.0 in n 0.806 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.806 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.806 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.806 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.806 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.806 * [taylor]: Taking taylor expansion of 0.5 in n 0.806 * [backup-simplify]: Simplify 0.5 into 0.5 0.806 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.806 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.806 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.806 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.806 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.806 * [taylor]: Taking taylor expansion of 1.0 in n 0.806 * [backup-simplify]: Simplify 1.0 into 1.0 0.806 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.806 * [taylor]: Taking taylor expansion of 2.0 in n 0.806 * [backup-simplify]: Simplify 2.0 into 2.0 0.807 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.807 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.808 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.808 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.808 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.808 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.809 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.809 * [taylor]: Taking taylor expansion of 1.0 in n 0.809 * [backup-simplify]: Simplify 1.0 into 1.0 0.809 * [taylor]: Taking taylor expansion of (log PI) in n 0.809 * [taylor]: Taking taylor expansion of PI in n 0.809 * [backup-simplify]: Simplify PI into PI 0.809 * [backup-simplify]: Simplify (log PI) into (log PI) 0.809 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.810 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.810 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.811 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.811 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.811 * [taylor]: Taking taylor expansion of 1.0 in n 0.811 * [backup-simplify]: Simplify 1.0 into 1.0 0.811 * [taylor]: Taking taylor expansion of (log n) in n 0.811 * [taylor]: Taking taylor expansion of n in n 0.811 * [backup-simplify]: Simplify 0 into 0 0.811 * [backup-simplify]: Simplify 1 into 1 0.811 * [backup-simplify]: Simplify (log 1) into 0 0.811 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.811 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.811 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.812 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.812 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.813 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.814 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.815 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.815 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.815 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.815 * [taylor]: Taking taylor expansion of 2.0 in n 0.815 * [backup-simplify]: Simplify 2.0 into 2.0 0.815 * [taylor]: Taking taylor expansion of (* n PI) in n 0.815 * [taylor]: Taking taylor expansion of n in n 0.815 * [backup-simplify]: Simplify 0 into 0 0.815 * [backup-simplify]: Simplify 1 into 1 0.815 * [taylor]: Taking taylor expansion of PI in n 0.815 * [backup-simplify]: Simplify PI into PI 0.816 * [backup-simplify]: Simplify (* 0 PI) into 0 0.816 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.817 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.818 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.819 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.820 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 0.821 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.827 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.829 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.830 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 0.834 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.838 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.841 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.842 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 0.843 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 0.844 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 0.845 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 0.845 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.845 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 0.846 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 0.846 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 0.847 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 0.848 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 0.849 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 0.850 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 0.852 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 0.854 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 0.856 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 0.859 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 0.859 * [backup-simplify]: Simplify (- 0) into 0 0.859 * [backup-simplify]: Simplify 0 into 0 0.859 * [backup-simplify]: Simplify 0 into 0 0.860 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 0.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 0.865 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 0.865 * [backup-simplify]: Simplify (- 0) into 0 0.866 * [backup-simplify]: Simplify (+ 0 0) into 0 0.867 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 0.869 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 0.871 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.872 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 0.876 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 0.882 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 0.892 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 0.893 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 0.893 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 0.893 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 0.893 * [taylor]: Taking taylor expansion of +nan.0 in n 0.893 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.893 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 0.893 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 0.893 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 0.893 * [taylor]: Taking taylor expansion of 0.5 in n 0.893 * [backup-simplify]: Simplify 0.5 into 0.5 0.893 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 0.893 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 0.893 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.893 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.893 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.893 * [taylor]: Taking taylor expansion of 1.0 in n 0.893 * [backup-simplify]: Simplify 1.0 into 1.0 0.893 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.893 * [taylor]: Taking taylor expansion of 2.0 in n 0.893 * [backup-simplify]: Simplify 2.0 into 2.0 0.894 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.895 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.897 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.897 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 0.897 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.897 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.897 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.897 * [taylor]: Taking taylor expansion of 1.0 in n 0.897 * [backup-simplify]: Simplify 1.0 into 1.0 0.897 * [taylor]: Taking taylor expansion of (log n) in n 0.897 * [taylor]: Taking taylor expansion of n in n 0.897 * [backup-simplify]: Simplify 0 into 0 0.897 * [backup-simplify]: Simplify 1 into 1 0.897 * [backup-simplify]: Simplify (log 1) into 0 0.898 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.898 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.898 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.898 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.898 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.898 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.898 * [taylor]: Taking taylor expansion of 1.0 in n 0.898 * [backup-simplify]: Simplify 1.0 into 1.0 0.898 * [taylor]: Taking taylor expansion of (log PI) in n 0.898 * [taylor]: Taking taylor expansion of PI in n 0.898 * [backup-simplify]: Simplify PI into PI 0.899 * [backup-simplify]: Simplify (log PI) into (log PI) 0.900 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.901 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.902 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.903 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.905 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.906 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.908 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.908 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 0.908 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 0.908 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 0.908 * [taylor]: Taking taylor expansion of +nan.0 in n 0.908 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.908 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 0.908 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.908 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.908 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.908 * [taylor]: Taking taylor expansion of 0.5 in n 0.908 * [backup-simplify]: Simplify 0.5 into 0.5 0.908 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.909 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.909 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.909 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.909 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.909 * [taylor]: Taking taylor expansion of 1.0 in n 0.909 * [backup-simplify]: Simplify 1.0 into 1.0 0.909 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.909 * [taylor]: Taking taylor expansion of 2.0 in n 0.909 * [backup-simplify]: Simplify 2.0 into 2.0 0.909 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.910 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.912 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.912 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.912 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.912 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.912 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.912 * [taylor]: Taking taylor expansion of 1.0 in n 0.912 * [backup-simplify]: Simplify 1.0 into 1.0 0.912 * [taylor]: Taking taylor expansion of (log PI) in n 0.912 * [taylor]: Taking taylor expansion of PI in n 0.912 * [backup-simplify]: Simplify PI into PI 0.913 * [backup-simplify]: Simplify (log PI) into (log PI) 0.914 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.915 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.915 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.915 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.915 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.916 * [taylor]: Taking taylor expansion of 1.0 in n 0.916 * [backup-simplify]: Simplify 1.0 into 1.0 0.916 * [taylor]: Taking taylor expansion of (log n) in n 0.916 * [taylor]: Taking taylor expansion of n in n 0.916 * [backup-simplify]: Simplify 0 into 0 0.916 * [backup-simplify]: Simplify 1 into 1 0.916 * [backup-simplify]: Simplify (log 1) into 0 0.917 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.917 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.917 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.917 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.919 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.920 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.921 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.923 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.923 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.923 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.923 * [taylor]: Taking taylor expansion of 2.0 in n 0.923 * [backup-simplify]: Simplify 2.0 into 2.0 0.923 * [taylor]: Taking taylor expansion of (* n PI) in n 0.923 * [taylor]: Taking taylor expansion of n in n 0.923 * [backup-simplify]: Simplify 0 into 0 0.923 * [backup-simplify]: Simplify 1 into 1 0.923 * [taylor]: Taking taylor expansion of PI in n 0.923 * [backup-simplify]: Simplify PI into PI 0.924 * [backup-simplify]: Simplify (* 0 PI) into 0 0.924 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.926 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.927 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.928 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.928 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 0.928 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 0.928 * [taylor]: Taking taylor expansion of +nan.0 in n 0.928 * [backup-simplify]: Simplify +nan.0 into +nan.0 0.928 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 0.928 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 0.928 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 0.928 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 0.928 * [taylor]: Taking taylor expansion of 0.5 in n 0.929 * [backup-simplify]: Simplify 0.5 into 0.5 0.929 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 0.929 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 0.929 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 0.929 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 0.929 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 0.929 * [taylor]: Taking taylor expansion of 1.0 in n 0.929 * [backup-simplify]: Simplify 1.0 into 1.0 0.929 * [taylor]: Taking taylor expansion of (log 2.0) in n 0.929 * [taylor]: Taking taylor expansion of 2.0 in n 0.929 * [backup-simplify]: Simplify 2.0 into 2.0 0.929 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 0.930 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 0.932 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 0.932 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 0.932 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 0.932 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 0.932 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 0.932 * [taylor]: Taking taylor expansion of 1.0 in n 0.932 * [backup-simplify]: Simplify 1.0 into 1.0 0.932 * [taylor]: Taking taylor expansion of (log PI) in n 0.932 * [taylor]: Taking taylor expansion of PI in n 0.932 * [backup-simplify]: Simplify PI into PI 0.932 * [backup-simplify]: Simplify (log PI) into (log PI) 0.933 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 0.935 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 0.935 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 0.935 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 0.935 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 0.935 * [taylor]: Taking taylor expansion of 1.0 in n 0.935 * [backup-simplify]: Simplify 1.0 into 1.0 0.935 * [taylor]: Taking taylor expansion of (log n) in n 0.935 * [taylor]: Taking taylor expansion of n in n 0.935 * [backup-simplify]: Simplify 0 into 0 0.935 * [backup-simplify]: Simplify 1 into 1 0.936 * [backup-simplify]: Simplify (log 1) into 0 0.936 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 0.936 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 0.936 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 0.937 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 0.938 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 0.940 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 0.941 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 0.943 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0.943 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 0.943 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 0.943 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 0.943 * [taylor]: Taking taylor expansion of 2.0 in n 0.943 * [backup-simplify]: Simplify 2.0 into 2.0 0.943 * [taylor]: Taking taylor expansion of (* n PI) in n 0.943 * [taylor]: Taking taylor expansion of n in n 0.943 * [backup-simplify]: Simplify 0 into 0 0.943 * [backup-simplify]: Simplify 1 into 1 0.943 * [taylor]: Taking taylor expansion of PI in n 0.943 * [backup-simplify]: Simplify PI into PI 0.944 * [backup-simplify]: Simplify (* 0 PI) into 0 0.944 * [backup-simplify]: Simplify (* 2.0 0) into 0 0.946 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 0.947 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 0.949 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 0.950 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.951 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.953 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.956 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.958 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.960 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.961 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 0.968 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 0.971 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 0.973 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0.976 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 0.987 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 0.996 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 1.006 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 1.016 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 1.029 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 1.058 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 1.060 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 1.060 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 1.060 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 1.060 * [taylor]: Taking taylor expansion of 1.0 in n 1.060 * [backup-simplify]: Simplify 1.0 into 1.0 1.060 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 1.060 * [taylor]: Taking taylor expansion of (sqrt k) in n 1.060 * [taylor]: Taking taylor expansion of k in n 1.060 * [backup-simplify]: Simplify k into k 1.060 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 1.060 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 1.060 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.060 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.060 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.060 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.060 * [taylor]: Taking taylor expansion of 0.5 in n 1.060 * [backup-simplify]: Simplify 0.5 into 0.5 1.060 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.060 * [taylor]: Taking taylor expansion of 1.0 in n 1.060 * [backup-simplify]: Simplify 1.0 into 1.0 1.060 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.061 * [taylor]: Taking taylor expansion of k in n 1.061 * [backup-simplify]: Simplify k into k 1.061 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.061 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.061 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.061 * [taylor]: Taking taylor expansion of 2.0 in n 1.061 * [backup-simplify]: Simplify 2.0 into 2.0 1.061 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.061 * [taylor]: Taking taylor expansion of PI in n 1.061 * [backup-simplify]: Simplify PI into PI 1.061 * [taylor]: Taking taylor expansion of n in n 1.061 * [backup-simplify]: Simplify 0 into 0 1.061 * [backup-simplify]: Simplify 1 into 1 1.061 * [backup-simplify]: Simplify (/ PI 1) into PI 1.062 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.063 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.063 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.063 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.063 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.066 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.067 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.067 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 1.067 * [taylor]: Taking taylor expansion of 1.0 in k 1.067 * [backup-simplify]: Simplify 1.0 into 1.0 1.067 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 1.067 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.067 * [taylor]: Taking taylor expansion of k in k 1.067 * [backup-simplify]: Simplify 0 into 0 1.067 * [backup-simplify]: Simplify 1 into 1 1.067 * [backup-simplify]: Simplify (sqrt 0) into 0 1.068 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.068 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.068 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.068 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.068 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.068 * [taylor]: Taking taylor expansion of 0.5 in k 1.068 * [backup-simplify]: Simplify 0.5 into 0.5 1.068 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.068 * [taylor]: Taking taylor expansion of 1.0 in k 1.068 * [backup-simplify]: Simplify 1.0 into 1.0 1.068 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.068 * [taylor]: Taking taylor expansion of k in k 1.068 * [backup-simplify]: Simplify 0 into 0 1.068 * [backup-simplify]: Simplify 1 into 1 1.069 * [backup-simplify]: Simplify (/ 1 1) into 1 1.069 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.069 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.069 * [taylor]: Taking taylor expansion of 2.0 in k 1.069 * [backup-simplify]: Simplify 2.0 into 2.0 1.069 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.069 * [taylor]: Taking taylor expansion of PI in k 1.069 * [backup-simplify]: Simplify PI into PI 1.069 * [taylor]: Taking taylor expansion of n in k 1.069 * [backup-simplify]: Simplify n into n 1.069 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.069 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.069 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.069 * [backup-simplify]: Simplify (- 1) into -1 1.070 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.070 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.070 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.070 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.070 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 1.070 * [taylor]: Taking taylor expansion of 1.0 in k 1.070 * [backup-simplify]: Simplify 1.0 into 1.0 1.070 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 1.070 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.070 * [taylor]: Taking taylor expansion of k in k 1.070 * [backup-simplify]: Simplify 0 into 0 1.070 * [backup-simplify]: Simplify 1 into 1 1.071 * [backup-simplify]: Simplify (sqrt 0) into 0 1.071 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.071 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.071 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.071 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.071 * [taylor]: Taking taylor expansion of 0.5 in k 1.071 * [backup-simplify]: Simplify 0.5 into 0.5 1.071 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.072 * [taylor]: Taking taylor expansion of 1.0 in k 1.072 * [backup-simplify]: Simplify 1.0 into 1.0 1.072 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.072 * [taylor]: Taking taylor expansion of k in k 1.072 * [backup-simplify]: Simplify 0 into 0 1.072 * [backup-simplify]: Simplify 1 into 1 1.072 * [backup-simplify]: Simplify (/ 1 1) into 1 1.072 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.072 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.072 * [taylor]: Taking taylor expansion of 2.0 in k 1.072 * [backup-simplify]: Simplify 2.0 into 2.0 1.072 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.072 * [taylor]: Taking taylor expansion of PI in k 1.072 * [backup-simplify]: Simplify PI into PI 1.072 * [taylor]: Taking taylor expansion of n in k 1.072 * [backup-simplify]: Simplify n into n 1.072 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.072 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.072 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.072 * [backup-simplify]: Simplify (- 1) into -1 1.073 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.073 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.073 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.073 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.073 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 1.074 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.074 * [taylor]: Taking taylor expansion of 0 in n 1.074 * [backup-simplify]: Simplify 0 into 0 1.074 * [backup-simplify]: Simplify 0 into 0 1.074 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 1.075 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 1.075 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 1.075 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 1.075 * [taylor]: Taking taylor expansion of +nan.0 in n 1.075 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.075 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 1.075 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 1.075 * [taylor]: Taking taylor expansion of 0.5 in n 1.075 * [backup-simplify]: Simplify 0.5 into 0.5 1.075 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 1.075 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.075 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.075 * [taylor]: Taking taylor expansion of 2.0 in n 1.075 * [backup-simplify]: Simplify 2.0 into 2.0 1.075 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.075 * [taylor]: Taking taylor expansion of PI in n 1.075 * [backup-simplify]: Simplify PI into PI 1.075 * [taylor]: Taking taylor expansion of n in n 1.075 * [backup-simplify]: Simplify 0 into 0 1.075 * [backup-simplify]: Simplify 1 into 1 1.075 * [backup-simplify]: Simplify (/ PI 1) into PI 1.076 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.076 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.076 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.076 * [taylor]: Taking taylor expansion of 1.0 in n 1.076 * [backup-simplify]: Simplify 1.0 into 1.0 1.077 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.077 * [taylor]: Taking taylor expansion of k in n 1.077 * [backup-simplify]: Simplify k into k 1.077 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.078 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.078 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.078 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.078 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 1.079 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.080 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.081 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 1.082 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.083 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.083 * [backup-simplify]: Simplify 0 into 0 1.088 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.089 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 1.089 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 1.089 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 1.089 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 1.089 * [taylor]: Taking taylor expansion of +nan.0 in n 1.089 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.089 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 1.089 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 1.089 * [taylor]: Taking taylor expansion of 0.5 in n 1.089 * [backup-simplify]: Simplify 0.5 into 0.5 1.089 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 1.089 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.089 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.089 * [taylor]: Taking taylor expansion of 2.0 in n 1.089 * [backup-simplify]: Simplify 2.0 into 2.0 1.089 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.089 * [taylor]: Taking taylor expansion of PI in n 1.089 * [backup-simplify]: Simplify PI into PI 1.090 * [taylor]: Taking taylor expansion of n in n 1.090 * [backup-simplify]: Simplify 0 into 0 1.090 * [backup-simplify]: Simplify 1 into 1 1.090 * [backup-simplify]: Simplify (/ PI 1) into PI 1.090 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.091 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.091 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.091 * [taylor]: Taking taylor expansion of 1.0 in n 1.091 * [backup-simplify]: Simplify 1.0 into 1.0 1.091 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.091 * [taylor]: Taking taylor expansion of k in n 1.091 * [backup-simplify]: Simplify k into k 1.091 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.092 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.092 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.092 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.093 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 1.094 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.095 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.096 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 1.098 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.099 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.101 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.101 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.101 * [backup-simplify]: Simplify (- 0) into 0 1.102 * [backup-simplify]: Simplify (+ 0 0) into 0 1.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.103 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.105 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.107 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.108 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 1.111 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.113 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 1.113 * [backup-simplify]: Simplify (- 0) into 0 1.113 * [backup-simplify]: Simplify 0 into 0 1.113 * [backup-simplify]: Simplify 0 into 0 1.117 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.119 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 1.121 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 1.121 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 1.121 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 1.121 * [taylor]: Taking taylor expansion of +nan.0 in n 1.121 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.121 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 1.121 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 1.121 * [taylor]: Taking taylor expansion of 0.5 in n 1.121 * [backup-simplify]: Simplify 0.5 into 0.5 1.121 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 1.121 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.121 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.121 * [taylor]: Taking taylor expansion of 2.0 in n 1.121 * [backup-simplify]: Simplify 2.0 into 2.0 1.121 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.121 * [taylor]: Taking taylor expansion of PI in n 1.121 * [backup-simplify]: Simplify PI into PI 1.121 * [taylor]: Taking taylor expansion of n in n 1.121 * [backup-simplify]: Simplify 0 into 0 1.121 * [backup-simplify]: Simplify 1 into 1 1.122 * [backup-simplify]: Simplify (/ PI 1) into PI 1.122 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.123 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.123 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.123 * [taylor]: Taking taylor expansion of 1.0 in n 1.123 * [backup-simplify]: Simplify 1.0 into 1.0 1.124 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.124 * [taylor]: Taking taylor expansion of k in n 1.124 * [backup-simplify]: Simplify k into k 1.124 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.125 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.125 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.125 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.126 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 1.127 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.128 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.129 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 1.130 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.130 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 1.133 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 1.134 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 1.134 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 1.134 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 1.134 * [taylor]: Taking taylor expansion of 1.0 in n 1.134 * [backup-simplify]: Simplify 1.0 into 1.0 1.134 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 1.134 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.134 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.134 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.134 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.134 * [taylor]: Taking taylor expansion of 0.5 in n 1.134 * [backup-simplify]: Simplify 0.5 into 0.5 1.134 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.134 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.134 * [taylor]: Taking taylor expansion of k in n 1.134 * [backup-simplify]: Simplify k into k 1.134 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.134 * [taylor]: Taking taylor expansion of 1.0 in n 1.134 * [backup-simplify]: Simplify 1.0 into 1.0 1.134 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.134 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.134 * [taylor]: Taking taylor expansion of -2.0 in n 1.134 * [backup-simplify]: Simplify -2.0 into -2.0 1.134 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.134 * [taylor]: Taking taylor expansion of PI in n 1.134 * [backup-simplify]: Simplify PI into PI 1.135 * [taylor]: Taking taylor expansion of n in n 1.135 * [backup-simplify]: Simplify 0 into 0 1.135 * [backup-simplify]: Simplify 1 into 1 1.135 * [backup-simplify]: Simplify (/ PI 1) into PI 1.135 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.136 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.136 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.136 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.138 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.138 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.138 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 1.138 * [taylor]: Taking taylor expansion of (/ -1 k) in n 1.138 * [taylor]: Taking taylor expansion of -1 in n 1.138 * [backup-simplify]: Simplify -1 into -1 1.139 * [taylor]: Taking taylor expansion of k in n 1.139 * [backup-simplify]: Simplify k into k 1.139 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 1.139 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 1.139 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 1.139 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 1.140 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 1.140 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 1.140 * [taylor]: Taking taylor expansion of 1.0 in k 1.140 * [backup-simplify]: Simplify 1.0 into 1.0 1.140 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 1.140 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.140 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.140 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.140 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.140 * [taylor]: Taking taylor expansion of 0.5 in k 1.140 * [backup-simplify]: Simplify 0.5 into 0.5 1.140 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.140 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.140 * [taylor]: Taking taylor expansion of k in k 1.140 * [backup-simplify]: Simplify 0 into 0 1.140 * [backup-simplify]: Simplify 1 into 1 1.140 * [backup-simplify]: Simplify (/ 1 1) into 1 1.140 * [taylor]: Taking taylor expansion of 1.0 in k 1.140 * [backup-simplify]: Simplify 1.0 into 1.0 1.140 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.140 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.140 * [taylor]: Taking taylor expansion of -2.0 in k 1.140 * [backup-simplify]: Simplify -2.0 into -2.0 1.140 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.140 * [taylor]: Taking taylor expansion of PI in k 1.140 * [backup-simplify]: Simplify PI into PI 1.140 * [taylor]: Taking taylor expansion of n in k 1.140 * [backup-simplify]: Simplify n into n 1.140 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.140 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.140 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.141 * [backup-simplify]: Simplify (+ 1 0) into 1 1.141 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.141 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.141 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.141 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.141 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.141 * [taylor]: Taking taylor expansion of -1 in k 1.141 * [backup-simplify]: Simplify -1 into -1 1.141 * [taylor]: Taking taylor expansion of k in k 1.141 * [backup-simplify]: Simplify 0 into 0 1.141 * [backup-simplify]: Simplify 1 into 1 1.142 * [backup-simplify]: Simplify (/ -1 1) into -1 1.142 * [backup-simplify]: Simplify (sqrt 0) into 0 1.143 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.143 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 1.143 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 1.143 * [taylor]: Taking taylor expansion of 1.0 in k 1.143 * [backup-simplify]: Simplify 1.0 into 1.0 1.143 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 1.143 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.143 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.143 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.143 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.143 * [taylor]: Taking taylor expansion of 0.5 in k 1.143 * [backup-simplify]: Simplify 0.5 into 0.5 1.143 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.143 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.143 * [taylor]: Taking taylor expansion of k in k 1.143 * [backup-simplify]: Simplify 0 into 0 1.143 * [backup-simplify]: Simplify 1 into 1 1.143 * [backup-simplify]: Simplify (/ 1 1) into 1 1.143 * [taylor]: Taking taylor expansion of 1.0 in k 1.143 * [backup-simplify]: Simplify 1.0 into 1.0 1.144 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.144 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.144 * [taylor]: Taking taylor expansion of -2.0 in k 1.144 * [backup-simplify]: Simplify -2.0 into -2.0 1.144 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.144 * [taylor]: Taking taylor expansion of PI in k 1.144 * [backup-simplify]: Simplify PI into PI 1.144 * [taylor]: Taking taylor expansion of n in k 1.144 * [backup-simplify]: Simplify n into n 1.144 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.144 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.144 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.144 * [backup-simplify]: Simplify (+ 1 0) into 1 1.144 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.144 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.145 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.145 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.145 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.145 * [taylor]: Taking taylor expansion of -1 in k 1.145 * [backup-simplify]: Simplify -1 into -1 1.145 * [taylor]: Taking taylor expansion of k in k 1.145 * [backup-simplify]: Simplify 0 into 0 1.145 * [backup-simplify]: Simplify 1 into 1 1.145 * [backup-simplify]: Simplify (/ -1 1) into -1 1.145 * [backup-simplify]: Simplify (sqrt 0) into 0 1.146 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.146 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 1.146 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 1.146 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 1.147 * [taylor]: Taking taylor expansion of +nan.0 in n 1.147 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.147 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 1.147 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 1.147 * [taylor]: Taking taylor expansion of 0.5 in n 1.147 * [backup-simplify]: Simplify 0.5 into 0.5 1.147 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 1.147 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.147 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.147 * [taylor]: Taking taylor expansion of k in n 1.147 * [backup-simplify]: Simplify k into k 1.147 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.147 * [taylor]: Taking taylor expansion of 1.0 in n 1.147 * [backup-simplify]: Simplify 1.0 into 1.0 1.147 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.147 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.147 * [taylor]: Taking taylor expansion of -2.0 in n 1.147 * [backup-simplify]: Simplify -2.0 into -2.0 1.147 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.147 * [taylor]: Taking taylor expansion of PI in n 1.147 * [backup-simplify]: Simplify PI into PI 1.147 * [taylor]: Taking taylor expansion of n in n 1.147 * [backup-simplify]: Simplify 0 into 0 1.147 * [backup-simplify]: Simplify 1 into 1 1.147 * [backup-simplify]: Simplify (/ PI 1) into PI 1.148 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.148 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.148 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.150 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 1.151 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.151 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.152 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 1.153 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 1.154 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.156 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.156 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 1.157 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 1.157 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 1.157 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 1.157 * [taylor]: Taking taylor expansion of +nan.0 in n 1.157 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.157 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 1.157 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 1.157 * [taylor]: Taking taylor expansion of 0.5 in n 1.157 * [backup-simplify]: Simplify 0.5 into 0.5 1.157 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 1.157 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.157 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.157 * [taylor]: Taking taylor expansion of k in n 1.157 * [backup-simplify]: Simplify k into k 1.157 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.157 * [taylor]: Taking taylor expansion of 1.0 in n 1.157 * [backup-simplify]: Simplify 1.0 into 1.0 1.157 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.157 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.157 * [taylor]: Taking taylor expansion of -2.0 in n 1.157 * [backup-simplify]: Simplify -2.0 into -2.0 1.157 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.157 * [taylor]: Taking taylor expansion of PI in n 1.157 * [backup-simplify]: Simplify PI into PI 1.157 * [taylor]: Taking taylor expansion of n in n 1.157 * [backup-simplify]: Simplify 0 into 0 1.157 * [backup-simplify]: Simplify 1 into 1 1.157 * [backup-simplify]: Simplify (/ PI 1) into PI 1.158 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.158 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.159 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.160 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 1.161 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.162 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.163 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 1.163 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 1.164 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 1.165 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.165 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.166 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.167 * [backup-simplify]: Simplify (+ 0 0) into 0 1.