124.678 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.204 * * * [progress]: [2/2] Setting up program.
0.212 * [progress]: [Phase 2 of 3] Improving.
0.213 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.213 * * [simplify]: iteration 0: 13 enodes
0.220 * * [simplify]: iteration 1: 29 enodes
0.235 * * [simplify]: iteration 2: 58 enodes
0.265 * * [simplify]: iteration 3: 114 enodes
0.344 * * [simplify]: iteration 4: 285 enodes
0.565 * * [simplify]: iteration 5: 819 enodes
2.349 * * [simplify]: iteration 6: 2725 enodes
4.368 * * [simplify]: iteration complete: 5002 enodes
4.368 * * [simplify]: Extracting #0: cost 1 inf + 0
4.369 * * [simplify]: Extracting #1: cost 107 inf + 0
4.373 * * [simplify]: Extracting #2: cost 441 inf + 1
4.386 * * [simplify]: Extracting #3: cost 1037 inf + 92
4.401 * * [simplify]: Extracting #4: cost 1334 inf + 12205
4.441 * * [simplify]: Extracting #5: cost 655 inf + 86066
4.566 * * [simplify]: Extracting #6: cost 190 inf + 381239
4.762 * * [simplify]: Extracting #7: cost 0 inf + 587702
4.947 * * [simplify]: Extracting #8: cost 0 inf + 570924
5.136 * [simplify]: Simplified to:
  (/ (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
5.137 * * [progress]: iteration 1 / 4
5.137 * * * [progress]: picking best candidate
5.146 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
5.146 * * * [progress]: localizing error
5.194 * * * [progress]: generating rewritten candidates
5.195 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
5.248 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
5.284 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
5.297 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.394 * * * [progress]: generating series expansions
5.394 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
5.395 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
5.395 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
5.396 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
5.396 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
5.396 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
5.396 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
5.396 * [taylor]: Taking taylor expansion of 0.5 in k
5.396 * [backup-simplify]: Simplify 0.5 into 0.5
5.396 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.396 * [taylor]: Taking taylor expansion of 1.0 in k
5.396 * [backup-simplify]: Simplify 1.0 into 1.0
5.396 * [taylor]: Taking taylor expansion of k in k
5.396 * [backup-simplify]: Simplify 0 into 0
5.396 * [backup-simplify]: Simplify 1 into 1
5.396 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
5.396 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
5.396 * [taylor]: Taking taylor expansion of 2.0 in k
5.396 * [backup-simplify]: Simplify 2.0 into 2.0
5.396 * [taylor]: Taking taylor expansion of (* n PI) in k
5.396 * [taylor]: Taking taylor expansion of n in k
5.396 * [backup-simplify]: Simplify n into n
5.396 * [taylor]: Taking taylor expansion of PI in k
5.396 * [backup-simplify]: Simplify PI into PI
5.396 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.396 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
5.397 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
5.397 * [backup-simplify]: Simplify (- 0) into 0
5.398 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.398 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
5.398 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
5.399 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
5.399 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.399 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.399 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.399 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.399 * [taylor]: Taking taylor expansion of 0.5 in n
5.399 * [backup-simplify]: Simplify 0.5 into 0.5
5.399 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.399 * [taylor]: Taking taylor expansion of 1.0 in n
5.399 * [backup-simplify]: Simplify 1.0 into 1.0
5.399 * [taylor]: Taking taylor expansion of k in n
5.399 * [backup-simplify]: Simplify k into k
5.399 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.399 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.399 * [taylor]: Taking taylor expansion of 2.0 in n
5.399 * [backup-simplify]: Simplify 2.0 into 2.0
5.399 * [taylor]: Taking taylor expansion of (* n PI) in n
5.399 * [taylor]: Taking taylor expansion of n in n
5.399 * [backup-simplify]: Simplify 0 into 0
5.399 * [backup-simplify]: Simplify 1 into 1
5.399 * [taylor]: Taking taylor expansion of PI in n
5.399 * [backup-simplify]: Simplify PI into PI
5.400 * [backup-simplify]: Simplify (* 0 PI) into 0
5.400 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.402 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.404 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.406 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.406 * [backup-simplify]: Simplify (- k) into (- k)
5.406 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.406 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.408 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.409 * [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))))
5.410 * [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)))))
5.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.411 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.411 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.411 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.411 * [taylor]: Taking taylor expansion of 0.5 in n
5.411 * [backup-simplify]: Simplify 0.5 into 0.5
5.411 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.411 * [taylor]: Taking taylor expansion of 1.0 in n
5.411 * [backup-simplify]: Simplify 1.0 into 1.0
5.411 * [taylor]: Taking taylor expansion of k in n
5.411 * [backup-simplify]: Simplify k into k
5.411 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.411 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.411 * [taylor]: Taking taylor expansion of 2.0 in n
5.411 * [backup-simplify]: Simplify 2.0 into 2.0
5.411 * [taylor]: Taking taylor expansion of (* n PI) in n
5.411 * [taylor]: Taking taylor expansion of n in n
5.411 * [backup-simplify]: Simplify 0 into 0
5.411 * [backup-simplify]: Simplify 1 into 1
5.411 * [taylor]: Taking taylor expansion of PI in n
5.411 * [backup-simplify]: Simplify PI into PI
5.412 * [backup-simplify]: Simplify (* 0 PI) into 0
5.412 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.414 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.416 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.417 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.417 * [backup-simplify]: Simplify (- k) into (- k)
5.417 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.417 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.419 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.420 * [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))))
5.422 * [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)))))
5.422 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
5.422 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
5.422 * [taylor]: Taking taylor expansion of 0.5 in k
5.422 * [backup-simplify]: Simplify 0.5 into 0.5
5.422 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
5.422 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.422 * [taylor]: Taking taylor expansion of 1.0 in k
5.422 * [backup-simplify]: Simplify 1.0 into 1.0
5.422 * [taylor]: Taking taylor expansion of k in k
5.422 * [backup-simplify]: Simplify 0 into 0
5.422 * [backup-simplify]: Simplify 1 into 1
5.422 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
5.422 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
5.422 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
5.423 * [taylor]: Taking taylor expansion of 2.0 in k