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.168 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.169 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 1.171 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.172 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 1.172 * [backup-simplify]: Simplify 0 into 0 1.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.175 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.176 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 1.176 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 1.176 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 1.176 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 1.176 * [taylor]: Taking taylor expansion of +nan.0 in n 1.176 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.176 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 1.176 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 1.176 * [taylor]: Taking taylor expansion of 0.5 in n 1.176 * [backup-simplify]: Simplify 0.5 into 0.5 1.176 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 1.176 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.176 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.176 * [taylor]: Taking taylor expansion of k in n 1.176 * [backup-simplify]: Simplify k into k 1.177 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.177 * [taylor]: Taking taylor expansion of 1.0 in n 1.177 * [backup-simplify]: Simplify 1.0 into 1.0 1.177 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.177 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.177 * [taylor]: Taking taylor expansion of -2.0 in n 1.177 * [backup-simplify]: Simplify -2.0 into -2.0 1.177 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.177 * [taylor]: Taking taylor expansion of PI in n 1.177 * [backup-simplify]: Simplify PI into PI 1.177 * [taylor]: Taking taylor expansion of n in n 1.177 * [backup-simplify]: Simplify 0 into 0 1.177 * [backup-simplify]: Simplify 1 into 1 1.177 * [backup-simplify]: Simplify (/ PI 1) into PI 1.177 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.178 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.179 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.180 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.181 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 1.183 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.184 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.186 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 1.187 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 1.189 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 1.194 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 1.194 * * * [progress]: simplifying candidates 1.200 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 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(- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 1.207 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log 2.0) (log h2)) (log h1)) (/ (- 1.0 h0) 2.0)) (* (+ (log (* 2.0 h2)) (log h1)) (/ (- 1.0 h0) 2.0)) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0)) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (pow (* (* 2.0 h2) h1) (/ 1.0 2.0)) (pow (* (* 2.0 h2) h1) (/ h0 2.0)) (pow (* (* 2.0 h2) h1) (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0)))) (pow (* (* 2.0 h2) h1) (sqrt (/ (- 1.0 h0) 2.0))) (pow (* (* 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(log (sqrt h0))) (* (+ (log (* 2.0 h2)) (log h1)) (/ (- 1.0 h0) 2.0))) (+ (- (log 1.0) (log (sqrt h0))) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0))) (+ (- (log 1.0) (log (sqrt h0))) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0))) (+ (- (log 1.0) (log (sqrt h0))) (log (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (+ (log (/ 1.0 (sqrt h0))) (* (+ (+ (log 2.0) (log h2)) (log h1)) (/ (- 1.0 h0) 2.0))) (+ (log (/ 1.0 (sqrt h0))) (* (+ (log (* 2.0 h2)) (log h1)) (/ (- 1.0 h0) 2.0))) (+ (log (/ 1.0 (sqrt h0))) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0))) (+ (log (/ 1.0 (sqrt h0))) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0))) (+ (log (/ 1.0 (sqrt h0))) (log (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (log (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (exp (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt h0) (sqrt h0)) (sqrt h0))) (* (* (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (* (* (/ 1.0 (sqrt h0)) (/ 1.0 (sqrt h0))) (/ 1.0 (sqrt h0))) (* (* (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (cbrt (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))))) (cbrt (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (* (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (sqrt (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (sqrt (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* 1.0 (pow (* (* 2.0 h2) h1) (/ 1.0 2.0))) (* (sqrt h0) (pow (* (* 2.0 h2) h1) (/ h0 2.0))) (* (sqrt (/ 1.0 (sqrt h0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (sqrt (/ 1.0 (sqrt h0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (sqrt (/ 1.0 (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (/ 1.0 (sqrt h0)) (pow (* 2.0 h2) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt h0)) (* (cbrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (cbrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))))) (* (/ 1.0 (sqrt h0)) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (* (/ 1.0 (sqrt h0)) 1) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (sqrt (/ 1.0 (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (cbrt 1.0) (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (cbrt 1.0) (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (sqrt 1.0) (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ (sqrt 1.0) (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (cbrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt (cbrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt (sqrt h0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (/ 1.0 (sqrt h0)) (pow (* (* 2.0 h2) h1) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (- (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (pow (log h1) 2)))) (+ (* (/ 1.0 4.0) (* (pow h0 2) (* (log (* 2.0 h2)) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1))))) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 2.0) (* h0 (* (log (* 2.0 h2)) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (* (/ 1.0 2.0) (* h0 (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1)))))) (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (- (+ (* h3 h0) (- (+ (* h3 (pow h0 2)) (- h3))))) (- (+ (* h3 (/ 1 (pow h0 2))) (- (+ (* h3 (/ 1 h0)) (- (* h3 (/ 1 (pow h0 3)))))))) (- (+ (* h3 (/ 1 (pow h0 2))) (- (+ (* h3 (/ 1 h0)) (- h3))))) (- (+ (* h3 (* (* (pow h0 2) (pow (log (* 2.0 h2)) 2)) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (log (* 2.0 h2))) (pow (* (pow h2 1.0) (* (pow h1 1.0) (pow 2.0 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (* (log (* 2.0 h2)) (log h1))) (pow (* (pow h2 1.0) (* (pow 2.0 1.0) (pow h1 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (log h1)) (pow (* (pow 2.0 1.0) (* (pow h2 1.0) (pow h1 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* h0 (log (* 2.0 h2))) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (pow (log h1) 2)) (pow (* (pow 2.0 1.0) (* (pow h2 1.0) (pow h1 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* h0 (log h1)) (pow (* (pow 2.0 1.0) (* (pow h2 1.0) (pow h1 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0))) (- (+ (* h3 (* (pow h0 2) (pow (* (pow h2 1.0) (* (pow h1 1.0) (pow 2.0 1.0))) (/ 1.0 2.0)))) (- (* h3 (* h0 (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0))))))))))))))))))))))) (- (+ (* h3 (/ (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (pow h0 3))) (- (+ (* h3 (/ (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) h0)) (- (* h3 (/ (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (pow h0 2)))))))) (- (+ (* h3 (/ (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) h0)) (- (+ (* h3 (/ (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (pow h0 2))) (- (* h3 (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))))))))) 1.322 * * * [progress]: adding candidates to table 1.992 * * [progress]: iteration 2 / 4 1.992 * * * [progress]: picking best candidate 2.021 * * * * [pick]: Picked # 2.022 * * * [progress]: localizing error 2.049 * * * [progress]: generating rewritten candidates 2.049 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 2.084 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2) 2.130 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1) 2.164 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1) 2.210 * * * [progress]: generating series expansions 2.210 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 2.211 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.211 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.211 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.211 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.211 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.211 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.211 * [taylor]: Taking taylor expansion of 0.25 in k 2.211 * [backup-simplify]: Simplify 0.25 into 0.25 2.211 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.211 * [taylor]: Taking taylor expansion of 1.0 in k 2.211 * [backup-simplify]: Simplify 1.0 into 1.0 2.211 * [taylor]: Taking taylor expansion of k in k 2.211 * [backup-simplify]: Simplify 0 into 0 2.211 * [backup-simplify]: Simplify 1 into 1 2.211 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.211 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.211 * [taylor]: Taking taylor expansion of 2.0 in k 2.211 * [backup-simplify]: Simplify 2.0 into 2.0 2.211 * [taylor]: Taking taylor expansion of (* n PI) in k 2.211 * [taylor]: Taking taylor expansion of n in k 2.211 * [backup-simplify]: Simplify n into n 2.211 * [taylor]: Taking taylor expansion of PI in k 2.211 * [backup-simplify]: Simplify PI into PI 2.211 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.211 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.211 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.211 * [backup-simplify]: Simplify (- 0) into 0 2.212 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.212 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.212 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.212 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.212 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.212 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.212 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.212 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.212 * [taylor]: Taking taylor expansion of 0.25 in n 2.212 * [backup-simplify]: Simplify 0.25 into 0.25 2.212 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.212 * [taylor]: Taking taylor expansion of 1.0 in n 2.212 * [backup-simplify]: Simplify 1.0 into 1.0 2.212 * [taylor]: Taking taylor expansion of k in n 2.212 * [backup-simplify]: Simplify k into k 2.212 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.212 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.212 * [taylor]: Taking taylor expansion of 2.0 in n 2.212 * [backup-simplify]: Simplify 2.0 into 2.0 2.212 * [taylor]: Taking taylor expansion of (* n PI) in n 2.212 * [taylor]: Taking taylor expansion of n in n 2.212 * [backup-simplify]: Simplify 0 into 0 2.213 * [backup-simplify]: Simplify 1 into 1 2.213 * [taylor]: Taking taylor expansion of PI in n 2.213 * [backup-simplify]: Simplify PI into PI 2.213 * [backup-simplify]: Simplify (* 0 PI) into 0 2.213 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.214 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.215 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.216 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.216 * [backup-simplify]: Simplify (- k) into (- k) 2.216 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.216 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.217 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.217 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.218 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.218 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.218 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.218 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.218 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.218 * [taylor]: Taking taylor expansion of 0.25 in n 2.218 * [backup-simplify]: Simplify 0.25 into 0.25 2.218 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.218 * [taylor]: Taking taylor expansion of 1.0 in n 2.218 * [backup-simplify]: Simplify 1.0 into 1.0 2.218 * [taylor]: Taking taylor expansion of k in n 2.218 * [backup-simplify]: Simplify k into k 2.218 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.218 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.218 * [taylor]: Taking taylor expansion of 2.0 in n 2.218 * [backup-simplify]: Simplify 2.0 into 2.0 2.218 * [taylor]: Taking taylor expansion of (* n PI) in n 2.219 * [taylor]: Taking taylor expansion of n in n 2.219 * [backup-simplify]: Simplify 0 into 0 2.219 * [backup-simplify]: Simplify 1 into 1 2.219 * [taylor]: Taking taylor expansion of PI in n 2.219 * [backup-simplify]: Simplify PI into PI 2.219 * [backup-simplify]: Simplify (* 0 PI) into 0 2.219 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.220 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.221 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.222 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.222 * [backup-simplify]: Simplify (- k) into (- k) 2.222 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.222 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.224 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.225 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.231 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.231 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.231 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.231 * [taylor]: Taking taylor expansion of 0.25 in k 2.231 * [backup-simplify]: Simplify 0.25 into 0.25 2.231 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.231 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.231 * [taylor]: Taking taylor expansion of 1.0 in k 2.232 * [backup-simplify]: Simplify 1.0 into 1.0 2.232 * [taylor]: Taking taylor expansion of k in k 2.232 * [backup-simplify]: Simplify 0 into 0 2.232 * [backup-simplify]: Simplify 1 into 1 2.232 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.232 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.232 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.232 * [taylor]: Taking taylor expansion of 2.0 in k 2.232 * [backup-simplify]: Simplify 2.0 into 2.0 2.232 * [taylor]: Taking taylor expansion of PI in k 2.232 * [backup-simplify]: Simplify PI into PI 2.233 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.234 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.234 * [taylor]: Taking taylor expansion of (log n) in k 2.234 * [taylor]: Taking taylor expansion of n in k 2.234 * [backup-simplify]: Simplify n into n 2.234 * [backup-simplify]: Simplify (log n) into (log n) 2.235 * [backup-simplify]: Simplify (- 0) into 0 2.235 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.236 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.237 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.238 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.239 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.240 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.241 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.244 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.244 * [backup-simplify]: Simplify (- 0) into 0 2.245 * [backup-simplify]: Simplify (+ 0 0) into 0 2.245 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.247 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.249 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.249 * [taylor]: Taking taylor expansion of 0 in k 2.249 * [backup-simplify]: Simplify 0 into 0 2.249 * [backup-simplify]: Simplify 0 into 0 2.250 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.252 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.253 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.254 * [backup-simplify]: Simplify (+ 0 0) into 0 2.254 * [backup-simplify]: Simplify (- 1) into -1 2.254 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.256 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.258 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.262 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.266 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.268 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.272 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.272 * [backup-simplify]: Simplify (- 0) into 0 2.273 * [backup-simplify]: Simplify (+ 0 0) into 0 2.273 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.275 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.276 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.279 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.279 * [taylor]: Taking taylor expansion of 0 in k 2.279 * [backup-simplify]: Simplify 0 into 0 2.279 * [backup-simplify]: Simplify 0 into 0 2.279 * [backup-simplify]: Simplify 0 into 0 2.280 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.283 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.285 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.286 * [backup-simplify]: Simplify (+ 0 0) into 0 2.286 * [backup-simplify]: Simplify (- 0) into 0 2.286 * [backup-simplify]: Simplify (+ 0 0) into 0 2.288 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.291 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.295 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.301 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.311 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.312 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.312 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.312 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.312 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.312 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.312 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.312 * [taylor]: Taking taylor expansion of 0.25 in k 2.312 * [backup-simplify]: Simplify 0.25 into 0.25 2.312 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.312 * [taylor]: Taking taylor expansion of 1.0 in k 2.312 * [backup-simplify]: Simplify 1.0 into 1.0 2.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.312 * [taylor]: Taking taylor expansion of k in k 2.312 * [backup-simplify]: Simplify 0 into 0 2.312 * [backup-simplify]: Simplify 1 into 1 2.313 * [backup-simplify]: Simplify (/ 1 1) into 1 2.313 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.313 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.313 * [taylor]: Taking taylor expansion of 2.0 in k 2.313 * [backup-simplify]: Simplify 2.0 into 2.0 2.313 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.313 * [taylor]: Taking taylor expansion of PI in k 2.313 * [backup-simplify]: Simplify PI into PI 2.313 * [taylor]: Taking taylor expansion of n in k 2.313 * [backup-simplify]: Simplify n into n 2.313 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.313 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.313 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.314 * [backup-simplify]: Simplify (- 1) into -1 2.314 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.314 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.315 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.315 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.315 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.315 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.315 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.315 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.315 * [taylor]: Taking taylor expansion of 0.25 in n 2.315 * [backup-simplify]: Simplify 0.25 into 0.25 2.315 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.315 * [taylor]: Taking taylor expansion of 1.0 in n 2.315 * [backup-simplify]: Simplify 1.0 into 1.0 2.315 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.315 * [taylor]: Taking taylor expansion of k in n 2.315 * [backup-simplify]: Simplify k into k 2.315 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.315 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.315 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.315 * [taylor]: Taking taylor expansion of 2.0 in n 2.315 * [backup-simplify]: Simplify 2.0 into 2.0 2.315 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.315 * [taylor]: Taking taylor expansion of PI in n 2.315 * [backup-simplify]: Simplify PI into PI 2.315 * [taylor]: Taking taylor expansion of n in n 2.315 * [backup-simplify]: Simplify 0 into 0 2.316 * [backup-simplify]: Simplify 1 into 1 2.316 * [backup-simplify]: Simplify (/ PI 1) into PI 2.317 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.318 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.318 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.318 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.318 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.319 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.321 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.322 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.322 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.322 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.322 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.322 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.322 * [taylor]: Taking taylor expansion of 0.25 in n 2.322 * [backup-simplify]: Simplify 0.25 into 0.25 2.322 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.322 * [taylor]: Taking taylor expansion of 1.0 in n 2.322 * [backup-simplify]: Simplify 1.0 into 1.0 2.322 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.322 * [taylor]: Taking taylor expansion of k in n 2.322 * [backup-simplify]: Simplify k into k 2.322 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.322 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.322 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.322 * [taylor]: Taking taylor expansion of 2.0 in n 2.322 * [backup-simplify]: Simplify 2.0 into 2.0 2.322 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.322 * [taylor]: Taking taylor expansion of PI in n 2.323 * [backup-simplify]: Simplify PI into PI 2.323 * [taylor]: Taking taylor expansion of n in n 2.323 * [backup-simplify]: Simplify 0 into 0 2.323 * [backup-simplify]: Simplify 1 into 1 2.323 * [backup-simplify]: Simplify (/ PI 1) into PI 2.324 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.325 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.325 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.325 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.325 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.327 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.329 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.329 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.329 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.329 * [taylor]: Taking taylor expansion of 0.25 in k 2.329 * [backup-simplify]: Simplify 0.25 into 0.25 2.329 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.329 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.329 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.329 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.329 * [taylor]: Taking taylor expansion of 2.0 in k 2.329 * [backup-simplify]: Simplify 2.0 into 2.0 2.329 * [taylor]: Taking taylor expansion of PI in k 2.329 * [backup-simplify]: Simplify PI into PI 2.330 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.331 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.331 * [taylor]: Taking taylor expansion of (log n) in k 2.331 * [taylor]: Taking taylor expansion of n in k 2.331 * [backup-simplify]: Simplify n into n 2.331 * [backup-simplify]: Simplify (log n) into (log n) 2.331 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.331 * [taylor]: Taking taylor expansion of 1.0 in k 2.331 * [backup-simplify]: Simplify 1.0 into 1.0 2.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.331 * [taylor]: Taking taylor expansion of k in k 2.331 * [backup-simplify]: Simplify 0 into 0 2.331 * [backup-simplify]: Simplify 1 into 1 2.331 * [backup-simplify]: Simplify (/ 1 1) into 1 2.331 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.333 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.333 * [backup-simplify]: Simplify (- 1) into -1 2.334 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.335 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.336 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.337 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.338 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.339 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.340 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.342 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.342 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.342 * [backup-simplify]: Simplify (- 0) into 0 2.343 * [backup-simplify]: Simplify (+ 0 0) into 0 2.344 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.345 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.346 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.348 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.348 * [taylor]: Taking taylor expansion of 0 in k 2.348 * [backup-simplify]: Simplify 0 into 0 2.348 * [backup-simplify]: Simplify 0 into 0 2.348 * [backup-simplify]: Simplify 0 into 0 2.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.350 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.354 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.354 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.355 * [backup-simplify]: Simplify (- 0) into 0 2.355 * [backup-simplify]: Simplify (+ 0 0) into 0 2.356 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.359 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.361 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.361 * [taylor]: Taking taylor expansion of 0 in k 2.361 * [backup-simplify]: Simplify 0 into 0 2.361 * [backup-simplify]: Simplify 0 into 0 2.361 * [backup-simplify]: Simplify 0 into 0 2.361 * [backup-simplify]: Simplify 0 into 0 2.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.364 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.370 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.371 * [backup-simplify]: Simplify (- 0) into 0 2.371 * [backup-simplify]: Simplify (+ 0 0) into 0 2.372 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.372 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.374 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.380 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.380 * [taylor]: Taking taylor expansion of 0 in k 2.380 * [backup-simplify]: Simplify 0 into 0 2.380 * [backup-simplify]: Simplify 0 into 0 2.381 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.381 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.381 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.382 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.382 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.382 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.382 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.382 * [taylor]: Taking taylor expansion of 0.25 in k 2.382 * [backup-simplify]: Simplify 0.25 into 0.25 2.382 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.382 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.382 * [taylor]: Taking taylor expansion of k in k 2.382 * [backup-simplify]: Simplify 0 into 0 2.382 * [backup-simplify]: Simplify 1 into 1 2.382 * [backup-simplify]: Simplify (/ 1 1) into 1 2.382 * [taylor]: Taking taylor expansion of 1.0 in k 2.382 * [backup-simplify]: Simplify 1.0 into 1.0 2.382 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.382 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.382 * [taylor]: Taking taylor expansion of -2.0 in k 2.382 * [backup-simplify]: Simplify -2.0 into -2.0 2.382 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.382 * [taylor]: Taking taylor expansion of PI in k 2.382 * [backup-simplify]: Simplify PI into PI 2.382 * [taylor]: Taking taylor expansion of n in k 2.382 * [backup-simplify]: Simplify n into n 2.382 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.382 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.382 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.383 * [backup-simplify]: Simplify (+ 1 0) into 1 2.383 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.383 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.383 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.383 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.383 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.383 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.383 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.383 * [taylor]: Taking taylor expansion of 0.25 in n 2.383 * [backup-simplify]: Simplify 0.25 into 0.25 2.383 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.383 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.383 * [taylor]: Taking taylor expansion of k in n 2.383 * [backup-simplify]: Simplify k into k 2.383 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.383 * [taylor]: Taking taylor expansion of 1.0 in n 2.383 * [backup-simplify]: Simplify 1.0 into 1.0 2.383 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.383 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.383 * [taylor]: Taking taylor expansion of -2.0 in n 2.383 * [backup-simplify]: Simplify -2.0 into -2.0 2.383 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.383 * [taylor]: Taking taylor expansion of PI in n 2.383 * [backup-simplify]: Simplify PI into PI 2.384 * [taylor]: Taking taylor expansion of n in n 2.384 * [backup-simplify]: Simplify 0 into 0 2.384 * [backup-simplify]: Simplify 1 into 1 2.384 * [backup-simplify]: Simplify (/ PI 1) into PI 2.384 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.385 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.385 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.385 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.386 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.387 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.387 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.387 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.387 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.387 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.387 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.387 * [taylor]: Taking taylor expansion of 0.25 in n 2.387 * [backup-simplify]: Simplify 0.25 into 0.25 2.387 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.388 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.388 * [taylor]: Taking taylor expansion of k in n 2.388 * [backup-simplify]: Simplify k into k 2.388 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.388 * [taylor]: Taking taylor expansion of 1.0 in n 2.388 * [backup-simplify]: Simplify 1.0 into 1.0 2.388 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.388 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.388 * [taylor]: Taking taylor expansion of -2.0 in n 2.388 * [backup-simplify]: Simplify -2.0 into -2.0 2.388 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.388 * [taylor]: Taking taylor expansion of PI in n 2.388 * [backup-simplify]: Simplify PI into PI 2.388 * [taylor]: Taking taylor expansion of n in n 2.388 * [backup-simplify]: Simplify 0 into 0 2.388 * [backup-simplify]: Simplify 1 into 1 2.388 * [backup-simplify]: Simplify (/ PI 1) into PI 2.388 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.389 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.389 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.389 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.390 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.391 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.392 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.392 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.392 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.392 * [taylor]: Taking taylor expansion of 0.25 in k 2.392 * [backup-simplify]: Simplify 0.25 into 0.25 2.392 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.392 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.392 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.392 * [taylor]: Taking taylor expansion of k in k 2.392 * [backup-simplify]: Simplify 0 into 0 2.392 * [backup-simplify]: Simplify 1 into 1 2.392 * [backup-simplify]: Simplify (/ 1 1) into 1 2.392 * [taylor]: Taking taylor expansion of 1.0 in k 2.392 * [backup-simplify]: Simplify 1.0 into 1.0 2.392 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.392 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.392 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.392 * [taylor]: Taking taylor expansion of -2.0 in k 2.392 * [backup-simplify]: Simplify -2.0 into -2.0 2.392 * [taylor]: Taking taylor expansion of PI in k 2.392 * [backup-simplify]: Simplify PI into PI 2.393 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.393 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.393 * [taylor]: Taking taylor expansion of (log n) in k 2.393 * [taylor]: Taking taylor expansion of n in k 2.393 * [backup-simplify]: Simplify n into n 2.394 * [backup-simplify]: Simplify (log n) into (log n) 2.394 * [backup-simplify]: Simplify (+ 1 0) into 1 2.394 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.394 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.395 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.396 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.397 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.397 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.398 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.398 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.399 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.400 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.400 * [backup-simplify]: Simplify (+ 0 0) into 0 2.400 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.402 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.404 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.404 * [taylor]: Taking taylor expansion of 0 in k 2.404 * [backup-simplify]: Simplify 0 into 0 2.404 * [backup-simplify]: Simplify 0 into 0 2.404 * [backup-simplify]: Simplify 0 into 0 2.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.406 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.410 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.411 * [backup-simplify]: Simplify (+ 0 0) into 0 2.411 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.413 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.414 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.417 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.417 * [taylor]: Taking taylor expansion of 0 in k 2.417 * [backup-simplify]: Simplify 0 into 0 2.417 * [backup-simplify]: Simplify 0 into 0 2.417 * [backup-simplify]: Simplify 0 into 0 2.417 * [backup-simplify]: Simplify 0 into 0 2.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.419 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.426 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.426 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.426 * [backup-simplify]: Simplify (+ 0 0) into 0 2.428 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.429 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.431 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.434 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.434 * [taylor]: Taking taylor expansion of 0 in k 2.434 * [backup-simplify]: Simplify 0 into 0 2.434 * [backup-simplify]: Simplify 0 into 0 2.436 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.436 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2) 2.436 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2.436 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 2.436 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 2.437 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 2.437 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 2.437 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 2.437 * [taylor]: Taking taylor expansion of 0.25 in k 2.437 * [backup-simplify]: Simplify 0.25 into 0.25 2.437 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.437 * [taylor]: Taking taylor expansion of 1.0 in k 2.437 * [backup-simplify]: Simplify 1.0 into 1.0 2.437 * [taylor]: Taking taylor expansion of k in k 2.437 * [backup-simplify]: Simplify 0 into 0 2.437 * [backup-simplify]: Simplify 1 into 1 2.437 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 2.437 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 2.437 * [taylor]: Taking taylor expansion of 2.0 in k 2.437 * [backup-simplify]: Simplify 2.0 into 2.0 2.437 * [taylor]: Taking taylor expansion of (* n PI) in k 2.437 * [taylor]: Taking taylor expansion of n in k 2.437 * [backup-simplify]: Simplify n into n 2.437 * [taylor]: Taking taylor expansion of PI in k 2.437 * [backup-simplify]: Simplify PI into PI 2.437 * [backup-simplify]: Simplify (* n PI) into (* n PI) 2.437 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 2.437 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 2.438 * [backup-simplify]: Simplify (- 0) into 0 2.438 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.439 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 2.439 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 2.439 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 2.439 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.439 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.439 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.439 * [taylor]: Taking taylor expansion of 0.25 in n 2.439 * [backup-simplify]: Simplify 0.25 into 0.25 2.439 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.439 * [taylor]: Taking taylor expansion of 1.0 in n 2.439 * [backup-simplify]: Simplify 1.0 into 1.0 2.439 * [taylor]: Taking taylor expansion of k in n 2.439 * [backup-simplify]: Simplify k into k 2.439 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.439 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.439 * [taylor]: Taking taylor expansion of 2.0 in n 2.439 * [backup-simplify]: Simplify 2.0 into 2.0 2.439 * [taylor]: Taking taylor expansion of (* n PI) in n 2.439 * [taylor]: Taking taylor expansion of n in n 2.439 * [backup-simplify]: Simplify 0 into 0 2.439 * [backup-simplify]: Simplify 1 into 1 2.439 * [taylor]: Taking taylor expansion of PI in n 2.439 * [backup-simplify]: Simplify PI into PI 2.440 * [backup-simplify]: Simplify (* 0 PI) into 0 2.440 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.442 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.444 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.445 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.445 * [backup-simplify]: Simplify (- k) into (- k) 2.445 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.445 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.447 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.448 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.449 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.449 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 2.450 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 2.450 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 2.450 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 2.450 * [taylor]: Taking taylor expansion of 0.25 in n 2.450 * [backup-simplify]: Simplify 0.25 into 0.25 2.450 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 2.450 * [taylor]: Taking taylor expansion of 1.0 in n 2.450 * [backup-simplify]: Simplify 1.0 into 1.0 2.450 * [taylor]: Taking taylor expansion of k in n 2.450 * [backup-simplify]: Simplify k into k 2.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.450 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.450 * [taylor]: Taking taylor expansion of 2.0 in n 2.450 * [backup-simplify]: Simplify 2.0 into 2.0 2.450 * [taylor]: Taking taylor expansion of (* n PI) in n 2.450 * [taylor]: Taking taylor expansion of n in n 2.450 * [backup-simplify]: Simplify 0 into 0 2.450 * [backup-simplify]: Simplify 1 into 1 2.450 * [taylor]: Taking taylor expansion of PI in n 2.450 * [backup-simplify]: Simplify PI into PI 2.450 * [backup-simplify]: Simplify (* 0 PI) into 0 2.451 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.452 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.454 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.455 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.455 * [backup-simplify]: Simplify (- k) into (- k) 2.455 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 2.455 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 2.457 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.458 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 2.459 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2.459 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 2.459 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 2.460 * [taylor]: Taking taylor expansion of 0.25 in k 2.460 * [backup-simplify]: Simplify 0.25 into 0.25 2.460 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 2.460 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 2.460 * [taylor]: Taking taylor expansion of 1.0 in k 2.460 * [backup-simplify]: Simplify 1.0 into 1.0 2.460 * [taylor]: Taking taylor expansion of k in k 2.460 * [backup-simplify]: Simplify 0 into 0 2.460 * [backup-simplify]: Simplify 1 into 1 2.460 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 2.460 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.460 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.460 * [taylor]: Taking taylor expansion of 2.0 in k 2.460 * [backup-simplify]: Simplify 2.0 into 2.0 2.460 * [taylor]: Taking taylor expansion of PI in k 2.460 * [backup-simplify]: Simplify PI into PI 2.461 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.462 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.462 * [taylor]: Taking taylor expansion of (log n) in k 2.462 * [taylor]: Taking taylor expansion of n in k 2.462 * [backup-simplify]: Simplify n into n 2.462 * [backup-simplify]: Simplify (log n) into (log n) 2.462 * [backup-simplify]: Simplify (- 0) into 0 2.463 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 2.464 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 2.465 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 2.466 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 2.467 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.468 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.471 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.473 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.473 * [backup-simplify]: Simplify (- 0) into 0 2.473 * [backup-simplify]: Simplify (+ 0 0) into 0 2.474 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 2.475 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.477 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 2.479 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.479 * [taylor]: Taking taylor expansion of 0 in k 2.479 * [backup-simplify]: Simplify 0 into 0 2.479 * [backup-simplify]: Simplify 0 into 0 2.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.481 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.482 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 2.483 * [backup-simplify]: Simplify (+ 0 0) into 0 2.483 * [backup-simplify]: Simplify (- 1) into -1 2.484 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.485 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 2.487 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2.489 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.490 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 2.491 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.492 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.494 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.494 * [backup-simplify]: Simplify (- 0) into 0 2.495 * [backup-simplify]: Simplify (+ 0 0) into 0 2.495 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 2.496 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.497 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.499 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.499 * [taylor]: Taking taylor expansion of 0 in k 2.499 * [backup-simplify]: Simplify 0 into 0 2.499 * [backup-simplify]: Simplify 0 into 0 2.499 * [backup-simplify]: Simplify 0 into 0 2.499 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.501 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.502 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 2.503 * [backup-simplify]: Simplify (+ 0 0) into 0 2.508 * [backup-simplify]: Simplify (- 0) into 0 2.508 * [backup-simplify]: Simplify (+ 0 0) into 0 2.509 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 2.511 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 2.514 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.519 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 2.530 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 2.531 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2.531 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 2.532 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 2.532 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.532 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.532 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 2.532 * [taylor]: Taking taylor expansion of 0.25 in k 2.532 * [backup-simplify]: Simplify 0.25 into 0.25 2.532 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.532 * [taylor]: Taking taylor expansion of 1.0 in k 2.532 * [backup-simplify]: Simplify 1.0 into 1.0 2.532 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.532 * [taylor]: Taking taylor expansion of k in k 2.532 * [backup-simplify]: Simplify 0 into 0 2.532 * [backup-simplify]: Simplify 1 into 1 2.532 * [backup-simplify]: Simplify (/ 1 1) into 1 2.533 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.533 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.533 * [taylor]: Taking taylor expansion of 2.0 in k 2.533 * [backup-simplify]: Simplify 2.0 into 2.0 2.533 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.533 * [taylor]: Taking taylor expansion of PI in k 2.533 * [backup-simplify]: Simplify PI into PI 2.533 * [taylor]: Taking taylor expansion of n in k 2.533 * [backup-simplify]: Simplify n into n 2.533 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.533 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.533 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.534 * [backup-simplify]: Simplify (- 1) into -1 2.534 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.534 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 2.535 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 2.535 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.535 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.535 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.535 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.535 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.535 * [taylor]: Taking taylor expansion of 0.25 in n 2.535 * [backup-simplify]: Simplify 0.25 into 0.25 2.535 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.535 * [taylor]: Taking taylor expansion of 1.0 in n 2.535 * [backup-simplify]: Simplify 1.0 into 1.0 2.535 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.535 * [taylor]: Taking taylor expansion of k in n 2.535 * [backup-simplify]: Simplify k into k 2.535 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.535 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.536 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.536 * [taylor]: Taking taylor expansion of 2.0 in n 2.536 * [backup-simplify]: Simplify 2.0 into 2.0 2.536 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.536 * [taylor]: Taking taylor expansion of PI in n 2.536 * [backup-simplify]: Simplify PI into PI 2.536 * [taylor]: Taking taylor expansion of n in n 2.536 * [backup-simplify]: Simplify 0 into 0 2.536 * [backup-simplify]: Simplify 1 into 1 2.536 * [backup-simplify]: Simplify (/ PI 1) into PI 2.537 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.538 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.538 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.538 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.539 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.541 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.543 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.543 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 2.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.543 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.543 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 2.543 * [taylor]: Taking taylor expansion of 0.25 in n 2.543 * [backup-simplify]: Simplify 0.25 into 0.25 2.543 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.543 * [taylor]: Taking taylor expansion of 1.0 in n 2.543 * [backup-simplify]: Simplify 1.0 into 1.0 2.543 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.543 * [taylor]: Taking taylor expansion of k in n 2.543 * [backup-simplify]: Simplify k into k 2.543 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.543 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.543 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.543 * [taylor]: Taking taylor expansion of 2.0 in n 2.543 * [backup-simplify]: Simplify 2.0 into 2.0 2.543 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.544 * [taylor]: Taking taylor expansion of PI in n 2.544 * [backup-simplify]: Simplify PI into PI 2.544 * [taylor]: Taking taylor expansion of n in n 2.544 * [backup-simplify]: Simplify 0 into 0 2.544 * [backup-simplify]: Simplify 1 into 1 2.545 * [backup-simplify]: Simplify (/ PI 1) into PI 2.545 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.546 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.546 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.546 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.546 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 2.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.548 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.549 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.549 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 2.549 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 2.549 * [taylor]: Taking taylor expansion of 0.25 in k 2.549 * [backup-simplify]: Simplify 0.25 into 0.25 2.549 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 2.549 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 2.549 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 2.549 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 2.549 * [taylor]: Taking taylor expansion of 2.0 in k 2.549 * [backup-simplify]: Simplify 2.0 into 2.0 2.549 * [taylor]: Taking taylor expansion of PI in k 2.549 * [backup-simplify]: Simplify PI into PI 2.550 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.550 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.550 * [taylor]: Taking taylor expansion of (log n) in k 2.550 * [taylor]: Taking taylor expansion of n in k 2.550 * [backup-simplify]: Simplify n into n 2.550 * [backup-simplify]: Simplify (log n) into (log n) 2.550 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.550 * [taylor]: Taking taylor expansion of 1.0 in k 2.550 * [backup-simplify]: Simplify 1.0 into 1.0 2.550 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.550 * [taylor]: Taking taylor expansion of k in k 2.550 * [backup-simplify]: Simplify 0 into 0 2.550 * [backup-simplify]: Simplify 1 into 1 2.551 * [backup-simplify]: Simplify (/ 1 1) into 1 2.551 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.551 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 2.552 * [backup-simplify]: Simplify (- 1) into -1 2.552 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.553 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 2.553 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 2.554 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.555 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.556 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.557 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.557 * [backup-simplify]: Simplify (- 0) into 0 2.557 * [backup-simplify]: Simplify (+ 0 0) into 0 2.558 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.560 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 2.561 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.561 * [taylor]: Taking taylor expansion of 0 in k 2.561 * [backup-simplify]: Simplify 0 into 0 2.562 * [backup-simplify]: Simplify 0 into 0 2.562 * [backup-simplify]: Simplify 0 into 0 2.563 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.563 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.567 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 2.567 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.568 * [backup-simplify]: Simplify (- 0) into 0 2.568 * [backup-simplify]: Simplify (+ 0 0) into 0 2.569 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 2.570 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.572 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 2.575 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.575 * [taylor]: Taking taylor expansion of 0 in k 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.575 * [backup-simplify]: Simplify 0 into 0 2.576 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.577 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.583 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 2.583 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.583 * [backup-simplify]: Simplify (- 0) into 0 2.584 * [backup-simplify]: Simplify (+ 0 0) into 0 2.585 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 2.586 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.588 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 2.590 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.591 * [taylor]: Taking taylor expansion of 0 in k 2.591 * [backup-simplify]: Simplify 0 into 0 2.591 * [backup-simplify]: Simplify 0 into 0 2.592 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2.593 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2.593 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 2.593 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 2.593 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.593 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.593 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 2.593 * [taylor]: Taking taylor expansion of 0.25 in k 2.593 * [backup-simplify]: Simplify 0.25 into 0.25 2.593 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.593 * [taylor]: Taking taylor expansion of k in k 2.593 * [backup-simplify]: Simplify 0 into 0 2.593 * [backup-simplify]: Simplify 1 into 1 2.593 * [backup-simplify]: Simplify (/ 1 1) into 1 2.593 * [taylor]: Taking taylor expansion of 1.0 in k 2.593 * [backup-simplify]: Simplify 1.0 into 1.0 2.593 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.593 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.594 * [taylor]: Taking taylor expansion of -2.0 in k 2.594 * [backup-simplify]: Simplify -2.0 into -2.0 2.594 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.594 * [taylor]: Taking taylor expansion of PI in k 2.594 * [backup-simplify]: Simplify PI into PI 2.594 * [taylor]: Taking taylor expansion of n in k 2.594 * [backup-simplify]: Simplify n into n 2.594 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.594 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.594 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.594 * [backup-simplify]: Simplify (+ 1 0) into 1 2.595 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 2.595 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 2.595 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.595 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.595 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.595 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.595 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.595 * [taylor]: Taking taylor expansion of 0.25 in n 2.595 * [backup-simplify]: Simplify 0.25 into 0.25 2.595 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.595 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.595 * [taylor]: Taking taylor expansion of k in n 2.595 * [backup-simplify]: Simplify k into k 2.595 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.595 * [taylor]: Taking taylor expansion of 1.0 in n 2.596 * [backup-simplify]: Simplify 1.0 into 1.0 2.596 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.596 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.596 * [taylor]: Taking taylor expansion of -2.0 in n 2.596 * [backup-simplify]: Simplify -2.0 into -2.0 2.596 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.596 * [taylor]: Taking taylor expansion of PI in n 2.596 * [backup-simplify]: Simplify PI into PI 2.596 * [taylor]: Taking taylor expansion of n in n 2.596 * [backup-simplify]: Simplify 0 into 0 2.596 * [backup-simplify]: Simplify 1 into 1 2.596 * [backup-simplify]: Simplify (/ PI 1) into PI 2.597 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.598 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.598 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.598 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.600 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.602 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.602 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 2.602 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.602 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.602 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 2.602 * [taylor]: Taking taylor expansion of 0.25 in n 2.602 * [backup-simplify]: Simplify 0.25 into 0.25 2.602 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.602 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.602 * [taylor]: Taking taylor expansion of k in n 2.602 * [backup-simplify]: Simplify k into k 2.602 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.602 * [taylor]: Taking taylor expansion of 1.0 in n 2.602 * [backup-simplify]: Simplify 1.0 into 1.0 2.602 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.602 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.602 * [taylor]: Taking taylor expansion of -2.0 in n 2.602 * [backup-simplify]: Simplify -2.0 into -2.0 2.602 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.602 * [taylor]: Taking taylor expansion of PI in n 2.602 * [backup-simplify]: Simplify PI into PI 2.602 * [taylor]: Taking taylor expansion of n in n 2.602 * [backup-simplify]: Simplify 0 into 0 2.602 * [backup-simplify]: Simplify 1 into 1 2.603 * [backup-simplify]: Simplify (/ PI 1) into PI 2.603 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.604 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.605 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.605 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 2.606 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.607 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.608 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.608 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 2.608 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 2.608 * [taylor]: Taking taylor expansion of 0.25 in k 2.608 * [backup-simplify]: Simplify 0.25 into 0.25 2.608 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 2.609 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.609 * [taylor]: Taking taylor expansion of k in k 2.609 * [backup-simplify]: Simplify 0 into 0 2.609 * [backup-simplify]: Simplify 1 into 1 2.609 * [backup-simplify]: Simplify (/ 1 1) into 1 2.609 * [taylor]: Taking taylor expansion of 1.0 in k 2.609 * [backup-simplify]: Simplify 1.0 into 1.0 2.609 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 2.609 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 2.609 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 2.609 * [taylor]: Taking taylor expansion of -2.0 in k 2.609 * [backup-simplify]: Simplify -2.0 into -2.0 2.609 * [taylor]: Taking taylor expansion of PI in k 2.609 * [backup-simplify]: Simplify PI into PI 2.610 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.611 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.611 * [taylor]: Taking taylor expansion of (log n) in k 2.611 * [taylor]: Taking taylor expansion of n in k 2.611 * [backup-simplify]: Simplify n into n 2.611 * [backup-simplify]: Simplify (log n) into (log n) 2.611 * [backup-simplify]: Simplify (+ 1 0) into 1 2.611 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 2.613 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 2.614 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 2.615 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 2.616 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.617 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.618 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.619 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.620 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.620 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.621 * [backup-simplify]: Simplify (+ 0 0) into 0 2.621 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 2.622 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.624 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.625 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.625 * [taylor]: Taking taylor expansion of 0 in k 2.625 * [backup-simplify]: Simplify 0 into 0 2.625 * [backup-simplify]: Simplify 0 into 0 2.626 * [backup-simplify]: Simplify 0 into 0 2.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.627 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.631 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 2.631 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.631 * [backup-simplify]: Simplify (+ 0 0) into 0 2.632 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 2.633 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.634 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 2.636 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 2.636 * [taylor]: Taking taylor expansion of 0 in k 2.636 * [backup-simplify]: Simplify 0 into 0 2.636 * [backup-simplify]: Simplify 0 into 0 2.636 * [backup-simplify]: Simplify 0 into 0 2.636 * [backup-simplify]: Simplify 0 into 0 2.637 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.637 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.645 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 2.646 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 2.646 * [backup-simplify]: Simplify (+ 0 0) into 0 2.647 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 2.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.649 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 2.652 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 2.652 * [taylor]: Taking taylor expansion of 0 in k 2.652 * [backup-simplify]: Simplify 0 into 0 2.652 * [backup-simplify]: Simplify 0 into 0 2.653 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2.653 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1) 2.654 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.654 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.654 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.654 * [taylor]: Taking taylor expansion of 2.0 in n 2.654 * [backup-simplify]: Simplify 2.0 into 2.0 2.654 * [taylor]: Taking taylor expansion of (* n PI) in n 2.654 * [taylor]: Taking taylor expansion of n in n 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify 1 into 1 2.654 * [taylor]: Taking taylor expansion of PI in n 2.654 * [backup-simplify]: Simplify PI into PI 2.654 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.654 * [taylor]: Taking taylor expansion of 2.0 in n 2.654 * [backup-simplify]: Simplify 2.0 into 2.0 2.654 * [taylor]: Taking taylor expansion of (* n PI) in n 2.654 * [taylor]: Taking taylor expansion of n in n 2.654 * [backup-simplify]: Simplify 0 into 0 2.654 * [backup-simplify]: Simplify 1 into 1 2.654 * [taylor]: Taking taylor expansion of PI in n 2.654 * [backup-simplify]: Simplify PI into PI 2.654 * [backup-simplify]: Simplify (* 0 PI) into 0 2.655 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.655 * [backup-simplify]: Simplify 0 into 0 2.656 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.657 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.657 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.658 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.658 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.658 * [backup-simplify]: Simplify 0 into 0 2.659 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.660 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.660 * [backup-simplify]: Simplify 0 into 0 2.660 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.661 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.661 * [backup-simplify]: Simplify 0 into 0 2.662 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.663 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.663 * [backup-simplify]: Simplify 0 into 0 2.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.665 * [backup-simplify]: Simplify 0 into 0 2.666 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.667 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.667 * [backup-simplify]: Simplify 0 into 0 2.667 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.668 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.668 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.668 * [taylor]: Taking taylor expansion of 2.0 in n 2.668 * [backup-simplify]: Simplify 2.0 into 2.0 2.668 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.668 * [taylor]: Taking taylor expansion of PI in n 2.668 * [backup-simplify]: Simplify PI into PI 2.668 * [taylor]: Taking taylor expansion of n in n 2.668 * [backup-simplify]: Simplify 0 into 0 2.668 * [backup-simplify]: Simplify 1 into 1 2.668 * [backup-simplify]: Simplify (/ PI 1) into PI 2.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.668 * [taylor]: Taking taylor expansion of 2.0 in n 2.668 * [backup-simplify]: Simplify 2.0 into 2.0 2.668 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.668 * [taylor]: Taking taylor expansion of PI in n 2.668 * [backup-simplify]: Simplify PI into PI 2.668 * [taylor]: Taking taylor expansion of n in n 2.668 * [backup-simplify]: Simplify 0 into 0 2.668 * [backup-simplify]: Simplify 1 into 1 2.669 * [backup-simplify]: Simplify (/ PI 1) into PI 2.669 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.669 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.670 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.670 * [backup-simplify]: Simplify 0 into 0 2.671 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.672 * [backup-simplify]: Simplify 0 into 0 2.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.673 * [backup-simplify]: Simplify 0 into 0 2.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.674 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.674 * [backup-simplify]: Simplify 0 into 0 2.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.676 * [backup-simplify]: Simplify 0 into 0 2.677 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.678 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.678 * [backup-simplify]: Simplify 0 into 0 2.678 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.678 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.678 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.678 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.678 * [taylor]: Taking taylor expansion of -2.0 in n 2.678 * [backup-simplify]: Simplify -2.0 into -2.0 2.678 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.678 * [taylor]: Taking taylor expansion of PI in n 2.678 * [backup-simplify]: Simplify PI into PI 2.678 * [taylor]: Taking taylor expansion of n in n 2.679 * [backup-simplify]: Simplify 0 into 0 2.679 * [backup-simplify]: Simplify 1 into 1 2.679 * [backup-simplify]: Simplify (/ PI 1) into PI 2.679 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.679 * [taylor]: Taking taylor expansion of -2.0 in n 2.679 * [backup-simplify]: Simplify -2.0 into -2.0 2.679 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.679 * [taylor]: Taking taylor expansion of PI in n 2.679 * [backup-simplify]: Simplify PI into PI 2.679 * [taylor]: Taking taylor expansion of n in n 2.679 * [backup-simplify]: Simplify 0 into 0 2.679 * [backup-simplify]: Simplify 1 into 1 2.679 * [backup-simplify]: Simplify (/ PI 1) into PI 2.680 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.680 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.680 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.681 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.681 * [backup-simplify]: Simplify 0 into 0 2.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.682 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.682 * [backup-simplify]: Simplify 0 into 0 2.683 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.683 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.684 * [backup-simplify]: Simplify 0 into 0 2.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.685 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.685 * [backup-simplify]: Simplify 0 into 0 2.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.687 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.688 * [backup-simplify]: Simplify 0 into 0 2.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.691 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.691 * [backup-simplify]: Simplify 0 into 0 2.691 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.691 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1) 2.692 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.692 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 2.692 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.692 * [taylor]: Taking taylor expansion of 2.0 in n 2.692 * [backup-simplify]: Simplify 2.0 into 2.0 2.692 * [taylor]: Taking taylor expansion of (* n PI) in n 2.692 * [taylor]: Taking taylor expansion of n in n 2.692 * [backup-simplify]: Simplify 0 into 0 2.692 * [backup-simplify]: Simplify 1 into 1 2.692 * [taylor]: Taking taylor expansion of PI in n 2.692 * [backup-simplify]: Simplify PI into PI 2.692 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.692 * [taylor]: Taking taylor expansion of 2.0 in n 2.692 * [backup-simplify]: Simplify 2.0 into 2.0 2.692 * [taylor]: Taking taylor expansion of (* n PI) in n 2.692 * [taylor]: Taking taylor expansion of n in n 2.692 * [backup-simplify]: Simplify 0 into 0 2.692 * [backup-simplify]: Simplify 1 into 1 2.693 * [taylor]: Taking taylor expansion of PI in n 2.693 * [backup-simplify]: Simplify PI into PI 2.693 * [backup-simplify]: Simplify (* 0 PI) into 0 2.694 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.694 * [backup-simplify]: Simplify 0 into 0 2.695 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.697 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.697 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.698 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 2.699 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 2.699 * [backup-simplify]: Simplify 0 into 0 2.701 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 2.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 2.702 * [backup-simplify]: Simplify 0 into 0 2.703 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.705 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 2.705 * [backup-simplify]: Simplify 0 into 0 2.707 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.708 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 2.708 * [backup-simplify]: Simplify 0 into 0 2.710 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 2.712 * [backup-simplify]: Simplify 0 into 0 2.714 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 2.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 2.716 * [backup-simplify]: Simplify 0 into 0 2.717 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 2.717 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 2.717 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 2.717 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.717 * [taylor]: Taking taylor expansion of 2.0 in n 2.717 * [backup-simplify]: Simplify 2.0 into 2.0 2.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.717 * [taylor]: Taking taylor expansion of PI in n 2.717 * [backup-simplify]: Simplify PI into PI 2.717 * [taylor]: Taking taylor expansion of n in n 2.717 * [backup-simplify]: Simplify 0 into 0 2.717 * [backup-simplify]: Simplify 1 into 1 2.718 * [backup-simplify]: Simplify (/ PI 1) into PI 2.718 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.718 * [taylor]: Taking taylor expansion of 2.0 in n 2.718 * [backup-simplify]: Simplify 2.0 into 2.0 2.718 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.718 * [taylor]: Taking taylor expansion of PI in n 2.718 * [backup-simplify]: Simplify PI into PI 2.718 * [taylor]: Taking taylor expansion of n in n 2.718 * [backup-simplify]: Simplify 0 into 0 2.718 * [backup-simplify]: Simplify 1 into 1 2.718 * [backup-simplify]: Simplify (/ PI 1) into PI 2.719 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.719 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.721 * [backup-simplify]: Simplify 0 into 0 2.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.723 * [backup-simplify]: Simplify 0 into 0 2.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.726 * [backup-simplify]: Simplify 0 into 0 2.727 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.728 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.728 * [backup-simplify]: Simplify 0 into 0 2.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.731 * [backup-simplify]: Simplify 0 into 0 2.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.734 * [backup-simplify]: Simplify 0 into 0 2.735 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 2.735 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 2.735 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 2.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.735 * [taylor]: Taking taylor expansion of -2.0 in n 2.735 * [backup-simplify]: Simplify -2.0 into -2.0 2.735 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.735 * [taylor]: Taking taylor expansion of PI in n 2.735 * [backup-simplify]: Simplify PI into PI 2.736 * [taylor]: Taking taylor expansion of n in n 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 1 into 1 2.736 * [backup-simplify]: Simplify (/ PI 1) into PI 2.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.736 * [taylor]: Taking taylor expansion of -2.0 in n 2.736 * [backup-simplify]: Simplify -2.0 into -2.0 2.736 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.736 * [taylor]: Taking taylor expansion of PI in n 2.736 * [backup-simplify]: Simplify PI into PI 2.736 * [taylor]: Taking taylor expansion of n in n 2.736 * [backup-simplify]: Simplify 0 into 0 2.736 * [backup-simplify]: Simplify 1 into 1 2.737 * [backup-simplify]: Simplify (/ PI 1) into PI 2.737 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.738 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.740 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.740 * [backup-simplify]: Simplify 0 into 0 2.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.742 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 2.742 * [backup-simplify]: Simplify 0 into 0 2.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.744 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.744 * [backup-simplify]: Simplify 0 into 0 2.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.747 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 2.747 * [backup-simplify]: Simplify 0 into 0 2.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.750 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 2.750 * [backup-simplify]: Simplify 0 into 0 2.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.753 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 2.753 * [backup-simplify]: Simplify 0 into 0 2.753 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 2.754 * * * [progress]: simplifying candidates 2.760 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ 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1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 2.763 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log 2.0) (log h2)) (log h1)) (/ (/ (- 1.0 h0) 2.0) 2)) (* (+ (log (* 2.0 h2)) (log h1)) (/ (/ (- 1.0 h0) 2.0) 2)) (* (log (* (* 2.0 h2) h1)) (/ (/ (- 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2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) 1) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) 1) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 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h1) (/ (/ (- 1.0 h0) 2.0) 2))) (sqrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (sqrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (pow (* (* 2.0 h2) h1) (/ (/ (/ (- 1.0 h0) 2.0) 2) 2)) (pow (* (* 2.0 h2) h1) (/ (/ (/ (- 1.0 h0) 2.0) 2) 2)) (* (+ (+ (log 2.0) (log h2)) (log h1)) (/ (/ (- 1.0 h0) 2.0) 2)) (* (+ (log (* 2.0 h2)) (log h1)) (/ (/ (- 1.0 h0) 2.0) 2)) (* (log (* (* 2.0 h2) h1)) (/ (/ (- 1.0 h0) 2.0) 2)) (* (log (* (* 2.0 h2) h1)) (/ (/ (- 1.0 h0) 2.0) 2)) (* 1 (/ (/ (- 1.0 h0) 2.0) 2)) (* 1 (/ (/ (- 1.0 h0) 2.0) 2)) (* 1 (/ (/ (- 1.0 h0) 2.0) 2)) (pow (* (* 2.0 h2) h1) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 h2) h1) (/ (/ h0 2.0) 2)) (pow (* (* 2.0 h2) h1) (* (cbrt (/ (/ (- 1.0 h0) 2.0) 2)) (cbrt (/ (/ (- 1.0 h0) 2.0) 2)))) (pow (* (* 2.0 h2) h1) (sqrt (/ (/ (- 1.0 h0) 2.0) 2))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (sqrt (/ (- 1.0 h0) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (sqrt (/ (- 1.0 h0) 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (sqrt (/ (- 1.0 h0) 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (sqrt 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) 1) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) 1) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) (sqrt 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) 1) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (sqrt (- 1.0 h0)) 1) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 1) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) 1) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ (+ (sqrt 1.0) (sqrt h0)) 1) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 h2) h1) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (/ 1 1) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ 1 (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ 1 1)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) (sqrt 2))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 1)) (pow (* (* 2.0 h2) h1) 1) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)) (pow (* 2.0 h2) (/ (/ (- 1.0 h0) 2.0) 2)) (pow h1 (/ (/ (- 1.0 h0) 2.0) 2)) (log (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (exp (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (cbrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (cbrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2)))) (cbrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (* (* (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2)) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (sqrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (sqrt (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2))) (pow (* (* 2.0 h2) h1) (/ (/ (/ (- 1.0 h0) 2.0) 2) 2)) (pow (* (* 2.0 h2) h1) (/ (/ (/ (- 1.0 h0) 2.0) 2) 2)) (* (* 2.0 h2) h1) (* (* 2.0 h2) h1) (+ (+ (log 2.0) (log h2)) (log h1)) (+ (log (* 2.0 h2)) (log h1)) (log (* (* 2.0 h2) h1)) (exp (* (* 2.0 h2) h1)) (* (* (* (* 2.0 2.0) 2.0) (* (* h2 h2) h2)) (* (* h1 h1) h1)) (* (* (* (* 2.0 h2) (* 2.0 h2)) (* 2.0 h2)) (* (* h1 h1) h1)) (* (cbrt (* (* 2.0 h2) h1)) (cbrt (* (* 2.0 h2) h1))) (cbrt (* (* 2.0 h2) h1)) (* (* (* (* 2.0 h2) h1) (* (* 2.0 h2) h1)) (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (* (* 2.0 h2) (* (cbrt h1) (cbrt h1))) (* (* 2.0 h2) (sqrt h1)) (* (* 2.0 h2) 1) (* h2 h1) (* (* 2.0 h2) h1) (* (* 2.0 h2) h1) (+ (+ (log 2.0) (log h2)) (log h1)) (+ (log (* 2.0 h2)) (log h1)) (log (* (* 2.0 h2) h1)) (exp (* (* 2.0 h2) h1)) (* (* (* (* 2.0 2.0) 2.0) (* (* h2 h2) h2)) (* (* h1 h1) h1)) (* (* (* (* 2.0 h2) (* 2.0 h2)) (* 2.0 h2)) (* (* h1 h1) h1)) (* (cbrt (* (* 2.0 h2) h1)) (cbrt (* (* 2.0 h2) h1))) (cbrt (* (* 2.0 h2) h1)) (* (* (* (* 2.0 h2) h1) (* (* 2.0 h2) h1)) (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (* (* 2.0 h2) (* (cbrt h1) (cbrt h1))) (* (* 2.0 h2) (sqrt h1)) (* (* 2.0 h2) 1) (* h2 h1) (- (+ (* (/ 1.0 32.0) (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (+ (* (/ 1.0 16.0) (* (pow h0 2) (* (log (* 2.0 h2)) (* (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1))))) (* (/ 1.0 32.0) (* (pow h0 2) (* (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (pow (log h1) 2))))))) (+ (* (/ 1.0 4.0) (* h0 (* (log (* 2.0 h2)) (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1))))))) (* (/ 1.0 4.0) (* h0 (* (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1)))))) (exp (* (/ 1.0 4.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (exp (* (/ 1.0 4.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (- (+ (* (/ 1.0 32.0) (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (+ (* (/ 1.0 16.0) (* (pow h0 2) (* (log (* 2.0 h2)) (* (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1))))) (* (/ 1.0 32.0) (* (pow h0 2) (* (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (pow (log h1) 2))))))) (+ (* (/ 1.0 4.0) (* h0 (* (log (* 2.0 h2)) (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1))))))) (* (/ 1.0 4.0) (* h0 (* (exp (* (/ 1.0 4.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1)))))) (exp (* (/ 1.0 4.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (exp (* (/ 1.0 4.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) 2.852 * * * [progress]: adding candidates to table 3.883 * * [progress]: iteration 3 / 4 3.883 * * * [progress]: picking best candidate 3.915 * * * * [pick]: Picked # 3.915 * * * [progress]: localizing error 3.935 * * * [progress]: generating rewritten candidates 3.935 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2) 3.970 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 4.015 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1) 4.028 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1) 4.050 * * * [progress]: generating series expansions 4.050 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2) 4.051 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 4.052 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 4.052 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 4.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 4.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 4.052 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 4.052 * [taylor]: Taking taylor expansion of 0.5 in k 4.052 * [backup-simplify]: Simplify 0.5 into 0.5 4.052 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.052 * [taylor]: Taking taylor expansion of 1.0 in k 4.052 * [backup-simplify]: Simplify 1.0 into 1.0 4.052 * [taylor]: Taking taylor expansion of k in k 4.052 * [backup-simplify]: Simplify 0 into 0 4.052 * [backup-simplify]: Simplify 1 into 1 4.052 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 4.052 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 4.052 * [taylor]: Taking taylor expansion of 2.0 in k 4.052 * [backup-simplify]: Simplify 2.0 into 2.0 4.052 * [taylor]: Taking taylor expansion of (* n PI) in k 4.052 * [taylor]: Taking taylor expansion of n in k 4.052 * [backup-simplify]: Simplify n into n 4.052 * [taylor]: Taking taylor expansion of PI in k 4.052 * [backup-simplify]: Simplify PI into PI 4.052 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.052 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 4.052 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 4.053 * [backup-simplify]: Simplify (- 0) into 0 4.053 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.054 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 4.054 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 4.054 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 4.054 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.054 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.054 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.054 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.054 * [taylor]: Taking taylor expansion of 0.5 in n 4.054 * [backup-simplify]: Simplify 0.5 into 0.5 4.054 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.054 * [taylor]: Taking taylor expansion of 1.0 in n 4.055 * [backup-simplify]: Simplify 1.0 into 1.0 4.055 * [taylor]: Taking taylor expansion of k in n 4.055 * [backup-simplify]: Simplify k into k 4.055 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.055 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.055 * [taylor]: Taking taylor expansion of 2.0 in n 4.055 * [backup-simplify]: Simplify 2.0 into 2.0 4.055 * [taylor]: Taking taylor expansion of (* n PI) in n 4.055 * [taylor]: Taking taylor expansion of n in n 4.055 * [backup-simplify]: Simplify 0 into 0 4.055 * [backup-simplify]: Simplify 1 into 1 4.055 * [taylor]: Taking taylor expansion of PI in n 4.055 * [backup-simplify]: Simplify PI into PI 4.055 * [backup-simplify]: Simplify (* 0 PI) into 0 4.056 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.058 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.059 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.061 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.061 * [backup-simplify]: Simplify (- k) into (- k) 4.061 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.061 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.063 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.064 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.065 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.065 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 4.065 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 4.065 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 4.065 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 4.065 * [taylor]: Taking taylor expansion of 0.5 in n 4.065 * [backup-simplify]: Simplify 0.5 into 0.5 4.065 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 4.065 * [taylor]: Taking taylor expansion of 1.0 in n 4.065 * [backup-simplify]: Simplify 1.0 into 1.0 4.065 * [taylor]: Taking taylor expansion of k in n 4.065 * [backup-simplify]: Simplify k into k 4.065 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 4.065 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.065 * [taylor]: Taking taylor expansion of 2.0 in n 4.066 * [backup-simplify]: Simplify 2.0 into 2.0 4.066 * [taylor]: Taking taylor expansion of (* n PI) in n 4.066 * [taylor]: Taking taylor expansion of n in n 4.066 * [backup-simplify]: Simplify 0 into 0 4.066 * [backup-simplify]: Simplify 1 into 1 4.066 * [taylor]: Taking taylor expansion of PI in n 4.066 * [backup-simplify]: Simplify PI into PI 4.066 * [backup-simplify]: Simplify (* 0 PI) into 0 4.067 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.068 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.069 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.071 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.071 * [backup-simplify]: Simplify (- k) into (- k) 4.071 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 4.071 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 4.072 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.074 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 4.075 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 4.075 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 4.075 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 4.075 * [taylor]: Taking taylor expansion of 0.5 in k 4.075 * [backup-simplify]: Simplify 0.5 into 0.5 4.075 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 4.075 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 4.075 * [taylor]: Taking taylor expansion of 1.0 in k 4.075 * [backup-simplify]: Simplify 1.0 into 1.0 4.075 * [taylor]: Taking taylor expansion of k in k 4.075 * [backup-simplify]: Simplify 0 into 0 4.075 * [backup-simplify]: Simplify 1 into 1 4.076 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 4.076 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.076 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.076 * [taylor]: Taking taylor expansion of 2.0 in k 4.076 * [backup-simplify]: Simplify 2.0 into 2.0 4.076 * [taylor]: Taking taylor expansion of PI in k 4.076 * [backup-simplify]: Simplify PI into PI 4.076 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.077 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.077 * [taylor]: Taking taylor expansion of (log n) in k 4.077 * [taylor]: Taking taylor expansion of n in k 4.077 * [backup-simplify]: Simplify n into n 4.078 * [backup-simplify]: Simplify (log n) into (log n) 4.078 * [backup-simplify]: Simplify (- 0) into 0 4.078 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 4.079 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 4.081 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 4.082 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 4.083 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.084 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 4.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.086 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.088 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.089 * [backup-simplify]: Simplify (- 0) into 0 4.089 * [backup-simplify]: Simplify (+ 0 0) into 0 4.090 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 4.090 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.091 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 4.092 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.092 * [taylor]: Taking taylor expansion of 0 in k 4.092 * [backup-simplify]: Simplify 0 into 0 4.092 * [backup-simplify]: Simplify 0 into 0 4.093 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.095 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.095 * [backup-simplify]: Simplify (+ 0 0) into 0 4.095 * [backup-simplify]: Simplify (- 1) into -1 4.095 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.096 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 4.098 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 4.100 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.102 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 4.102 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.103 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.105 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.106 * [backup-simplify]: Simplify (- 0) into 0 4.106 * [backup-simplify]: Simplify (+ 0 0) into 0 4.106 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 4.107 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 4.108 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.110 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.110 * [taylor]: Taking taylor expansion of 0 in k 4.110 * [backup-simplify]: Simplify 0 into 0 4.110 * [backup-simplify]: Simplify 0 into 0 4.110 * [backup-simplify]: Simplify 0 into 0 4.111 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.113 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.114 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.114 * [backup-simplify]: Simplify (+ 0 0) into 0 4.115 * [backup-simplify]: Simplify (- 0) into 0 4.115 * [backup-simplify]: Simplify (+ 0 0) into 0 4.116 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 4.118 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 4.123 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.129 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 4.152 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 4.152 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 4.153 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 4.153 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 4.153 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 4.153 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 4.153 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 4.153 * [taylor]: Taking taylor expansion of 0.5 in k 4.153 * [backup-simplify]: Simplify 0.5 into 0.5 4.153 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.153 * [taylor]: Taking taylor expansion of 1.0 in k 4.153 * [backup-simplify]: Simplify 1.0 into 1.0 4.153 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.153 * [taylor]: Taking taylor expansion of k in k 4.153 * [backup-simplify]: Simplify 0 into 0 4.153 * [backup-simplify]: Simplify 1 into 1 4.153 * [backup-simplify]: Simplify (/ 1 1) into 1 4.153 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 4.153 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 4.154 * [taylor]: Taking taylor expansion of 2.0 in k 4.154 * [backup-simplify]: Simplify 2.0 into 2.0 4.154 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.154 * [taylor]: Taking taylor expansion of PI in k 4.154 * [backup-simplify]: Simplify PI into PI 4.154 * [taylor]: Taking taylor expansion of n in k 4.154 * [backup-simplify]: Simplify n into n 4.154 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.154 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 4.154 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 4.155 * [backup-simplify]: Simplify (- 1) into -1 4.155 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.155 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 4.156 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 4.156 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 4.156 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.156 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.156 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.156 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.156 * [taylor]: Taking taylor expansion of 0.5 in n 4.156 * [backup-simplify]: Simplify 0.5 into 0.5 4.156 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.156 * [taylor]: Taking taylor expansion of 1.0 in n 4.156 * [backup-simplify]: Simplify 1.0 into 1.0 4.156 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.156 * [taylor]: Taking taylor expansion of k in n 4.156 * [backup-simplify]: Simplify k into k 4.156 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.156 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.157 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.157 * [taylor]: Taking taylor expansion of 2.0 in n 4.157 * [backup-simplify]: Simplify 2.0 into 2.0 4.157 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.157 * [taylor]: Taking taylor expansion of PI in n 4.157 * [backup-simplify]: Simplify PI into PI 4.157 * [taylor]: Taking taylor expansion of n in n 4.157 * [backup-simplify]: Simplify 0 into 0 4.157 * [backup-simplify]: Simplify 1 into 1 4.157 * [backup-simplify]: Simplify (/ PI 1) into PI 4.158 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.159 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.159 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.159 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.159 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.161 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.162 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.163 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.164 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 4.164 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 4.164 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 4.164 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 4.164 * [taylor]: Taking taylor expansion of 0.5 in n 4.164 * [backup-simplify]: Simplify 0.5 into 0.5 4.164 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 4.164 * [taylor]: Taking taylor expansion of 1.0 in n 4.164 * [backup-simplify]: Simplify 1.0 into 1.0 4.164 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.164 * [taylor]: Taking taylor expansion of k in n 4.164 * [backup-simplify]: Simplify k into k 4.164 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.164 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 4.164 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.164 * [taylor]: Taking taylor expansion of 2.0 in n 4.164 * [backup-simplify]: Simplify 2.0 into 2.0 4.164 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.164 * [taylor]: Taking taylor expansion of PI in n 4.164 * [backup-simplify]: Simplify PI into PI 4.164 * [taylor]: Taking taylor expansion of n in n 4.164 * [backup-simplify]: Simplify 0 into 0 4.164 * [backup-simplify]: Simplify 1 into 1 4.165 * [backup-simplify]: Simplify (/ PI 1) into PI 4.165 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.166 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.167 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 4.167 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 4.167 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 4.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.170 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 4.171 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.171 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 4.171 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 4.171 * [taylor]: Taking taylor expansion of 0.5 in k 4.171 * [backup-simplify]: Simplify 0.5 into 0.5 4.171 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 4.171 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 4.171 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 4.171 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 4.171 * [taylor]: Taking taylor expansion of 2.0 in k 4.171 * [backup-simplify]: Simplify 2.0 into 2.0 4.171 * [taylor]: Taking taylor expansion of PI in k 4.171 * [backup-simplify]: Simplify PI into PI 4.172 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.173 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 4.173 * [taylor]: Taking taylor expansion of (log n) in k 4.173 * [taylor]: Taking taylor expansion of n in k 4.173 * [backup-simplify]: Simplify n into n 4.173 * [backup-simplify]: Simplify (log n) into (log n) 4.173 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 4.173 * [taylor]: Taking taylor expansion of 1.0 in k 4.173 * [backup-simplify]: Simplify 1.0 into 1.0 4.173 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.173 * [taylor]: Taking taylor expansion of k in k 4.173 * [backup-simplify]: Simplify 0 into 0 4.173 * [backup-simplify]: Simplify 1 into 1 4.174 * [backup-simplify]: Simplify (/ 1 1) into 1 4.174 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.175 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 4.175 * [backup-simplify]: Simplify (- 1) into -1 4.176 * [backup-simplify]: Simplify (+ 0 -1) into -1 4.177 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 4.178 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 4.179 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.180 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 4.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.182 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.184 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 4.184 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.185 * [backup-simplify]: Simplify (- 0) into 0 4.185 * [backup-simplify]: Simplify (+ 0 0) into 0 4.186 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 4.187 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.188 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 4.191 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.191 * [taylor]: Taking taylor expansion of 0 in k 4.191 * [backup-simplify]: Simplify 0 into 0 4.191 * [backup-simplify]: Simplify 0 into 0 4.191 * [backup-simplify]: Simplify 0 into 0 4.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.193 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.197 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 4.197 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.198 * [backup-simplify]: Simplify (- 0) into 0 4.198 * [backup-simplify]: Simplify (+ 0 0) into 0 4.199 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 4.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.202 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 4.205 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.205 * [taylor]: Taking taylor expansion of 0 in k 4.205 * [backup-simplify]: Simplify 0 into 0 4.205 * [backup-simplify]: Simplify 0 into 0 4.205 * [backup-simplify]: Simplify 0 into 0 4.205 * [backup-simplify]: Simplify 0 into 0 4.206 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.208 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.214 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 4.215 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.215 * [backup-simplify]: Simplify (- 0) into 0 4.215 * [backup-simplify]: Simplify (+ 0 0) into 0 4.217 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 4.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 4.220 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 4.223 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.223 * [taylor]: Taking taylor expansion of 0 in k 4.223 * [backup-simplify]: Simplify 0 into 0 4.223 * [backup-simplify]: Simplify 0 into 0 4.225 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 4.225 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 4.226 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 4.226 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 4.226 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 4.226 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 4.226 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 4.226 * [taylor]: Taking taylor expansion of 0.5 in k 4.226 * [backup-simplify]: Simplify 0.5 into 0.5 4.226 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.226 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.226 * [taylor]: Taking taylor expansion of k in k 4.226 * [backup-simplify]: Simplify 0 into 0 4.226 * [backup-simplify]: Simplify 1 into 1 4.226 * [backup-simplify]: Simplify (/ 1 1) into 1 4.226 * [taylor]: Taking taylor expansion of 1.0 in k 4.226 * [backup-simplify]: Simplify 1.0 into 1.0 4.226 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 4.226 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 4.227 * [taylor]: Taking taylor expansion of -2.0 in k 4.227 * [backup-simplify]: Simplify -2.0 into -2.0 4.227 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.227 * [taylor]: Taking taylor expansion of PI in k 4.227 * [backup-simplify]: Simplify PI into PI 4.227 * [taylor]: Taking taylor expansion of n in k 4.227 * [backup-simplify]: Simplify n into n 4.227 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.227 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 4.227 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 4.227 * [backup-simplify]: Simplify (+ 1 0) into 1 4.228 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 4.228 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 4.228 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 4.228 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.228 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.228 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.228 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.228 * [taylor]: Taking taylor expansion of 0.5 in n 4.229 * [backup-simplify]: Simplify 0.5 into 0.5 4.229 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.229 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.229 * [taylor]: Taking taylor expansion of k in n 4.229 * [backup-simplify]: Simplify k into k 4.229 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.229 * [taylor]: Taking taylor expansion of 1.0 in n 4.229 * [backup-simplify]: Simplify 1.0 into 1.0 4.229 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.229 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.229 * [taylor]: Taking taylor expansion of -2.0 in n 4.229 * [backup-simplify]: Simplify -2.0 into -2.0 4.229 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.229 * [taylor]: Taking taylor expansion of PI in n 4.229 * [backup-simplify]: Simplify PI into PI 4.229 * [taylor]: Taking taylor expansion of n in n 4.229 * [backup-simplify]: Simplify 0 into 0 4.229 * [backup-simplify]: Simplify 1 into 1 4.230 * [backup-simplify]: Simplify (/ PI 1) into PI 4.230 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.231 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.231 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.231 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.233 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.234 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.236 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.236 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 4.237 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 4.237 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 4.237 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 4.237 * [taylor]: Taking taylor expansion of 0.5 in n 4.237 * [backup-simplify]: Simplify 0.5 into 0.5 4.237 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 4.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.237 * [taylor]: Taking taylor expansion of k in n 4.237 * [backup-simplify]: Simplify k into k 4.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.237 * [taylor]: Taking taylor expansion of 1.0 in n 4.237 * [backup-simplify]: Simplify 1.0 into 1.0 4.237 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 4.237 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.237 * [taylor]: Taking taylor expansion of -2.0 in n 4.237 * [backup-simplify]: Simplify -2.0 into -2.0 4.237 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.237 * [taylor]: Taking taylor expansion of PI in n 4.237 * [backup-simplify]: Simplify PI into PI 4.237 * [taylor]: Taking taylor expansion of n in n 4.237 * [backup-simplify]: Simplify 0 into 0 4.237 * [backup-simplify]: Simplify 1 into 1 4.238 * [backup-simplify]: Simplify (/ PI 1) into PI 4.238 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.239 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.239 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 4.239 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 4.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.240 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 4.241 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.241 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 4.241 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 4.241 * [taylor]: Taking taylor expansion of 0.5 in k 4.241 * [backup-simplify]: Simplify 0.5 into 0.5 4.241 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 4.241 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 4.241 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.241 * [taylor]: Taking taylor expansion of k in k 4.242 * [backup-simplify]: Simplify 0 into 0 4.242 * [backup-simplify]: Simplify 1 into 1 4.242 * [backup-simplify]: Simplify (/ 1 1) into 1 4.242 * [taylor]: Taking taylor expansion of 1.0 in k 4.242 * [backup-simplify]: Simplify 1.0 into 1.0 4.242 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 4.242 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 4.242 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 4.242 * [taylor]: Taking taylor expansion of -2.0 in k 4.242 * [backup-simplify]: Simplify -2.0 into -2.0 4.242 * [taylor]: Taking taylor expansion of PI in k 4.242 * [backup-simplify]: Simplify PI into PI 4.242 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.243 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 4.243 * [taylor]: Taking taylor expansion of (log n) in k 4.243 * [taylor]: Taking taylor expansion of n in k 4.243 * [backup-simplify]: Simplify n into n 4.243 * [backup-simplify]: Simplify (log n) into (log n) 4.243 * [backup-simplify]: Simplify (+ 1 0) into 1 4.243 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.244 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 4.245 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 4.246 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 4.246 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.247 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 4.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.248 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.249 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 4.249 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.249 * [backup-simplify]: Simplify (+ 0 0) into 0 4.250 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 4.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.251 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 4.253 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.253 * [taylor]: Taking taylor expansion of 0 in k 4.253 * [backup-simplify]: Simplify 0 into 0 4.253 * [backup-simplify]: Simplify 0 into 0 4.253 * [backup-simplify]: Simplify 0 into 0 4.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.254 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.256 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 4.256 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.257 * [backup-simplify]: Simplify (+ 0 0) into 0 4.257 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 4.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.259 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 4.261 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.261 * [taylor]: Taking taylor expansion of 0 in k 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 0 into 0 4.261 * [backup-simplify]: Simplify 0 into 0 4.262 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.262 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.266 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 4.266 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.267 * [backup-simplify]: Simplify (+ 0 0) into 0 4.268 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 4.270 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 4.272 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 4.275 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 4.275 * [taylor]: Taking taylor expansion of 0 in k 4.275 * [backup-simplify]: Simplify 0 into 0 4.275 * [backup-simplify]: Simplify 0 into 0 4.276 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 4.276 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 4.277 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.277 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 4.277 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.277 * [taylor]: Taking taylor expansion of 2.0 in n 4.277 * [backup-simplify]: Simplify 2.0 into 2.0 4.277 * [taylor]: Taking taylor expansion of (* n PI) in n 4.277 * [taylor]: Taking taylor expansion of n in n 4.277 * [backup-simplify]: Simplify 0 into 0 4.277 * [backup-simplify]: Simplify 1 into 1 4.277 * [taylor]: Taking taylor expansion of PI in n 4.277 * [backup-simplify]: Simplify PI into PI 4.278 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 4.278 * [taylor]: Taking taylor expansion of 2.0 in n 4.278 * [backup-simplify]: Simplify 2.0 into 2.0 4.278 * [taylor]: Taking taylor expansion of (* n PI) in n 4.278 * [taylor]: Taking taylor expansion of n in n 4.278 * [backup-simplify]: Simplify 0 into 0 4.278 * [backup-simplify]: Simplify 1 into 1 4.278 * [taylor]: Taking taylor expansion of PI in n 4.278 * [backup-simplify]: Simplify PI into PI 4.278 * [backup-simplify]: Simplify (* 0 PI) into 0 4.279 * [backup-simplify]: Simplify (* 2.0 0) into 0 4.279 * [backup-simplify]: Simplify 0 into 0 4.280 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.282 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 4.283 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.284 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.292 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 4.292 * [backup-simplify]: Simplify 0 into 0 4.293 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.294 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.294 * [backup-simplify]: Simplify 0 into 0 4.294 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.295 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 4.295 * [backup-simplify]: Simplify 0 into 0 4.296 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.297 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 4.297 * [backup-simplify]: Simplify 0 into 0 4.298 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.299 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 4.299 * [backup-simplify]: Simplify 0 into 0 4.300 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 4.301 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 4.302 * [backup-simplify]: Simplify 0 into 0 4.302 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 4.302 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 4.302 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 4.302 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.302 * [taylor]: Taking taylor expansion of 2.0 in n 4.303 * [backup-simplify]: Simplify 2.0 into 2.0 4.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.303 * [taylor]: Taking taylor expansion of PI in n 4.303 * [backup-simplify]: Simplify PI into PI 4.303 * [taylor]: Taking taylor expansion of n in n 4.303 * [backup-simplify]: Simplify 0 into 0 4.303 * [backup-simplify]: Simplify 1 into 1 4.303 * [backup-simplify]: Simplify (/ PI 1) into PI 4.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 4.303 * [taylor]: Taking taylor expansion of 2.0 in n 4.303 * [backup-simplify]: Simplify 2.0 into 2.0 4.303 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.303 * [taylor]: Taking taylor expansion of PI in n 4.303 * [backup-simplify]: Simplify PI into PI 4.303 * [taylor]: Taking taylor expansion of n in n 4.303 * [backup-simplify]: Simplify 0 into 0 4.303 * [backup-simplify]: Simplify 1 into 1 4.303 * [backup-simplify]: Simplify (/ PI 1) into PI 4.304 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.304 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 4.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.305 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 4.305 * [backup-simplify]: Simplify 0 into 0 4.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.307 * [backup-simplify]: Simplify 0 into 0 4.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.308 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.308 * [backup-simplify]: Simplify 0 into 0 4.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.310 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.310 * [backup-simplify]: Simplify 0 into 0 4.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.311 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.311 * [backup-simplify]: Simplify 0 into 0 4.312 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.313 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.313 * [backup-simplify]: Simplify 0 into 0 4.314 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 4.314 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 4.314 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 4.314 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.314 * [taylor]: Taking taylor expansion of -2.0 in n 4.314 * [backup-simplify]: Simplify -2.0 into -2.0 4.314 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.314 * [taylor]: Taking taylor expansion of PI in n 4.314 * [backup-simplify]: Simplify PI into PI 4.314 * [taylor]: Taking taylor expansion of n in n 4.314 * [backup-simplify]: Simplify 0 into 0 4.314 * [backup-simplify]: Simplify 1 into 1 4.315 * [backup-simplify]: Simplify (/ PI 1) into PI 4.315 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 4.315 * [taylor]: Taking taylor expansion of -2.0 in n 4.315 * [backup-simplify]: Simplify -2.0 into -2.0 4.315 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.315 * [taylor]: Taking taylor expansion of PI in n 4.315 * [backup-simplify]: Simplify PI into PI 4.315 * [taylor]: Taking taylor expansion of n in n 4.315 * [backup-simplify]: Simplify 0 into 0 4.315 * [backup-simplify]: Simplify 1 into 1 4.315 * [backup-simplify]: Simplify (/ PI 1) into PI 4.315 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.316 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 4.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.317 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 4.317 * [backup-simplify]: Simplify 0 into 0 4.317 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.318 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 4.319 * [backup-simplify]: Simplify 0 into 0 4.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.321 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.321 * [backup-simplify]: Simplify 0 into 0 4.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.324 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 4.324 * [backup-simplify]: Simplify 0 into 0 4.325 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.326 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 4.326 * [backup-simplify]: Simplify 0 into 0 4.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.330 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 4.330 * [backup-simplify]: Simplify 0 into 0 4.331 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 4.331 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1) 4.331 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.331 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.331 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.331 * [taylor]: Taking taylor expansion of 1.0 in k 4.331 * [backup-simplify]: Simplify 1.0 into 1.0 4.331 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.331 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.331 * [taylor]: Taking taylor expansion of k in k 4.331 * [backup-simplify]: Simplify 0 into 0 4.331 * [backup-simplify]: Simplify 1 into 1 4.332 * [backup-simplify]: Simplify (/ 1 1) into 1 4.332 * [backup-simplify]: Simplify (sqrt 0) into 0 4.334 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.334 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.334 * [taylor]: Taking taylor expansion of 1.0 in k 4.334 * [backup-simplify]: Simplify 1.0 into 1.0 4.334 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.334 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.334 * [taylor]: Taking taylor expansion of k in k 4.334 * [backup-simplify]: Simplify 0 into 0 4.334 * [backup-simplify]: Simplify 1 into 1 4.334 * [backup-simplify]: Simplify (/ 1 1) into 1 4.335 * [backup-simplify]: Simplify (sqrt 0) into 0 4.336 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.336 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.336 * [backup-simplify]: Simplify 0 into 0 4.338 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.338 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.339 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.343 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.345 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.345 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.346 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.350 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.351 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.351 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.352 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.352 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.352 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.352 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.352 * [taylor]: Taking taylor expansion of 1.0 in k 4.352 * [backup-simplify]: Simplify 1.0 into 1.0 4.352 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.352 * [taylor]: Taking taylor expansion of k in k 4.353 * [backup-simplify]: Simplify 0 into 0 4.353 * [backup-simplify]: Simplify 1 into 1 4.353 * [backup-simplify]: Simplify (sqrt 0) into 0 4.354 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.354 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.354 * [taylor]: Taking taylor expansion of 1.0 in k 4.354 * [backup-simplify]: Simplify 1.0 into 1.0 4.354 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.354 * [taylor]: Taking taylor expansion of k in k 4.354 * [backup-simplify]: Simplify 0 into 0 4.354 * [backup-simplify]: Simplify 1 into 1 4.354 * [backup-simplify]: Simplify (sqrt 0) into 0 4.355 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.355 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.355 * [backup-simplify]: Simplify 0 into 0 4.356 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.357 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.358 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.360 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.360 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.362 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.363 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.364 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.365 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.365 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.365 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.365 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.365 * [taylor]: Taking taylor expansion of 1.0 in k 4.365 * [backup-simplify]: Simplify 1.0 into 1.0 4.365 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.365 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.365 * [taylor]: Taking taylor expansion of -1 in k 4.365 * [backup-simplify]: Simplify -1 into -1 4.365 * [taylor]: Taking taylor expansion of k in k 4.365 * [backup-simplify]: Simplify 0 into 0 4.365 * [backup-simplify]: Simplify 1 into 1 4.365 * [backup-simplify]: Simplify (/ -1 1) into -1 4.366 * [backup-simplify]: Simplify (sqrt 0) into 0 4.366 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.367 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.367 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.367 * [taylor]: Taking taylor expansion of 1.0 in k 4.367 * [backup-simplify]: Simplify 1.0 into 1.0 4.367 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.367 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.367 * [taylor]: Taking taylor expansion of -1 in k 4.367 * [backup-simplify]: Simplify -1 into -1 4.367 * [taylor]: Taking taylor expansion of k in k 4.367 * [backup-simplify]: Simplify 0 into 0 4.367 * [backup-simplify]: Simplify 1 into 1 4.367 * [backup-simplify]: Simplify (/ -1 1) into -1 4.367 * [backup-simplify]: Simplify (sqrt 0) into 0 4.368 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.369 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.369 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.372 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.374 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.374 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.377 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.380 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.380 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.381 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.381 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1) 4.381 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 4.381 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 4.381 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.381 * [taylor]: Taking taylor expansion of 1.0 in k 4.381 * [backup-simplify]: Simplify 1.0 into 1.0 4.381 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.381 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.381 * [taylor]: Taking taylor expansion of k in k 4.381 * [backup-simplify]: Simplify 0 into 0 4.381 * [backup-simplify]: Simplify 1 into 1 4.382 * [backup-simplify]: Simplify (/ 1 1) into 1 4.382 * [backup-simplify]: Simplify (sqrt 0) into 0 4.383 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.383 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 4.383 * [taylor]: Taking taylor expansion of 1.0 in k 4.383 * [backup-simplify]: Simplify 1.0 into 1.0 4.383 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 4.383 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.383 * [taylor]: Taking taylor expansion of k in k 4.383 * [backup-simplify]: Simplify 0 into 0 4.383 * [backup-simplify]: Simplify 1 into 1 4.383 * [backup-simplify]: Simplify (/ 1 1) into 1 4.384 * [backup-simplify]: Simplify (sqrt 0) into 0 4.384 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.385 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.385 * [backup-simplify]: Simplify 0 into 0 4.386 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.386 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.387 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 4.390 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.392 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.393 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.393 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.396 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.397 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.397 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.398 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 4.398 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 4.398 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 4.398 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.398 * [taylor]: Taking taylor expansion of 1.0 in k 4.398 * [backup-simplify]: Simplify 1.0 into 1.0 4.398 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.398 * [taylor]: Taking taylor expansion of k in k 4.398 * [backup-simplify]: Simplify 0 into 0 4.398 * [backup-simplify]: Simplify 1 into 1 4.399 * [backup-simplify]: Simplify (sqrt 0) into 0 4.399 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.399 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 4.399 * [taylor]: Taking taylor expansion of 1.0 in k 4.399 * [backup-simplify]: Simplify 1.0 into 1.0 4.399 * [taylor]: Taking taylor expansion of (sqrt k) in k 4.399 * [taylor]: Taking taylor expansion of k in k 4.399 * [backup-simplify]: Simplify 0 into 0 4.399 * [backup-simplify]: Simplify 1 into 1 4.405 * [backup-simplify]: Simplify (sqrt 0) into 0 4.407 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 4.407 * [backup-simplify]: Simplify (* 1.0 0) into 0 4.407 * [backup-simplify]: Simplify 0 into 0 4.408 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 4.408 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.410 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.411 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 4.411 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.414 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.415 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 4.415 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.416 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) 4.416 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 4.416 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 4.416 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.416 * [taylor]: Taking taylor expansion of 1.0 in k 4.416 * [backup-simplify]: Simplify 1.0 into 1.0 4.416 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.416 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.416 * [taylor]: Taking taylor expansion of -1 in k 4.416 * [backup-simplify]: Simplify -1 into -1 4.417 * [taylor]: Taking taylor expansion of k in k 4.417 * [backup-simplify]: Simplify 0 into 0 4.417 * [backup-simplify]: Simplify 1 into 1 4.417 * [backup-simplify]: Simplify (/ -1 1) into -1 4.417 * [backup-simplify]: Simplify (sqrt 0) into 0 4.418 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.418 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.418 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 4.418 * [taylor]: Taking taylor expansion of 1.0 in k 4.418 * [backup-simplify]: Simplify 1.0 into 1.0 4.418 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 4.418 * [taylor]: Taking taylor expansion of (/ -1 k) in k 4.418 * [taylor]: Taking taylor expansion of -1 in k 4.418 * [backup-simplify]: Simplify -1 into -1 4.418 * [taylor]: Taking taylor expansion of k in k 4.418 * [backup-simplify]: Simplify 0 into 0 4.418 * [backup-simplify]: Simplify 1 into 1 4.419 * [backup-simplify]: Simplify (/ -1 1) into -1 4.419 * [backup-simplify]: Simplify (sqrt 0) into 0 4.420 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 4.420 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 4.420 * [backup-simplify]: Simplify +nan.0 into +nan.0 4.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.423 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.425 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 4.426 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.427 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.431 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.435 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 4.435 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 4.437 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.437 * * * [progress]: simplifying candidates 4.440 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) 4.442 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log 2.0) (log h2)) (log h1)) (/ (- 1.0 h0) 2.0)) (* (+ (log (* 2.0 h2)) (log h1)) (/ (- 1.0 h0) 2.0)) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0)) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (pow (* (* 2.0 h2) h1) (/ 1.0 2.0)) (pow (* (* 2.0 h2) h1) (/ h0 2.0)) (pow (* (* 2.0 h2) h1) (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0)))) (pow (* (* 2.0 h2) h1) (sqrt (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) 1)) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ 1 1)) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ 1 1)) (pow (* (* 2.0 h2) h1) 1) (pow (* (* 2.0 h2) h1) (- 1.0 h0)) (pow (* 2.0 h2) (/ (- 1.0 h0) 2.0)) (pow h1 (/ (- 1.0 h0) 2.0)) (log (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (exp (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (cbrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (cbrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)))) (cbrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (* (* (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0)) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (sqrt (pow (* (* 2.0 h2) h1) (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2)) (pow (* (* 2.0 h2) h1) (/ (/ (- 1.0 h0) 2.0) 2)) (* (* 2.0 h2) h1) (* (* 2.0 h2) h1) (+ (+ (log 2.0) (log h2)) (log h1)) (+ (log (* 2.0 h2)) (log h1)) (log (* (* 2.0 h2) h1)) (exp (* (* 2.0 h2) h1)) (* (* (* (* 2.0 2.0) 2.0) (* (* h2 h2) h2)) (* (* h1 h1) h1)) (* (* (* (* 2.0 h2) (* 2.0 h2)) (* 2.0 h2)) (* (* h1 h1) h1)) (* (cbrt (* (* 2.0 h2) h1)) (cbrt (* (* 2.0 h2) h1))) (cbrt (* (* 2.0 h2) h1)) (* (* (* (* 2.0 h2) h1) (* (* 2.0 h2) h1)) (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (* (* 2.0 h2) (* (cbrt h1) (cbrt h1))) (* (* 2.0 h2) (sqrt h1)) (* (* 2.0 h2) 1) (* h2 h1) (- (log 1.0) (log (sqrt h0))) (log (/ 1.0 (sqrt h0))) (exp (/ 1.0 (sqrt h0))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt h0) (sqrt h0)) (sqrt h0))) (* (cbrt (/ 1.0 (sqrt h0))) (cbrt (/ 1.0 (sqrt h0)))) (cbrt (/ 1.0 (sqrt h0))) (* (* (/ 1.0 (sqrt h0)) (/ 1.0 (sqrt h0))) (/ 1.0 (sqrt h0))) (sqrt (/ 1.0 (sqrt h0))) (sqrt (/ 1.0 (sqrt h0))) (- 1.0) (- (sqrt h0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ (cbrt 1.0) (cbrt (sqrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt h0) (cbrt h0)))) (/ (cbrt 1.0) (sqrt (cbrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt h0))) (/ (cbrt 1.0) (sqrt (sqrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt h0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt h0))) (/ (cbrt 1.0) (sqrt (sqrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt h0)) (/ (sqrt 1.0) (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ (sqrt 1.0) (cbrt (sqrt h0))) (/ (sqrt 1.0) (sqrt (* (cbrt h0) (cbrt h0)))) (/ (sqrt 1.0) (sqrt (cbrt h0))) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt h0)) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt h0)) (/ 1 (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ 1.0 (cbrt (sqrt h0))) (/ 1 (sqrt (* (cbrt h0) (cbrt h0)))) (/ 1.0 (sqrt (cbrt h0))) (/ 1 (sqrt (sqrt h0))) (/ 1.0 (sqrt (sqrt h0))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt h0)) (/ 1 (sqrt (sqrt h0))) (/ 1.0 (sqrt (sqrt h0))) (/ 1 1) (/ 1.0 (sqrt h0)) (/ 1 (sqrt h0)) (/ (sqrt h0) 1.0) (/ 1.0 (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ 1.0 (sqrt (* (cbrt h0) (cbrt h0)))) (/ 1.0 (sqrt (sqrt h0))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt h0))) (/ 1.0 1) (/ (sqrt h0) (cbrt 1.0)) (/ (sqrt h0) (sqrt 1.0)) (/ (sqrt h0) 1.0) (- (log 1.0) (log (sqrt h0))) (log (/ 1.0 (sqrt h0))) (exp (/ 1.0 (sqrt h0))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt h0) (sqrt h0)) (sqrt h0))) (* (cbrt (/ 1.0 (sqrt h0))) (cbrt (/ 1.0 (sqrt h0)))) (cbrt (/ 1.0 (sqrt h0))) (* (* (/ 1.0 (sqrt h0)) (/ 1.0 (sqrt h0))) (/ 1.0 (sqrt h0))) (sqrt (/ 1.0 (sqrt h0))) (sqrt (/ 1.0 (sqrt h0))) (- 1.0) (- (sqrt h0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ (cbrt 1.0) (cbrt (sqrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt h0) (cbrt h0)))) (/ (cbrt 1.0) (sqrt (cbrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt h0))) (/ (cbrt 1.0) (sqrt (sqrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt h0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt h0))) (/ (cbrt 1.0) (sqrt (sqrt h0))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt h0)) (/ (sqrt 1.0) (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ (sqrt 1.0) (cbrt (sqrt h0))) (/ (sqrt 1.0) (sqrt (* (cbrt h0) (cbrt h0)))) (/ (sqrt 1.0) (sqrt (cbrt h0))) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt h0)) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) (sqrt (sqrt h0))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt h0)) (/ 1 (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ 1.0 (cbrt (sqrt h0))) (/ 1 (sqrt (* (cbrt h0) (cbrt h0)))) (/ 1.0 (sqrt (cbrt h0))) (/ 1 (sqrt (sqrt h0))) (/ 1.0 (sqrt (sqrt h0))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt h0)) (/ 1 (sqrt (sqrt h0))) (/ 1.0 (sqrt (sqrt h0))) (/ 1 1) (/ 1.0 (sqrt h0)) (/ 1 (sqrt h0)) (/ (sqrt h0) 1.0) (/ 1.0 (* (cbrt (sqrt h0)) (cbrt (sqrt h0)))) (/ 1.0 (sqrt (* (cbrt h0) (cbrt h0)))) (/ 1.0 (sqrt (sqrt h0))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt h0))) (/ 1.0 1) (/ (sqrt h0) (cbrt 1.0)) (/ (sqrt h0) (sqrt 1.0)) (/ (sqrt h0) 1.0) (- (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (pow (log h1) 2)))) (+ (* (/ 1.0 4.0) (* (pow h0 2) (* (log (* 2.0 h2)) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1))))) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 2.0) (* h0 (* (log (* 2.0 h2)) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (* (/ 1.0 2.0) (* h0 (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1)))))) (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (- (+ (* h3 h0) (- (+ (* h3 (pow h0 2)) (- h3))))) (- (+ (* h3 (/ 1 (pow h0 2))) (- (+ (* h3 (/ 1 h0)) (- (* h3 (/ 1 (pow h0 3)))))))) (- (+ (* h3 (/ 1 (pow h0 2))) (- (+ (* h3 (/ 1 h0)) (- h3))))) (- (+ (* h3 h0) (- (+ (* h3 (pow h0 2)) (- h3))))) (- (+ (* h3 (/ 1 (pow h0 2))) (- (+ (* h3 (/ 1 h0)) (- (* h3 (/ 1 (pow h0 3)))))))) (- (+ (* h3 (/ 1 (pow h0 2))) (- (+ (* h3 (/ 1 h0)) (- h3))))) 4.514 * * * [progress]: adding candidates to table 5.289 * * [progress]: iteration 4 / 4 5.290 * * * [progress]: picking best candidate 5.312 * * * * [pick]: Picked # 5.312 * * * [progress]: localizing error 5.340 * * * [progress]: generating rewritten candidates 5.340 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 2) 5.372 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 2) 5.399 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 5.644 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 2 1) 5.670 * * * [progress]: generating series expansions 5.670 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 2) 5.671 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 5.671 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 5.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 5.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 5.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 5.671 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 5.671 * [taylor]: Taking taylor expansion of 0.5 in k 5.671 * [backup-simplify]: Simplify 0.5 into 0.5 5.671 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.671 * [taylor]: Taking taylor expansion of 1.0 in k 5.671 * [backup-simplify]: Simplify 1.0 into 1.0 5.671 * [taylor]: Taking taylor expansion of k in k 5.671 * [backup-simplify]: Simplify 0 into 0 5.671 * [backup-simplify]: Simplify 1 into 1 5.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 5.671 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 5.671 * [taylor]: Taking taylor expansion of 2.0 in k 5.671 * [backup-simplify]: Simplify 2.0 into 2.0 5.671 * [taylor]: Taking taylor expansion of (* n PI) in k 5.671 * [taylor]: Taking taylor expansion of n in k 5.671 * [backup-simplify]: Simplify n into n 5.671 * [taylor]: Taking taylor expansion of PI in k 5.671 * [backup-simplify]: Simplify PI into PI 5.671 * [backup-simplify]: Simplify (* n PI) into (* n PI) 5.672 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 5.672 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 5.672 * [backup-simplify]: Simplify (- 0) into 0 5.672 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.673 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 5.673 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 5.673 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 5.673 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.673 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.673 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.673 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.673 * [taylor]: Taking taylor expansion of 0.5 in n 5.673 * [backup-simplify]: Simplify 0.5 into 0.5 5.673 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.673 * [taylor]: Taking taylor expansion of 1.0 in n 5.673 * [backup-simplify]: Simplify 1.0 into 1.0 5.673 * [taylor]: Taking taylor expansion of k in n 5.673 * [backup-simplify]: Simplify k into k 5.673 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.673 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.673 * [taylor]: Taking taylor expansion of 2.0 in n 5.673 * [backup-simplify]: Simplify 2.0 into 2.0 5.673 * [taylor]: Taking taylor expansion of (* n PI) in n 5.673 * [taylor]: Taking taylor expansion of n in n 5.673 * [backup-simplify]: Simplify 0 into 0 5.673 * [backup-simplify]: Simplify 1 into 1 5.673 * [taylor]: Taking taylor expansion of PI in n 5.673 * [backup-simplify]: Simplify PI into PI 5.674 * [backup-simplify]: Simplify (* 0 PI) into 0 5.674 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.675 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.676 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.677 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.677 * [backup-simplify]: Simplify (- k) into (- k) 5.677 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.677 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 5.678 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.679 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.679 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.680 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.680 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.680 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.680 * [taylor]: Taking taylor expansion of 0.5 in n 5.680 * [backup-simplify]: Simplify 0.5 into 0.5 5.680 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.680 * [taylor]: Taking taylor expansion of 1.0 in n 5.680 * [backup-simplify]: Simplify 1.0 into 1.0 5.680 * [taylor]: Taking taylor expansion of k in n 5.680 * [backup-simplify]: Simplify k into k 5.680 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.680 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.680 * [taylor]: Taking taylor expansion of 2.0 in n 5.680 * [backup-simplify]: Simplify 2.0 into 2.0 5.680 * [taylor]: Taking taylor expansion of (* n PI) in n 5.680 * [taylor]: Taking taylor expansion of n in n 5.680 * [backup-simplify]: Simplify 0 into 0 5.680 * [backup-simplify]: Simplify 1 into 1 5.680 * [taylor]: Taking taylor expansion of PI in n 5.680 * [backup-simplify]: Simplify PI into PI 5.680 * [backup-simplify]: Simplify (* 0 PI) into 0 5.680 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.681 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.682 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.683 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.683 * [backup-simplify]: Simplify (- k) into (- k) 5.683 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.683 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 5.684 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.685 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.686 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.686 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 5.686 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 5.686 * [taylor]: Taking taylor expansion of 0.5 in k 5.686 * [backup-simplify]: Simplify 0.5 into 0.5 5.686 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 5.686 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.686 * [taylor]: Taking taylor expansion of 1.0 in k 5.686 * [backup-simplify]: Simplify 1.0 into 1.0 5.686 * [taylor]: Taking taylor expansion of k in k 5.686 * [backup-simplify]: Simplify 0 into 0 5.686 * [backup-simplify]: Simplify 1 into 1 5.686 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 5.686 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.686 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.686 * [taylor]: Taking taylor expansion of 2.0 in k 5.686 * [backup-simplify]: Simplify 2.0 into 2.0 5.686 * [taylor]: Taking taylor expansion of PI in k 5.686 * [backup-simplify]: Simplify PI into PI 5.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.687 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.687 * [taylor]: Taking taylor expansion of (log n) in k 5.687 * [taylor]: Taking taylor expansion of n in k 5.687 * [backup-simplify]: Simplify n into n 5.687 * [backup-simplify]: Simplify (log n) into (log n) 5.687 * [backup-simplify]: Simplify (- 0) into 0 5.688 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.688 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 5.689 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 5.690 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 5.691 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 5.691 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 5.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 5.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 5.694 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.694 * [backup-simplify]: Simplify (- 0) into 0 5.695 * [backup-simplify]: Simplify (+ 0 0) into 0 5.695 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 5.697 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.698 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 5.700 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.700 * [taylor]: Taking taylor expansion of 0 in k 5.701 * [backup-simplify]: Simplify 0 into 0 5.701 * [backup-simplify]: Simplify 0 into 0 5.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.703 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.703 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 5.703 * [backup-simplify]: Simplify (+ 0 0) into 0 5.704 * [backup-simplify]: Simplify (- 1) into -1 5.704 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.705 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 5.706 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 5.709 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 5.718 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 5.719 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 5.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 5.722 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.722 * [backup-simplify]: Simplify (- 0) into 0 5.723 * [backup-simplify]: Simplify (+ 0 0) into 0 5.723 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 5.724 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.725 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.727 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.727 * [taylor]: Taking taylor expansion of 0 in k 5.727 * [backup-simplify]: Simplify 0 into 0 5.727 * [backup-simplify]: Simplify 0 into 0 5.727 * [backup-simplify]: Simplify 0 into 0 5.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.732 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.734 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 5.735 * [backup-simplify]: Simplify (+ 0 0) into 0 5.735 * [backup-simplify]: Simplify (- 0) into 0 5.736 * [backup-simplify]: Simplify (+ 0 0) into 0 5.738 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.740 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 5.745 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 5.750 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 5.761 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 5.762 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 5.762 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 5.762 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 5.763 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.763 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.763 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 5.763 * [taylor]: Taking taylor expansion of 0.5 in k 5.763 * [backup-simplify]: Simplify 0.5 into 0.5 5.763 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.763 * [taylor]: Taking taylor expansion of 1.0 in k 5.763 * [backup-simplify]: Simplify 1.0 into 1.0 5.763 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.763 * [taylor]: Taking taylor expansion of k in k 5.763 * [backup-simplify]: Simplify 0 into 0 5.763 * [backup-simplify]: Simplify 1 into 1 5.763 * [backup-simplify]: Simplify (/ 1 1) into 1 5.763 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.763 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.763 * [taylor]: Taking taylor expansion of 2.0 in k 5.763 * [backup-simplify]: Simplify 2.0 into 2.0 5.763 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.764 * [taylor]: Taking taylor expansion of PI in k 5.764 * [backup-simplify]: Simplify PI into PI 5.764 * [taylor]: Taking taylor expansion of n in k 5.764 * [backup-simplify]: Simplify n into n 5.764 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.764 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 5.764 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 5.764 * [backup-simplify]: Simplify (- 1) into -1 5.765 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.765 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 5.765 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 5.766 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 5.766 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.766 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.766 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.766 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.766 * [taylor]: Taking taylor expansion of 0.5 in n 5.766 * [backup-simplify]: Simplify 0.5 into 0.5 5.766 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.766 * [taylor]: Taking taylor expansion of 1.0 in n 5.766 * [backup-simplify]: Simplify 1.0 into 1.0 5.766 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.766 * [taylor]: Taking taylor expansion of k in n 5.766 * [backup-simplify]: Simplify k into k 5.766 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.766 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.766 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.766 * [taylor]: Taking taylor expansion of 2.0 in n 5.766 * [backup-simplify]: Simplify 2.0 into 2.0 5.766 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.766 * [taylor]: Taking taylor expansion of PI in n 5.766 * [backup-simplify]: Simplify PI into PI 5.766 * [taylor]: Taking taylor expansion of n in n 5.766 * [backup-simplify]: Simplify 0 into 0 5.766 * [backup-simplify]: Simplify 1 into 1 5.767 * [backup-simplify]: Simplify (/ PI 1) into PI 5.768 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.769 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.769 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.769 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.769 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 5.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.772 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.773 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.773 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.773 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.773 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.773 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.773 * [taylor]: Taking taylor expansion of 0.5 in n 5.773 * [backup-simplify]: Simplify 0.5 into 0.5 5.773 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.773 * [taylor]: Taking taylor expansion of 1.0 in n 5.773 * [backup-simplify]: Simplify 1.0 into 1.0 5.773 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.773 * [taylor]: Taking taylor expansion of k in n 5.773 * [backup-simplify]: Simplify k into k 5.774 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.774 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.774 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.774 * [taylor]: Taking taylor expansion of 2.0 in n 5.774 * [backup-simplify]: Simplify 2.0 into 2.0 5.774 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.774 * [taylor]: Taking taylor expansion of PI in n 5.774 * [backup-simplify]: Simplify PI into PI 5.774 * [taylor]: Taking taylor expansion of n in n 5.774 * [backup-simplify]: Simplify 0 into 0 5.774 * [backup-simplify]: Simplify 1 into 1 5.774 * [backup-simplify]: Simplify (/ PI 1) into PI 5.775 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.776 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.776 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.776 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.776 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 5.778 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.779 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.780 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.781 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 5.781 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 5.781 * [taylor]: Taking taylor expansion of 0.5 in k 5.781 * [backup-simplify]: Simplify 0.5 into 0.5 5.781 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 5.781 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 5.781 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.781 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.781 * [taylor]: Taking taylor expansion of 2.0 in k 5.781 * [backup-simplify]: Simplify 2.0 into 2.0 5.781 * [taylor]: Taking taylor expansion of PI in k 5.781 * [backup-simplify]: Simplify PI into PI 5.781 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.782 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.782 * [taylor]: Taking taylor expansion of (log n) in k 5.782 * [taylor]: Taking taylor expansion of n in k 5.782 * [backup-simplify]: Simplify n into n 5.782 * [backup-simplify]: Simplify (log n) into (log n) 5.782 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.782 * [taylor]: Taking taylor expansion of 1.0 in k 5.782 * [backup-simplify]: Simplify 1.0 into 1.0 5.782 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.782 * [taylor]: Taking taylor expansion of k in k 5.782 * [backup-simplify]: Simplify 0 into 0 5.782 * [backup-simplify]: Simplify 1 into 1 5.782 * [backup-simplify]: Simplify (/ 1 1) into 1 5.783 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.783 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 5.783 * [backup-simplify]: Simplify (- 1) into -1 5.784 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.785 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 5.785 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 5.786 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.787 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.787 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.788 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.789 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.789 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.789 * [backup-simplify]: Simplify (- 0) into 0 5.790 * [backup-simplify]: Simplify (+ 0 0) into 0 5.790 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 5.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.792 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 5.793 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.793 * [taylor]: Taking taylor expansion of 0 in k 5.793 * [backup-simplify]: Simplify 0 into 0 5.793 * [backup-simplify]: Simplify 0 into 0 5.793 * [backup-simplify]: Simplify 0 into 0 5.794 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.794 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.796 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.796 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.796 * [backup-simplify]: Simplify (- 0) into 0 5.797 * [backup-simplify]: Simplify (+ 0 0) into 0 5.797 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 5.798 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.799 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 5.801 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.801 * [taylor]: Taking taylor expansion of 0 in k 5.801 * [backup-simplify]: Simplify 0 into 0 5.801 * [backup-simplify]: Simplify 0 into 0 5.801 * [backup-simplify]: Simplify 0 into 0 5.801 * [backup-simplify]: Simplify 0 into 0 5.801 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.802 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.806 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 5.806 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.806 * [backup-simplify]: Simplify (- 0) into 0 5.806 * [backup-simplify]: Simplify (+ 0 0) into 0 5.807 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 5.808 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.810 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 5.813 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 5.813 * [taylor]: Taking taylor expansion of 0 in k 5.813 * [backup-simplify]: Simplify 0 into 0 5.813 * [backup-simplify]: Simplify 0 into 0 5.815 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 5.815 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 5.816 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 5.816 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.816 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.816 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.816 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.816 * [taylor]: Taking taylor expansion of 0.5 in k 5.816 * [backup-simplify]: Simplify 0.5 into 0.5 5.816 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.816 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.816 * [taylor]: Taking taylor expansion of k in k 5.816 * [backup-simplify]: Simplify 0 into 0 5.816 * [backup-simplify]: Simplify 1 into 1 5.816 * [backup-simplify]: Simplify (/ 1 1) into 1 5.816 * [taylor]: Taking taylor expansion of 1.0 in k 5.816 * [backup-simplify]: Simplify 1.0 into 1.0 5.816 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.816 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.817 * [taylor]: Taking taylor expansion of -2.0 in k 5.817 * [backup-simplify]: Simplify -2.0 into -2.0 5.817 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.817 * [taylor]: Taking taylor expansion of PI in k 5.817 * [backup-simplify]: Simplify PI into PI 5.817 * [taylor]: Taking taylor expansion of n in k 5.817 * [backup-simplify]: Simplify n into n 5.817 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.817 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.817 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.817 * [backup-simplify]: Simplify (+ 1 0) into 1 5.818 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.818 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.818 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.818 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.818 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.818 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.819 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.819 * [taylor]: Taking taylor expansion of 0.5 in n 5.819 * [backup-simplify]: Simplify 0.5 into 0.5 5.819 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.819 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.819 * [taylor]: Taking taylor expansion of k in n 5.819 * [backup-simplify]: Simplify k into k 5.819 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.819 * [taylor]: Taking taylor expansion of 1.0 in n 5.819 * [backup-simplify]: Simplify 1.0 into 1.0 5.819 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.819 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.819 * [taylor]: Taking taylor expansion of -2.0 in n 5.819 * [backup-simplify]: Simplify -2.0 into -2.0 5.819 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.819 * [taylor]: Taking taylor expansion of PI in n 5.819 * [backup-simplify]: Simplify PI into PI 5.819 * [taylor]: Taking taylor expansion of n in n 5.819 * [backup-simplify]: Simplify 0 into 0 5.819 * [backup-simplify]: Simplify 1 into 1 5.820 * [backup-simplify]: Simplify (/ PI 1) into PI 5.820 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.821 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.822 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.822 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.825 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.826 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.826 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.826 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.826 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.826 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.826 * [taylor]: Taking taylor expansion of 0.5 in n 5.826 * [backup-simplify]: Simplify 0.5 into 0.5 5.826 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.826 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.826 * [taylor]: Taking taylor expansion of k in n 5.826 * [backup-simplify]: Simplify k into k 5.826 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.826 * [taylor]: Taking taylor expansion of 1.0 in n 5.826 * [backup-simplify]: Simplify 1.0 into 1.0 5.826 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.826 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.826 * [taylor]: Taking taylor expansion of -2.0 in n 5.826 * [backup-simplify]: Simplify -2.0 into -2.0 5.827 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.827 * [taylor]: Taking taylor expansion of PI in n 5.827 * [backup-simplify]: Simplify PI into PI 5.827 * [taylor]: Taking taylor expansion of n in n 5.827 * [backup-simplify]: Simplify 0 into 0 5.827 * [backup-simplify]: Simplify 1 into 1 5.827 * [backup-simplify]: Simplify (/ PI 1) into PI 5.828 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.829 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.829 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.829 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.831 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.832 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.833 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.833 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 5.833 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 5.833 * [taylor]: Taking taylor expansion of 0.5 in k 5.833 * [backup-simplify]: Simplify 0.5 into 0.5 5.833 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 5.833 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.834 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.834 * [taylor]: Taking taylor expansion of k in k 5.834 * [backup-simplify]: Simplify 0 into 0 5.834 * [backup-simplify]: Simplify 1 into 1 5.834 * [backup-simplify]: Simplify (/ 1 1) into 1 5.834 * [taylor]: Taking taylor expansion of 1.0 in k 5.834 * [backup-simplify]: Simplify 1.0 into 1.0 5.834 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 5.834 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 5.834 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 5.834 * [taylor]: Taking taylor expansion of -2.0 in k 5.834 * [backup-simplify]: Simplify -2.0 into -2.0 5.834 * [taylor]: Taking taylor expansion of PI in k 5.834 * [backup-simplify]: Simplify PI into PI 5.835 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.836 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.836 * [taylor]: Taking taylor expansion of (log n) in k 5.836 * [taylor]: Taking taylor expansion of n in k 5.836 * [backup-simplify]: Simplify n into n 5.836 * [backup-simplify]: Simplify (log n) into (log n) 5.837 * [backup-simplify]: Simplify (+ 1 0) into 1 5.837 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.838 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 5.839 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 5.840 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 5.841 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.843 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.844 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.844 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.846 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 5.846 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.854 * [backup-simplify]: Simplify (+ 0 0) into 0 5.855 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 5.856 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.857 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 5.858 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.858 * [taylor]: Taking taylor expansion of 0 in k 5.858 * [backup-simplify]: Simplify 0 into 0 5.858 * [backup-simplify]: Simplify 0 into 0 5.858 * [backup-simplify]: Simplify 0 into 0 5.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.859 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.861 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 5.862 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.862 * [backup-simplify]: Simplify (+ 0 0) into 0 5.862 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 5.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.864 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 5.866 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.866 * [taylor]: Taking taylor expansion of 0 in k 5.866 * [backup-simplify]: Simplify 0 into 0 5.866 * [backup-simplify]: Simplify 0 into 0 5.866 * [backup-simplify]: Simplify 0 into 0 5.866 * [backup-simplify]: Simplify 0 into 0 5.867 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.867 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.870 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 5.871 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.871 * [backup-simplify]: Simplify (+ 0 0) into 0 5.872 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 5.873 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.874 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 5.877 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 5.877 * [taylor]: Taking taylor expansion of 0 in k 5.877 * [backup-simplify]: Simplify 0 into 0 5.877 * [backup-simplify]: Simplify 0 into 0 5.879 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 5.879 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 2) 5.880 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 5.880 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 5.880 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 5.880 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 5.880 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 5.880 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 5.880 * [taylor]: Taking taylor expansion of 0.5 in k 5.880 * [backup-simplify]: Simplify 0.5 into 0.5 5.880 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.880 * [taylor]: Taking taylor expansion of 1.0 in k 5.880 * [backup-simplify]: Simplify 1.0 into 1.0 5.880 * [taylor]: Taking taylor expansion of k in k 5.880 * [backup-simplify]: Simplify 0 into 0 5.880 * [backup-simplify]: Simplify 1 into 1 5.880 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 5.880 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 5.880 * [taylor]: Taking taylor expansion of 2.0 in k 5.880 * [backup-simplify]: Simplify 2.0 into 2.0 5.880 * [taylor]: Taking taylor expansion of (* n PI) in k 5.880 * [taylor]: Taking taylor expansion of n in k 5.880 * [backup-simplify]: Simplify n into n 5.880 * [taylor]: Taking taylor expansion of PI in k 5.880 * [backup-simplify]: Simplify PI into PI 5.880 * [backup-simplify]: Simplify (* n PI) into (* n PI) 5.880 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 5.881 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 5.881 * [backup-simplify]: Simplify (- 0) into 0 5.882 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.882 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 5.882 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 5.882 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 5.882 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.882 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.882 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.883 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.883 * [taylor]: Taking taylor expansion of 0.5 in n 5.883 * [backup-simplify]: Simplify 0.5 into 0.5 5.883 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.883 * [taylor]: Taking taylor expansion of 1.0 in n 5.883 * [backup-simplify]: Simplify 1.0 into 1.0 5.883 * [taylor]: Taking taylor expansion of k in n 5.883 * [backup-simplify]: Simplify k into k 5.883 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.883 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.883 * [taylor]: Taking taylor expansion of 2.0 in n 5.883 * [backup-simplify]: Simplify 2.0 into 2.0 5.883 * [taylor]: Taking taylor expansion of (* n PI) in n 5.883 * [taylor]: Taking taylor expansion of n in n 5.883 * [backup-simplify]: Simplify 0 into 0 5.883 * [backup-simplify]: Simplify 1 into 1 5.883 * [taylor]: Taking taylor expansion of PI in n 5.883 * [backup-simplify]: Simplify PI into PI 5.884 * [backup-simplify]: Simplify (* 0 PI) into 0 5.884 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.886 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.888 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.889 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.889 * [backup-simplify]: Simplify (- k) into (- k) 5.889 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.889 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 5.890 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.892 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.893 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.893 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.893 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.893 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.893 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.893 * [taylor]: Taking taylor expansion of 0.5 in n 5.893 * [backup-simplify]: Simplify 0.5 into 0.5 5.893 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.893 * [taylor]: Taking taylor expansion of 1.0 in n 5.893 * [backup-simplify]: Simplify 1.0 into 1.0 5.893 * [taylor]: Taking taylor expansion of k in n 5.893 * [backup-simplify]: Simplify k into k 5.893 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.893 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.894 * [taylor]: Taking taylor expansion of 2.0 in n 5.894 * [backup-simplify]: Simplify 2.0 into 2.0 5.894 * [taylor]: Taking taylor expansion of (* n PI) in n 5.894 * [taylor]: Taking taylor expansion of n in n 5.894 * [backup-simplify]: Simplify 0 into 0 5.894 * [backup-simplify]: Simplify 1 into 1 5.894 * [taylor]: Taking taylor expansion of PI in n 5.894 * [backup-simplify]: Simplify PI into PI 5.894 * [backup-simplify]: Simplify (* 0 PI) into 0 5.895 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.896 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.898 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.899 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.899 * [backup-simplify]: Simplify (- k) into (- k) 5.899 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.899 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 5.901 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.902 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.903 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.903 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 5.904 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 5.904 * [taylor]: Taking taylor expansion of 0.5 in k 5.904 * [backup-simplify]: Simplify 0.5 into 0.5 5.904 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 5.904 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.904 * [taylor]: Taking taylor expansion of 1.0 in k 5.904 * [backup-simplify]: Simplify 1.0 into 1.0 5.904 * [taylor]: Taking taylor expansion of k in k 5.904 * [backup-simplify]: Simplify 0 into 0 5.904 * [backup-simplify]: Simplify 1 into 1 5.904 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 5.904 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.904 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.904 * [taylor]: Taking taylor expansion of 2.0 in k 5.904 * [backup-simplify]: Simplify 2.0 into 2.0 5.904 * [taylor]: Taking taylor expansion of PI in k 5.904 * [backup-simplify]: Simplify PI into PI 5.905 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.906 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.906 * [taylor]: Taking taylor expansion of (log n) in k 5.906 * [taylor]: Taking taylor expansion of n in k 5.906 * [backup-simplify]: Simplify n into n 5.906 * [backup-simplify]: Simplify (log n) into (log n) 5.906 * [backup-simplify]: Simplify (- 0) into 0 5.907 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.908 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 5.909 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 5.910 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 5.911 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 5.913 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 5.914 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 5.915 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 5.917 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.917 * [backup-simplify]: Simplify (- 0) into 0 5.917 * [backup-simplify]: Simplify (+ 0 0) into 0 5.918 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 5.920 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.921 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 5.923 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.923 * [taylor]: Taking taylor expansion of 0 in k 5.923 * [backup-simplify]: Simplify 0 into 0 5.923 * [backup-simplify]: Simplify 0 into 0 5.924 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.926 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.927 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 5.927 * [backup-simplify]: Simplify (+ 0 0) into 0 5.927 * [backup-simplify]: Simplify (- 1) into -1 5.928 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.929 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 5.932 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 5.936 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 5.939 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 5.940 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 5.942 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 5.945 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.946 * [backup-simplify]: Simplify (- 0) into 0 5.946 * [backup-simplify]: Simplify (+ 0 0) into 0 5.947 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 5.948 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.950 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.953 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.953 * [taylor]: Taking taylor expansion of 0 in k 5.953 * [backup-simplify]: Simplify 0 into 0 5.953 * [backup-simplify]: Simplify 0 into 0 5.953 * [backup-simplify]: Simplify 0 into 0 5.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.957 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.959 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 5.960 * [backup-simplify]: Simplify (+ 0 0) into 0 5.960 * [backup-simplify]: Simplify (- 0) into 0 5.961 * [backup-simplify]: Simplify (+ 0 0) into 0 5.962 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.965 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 5.970 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 5.975 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 5.986 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 5.987 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 5.987 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 5.987 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 5.988 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.988 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.988 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 5.988 * [taylor]: Taking taylor expansion of 0.5 in k 5.988 * [backup-simplify]: Simplify 0.5 into 0.5 5.988 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.988 * [taylor]: Taking taylor expansion of 1.0 in k 5.988 * [backup-simplify]: Simplify 1.0 into 1.0 5.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.988 * [taylor]: Taking taylor expansion of k in k 5.988 * [backup-simplify]: Simplify 0 into 0 5.988 * [backup-simplify]: Simplify 1 into 1 5.988 * [backup-simplify]: Simplify (/ 1 1) into 1 5.988 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.988 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.989 * [taylor]: Taking taylor expansion of 2.0 in k 5.989 * [backup-simplify]: Simplify 2.0 into 2.0 5.989 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.989 * [taylor]: Taking taylor expansion of PI in k 5.989 * [backup-simplify]: Simplify PI into PI 5.989 * [taylor]: Taking taylor expansion of n in k 5.989 * [backup-simplify]: Simplify n into n 5.989 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.989 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 5.989 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 5.990 * [backup-simplify]: Simplify (- 1) into -1 5.990 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.991 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 5.991 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 5.991 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 5.991 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.991 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.991 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.991 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.991 * [taylor]: Taking taylor expansion of 0.5 in n 5.991 * [backup-simplify]: Simplify 0.5 into 0.5 5.991 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.991 * [taylor]: Taking taylor expansion of 1.0 in n 5.991 * [backup-simplify]: Simplify 1.0 into 1.0 5.991 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.991 * [taylor]: Taking taylor expansion of k in n 5.991 * [backup-simplify]: Simplify k into k 5.992 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.992 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.992 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.992 * [taylor]: Taking taylor expansion of 2.0 in n 5.992 * [backup-simplify]: Simplify 2.0 into 2.0 5.992 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.992 * [taylor]: Taking taylor expansion of PI in n 5.992 * [backup-simplify]: Simplify PI into PI 5.992 * [taylor]: Taking taylor expansion of n in n 5.992 * [backup-simplify]: Simplify 0 into 0 5.992 * [backup-simplify]: Simplify 1 into 1 5.992 * [backup-simplify]: Simplify (/ PI 1) into PI 5.993 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.994 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.994 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.994 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.994 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.005 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.007 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.007 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.007 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.007 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.007 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.007 * [taylor]: Taking taylor expansion of 0.5 in n 6.007 * [backup-simplify]: Simplify 0.5 into 0.5 6.007 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.007 * [taylor]: Taking taylor expansion of 1.0 in n 6.007 * [backup-simplify]: Simplify 1.0 into 1.0 6.007 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.007 * [taylor]: Taking taylor expansion of k in n 6.007 * [backup-simplify]: Simplify k into k 6.007 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.007 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.007 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.007 * [taylor]: Taking taylor expansion of 2.0 in n 6.007 * [backup-simplify]: Simplify 2.0 into 2.0 6.007 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.007 * [taylor]: Taking taylor expansion of PI in n 6.007 * [backup-simplify]: Simplify PI into PI 6.007 * [taylor]: Taking taylor expansion of n in n 6.007 * [backup-simplify]: Simplify 0 into 0 6.007 * [backup-simplify]: Simplify 1 into 1 6.008 * [backup-simplify]: Simplify (/ PI 1) into PI 6.008 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.009 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.010 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.010 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.010 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.011 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.012 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.012 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.013 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.013 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.013 * [taylor]: Taking taylor expansion of 0.5 in k 6.013 * [backup-simplify]: Simplify 0.5 into 0.5 6.013 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.013 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.013 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.013 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.013 * [taylor]: Taking taylor expansion of 2.0 in k 6.013 * [backup-simplify]: Simplify 2.0 into 2.0 6.013 * [taylor]: Taking taylor expansion of PI in k 6.013 * [backup-simplify]: Simplify PI into PI 6.013 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.014 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.014 * [taylor]: Taking taylor expansion of (log n) in k 6.014 * [taylor]: Taking taylor expansion of n in k 6.014 * [backup-simplify]: Simplify n into n 6.014 * [backup-simplify]: Simplify (log n) into (log n) 6.014 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.014 * [taylor]: Taking taylor expansion of 1.0 in k 6.014 * [backup-simplify]: Simplify 1.0 into 1.0 6.014 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.014 * [taylor]: Taking taylor expansion of k in k 6.014 * [backup-simplify]: Simplify 0 into 0 6.014 * [backup-simplify]: Simplify 1 into 1 6.014 * [backup-simplify]: Simplify (/ 1 1) into 1 6.014 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.015 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.015 * [backup-simplify]: Simplify (- 1) into -1 6.016 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.016 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.017 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.018 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.019 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.020 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.021 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.022 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.022 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.022 * [backup-simplify]: Simplify (- 0) into 0 6.022 * [backup-simplify]: Simplify (+ 0 0) into 0 6.023 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.024 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.025 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.026 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.026 * [taylor]: Taking taylor expansion of 0 in k 6.026 * [backup-simplify]: Simplify 0 into 0 6.026 * [backup-simplify]: Simplify 0 into 0 6.026 * [backup-simplify]: Simplify 0 into 0 6.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.027 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.029 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.030 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.030 * [backup-simplify]: Simplify (- 0) into 0 6.030 * [backup-simplify]: Simplify (+ 0 0) into 0 6.031 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.032 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.033 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.034 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.034 * [taylor]: Taking taylor expansion of 0 in k 6.034 * [backup-simplify]: Simplify 0 into 0 6.034 * [backup-simplify]: Simplify 0 into 0 6.034 * [backup-simplify]: Simplify 0 into 0 6.034 * [backup-simplify]: Simplify 0 into 0 6.035 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.036 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.039 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.040 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.040 * [backup-simplify]: Simplify (- 0) into 0 6.040 * [backup-simplify]: Simplify (+ 0 0) into 0 6.042 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.044 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.047 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.050 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.050 * [taylor]: Taking taylor expansion of 0 in k 6.050 * [backup-simplify]: Simplify 0 into 0 6.050 * [backup-simplify]: Simplify 0 into 0 6.052 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 6.052 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 6.053 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.053 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.053 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.053 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.053 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.053 * [taylor]: Taking taylor expansion of 0.5 in k 6.053 * [backup-simplify]: Simplify 0.5 into 0.5 6.053 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.053 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.053 * [taylor]: Taking taylor expansion of k in k 6.053 * [backup-simplify]: Simplify 0 into 0 6.053 * [backup-simplify]: Simplify 1 into 1 6.053 * [backup-simplify]: Simplify (/ 1 1) into 1 6.053 * [taylor]: Taking taylor expansion of 1.0 in k 6.053 * [backup-simplify]: Simplify 1.0 into 1.0 6.054 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.054 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.054 * [taylor]: Taking taylor expansion of -2.0 in k 6.054 * [backup-simplify]: Simplify -2.0 into -2.0 6.054 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.054 * [taylor]: Taking taylor expansion of PI in k 6.054 * [backup-simplify]: Simplify PI into PI 6.054 * [taylor]: Taking taylor expansion of n in k 6.054 * [backup-simplify]: Simplify n into n 6.054 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.054 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.054 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.055 * [backup-simplify]: Simplify (+ 1 0) into 1 6.055 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.055 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.055 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.055 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.056 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.056 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.056 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.056 * [taylor]: Taking taylor expansion of 0.5 in n 6.056 * [backup-simplify]: Simplify 0.5 into 0.5 6.056 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.056 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.056 * [taylor]: Taking taylor expansion of k in n 6.056 * [backup-simplify]: Simplify k into k 6.056 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.056 * [taylor]: Taking taylor expansion of 1.0 in n 6.056 * [backup-simplify]: Simplify 1.0 into 1.0 6.056 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.056 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.056 * [taylor]: Taking taylor expansion of -2.0 in n 6.056 * [backup-simplify]: Simplify -2.0 into -2.0 6.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.056 * [taylor]: Taking taylor expansion of PI in n 6.056 * [backup-simplify]: Simplify PI into PI 6.056 * [taylor]: Taking taylor expansion of n in n 6.056 * [backup-simplify]: Simplify 0 into 0 6.056 * [backup-simplify]: Simplify 1 into 1 6.057 * [backup-simplify]: Simplify (/ PI 1) into PI 6.057 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.058 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.059 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.059 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.061 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.062 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.063 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.063 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.063 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.063 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.063 * [taylor]: Taking taylor expansion of 0.5 in n 6.063 * [backup-simplify]: Simplify 0.5 into 0.5 6.063 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.064 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.064 * [taylor]: Taking taylor expansion of k in n 6.064 * [backup-simplify]: Simplify k into k 6.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.064 * [taylor]: Taking taylor expansion of 1.0 in n 6.064 * [backup-simplify]: Simplify 1.0 into 1.0 6.064 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.064 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.064 * [taylor]: Taking taylor expansion of -2.0 in n 6.064 * [backup-simplify]: Simplify -2.0 into -2.0 6.064 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.064 * [taylor]: Taking taylor expansion of PI in n 6.064 * [backup-simplify]: Simplify PI into PI 6.064 * [taylor]: Taking taylor expansion of n in n 6.064 * [backup-simplify]: Simplify 0 into 0 6.064 * [backup-simplify]: Simplify 1 into 1 6.065 * [backup-simplify]: Simplify (/ PI 1) into PI 6.065 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.066 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.066 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.067 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.068 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.070 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.071 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.071 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.071 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.071 * [taylor]: Taking taylor expansion of 0.5 in k 6.071 * [backup-simplify]: Simplify 0.5 into 0.5 6.071 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.071 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.071 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.071 * [taylor]: Taking taylor expansion of k in k 6.071 * [backup-simplify]: Simplify 0 into 0 6.071 * [backup-simplify]: Simplify 1 into 1 6.072 * [backup-simplify]: Simplify (/ 1 1) into 1 6.072 * [taylor]: Taking taylor expansion of 1.0 in k 6.072 * [backup-simplify]: Simplify 1.0 into 1.0 6.072 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.072 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.072 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.072 * [taylor]: Taking taylor expansion of -2.0 in k 6.072 * [backup-simplify]: Simplify -2.0 into -2.0 6.072 * [taylor]: Taking taylor expansion of PI in k 6.072 * [backup-simplify]: Simplify PI into PI 6.073 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.074 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.074 * [taylor]: Taking taylor expansion of (log n) in k 6.074 * [taylor]: Taking taylor expansion of n in k 6.074 * [backup-simplify]: Simplify n into n 6.074 * [backup-simplify]: Simplify (log n) into (log n) 6.074 * [backup-simplify]: Simplify (+ 1 0) into 1 6.075 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.076 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.077 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.078 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.080 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.081 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.083 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.085 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.086 * [backup-simplify]: Simplify (+ 0 0) into 0 6.087 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.089 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.092 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.092 * [taylor]: Taking taylor expansion of 0 in k 6.092 * [backup-simplify]: Simplify 0 into 0 6.092 * [backup-simplify]: Simplify 0 into 0 6.092 * [backup-simplify]: Simplify 0 into 0 6.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.094 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.097 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.098 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.098 * [backup-simplify]: Simplify (+ 0 0) into 0 6.099 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.101 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.102 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.105 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.105 * [taylor]: Taking taylor expansion of 0 in k 6.105 * [backup-simplify]: Simplify 0 into 0 6.105 * [backup-simplify]: Simplify 0 into 0 6.105 * [backup-simplify]: Simplify 0 into 0 6.105 * [backup-simplify]: Simplify 0 into 0 6.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.108 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.114 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 6.114 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.115 * [backup-simplify]: Simplify (+ 0 0) into 0 6.116 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.118 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.120 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.123 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.123 * [taylor]: Taking taylor expansion of 0 in k 6.123 * [backup-simplify]: Simplify 0 into 0 6.123 * [backup-simplify]: Simplify 0 into 0 6.125 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.125 * * * * [progress]: [ 3 / 4 ] generating series at (2) 6.127 * [backup-simplify]: Simplify (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) into (* (sqrt (/ 1 k)) (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2))) 6.127 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2))) in (k n) around 0 6.127 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2))) in n 6.127 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.127 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.127 * [taylor]: Taking taylor expansion of k in n 6.127 * [backup-simplify]: Simplify k into k 6.127 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.127 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.127 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.127 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.127 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n 6.127 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.127 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.127 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.127 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.127 * [taylor]: Taking taylor expansion of 0.5 in n 6.127 * [backup-simplify]: Simplify 0.5 into 0.5 6.128 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.128 * [taylor]: Taking taylor expansion of 1.0 in n 6.128 * [backup-simplify]: Simplify 1.0 into 1.0 6.128 * [taylor]: Taking taylor expansion of k in n 6.128 * [backup-simplify]: Simplify k into k 6.128 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.128 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.128 * [taylor]: Taking taylor expansion of 2.0 in n 6.128 * [backup-simplify]: Simplify 2.0 into 2.0 6.128 * [taylor]: Taking taylor expansion of (* n PI) in n 6.128 * [taylor]: Taking taylor expansion of n in n 6.128 * [backup-simplify]: Simplify 0 into 0 6.128 * [backup-simplify]: Simplify 1 into 1 6.128 * [taylor]: Taking taylor expansion of PI in n 6.128 * [backup-simplify]: Simplify PI into PI 6.128 * [backup-simplify]: Simplify (* 0 PI) into 0 6.129 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.130 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.132 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.133 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.133 * [backup-simplify]: Simplify (- k) into (- k) 6.133 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.133 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.135 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.136 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.138 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.138 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.138 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.138 * [taylor]: Taking taylor expansion of 1.0 in n 6.138 * [backup-simplify]: Simplify 1.0 into 1.0 6.138 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.139 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.139 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2))) in k 6.139 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.139 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.139 * [taylor]: Taking taylor expansion of k in k 6.139 * [backup-simplify]: Simplify 0 into 0 6.139 * [backup-simplify]: Simplify 1 into 1 6.140 * [backup-simplify]: Simplify (/ 1 1) into 1 6.140 * [backup-simplify]: Simplify (sqrt 0) into 0 6.141 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.141 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k 6.142 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.142 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.142 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.142 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.142 * [taylor]: Taking taylor expansion of 0.5 in k 6.142 * [backup-simplify]: Simplify 0.5 into 0.5 6.142 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.142 * [taylor]: Taking taylor expansion of 1.0 in k 6.142 * [backup-simplify]: Simplify 1.0 into 1.0 6.142 * [taylor]: Taking taylor expansion of k in k 6.142 * [backup-simplify]: Simplify 0 into 0 6.142 * [backup-simplify]: Simplify 1 into 1 6.142 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.142 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.142 * [taylor]: Taking taylor expansion of 2.0 in k 6.142 * [backup-simplify]: Simplify 2.0 into 2.0 6.142 * [taylor]: Taking taylor expansion of (* n PI) in k 6.142 * [taylor]: Taking taylor expansion of n in k 6.142 * [backup-simplify]: Simplify n into n 6.142 * [taylor]: Taking taylor expansion of PI in k 6.142 * [backup-simplify]: Simplify PI into PI 6.142 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.142 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.142 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.143 * [backup-simplify]: Simplify (- 0) into 0 6.143 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.144 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.144 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.144 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.144 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 6.144 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 6.144 * [taylor]: Taking taylor expansion of 1.0 in k 6.144 * [backup-simplify]: Simplify 1.0 into 1.0 6.144 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.153 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.153 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2))) in k 6.153 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.153 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.153 * [taylor]: Taking taylor expansion of k in k 6.153 * [backup-simplify]: Simplify 0 into 0 6.153 * [backup-simplify]: Simplify 1 into 1 6.154 * [backup-simplify]: Simplify (/ 1 1) into 1 6.154 * [backup-simplify]: Simplify (sqrt 0) into 0 6.155 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.155 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k 6.155 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.155 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.155 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.156 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.156 * [taylor]: Taking taylor expansion of 0.5 in k 6.156 * [backup-simplify]: Simplify 0.5 into 0.5 6.156 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.156 * [taylor]: Taking taylor expansion of 1.0 in k 6.156 * [backup-simplify]: Simplify 1.0 into 1.0 6.156 * [taylor]: Taking taylor expansion of k in k 6.156 * [backup-simplify]: Simplify 0 into 0 6.156 * [backup-simplify]: Simplify 1 into 1 6.156 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.156 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.156 * [taylor]: Taking taylor expansion of 2.0 in k 6.156 * [backup-simplify]: Simplify 2.0 into 2.0 6.156 * [taylor]: Taking taylor expansion of (* n PI) in k 6.156 * [taylor]: Taking taylor expansion of n in k 6.156 * [backup-simplify]: Simplify n into n 6.156 * [taylor]: Taking taylor expansion of PI in k 6.156 * [backup-simplify]: Simplify PI into PI 6.156 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.156 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.156 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.157 * [backup-simplify]: Simplify (- 0) into 0 6.157 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.158 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.158 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.158 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.158 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 6.158 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 6.158 * [taylor]: Taking taylor expansion of 1.0 in k 6.158 * [backup-simplify]: Simplify 1.0 into 1.0 6.159 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.159 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.161 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.162 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) (pow (sqrt 1.0) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)) 6.164 * [backup-simplify]: Simplify (* 0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) into 0 6.164 * [taylor]: Taking taylor expansion of 0 in n 6.164 * [backup-simplify]: Simplify 0 into 0 6.164 * [backup-simplify]: Simplify 0 into 0 6.165 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 6.166 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 6.166 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 6.167 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 6.167 * [backup-simplify]: Simplify (- 1) into -1 6.168 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.170 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 6.171 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 6.171 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 6.174 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) 0) (* (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (sqrt 1.0) 2))) into (- (* 0.5 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 (* n PI))))))) 6.179 * [backup-simplify]: Simplify (+ (* 0 (- (* 0.5 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 (* n PI)))))))) (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) 6.179 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) in n 6.179 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) in n 6.179 * [taylor]: Taking taylor expansion of +nan.0 in n 6.179 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.179 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)) in n 6.179 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 6.179 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 6.179 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 6.179 * [taylor]: Taking taylor expansion of 0.5 in n 6.179 * [backup-simplify]: Simplify 0.5 into 0.5 6.179 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 6.179 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 6.179 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 6.179 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 6.179 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 6.179 * [taylor]: Taking taylor expansion of 1.0 in n 6.179 * [backup-simplify]: Simplify 1.0 into 1.0 6.179 * [taylor]: Taking taylor expansion of (log 2.0) in n 6.179 * [taylor]: Taking taylor expansion of 2.0 in n 6.179 * [backup-simplify]: Simplify 2.0 into 2.0 6.180 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 6.181 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 6.182 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 6.182 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 6.182 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 6.182 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 6.182 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 6.182 * [taylor]: Taking taylor expansion of 1.0 in n 6.182 * [backup-simplify]: Simplify 1.0 into 1.0 6.183 * [taylor]: Taking taylor expansion of (log n) in n 6.183 * [taylor]: Taking taylor expansion of n in n 6.183 * [backup-simplify]: Simplify 0 into 0 6.183 * [backup-simplify]: Simplify 1 into 1 6.183 * [backup-simplify]: Simplify (log 1) into 0 6.183 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.183 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 6.184 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 6.184 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 6.184 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 6.184 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 6.184 * [taylor]: Taking taylor expansion of 1.0 in n 6.184 * [backup-simplify]: Simplify 1.0 into 1.0 6.184 * [taylor]: Taking taylor expansion of (log PI) in n 6.184 * [taylor]: Taking taylor expansion of PI in n 6.184 * [backup-simplify]: Simplify PI into PI 6.184 * [backup-simplify]: Simplify (log PI) into (log PI) 6.185 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 6.186 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 6.187 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 6.187 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 6.188 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 6.189 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 6.190 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 6.190 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.190 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.190 * [taylor]: Taking taylor expansion of 1.0 in n 6.190 * [backup-simplify]: Simplify 1.0 into 1.0 6.190 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.191 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.192 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.193 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (sqrt 1.0) 2)) into (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)) 6.195 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) 6.196 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) 6.198 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))) 6.198 * [backup-simplify]: Simplify 0 into 0 6.198 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 6.199 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 6.199 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 6.200 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 6.201 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 6.201 * [backup-simplify]: Simplify (- 0) into 0 6.202 * [backup-simplify]: Simplify (+ 0 0) into 0 6.202 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 6.203 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 6.204 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 6.206 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) 0) (+ (* (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0) (* (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (sqrt 1.0) 2)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 (* n PI))) 2)))) 6.207 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.209 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.214 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (- (* 0.5 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 (* n PI)))))))) (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))) 6.214 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))) in n 6.214 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))))) in n 6.214 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) in n 6.214 * [taylor]: Taking taylor expansion of +nan.0 in n 6.214 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.214 * [taylor]: Taking taylor expansion of (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 6.214 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) in n 6.214 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.214 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.214 * [taylor]: Taking taylor expansion of 2.0 in n 6.214 * [backup-simplify]: Simplify 2.0 into 2.0 6.214 * [taylor]: Taking taylor expansion of (* n PI) in n 6.214 * [taylor]: Taking taylor expansion of n in n 6.214 * [backup-simplify]: Simplify 0 into 0 6.214 * [backup-simplify]: Simplify 1 into 1 6.214 * [taylor]: Taking taylor expansion of PI in n 6.214 * [backup-simplify]: Simplify PI into PI 6.215 * [backup-simplify]: Simplify (* 0 PI) into 0 6.215 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.217 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.219 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.220 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.220 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.220 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.220 * [taylor]: Taking taylor expansion of 1.0 in n 6.220 * [backup-simplify]: Simplify 1.0 into 1.0 6.220 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.221 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.221 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 6.221 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 6.221 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 6.221 * [taylor]: Taking taylor expansion of 0.5 in n 6.221 * [backup-simplify]: Simplify 0.5 into 0.5 6.221 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 6.221 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 6.221 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 6.221 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 6.221 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 6.221 * [taylor]: Taking taylor expansion of 1.0 in n 6.221 * [backup-simplify]: Simplify 1.0 into 1.0 6.221 * [taylor]: Taking taylor expansion of (log 2.0) in n 6.221 * [taylor]: Taking taylor expansion of 2.0 in n 6.221 * [backup-simplify]: Simplify 2.0 into 2.0 6.222 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 6.223 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 6.224 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 6.224 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 6.225 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 6.225 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 6.225 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 6.225 * [taylor]: Taking taylor expansion of 1.0 in n 6.225 * [backup-simplify]: Simplify 1.0 into 1.0 6.225 * [taylor]: Taking taylor expansion of (log n) in n 6.225 * [taylor]: Taking taylor expansion of n in n 6.225 * [backup-simplify]: Simplify 0 into 0 6.225 * [backup-simplify]: Simplify 1 into 1 6.225 * [backup-simplify]: Simplify (log 1) into 0 6.226 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.226 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 6.226 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 6.226 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 6.226 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 6.226 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 6.226 * [taylor]: Taking taylor expansion of 1.0 in n 6.226 * [backup-simplify]: Simplify 1.0 into 1.0 6.226 * [taylor]: Taking taylor expansion of (log PI) in n 6.226 * [taylor]: Taking taylor expansion of PI in n 6.226 * [backup-simplify]: Simplify PI into PI 6.227 * [backup-simplify]: Simplify (log PI) into (log PI) 6.228 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 6.229 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 6.230 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 6.232 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 6.233 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 6.234 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 6.235 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 6.235 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) in n 6.235 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) in n 6.235 * [taylor]: Taking taylor expansion of +nan.0 in n 6.235 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.235 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)) in n 6.235 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 6.235 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 6.235 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 6.235 * [taylor]: Taking taylor expansion of 0.5 in n 6.235 * [backup-simplify]: Simplify 0.5 into 0.5 6.235 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 6.235 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 6.235 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 6.235 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 6.235 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 6.235 * [taylor]: Taking taylor expansion of 1.0 in n 6.235 * [backup-simplify]: Simplify 1.0 into 1.0 6.235 * [taylor]: Taking taylor expansion of (log 2.0) in n 6.235 * [taylor]: Taking taylor expansion of 2.0 in n 6.235 * [backup-simplify]: Simplify 2.0 into 2.0 6.236 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 6.236 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 6.237 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 6.237 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 6.237 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 6.237 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 6.237 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 6.237 * [taylor]: Taking taylor expansion of 1.0 in n 6.237 * [backup-simplify]: Simplify 1.0 into 1.0 6.237 * [taylor]: Taking taylor expansion of (log n) in n 6.237 * [taylor]: Taking taylor expansion of n in n 6.237 * [backup-simplify]: Simplify 0 into 0 6.237 * [backup-simplify]: Simplify 1 into 1 6.238 * [backup-simplify]: Simplify (log 1) into 0 6.238 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.238 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 6.238 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 6.238 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 6.238 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 6.238 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 6.238 * [taylor]: Taking taylor expansion of 1.0 in n 6.238 * [backup-simplify]: Simplify 1.0 into 1.0 6.238 * [taylor]: Taking taylor expansion of (log PI) in n 6.238 * [taylor]: Taking taylor expansion of PI in n 6.238 * [backup-simplify]: Simplify PI into PI 6.238 * [backup-simplify]: Simplify (log PI) into (log PI) 6.239 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 6.240 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 6.240 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 6.241 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 6.242 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 6.243 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 6.244 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 6.244 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.244 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.244 * [taylor]: Taking taylor expansion of 1.0 in n 6.244 * [backup-simplify]: Simplify 1.0 into 1.0 6.244 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.245 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.246 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.247 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.248 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) 6.250 * [backup-simplify]: Simplify (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 6.252 * [backup-simplify]: Simplify (* +nan.0 (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 6.253 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.255 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (sqrt 1.0) 2)) into (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)) 6.256 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) 6.258 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) 6.261 * [backup-simplify]: Simplify (+ (* +nan.0 (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))))))) 6.281 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))))))))) into (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))))))))) 6.293 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) 6.294 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 6.296 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 6.297 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 6.298 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 6.299 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 6.300 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.300 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 6.300 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 6.301 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow PI 1.0))) into 0 6.302 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 6.303 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 6.304 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 6.305 * [backup-simplify]: Simplify (+ (* (pow 2.0 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow PI 1.0)) 1.0))) into 0 6.306 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1)))) 1) into 0 6.307 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)))) into 0 6.309 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 6.310 * [backup-simplify]: Simplify (+ (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 0) (* 0 (pow (sqrt 1.0) 2))) into 0 6.312 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) into 0 6.312 * [backup-simplify]: Simplify (- 0) into 0 6.312 * [backup-simplify]: Simplify 0 into 0 6.312 * [backup-simplify]: Simplify 0 into 0 6.313 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 6.314 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 6.315 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.316 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 6.319 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 6.320 * [backup-simplify]: Simplify (- 0) into 0 6.320 * [backup-simplify]: Simplify (+ 0 0) into 0 6.321 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 6.323 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 6.325 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 6.331 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) 0) (+ (* (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0) (+ (* (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 0) (* (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (sqrt 1.0) 2))))) into (- (* 0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 (* n PI))) 3))))) 6.332 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.336 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.346 * [backup-simplify]: Simplify (+ (* 0 (- (* 0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 (* n PI))) 3)))))) (+ (* +nan.0 (* 0.125 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (- (* 0.5 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (pow (sqrt 1.0) 2) (log (* 2.0 (* n PI)))))))) (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))))) into (- (+ (* +nan.0 (* (* (pow (log (* 2.0 (* n PI))) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))))) 6.346 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (pow (log (* 2.0 (* n PI))) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))))) in n 6.347 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (pow (log (* 2.0 (* n PI))) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))))))) in n 6.347 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (pow (log (* 2.0 (* n PI))) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) in n 6.347 * [taylor]: Taking taylor expansion of +nan.0 in n 6.347 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.347 * [taylor]: Taking taylor expansion of (* (* (pow (log (* 2.0 (* n PI))) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 6.347 * [taylor]: Taking taylor expansion of (* (pow (log (* 2.0 (* n PI))) 2) (pow (sqrt 1.0) 2)) in n 6.347 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 6.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.347 * [taylor]: Taking taylor expansion of 2.0 in n 6.347 * [backup-simplify]: Simplify 2.0 into 2.0 6.347 * [taylor]: Taking taylor expansion of (* n PI) in n 6.347 * [taylor]: Taking taylor expansion of n in n 6.347 * [backup-simplify]: Simplify 0 into 0 6.347 * [backup-simplify]: Simplify 1 into 1 6.347 * [taylor]: Taking taylor expansion of PI in n 6.347 * [backup-simplify]: Simplify PI into PI 6.348 * [backup-simplify]: Simplify (* 0 PI) into 0 6.348 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.349 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.350 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.352 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.352 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.352 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.352 * [taylor]: Taking taylor expansion of 1.0 in n 6.352 * [backup-simplify]: Simplify 1.0 into 1.0 6.353 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.353 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.353 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 6.353 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 6.353 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 6.353 * [taylor]: Taking taylor expansion of 0.5 in n 6.353 * [backup-simplify]: Simplify 0.5 into 0.5 6.353 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 6.353 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 6.353 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 6.353 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 6.353 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 6.353 * [taylor]: Taking taylor expansion of 1.0 in n 6.353 * [backup-simplify]: Simplify 1.0 into 1.0 6.353 * [taylor]: Taking taylor expansion of (log 2.0) in n 6.353 * [taylor]: Taking taylor expansion of 2.0 in n 6.353 * [backup-simplify]: Simplify 2.0 into 2.0 6.354 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 6.354 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 6.355 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 6.355 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 6.356 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 6.356 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 6.356 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 6.356 * [taylor]: Taking taylor expansion of 1.0 in n 6.356 * [backup-simplify]: Simplify 1.0 into 1.0 6.356 * [taylor]: Taking taylor expansion of (log n) in n 6.356 * [taylor]: Taking taylor expansion of n in n 6.356 * [backup-simplify]: Simplify 0 into 0 6.356 * [backup-simplify]: Simplify 1 into 1 6.356 * [backup-simplify]: Simplify (log 1) into 0 6.356 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.356 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 6.356 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 6.356 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 6.356 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 6.356 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 6.356 * [taylor]: Taking taylor expansion of 1.0 in n 6.356 * [backup-simplify]: Simplify 1.0 into 1.0 6.356 * [taylor]: Taking taylor expansion of (log PI) in n 6.356 * [taylor]: Taking taylor expansion of PI in n 6.356 * [backup-simplify]: Simplify PI into PI 6.357 * [backup-simplify]: Simplify (log PI) into (log PI) 6.357 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 6.358 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 6.359 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 6.360 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 6.360 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 6.361 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 6.363 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 6.363 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))) in n 6.363 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))))) in n 6.363 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) in n 6.363 * [taylor]: Taking taylor expansion of +nan.0 in n 6.363 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.363 * [taylor]: Taking taylor expansion of (* (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 6.363 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (sqrt 1.0) 2)) in n 6.363 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.363 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.363 * [taylor]: Taking taylor expansion of 2.0 in n 6.363 * [backup-simplify]: Simplify 2.0 into 2.0 6.363 * [taylor]: Taking taylor expansion of (* n PI) in n 6.363 * [taylor]: Taking taylor expansion of n in n 6.363 * [backup-simplify]: Simplify 0 into 0 6.363 * [backup-simplify]: Simplify 1 into 1 6.363 * [taylor]: Taking taylor expansion of PI in n 6.363 * [backup-simplify]: Simplify PI into PI 6.364 * [backup-simplify]: Simplify (* 0 PI) into 0 6.364 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.366 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.368 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.369 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.369 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.369 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.369 * [taylor]: Taking taylor expansion of 1.0 in n 6.369 * [backup-simplify]: Simplify 1.0 into 1.0 6.369 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.370 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.370 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 6.370 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 6.370 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 6.370 * [taylor]: Taking taylor expansion of 0.5 in n 6.370 * [backup-simplify]: Simplify 0.5 into 0.5 6.370 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 6.370 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 6.370 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 6.370 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 6.370 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 6.370 * [taylor]: Taking taylor expansion of 1.0 in n 6.370 * [backup-simplify]: Simplify 1.0 into 1.0 6.371 * [taylor]: Taking taylor expansion of (log 2.0) in n 6.371 * [taylor]: Taking taylor expansion of 2.0 in n 6.371 * [backup-simplify]: Simplify 2.0 into 2.0 6.371 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 6.372 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 6.374 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 6.374 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 6.374 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 6.374 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 6.374 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 6.374 * [taylor]: Taking taylor expansion of 1.0 in n 6.374 * [backup-simplify]: Simplify 1.0 into 1.0 6.374 * [taylor]: Taking taylor expansion of (log n) in n 6.374 * [taylor]: Taking taylor expansion of n in n 6.374 * [backup-simplify]: Simplify 0 into 0 6.374 * [backup-simplify]: Simplify 1 into 1 6.374 * [backup-simplify]: Simplify (log 1) into 0 6.375 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.375 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 6.375 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 6.375 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 6.375 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 6.375 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 6.375 * [taylor]: Taking taylor expansion of 1.0 in n 6.375 * [backup-simplify]: Simplify 1.0 into 1.0 6.375 * [taylor]: Taking taylor expansion of (log PI) in n 6.375 * [taylor]: Taking taylor expansion of PI in n 6.375 * [backup-simplify]: Simplify PI into PI 6.376 * [backup-simplify]: Simplify (log PI) into (log PI) 6.377 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 6.378 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 6.379 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 6.381 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 6.382 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 6.383 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 6.385 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 6.385 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) in n 6.385 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) in n 6.385 * [taylor]: Taking taylor expansion of +nan.0 in n 6.385 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.385 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)) in n 6.385 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 6.385 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 6.385 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 6.385 * [taylor]: Taking taylor expansion of 0.5 in n 6.385 * [backup-simplify]: Simplify 0.5 into 0.5 6.385 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 6.385 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 6.385 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 6.385 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 6.385 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 6.385 * [taylor]: Taking taylor expansion of 1.0 in n 6.386 * [backup-simplify]: Simplify 1.0 into 1.0 6.386 * [taylor]: Taking taylor expansion of (log 2.0) in n 6.386 * [taylor]: Taking taylor expansion of 2.0 in n 6.386 * [backup-simplify]: Simplify 2.0 into 2.0 6.386 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 6.387 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 6.389 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 6.389 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 6.389 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 6.389 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 6.389 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 6.389 * [taylor]: Taking taylor expansion of 1.0 in n 6.389 * [backup-simplify]: Simplify 1.0 into 1.0 6.389 * [taylor]: Taking taylor expansion of (log n) in n 6.389 * [taylor]: Taking taylor expansion of n in n 6.389 * [backup-simplify]: Simplify 0 into 0 6.389 * [backup-simplify]: Simplify 1 into 1 6.389 * [backup-simplify]: Simplify (log 1) into 0 6.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 6.390 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 6.390 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 6.390 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 6.390 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 6.390 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 6.390 * [taylor]: Taking taylor expansion of 1.0 in n 6.390 * [backup-simplify]: Simplify 1.0 into 1.0 6.390 * [taylor]: Taking taylor expansion of (log PI) in n 6.390 * [taylor]: Taking taylor expansion of PI in n 6.391 * [backup-simplify]: Simplify PI into PI 6.391 * [backup-simplify]: Simplify (log PI) into (log PI) 6.392 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 6.394 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 6.395 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 6.396 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 6.397 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 6.398 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 6.400 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 6.400 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.400 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.400 * [taylor]: Taking taylor expansion of 1.0 in n 6.400 * [backup-simplify]: Simplify 1.0 into 1.0 6.400 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.401 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.403 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.404 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.406 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 6.408 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.410 * [backup-simplify]: Simplify (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) 6.414 * [backup-simplify]: Simplify (* (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 6.424 * [backup-simplify]: Simplify (* +nan.0 (* (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 6.425 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.426 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.427 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) 6.429 * [backup-simplify]: Simplify (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 6.431 * [backup-simplify]: Simplify (* +nan.0 (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 6.432 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.434 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (sqrt 1.0) 2)) into (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)) 6.436 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) 6.437 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))) 6.441 * [backup-simplify]: Simplify (+ (* +nan.0 (* (* (+ (log (* 2.0 PI)) (log n)) (pow (sqrt 1.0) 2)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))))))) 6.448 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))))))))) into (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))))))))) 6.459 * [backup-simplify]: Simplify (+ (* +nan.0 (* (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (log n) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (* (log n) (pow (sqrt 1.0) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) 6.489 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (log n) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (* (log n) (pow (sqrt 1.0) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2)))) (- (+ (* +nan.0 (* (* (pow (log n) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (* (log n) (pow (sqrt 1.0) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))))))))))))))) 6.508 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2)))) (- (+ (* +nan.0 (* (* (pow (log n) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (* (log n) (pow (sqrt 1.0) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (log n) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (* (log n) (pow (sqrt 1.0) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) 6.555 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (log n) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (* (log n) (pow (sqrt 1.0) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2))) (- (+ (* +nan.0 (* (* (log n) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (sqrt 1.0) 2)))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (pow (sqrt 1.0) 2) (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (sqrt 1.0) 2) (* (pow k 2) (* (log (* 2.0 PI)) (log n)))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (pow (sqrt 1.0) 2) (pow (log n) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (* (pow (sqrt 1.0) 2) (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))))))))))))))))))) 6.557 * [backup-simplify]: Simplify (* (sqrt (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)))) (sqrt (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))))) into (* (sqrt k) (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 6.557 * [approximate]: Taking taylor expansion of (* (sqrt k) (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 6.557 * [taylor]: Taking taylor expansion of (* (sqrt k) (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 6.557 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.557 * [taylor]: Taking taylor expansion of k in n 6.557 * [backup-simplify]: Simplify k into k 6.558 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.558 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.558 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.558 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.558 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.558 * [taylor]: Taking taylor expansion of 1.0 in n 6.558 * [backup-simplify]: Simplify 1.0 into 1.0 6.558 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.559 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.559 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.559 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.559 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.559 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.559 * [taylor]: Taking taylor expansion of 0.5 in n 6.559 * [backup-simplify]: Simplify 0.5 into 0.5 6.559 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.559 * [taylor]: Taking taylor expansion of 1.0 in n 6.559 * [backup-simplify]: Simplify 1.0 into 1.0 6.559 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.559 * [taylor]: Taking taylor expansion of k in n 6.559 * [backup-simplify]: Simplify k into k 6.559 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.559 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.559 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.559 * [taylor]: Taking taylor expansion of 2.0 in n 6.559 * [backup-simplify]: Simplify 2.0 into 2.0 6.559 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.559 * [taylor]: Taking taylor expansion of PI in n 6.559 * [backup-simplify]: Simplify PI into PI 6.559 * [taylor]: Taking taylor expansion of n in n 6.559 * [backup-simplify]: Simplify 0 into 0 6.559 * [backup-simplify]: Simplify 1 into 1 6.559 * [backup-simplify]: Simplify (/ PI 1) into PI 6.560 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.560 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.560 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.561 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.561 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.562 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.563 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.563 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.563 * [taylor]: Taking taylor expansion of (* (sqrt k) (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 6.563 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.563 * [taylor]: Taking taylor expansion of k in k 6.563 * [backup-simplify]: Simplify 0 into 0 6.564 * [backup-simplify]: Simplify 1 into 1 6.564 * [backup-simplify]: Simplify (sqrt 0) into 0 6.565 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.565 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 6.565 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 6.565 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 6.565 * [taylor]: Taking taylor expansion of 1.0 in k 6.565 * [backup-simplify]: Simplify 1.0 into 1.0 6.565 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.566 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.566 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.566 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.566 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.566 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.566 * [taylor]: Taking taylor expansion of 0.5 in k 6.566 * [backup-simplify]: Simplify 0.5 into 0.5 6.566 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.566 * [taylor]: Taking taylor expansion of 1.0 in k 6.566 * [backup-simplify]: Simplify 1.0 into 1.0 6.566 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.566 * [taylor]: Taking taylor expansion of k in k 6.566 * [backup-simplify]: Simplify 0 into 0 6.566 * [backup-simplify]: Simplify 1 into 1 6.566 * [backup-simplify]: Simplify (/ 1 1) into 1 6.566 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.566 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.566 * [taylor]: Taking taylor expansion of 2.0 in k 6.566 * [backup-simplify]: Simplify 2.0 into 2.0 6.566 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.566 * [taylor]: Taking taylor expansion of PI in k 6.566 * [backup-simplify]: Simplify PI into PI 6.566 * [taylor]: Taking taylor expansion of n in k 6.566 * [backup-simplify]: Simplify n into n 6.566 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.566 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.566 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.567 * [backup-simplify]: Simplify (- 1) into -1 6.567 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.567 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.567 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.567 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.568 * [taylor]: Taking taylor expansion of (* (sqrt k) (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 6.568 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.568 * [taylor]: Taking taylor expansion of k in k 6.568 * [backup-simplify]: Simplify 0 into 0 6.568 * [backup-simplify]: Simplify 1 into 1 6.568 * [backup-simplify]: Simplify (sqrt 0) into 0 6.569 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.569 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 6.569 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 6.569 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 6.569 * [taylor]: Taking taylor expansion of 1.0 in k 6.569 * [backup-simplify]: Simplify 1.0 into 1.0 6.569 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.570 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.570 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.570 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.570 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.570 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.570 * [taylor]: Taking taylor expansion of 0.5 in k 6.570 * [backup-simplify]: Simplify 0.5 into 0.5 6.570 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.570 * [taylor]: Taking taylor expansion of 1.0 in k 6.570 * [backup-simplify]: Simplify 1.0 into 1.0 6.570 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.570 * [taylor]: Taking taylor expansion of k in k 6.570 * [backup-simplify]: Simplify 0 into 0 6.570 * [backup-simplify]: Simplify 1 into 1 6.570 * [backup-simplify]: Simplify (/ 1 1) into 1 6.570 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.570 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.570 * [taylor]: Taking taylor expansion of 2.0 in k 6.570 * [backup-simplify]: Simplify 2.0 into 2.0 6.570 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.570 * [taylor]: Taking taylor expansion of PI in k 6.570 * [backup-simplify]: Simplify PI into PI 6.570 * [taylor]: Taking taylor expansion of n in k 6.570 * [backup-simplify]: Simplify n into n 6.570 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.570 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.570 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.571 * [backup-simplify]: Simplify (- 1) into -1 6.571 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.571 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.571 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.572 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.572 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.573 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) 6.574 * [backup-simplify]: Simplify (* 0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into 0 6.574 * [taylor]: Taking taylor expansion of 0 in n 6.574 * [backup-simplify]: Simplify 0 into 0 6.574 * [backup-simplify]: Simplify 0 into 0 6.575 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 6.576 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into 0 6.578 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) 6.578 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n 6.578 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 6.578 * [taylor]: Taking taylor expansion of +nan.0 in n 6.578 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.578 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 6.578 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.578 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.579 * [taylor]: Taking taylor expansion of 1.0 in n 6.579 * [backup-simplify]: Simplify 1.0 into 1.0 6.579 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.580 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.580 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 6.580 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 6.580 * [taylor]: Taking taylor expansion of 0.5 in n 6.580 * [backup-simplify]: Simplify 0.5 into 0.5 6.580 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 6.580 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.580 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.580 * [taylor]: Taking taylor expansion of 2.0 in n 6.580 * [backup-simplify]: Simplify 2.0 into 2.0 6.580 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.580 * [taylor]: Taking taylor expansion of PI in n 6.580 * [backup-simplify]: Simplify PI into PI 6.580 * [taylor]: Taking taylor expansion of n in n 6.580 * [backup-simplify]: Simplify 0 into 0 6.580 * [backup-simplify]: Simplify 1 into 1 6.581 * [backup-simplify]: Simplify (/ PI 1) into PI 6.581 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.582 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.582 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.582 * [taylor]: Taking taylor expansion of 1.0 in n 6.583 * [backup-simplify]: Simplify 1.0 into 1.0 6.583 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.583 * [taylor]: Taking taylor expansion of k in n 6.583 * [backup-simplify]: Simplify k into k 6.583 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.584 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.584 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.586 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 6.587 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.588 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.589 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.592 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 6.594 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.597 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 6.599 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 6.599 * [backup-simplify]: Simplify 0 into 0 6.600 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 6.601 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 6.603 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into 0 6.606 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.608 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) 6.609 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n 6.609 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 6.609 * [taylor]: Taking taylor expansion of +nan.0 in n 6.609 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.609 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 6.609 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.609 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.609 * [taylor]: Taking taylor expansion of 1.0 in n 6.609 * [backup-simplify]: Simplify 1.0 into 1.0 6.609 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.610 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.610 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 6.610 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 6.610 * [taylor]: Taking taylor expansion of 0.5 in n 6.610 * [backup-simplify]: Simplify 0.5 into 0.5 6.610 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 6.610 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.610 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.610 * [taylor]: Taking taylor expansion of 2.0 in n 6.610 * [backup-simplify]: Simplify 2.0 into 2.0 6.610 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.610 * [taylor]: Taking taylor expansion of PI in n 6.611 * [backup-simplify]: Simplify PI into PI 6.611 * [taylor]: Taking taylor expansion of n in n 6.611 * [backup-simplify]: Simplify 0 into 0 6.611 * [backup-simplify]: Simplify 1 into 1 6.611 * [backup-simplify]: Simplify (/ PI 1) into PI 6.612 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.613 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.613 * [taylor]: Taking taylor expansion of 1.0 in n 6.613 * [backup-simplify]: Simplify 1.0 into 1.0 6.613 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.613 * [taylor]: Taking taylor expansion of k in n 6.613 * [backup-simplify]: Simplify k into k 6.613 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.615 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.615 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.616 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 6.618 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.619 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.620 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.623 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 6.625 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.628 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 6.630 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 6.632 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.632 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.632 * [backup-simplify]: Simplify (- 0) into 0 6.633 * [backup-simplify]: Simplify (+ 0 0) into 0 6.634 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.634 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.636 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.638 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.639 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 6.641 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.642 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 6.644 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 6.647 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.647 * [backup-simplify]: Simplify (- 0) into 0 6.647 * [backup-simplify]: Simplify 0 into 0 6.647 * [backup-simplify]: Simplify 0 into 0 6.649 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0 6.650 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0 6.652 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0 6.656 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.659 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) 6.659 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n 6.659 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 6.659 * [taylor]: Taking taylor expansion of +nan.0 in n 6.659 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.659 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 6.659 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.659 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.659 * [taylor]: Taking taylor expansion of 1.0 in n 6.659 * [backup-simplify]: Simplify 1.0 into 1.0 6.660 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.660 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.660 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 6.661 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 6.661 * [taylor]: Taking taylor expansion of 0.5 in n 6.661 * [backup-simplify]: Simplify 0.5 into 0.5 6.661 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 6.661 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.661 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.661 * [taylor]: Taking taylor expansion of 2.0 in n 6.661 * [backup-simplify]: Simplify 2.0 into 2.0 6.661 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.661 * [taylor]: Taking taylor expansion of PI in n 6.661 * [backup-simplify]: Simplify PI into PI 6.661 * [taylor]: Taking taylor expansion of n in n 6.661 * [backup-simplify]: Simplify 0 into 0 6.661 * [backup-simplify]: Simplify 1 into 1 6.662 * [backup-simplify]: Simplify (/ PI 1) into PI 6.662 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.663 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.663 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.663 * [taylor]: Taking taylor expansion of 1.0 in n 6.663 * [backup-simplify]: Simplify 1.0 into 1.0 6.663 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.664 * [taylor]: Taking taylor expansion of k in n 6.664 * [backup-simplify]: Simplify k into k 6.664 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.665 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.665 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.665 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.667 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 6.668 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.669 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.671 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.673 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 6.675 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.678 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 6.680 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) 6.697 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow (sqrt 1.0) 2)) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow (sqrt 1.0) 2)) (pow k 3)))))))) 6.699 * [backup-simplify]: Simplify (* (sqrt (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)))) (sqrt (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))))) into (/ (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) 6.699 * [approximate]: Taking taylor expansion of (/ (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in (k n) around 0 6.699 * [taylor]: Taking taylor expansion of (/ (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in n 6.699 * [taylor]: Taking taylor expansion of (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) in n 6.699 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.700 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.700 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.700 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.700 * [taylor]: Taking taylor expansion of 0.5 in n 6.700 * [backup-simplify]: Simplify 0.5 into 0.5 6.700 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.700 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.700 * [taylor]: Taking taylor expansion of k in n 6.700 * [backup-simplify]: Simplify k into k 6.700 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.700 * [taylor]: Taking taylor expansion of 1.0 in n 6.700 * [backup-simplify]: Simplify 1.0 into 1.0 6.700 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.700 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.700 * [taylor]: Taking taylor expansion of -2.0 in n 6.700 * [backup-simplify]: Simplify -2.0 into -2.0 6.700 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.700 * [taylor]: Taking taylor expansion of PI in n 6.700 * [backup-simplify]: Simplify PI into PI 6.700 * [taylor]: Taking taylor expansion of n in n 6.700 * [backup-simplify]: Simplify 0 into 0 6.700 * [backup-simplify]: Simplify 1 into 1 6.701 * [backup-simplify]: Simplify (/ PI 1) into PI 6.701 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.702 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.703 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.703 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.704 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.705 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.707 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.707 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.707 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.707 * [taylor]: Taking taylor expansion of 1.0 in n 6.707 * [backup-simplify]: Simplify 1.0 into 1.0 6.707 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.708 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.708 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 6.708 * [taylor]: Taking taylor expansion of (/ -1 k) in n 6.708 * [taylor]: Taking taylor expansion of -1 in n 6.708 * [backup-simplify]: Simplify -1 into -1 6.708 * [taylor]: Taking taylor expansion of k in n 6.708 * [backup-simplify]: Simplify k into k 6.708 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 6.708 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 6.709 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 6.709 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 6.710 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.713 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) 6.715 * [backup-simplify]: Simplify (/ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) into (/ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) 6.715 * [taylor]: Taking taylor expansion of (/ (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in k 6.715 * [taylor]: Taking taylor expansion of (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) in k 6.715 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.716 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.716 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.716 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.716 * [taylor]: Taking taylor expansion of 0.5 in k 6.716 * [backup-simplify]: Simplify 0.5 into 0.5 6.716 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.716 * [taylor]: Taking taylor expansion of k in k 6.716 * [backup-simplify]: Simplify 0 into 0 6.716 * [backup-simplify]: Simplify 1 into 1 6.716 * [backup-simplify]: Simplify (/ 1 1) into 1 6.716 * [taylor]: Taking taylor expansion of 1.0 in k 6.716 * [backup-simplify]: Simplify 1.0 into 1.0 6.716 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.716 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.716 * [taylor]: Taking taylor expansion of -2.0 in k 6.717 * [backup-simplify]: Simplify -2.0 into -2.0 6.717 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.717 * [taylor]: Taking taylor expansion of PI in k 6.717 * [backup-simplify]: Simplify PI into PI 6.717 * [taylor]: Taking taylor expansion of n in k 6.717 * [backup-simplify]: Simplify n into n 6.717 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.717 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.717 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.718 * [backup-simplify]: Simplify (+ 1 0) into 1 6.718 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.718 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.718 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.718 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 6.719 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 6.719 * [taylor]: Taking taylor expansion of 1.0 in k 6.719 * [backup-simplify]: Simplify 1.0 into 1.0 6.719 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.720 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.720 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.720 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.720 * [taylor]: Taking taylor expansion of -1 in k 6.720 * [backup-simplify]: Simplify -1 into -1 6.720 * [taylor]: Taking taylor expansion of k in k 6.720 * [backup-simplify]: Simplify 0 into 0 6.720 * [backup-simplify]: Simplify 1 into 1 6.721 * [backup-simplify]: Simplify (/ -1 1) into -1 6.721 * [backup-simplify]: Simplify (sqrt 0) into 0 6.722 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.724 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.725 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) 6.727 * [backup-simplify]: Simplify (/ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) +nan.0) into (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) 6.727 * [taylor]: Taking taylor expansion of (/ (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) (sqrt (/ -1 k))) in k 6.727 * [taylor]: Taking taylor expansion of (* (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (pow (sqrt 1.0) 2)) in k 6.727 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.727 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.727 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.727 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.727 * [taylor]: Taking taylor expansion of 0.5 in k 6.727 * [backup-simplify]: Simplify 0.5 into 0.5 6.727 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.727 * [taylor]: Taking taylor expansion of k in k 6.727 * [backup-simplify]: Simplify 0 into 0 6.727 * [backup-simplify]: Simplify 1 into 1 6.727 * [backup-simplify]: Simplify (/ 1 1) into 1 6.728 * [taylor]: Taking taylor expansion of 1.0 in k 6.728 * [backup-simplify]: Simplify 1.0 into 1.0 6.728 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.728 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.728 * [taylor]: Taking taylor expansion of -2.0 in k 6.728 * [backup-simplify]: Simplify -2.0 into -2.0 6.728 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.728 * [taylor]: Taking taylor expansion of PI in k 6.728 * [backup-simplify]: Simplify PI into PI 6.728 * [taylor]: Taking taylor expansion of n in k 6.728 * [backup-simplify]: Simplify n into n 6.728 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.728 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.728 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.729 * [backup-simplify]: Simplify (+ 1 0) into 1 6.729 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.729 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.730 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.730 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k 6.730 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k 6.730 * [taylor]: Taking taylor expansion of 1.0 in k 6.730 * [backup-simplify]: Simplify 1.0 into 1.0 6.730 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.731 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.731 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.731 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.731 * [taylor]: Taking taylor expansion of -1 in k 6.731 * [backup-simplify]: Simplify -1 into -1 6.731 * [taylor]: Taking taylor expansion of k in k 6.731 * [backup-simplify]: Simplify 0 into 0 6.731 * [backup-simplify]: Simplify 1 into 1 6.732 * [backup-simplify]: Simplify (/ -1 1) into -1 6.732 * [backup-simplify]: Simplify (sqrt 0) into 0 6.733 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.735 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.736 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) 6.737 * [backup-simplify]: Simplify (/ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) +nan.0) into (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) 6.737 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) in n 6.737 * [taylor]: Taking taylor expansion of +nan.0 in n 6.737 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.737 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) in n 6.738 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 6.738 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 6.738 * [taylor]: Taking taylor expansion of 0.5 in n 6.738 * [backup-simplify]: Simplify 0.5 into 0.5 6.738 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 6.738 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.738 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.738 * [taylor]: Taking taylor expansion of k in n 6.738 * [backup-simplify]: Simplify k into k 6.738 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.738 * [taylor]: Taking taylor expansion of 1.0 in n 6.738 * [backup-simplify]: Simplify 1.0 into 1.0 6.738 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.738 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.738 * [taylor]: Taking taylor expansion of -2.0 in n 6.738 * [backup-simplify]: Simplify -2.0 into -2.0 6.738 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.738 * [taylor]: Taking taylor expansion of PI in n 6.738 * [backup-simplify]: Simplify PI into PI 6.738 * [taylor]: Taking taylor expansion of n in n 6.738 * [backup-simplify]: Simplify 0 into 0 6.738 * [backup-simplify]: Simplify 1 into 1 6.739 * [backup-simplify]: Simplify (/ PI 1) into PI 6.739 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.740 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.740 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.742 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.743 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 6.745 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.746 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.746 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.746 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.746 * [taylor]: Taking taylor expansion of 1.0 in n 6.746 * [backup-simplify]: Simplify 1.0 into 1.0 6.747 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.747 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.749 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.751 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) 6.754 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) 6.757 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) 6.758 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 6.760 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0 6.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.765 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.768 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)))) 6.768 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)))) in n 6.768 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) in n 6.768 * [taylor]: Taking taylor expansion of +nan.0 in n 6.768 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.768 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) in n 6.768 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 6.768 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 6.768 * [taylor]: Taking taylor expansion of 0.5 in n 6.768 * [backup-simplify]: Simplify 0.5 into 0.5 6.768 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 6.768 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.768 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.768 * [taylor]: Taking taylor expansion of k in n 6.768 * [backup-simplify]: Simplify k into k 6.768 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.768 * [taylor]: Taking taylor expansion of 1.0 in n 6.768 * [backup-simplify]: Simplify 1.0 into 1.0 6.768 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.768 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.768 * [taylor]: Taking taylor expansion of -2.0 in n 6.769 * [backup-simplify]: Simplify -2.0 into -2.0 6.769 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.769 * [taylor]: Taking taylor expansion of PI in n 6.769 * [backup-simplify]: Simplify PI into PI 6.769 * [taylor]: Taking taylor expansion of n in n 6.769 * [backup-simplify]: Simplify 0 into 0 6.769 * [backup-simplify]: Simplify 1 into 1 6.769 * [backup-simplify]: Simplify (/ PI 1) into PI 6.770 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.771 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.771 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.773 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.774 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 6.775 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.777 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.777 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.777 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.777 * [taylor]: Taking taylor expansion of 1.0 in n 6.777 * [backup-simplify]: Simplify 1.0 into 1.0 6.777 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.778 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.779 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.782 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) 6.784 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) 6.787 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) 6.789 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) 6.790 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0 6.791 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.791 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.792 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.792 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.793 * [backup-simplify]: Simplify (+ 0 0) into 0 6.794 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.794 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.795 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 6.797 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.798 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0 6.800 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) into 0 6.800 * [backup-simplify]: Simplify 0 into 0 6.800 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0 6.801 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0 6.802 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2)))) into 0 6.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.805 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.808 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)))) 6.808 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)))) in n 6.808 * [taylor]: Taking taylor expansion of (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2))) in n 6.808 * [taylor]: Taking taylor expansion of +nan.0 in n 6.808 * [backup-simplify]: Simplify +nan.0 into +nan.0 6.808 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) (pow (sqrt 1.0) 2)) in n 6.808 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 6.808 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 6.808 * [taylor]: Taking taylor expansion of 0.5 in n 6.808 * [backup-simplify]: Simplify 0.5 into 0.5 6.808 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 6.808 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.808 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.808 * [taylor]: Taking taylor expansion of k in n 6.808 * [backup-simplify]: Simplify k into k 6.808 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.808 * [taylor]: Taking taylor expansion of 1.0 in n 6.808 * [backup-simplify]: Simplify 1.0 into 1.0 6.808 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.808 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.808 * [taylor]: Taking taylor expansion of -2.0 in n 6.808 * [backup-simplify]: Simplify -2.0 into -2.0 6.808 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.808 * [taylor]: Taking taylor expansion of PI in n 6.808 * [backup-simplify]: Simplify PI into PI 6.808 * [taylor]: Taking taylor expansion of n in n 6.808 * [backup-simplify]: Simplify 0 into 0 6.808 * [backup-simplify]: Simplify 1 into 1 6.808 * [backup-simplify]: Simplify (/ PI 1) into PI 6.809 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.809 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.810 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.811 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.811 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 6.812 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.813 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.813 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n 6.813 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n 6.813 * [taylor]: Taking taylor expansion of 1.0 in n 6.814 * [backup-simplify]: Simplify 1.0 into 1.0 6.814 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0) 6.814 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0 6.815 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2) 6.817 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) 6.818 * [backup-simplify]: Simplify (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) into (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2))) 6.820 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) 6.821 * [backup-simplify]: Simplify (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) into (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)))) 6.830 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) (pow (sqrt 1.0) 2)))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) (pow (sqrt 1.0) 2)))) (* 1 (/ 1 (- k)))) (* +nan.0 (* (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (pow k 2)))))))) 6.830 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 2 1) 6.831 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.831 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.831 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.831 * [taylor]: Taking taylor expansion of 2.0 in n 6.831 * [backup-simplify]: Simplify 2.0 into 2.0 6.831 * [taylor]: Taking taylor expansion of (* n PI) in n 6.831 * [taylor]: Taking taylor expansion of n in n 6.831 * [backup-simplify]: Simplify 0 into 0 6.831 * [backup-simplify]: Simplify 1 into 1 6.831 * [taylor]: Taking taylor expansion of PI in n 6.831 * [backup-simplify]: Simplify PI into PI 6.831 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.831 * [taylor]: Taking taylor expansion of 2.0 in n 6.831 * [backup-simplify]: Simplify 2.0 into 2.0 6.831 * [taylor]: Taking taylor expansion of (* n PI) in n 6.831 * [taylor]: Taking taylor expansion of n in n 6.831 * [backup-simplify]: Simplify 0 into 0 6.831 * [backup-simplify]: Simplify 1 into 1 6.831 * [taylor]: Taking taylor expansion of PI in n 6.831 * [backup-simplify]: Simplify PI into PI 6.832 * [backup-simplify]: Simplify (* 0 PI) into 0 6.832 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.832 * [backup-simplify]: Simplify 0 into 0 6.834 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.835 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.836 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.837 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.838 * [backup-simplify]: Simplify 0 into 0 6.845 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.846 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.846 * [backup-simplify]: Simplify 0 into 0 6.847 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.847 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.848 * [backup-simplify]: Simplify 0 into 0 6.848 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.849 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.849 * [backup-simplify]: Simplify 0 into 0 6.850 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.852 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.852 * [backup-simplify]: Simplify 0 into 0 6.853 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.854 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.854 * [backup-simplify]: Simplify 0 into 0 6.854 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.855 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.855 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.855 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.855 * [taylor]: Taking taylor expansion of 2.0 in n 6.855 * [backup-simplify]: Simplify 2.0 into 2.0 6.855 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.855 * [taylor]: Taking taylor expansion of PI in n 6.855 * [backup-simplify]: Simplify PI into PI 6.855 * [taylor]: Taking taylor expansion of n in n 6.855 * [backup-simplify]: Simplify 0 into 0 6.855 * [backup-simplify]: Simplify 1 into 1 6.855 * [backup-simplify]: Simplify (/ PI 1) into PI 6.855 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.855 * [taylor]: Taking taylor expansion of 2.0 in n 6.855 * [backup-simplify]: Simplify 2.0 into 2.0 6.855 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.855 * [taylor]: Taking taylor expansion of PI in n 6.856 * [backup-simplify]: Simplify PI into PI 6.856 * [taylor]: Taking taylor expansion of n in n 6.856 * [backup-simplify]: Simplify 0 into 0 6.856 * [backup-simplify]: Simplify 1 into 1 6.856 * [backup-simplify]: Simplify (/ PI 1) into PI 6.856 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.857 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.858 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.858 * [backup-simplify]: Simplify 0 into 0 6.858 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.859 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.859 * [backup-simplify]: Simplify 0 into 0 6.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.860 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.860 * [backup-simplify]: Simplify 0 into 0 6.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.862 * [backup-simplify]: Simplify 0 into 0 6.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.864 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.864 * [backup-simplify]: Simplify 0 into 0 6.864 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.865 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.865 * [backup-simplify]: Simplify 0 into 0 6.866 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.866 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.866 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.866 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.866 * [taylor]: Taking taylor expansion of -2.0 in n 6.866 * [backup-simplify]: Simplify -2.0 into -2.0 6.866 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.866 * [taylor]: Taking taylor expansion of PI in n 6.866 * [backup-simplify]: Simplify PI into PI 6.866 * [taylor]: Taking taylor expansion of n in n 6.866 * [backup-simplify]: Simplify 0 into 0 6.866 * [backup-simplify]: Simplify 1 into 1 6.867 * [backup-simplify]: Simplify (/ PI 1) into PI 6.867 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.867 * [taylor]: Taking taylor expansion of -2.0 in n 6.867 * [backup-simplify]: Simplify -2.0 into -2.0 6.867 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.867 * [taylor]: Taking taylor expansion of PI in n 6.867 * [backup-simplify]: Simplify PI into PI 6.867 * [taylor]: Taking taylor expansion of n in n 6.867 * [backup-simplify]: Simplify 0 into 0 6.867 * [backup-simplify]: Simplify 1 into 1 6.867 * [backup-simplify]: Simplify (/ PI 1) into PI 6.867 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.868 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.868 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.869 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.869 * [backup-simplify]: Simplify 0 into 0 6.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.870 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.870 * [backup-simplify]: Simplify 0 into 0 6.871 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.871 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.871 * [backup-simplify]: Simplify 0 into 0 6.872 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.873 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.873 * [backup-simplify]: Simplify 0 into 0 6.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.874 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.874 * [backup-simplify]: Simplify 0 into 0 6.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.876 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.876 * [backup-simplify]: Simplify 0 into 0 6.877 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.877 * * * [progress]: simplifying candidates 6.880 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (+ 1/2 1/2) (+ 1/2 (/ 1 2)) (+ 1 1) (+ (/ 1 2) 1/2) (+ (/ 1 2) (/ 1 2)) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ 1 1) (+ (log (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (log (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (log (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (exp (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (* (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (cbrt (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (cbrt (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))) (cbrt (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (* (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))) (sqrt (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))) (sqrt (pow (* (* 2.0 PI) n) (/ k 2.0)))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))) (sqrt (sqrt k))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (pow (* (* 2.0 PI) n) (/ k 2.0))) (sqrt (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (pow (* (* 2.0 PI) n) (/ k 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ k 2.0)))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (pow (* (* 2.0 PI) n) (/ k 2.0))) (sqrt (sqrt k))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (sqrt k)) (sqrt (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ k 2.0)))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (sqrt k)) (sqrt (sqrt k))) (* (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))) (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* 1 1) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* 2 1/2) (* 2 1) (* 2 (/ 1 2)) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) 1) (* (cbrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (pow (sqrt 1.0) 2) (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow (sqrt 1.0) 2) (* (pow k 2) (* (log (* 2.0 PI)) (log n)))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (sqrt 1.0) 2))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (pow (sqrt 1.0) 2) (pow (log n) 2))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (* (log (* 2.0 PI)) (pow (sqrt 1.0) 2))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (* (pow (sqrt 1.0) 2) (log n))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (sqrt 1.0) 2)))))))))))))))))))))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow (sqrt 1.0) 2)) (pow k 2))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow (sqrt 1.0) 2)) (pow k 3)))))))) (- (+ (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) k)) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (* +nan.0 (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (pow k 2)))))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 6.881 * [simplify]: Sending expressions to egg_math: (* (+ (+ (log 2.0) (log h2)) (log h1)) (/ (- 1.0 h0) 2.0)) (* (+ (log (* 2.0 h2)) (log h1)) (/ (- 1.0 h0) 2.0)) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0)) (* (log (* (* 2.0 h2) h1)) (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (* 1 (/ (- 1.0 h0) 2.0)) (pow (* (* 2.0 h2) h1) (/ 1.0 2.0)) (pow (* (* 2.0 h2) h1) (/ h0 2.0)) (pow (* (* 2.0 h2) h1) (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0)))) (pow (* (* 2.0 h2) h1) (sqrt (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) 1)) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ 1 1)) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ 1 1)) (pow (* (* 2.0 h2) h1) 1) 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2.0)) (pow (* (* 2.0 h2) h1) (/ h0 2.0)) (pow (* (* 2.0 h2) h1) (* (cbrt (/ (- 1.0 h0) 2.0)) (cbrt (/ (- 1.0 h0) 2.0)))) (pow (* (* 2.0 h2) h1) (sqrt (/ (- 1.0 h0) 2.0))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (* (cbrt (- 1.0 h0)) (cbrt (- 1.0 h0))) 1)) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (sqrt (- 1.0 h0)) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ 1 1)) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) (sqrt 2.0))) (pow (* (* 2.0 h2) h1) (/ (+ (sqrt 1.0) (sqrt h0)) 1)) (pow (* (* 2.0 h2) h1) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 h2) h1) (/ 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(* h2 h2) h2)) (* (* h1 h1) h1)) (* (* (* (* 2.0 h2) (* 2.0 h2)) (* 2.0 h2)) (* (* h1 h1) h1)) (* (cbrt (* (* 2.0 h2) h1)) (cbrt (* (* 2.0 h2) h1))) (cbrt (* (* 2.0 h2) h1)) (* (* (* (* 2.0 h2) h1) (* (* 2.0 h2) h1)) (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (sqrt (* (* 2.0 h2) h1)) (* (* 2.0 h2) (* (cbrt h1) (cbrt h1))) (* (* 2.0 h2) (sqrt h1)) (* (* 2.0 h2) 1) (* h2 h1) (- (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (pow (log h1) 2)))) (+ (* (/ 1.0 4.0) (* (pow h0 2) (* (log (* 2.0 h2)) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1))))) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 2.0) (* h0 (* (log (* 2.0 h2)) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (* (/ 1.0 2.0) (* h0 (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1)))))) (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (- (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 8.0) (* (pow h0 2) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (pow (log h1) 2)))) (+ (* (/ 1.0 4.0) (* (pow h0 2) (* (log (* 2.0 h2)) (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1))))) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (+ (* (/ 1.0 2.0) (* h0 (* (log (* 2.0 h2)) (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1))))))) (* (/ 1.0 2.0) (* h0 (* (exp (* (/ 1.0 2.0) (+ (log (* 2.0 h2)) (log h1)))) (log h1)))))) (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))) (- (+ (* h3 (* (* (pow h0 2) (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (* (pow (sqrt 1.0) 2) (log h1))) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow (sqrt 1.0) 2) (* (pow h0 2) (* (log (* 2.0 h2)) (log h1)))) (pow (* (pow h2 1.0) (* (pow h1 1.0) (pow 2.0 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (* (pow (log (* 2.0 h2)) 2) (pow (sqrt 1.0) 2))) (pow (* (pow h2 1.0) (* (pow h1 1.0) (pow 2.0 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (* (pow (sqrt 1.0) 2) (pow (log h1) 2))) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* h0 (pow (sqrt 1.0) 2)) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* (pow h0 2) (* (log (* 2.0 h2)) (pow (sqrt 1.0) 2))) (pow (* (pow h2 1.0) (* (pow h1 1.0) (pow 2.0 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* h0 (* (log (* 2.0 h2)) (pow (sqrt 1.0) 2))) (pow (* (pow h2 1.0) (* (pow h1 1.0) (pow 2.0 1.0))) (/ 1.0 2.0)))) (- (+ (* h3 (* (* h0 (* (pow (sqrt 1.0) 2) (log h1))) (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)))) (- (* h3 (* (pow (* (pow 2.0 1.0) (* (pow h1 1.0) (pow h2 1.0))) (/ 1.0 2.0)) (pow (sqrt 1.0) 2)))))))))))))))))))))) (- (+ (* h3 (/ (* (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (pow (sqrt 1.0) 2)) (pow h0 2))) (- (+ (* h3 (/ (* (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (pow (sqrt 1.0) 2)) h0)) (- (* h3 (/ (* (exp (* (/ 1.0 2.0) (* (- (log (* 2.0 h2)) (log (/ 1 h1))) (- 1.0 h0)))) (pow (sqrt 1.0) 2)) (pow h0 3)))))))) (- (+ (* h3 (/ (* (pow (sqrt 1.0) 2) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1))))))) h0)) (- (+ (* h3 (* (pow (sqrt 1.0) 2) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1)))))))) (- (* h3 (/ (* (pow (sqrt 1.0) 2) (exp (* (/ 1.0 2.0) (* (- 1.0 h0) (- (log (* -2.0 h2)) (log (/ -1 h1))))))) (pow h0 2)))))))) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) (* 2.0 (* h1 h2)) 6.990 * * * [progress]: adding candidates to table 7.672 * [progress]: [Phase 3 of 3] Extracting. 7.672 * * [regime]: Finding splitpoints for: (# # # # # # # #) 7.677 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2.0 PI) n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) n k) 7.677 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 7.728 * * * * [regimes]: Trying to branch on (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) from (# # # # # # # #) 7.796 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 7.846 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 7.889 * * * [regime]: Found split indices: #