5.423 * [backup-simplify]: Simplify 2.0 into 2.0
5.423 * [taylor]: Taking taylor expansion of PI in k
5.423 * [backup-simplify]: Simplify PI into PI
5.423 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.424 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.424 * [taylor]: Taking taylor expansion of (log n) in k
5.424 * [taylor]: Taking taylor expansion of n in k
5.424 * [backup-simplify]: Simplify n into n
5.425 * [backup-simplify]: Simplify (log n) into (log n)
5.425 * [backup-simplify]: Simplify (- 0) into 0
5.426 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.427 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
5.428 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
5.429 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
5.431 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
5.432 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
5.433 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.434 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
5.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.438 * [backup-simplify]: Simplify (- 0) into 0
5.438 * [backup-simplify]: Simplify (+ 0 0) into 0
5.439 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
5.440 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.442 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
5.444 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.444 * [taylor]: Taking taylor expansion of 0 in k
5.444 * [backup-simplify]: Simplify 0 into 0
5.444 * [backup-simplify]: Simplify 0 into 0
5.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.447 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.448 * [backup-simplify]: Simplify (+ 0 0) into 0
5.449 * [backup-simplify]: Simplify (- 1) into -1
5.449 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.451 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
5.453 * [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))))
5.457 * [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))))))
5.461 * [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))))))
5.463 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.468 * [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
5.469 * [backup-simplify]: Simplify (- 0) into 0
5.469 * [backup-simplify]: Simplify (+ 0 0) into 0
5.470 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
5.472 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.473 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
5.476 * [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
5.476 * [taylor]: Taking taylor expansion of 0 in k
5.476 * [backup-simplify]: Simplify 0 into 0
5.476 * [backup-simplify]: Simplify 0 into 0
5.476 * [backup-simplify]: Simplify 0 into 0
5.477 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.480 * [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
5.482 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.482 * [backup-simplify]: Simplify (+ 0 0) into 0
5.483 * [backup-simplify]: Simplify (- 0) into 0
5.483 * [backup-simplify]: Simplify (+ 0 0) into 0
5.485 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
5.488 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
5.502 * [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))))))
5.508 * [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))))))
5.521 * [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))))))
5.522 * [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))))
5.522 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
5.522 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
5.522 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
5.522 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
5.522 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
5.522 * [taylor]: Taking taylor expansion of 0.5 in k
5.522 * [backup-simplify]: Simplify 0.5 into 0.5
5.522 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.522 * [taylor]: Taking taylor expansion of 1.0 in k
5.522 * [backup-simplify]: Simplify 1.0 into 1.0
5.522 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.522 * [taylor]: Taking taylor expansion of k in k
5.522 * [backup-simplify]: Simplify 0 into 0
5.522 * [backup-simplify]: Simplify 1 into 1
5.523 * [backup-simplify]: Simplify (/ 1 1) into 1
5.523 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
5.523 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
5.523 * [taylor]: Taking taylor expansion of 2.0 in k
5.523 * [backup-simplify]: Simplify 2.0 into 2.0
5.523 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.523 * [taylor]: Taking taylor expansion of PI in k
5.523 * [backup-simplify]: Simplify PI into PI
5.523 * [taylor]: Taking taylor expansion of n in k
5.523 * [backup-simplify]: Simplify n into n
5.523 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.523 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
5.523 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
5.524 * [backup-simplify]: Simplify (- 1) into -1
5.524 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.525 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
5.525 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
5.525 * [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)))))
5.525 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.525 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.525 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.525 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.525 * [taylor]: Taking taylor expansion of 0.5 in n
5.525 * [backup-simplify]: Simplify 0.5 into 0.5
5.526 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.526 * [taylor]: Taking taylor expansion of 1.0 in n
5.526 * [backup-simplify]: Simplify 1.0 into 1.0
5.526 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.526 * [taylor]: Taking taylor expansion of k in n
5.526 * [backup-simplify]: Simplify k into k
5.526 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.526 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.526 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.526 * [taylor]: Taking taylor expansion of 2.0 in n
5.526 * [backup-simplify]: Simplify 2.0 into 2.0
5.526 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.526 * [taylor]: Taking taylor expansion of PI in n
5.526 * [backup-simplify]: Simplify PI into PI
5.526 * [taylor]: Taking taylor expansion of n in n
5.526 * [backup-simplify]: Simplify 0 into 0
5.526 * [backup-simplify]: Simplify 1 into 1
5.527 * [backup-simplify]: Simplify (/ PI 1) into PI
5.527 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.528 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.529 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.529 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.529 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.532 * [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))))
5.533 * [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)))))
5.533 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.533 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.533 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.533 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.533 * [taylor]: Taking taylor expansion of 0.5 in n
5.533 * [backup-simplify]: Simplify 0.5 into 0.5
5.533 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.533 * [taylor]: Taking taylor expansion of 1.0 in n
5.534 * [backup-simplify]: Simplify 1.0 into 1.0
5.534 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.534 * [taylor]: Taking taylor expansion of k in n
5.534 * [backup-simplify]: Simplify k into k
5.534 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.534 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.534 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.534 * [taylor]: Taking taylor expansion of 2.0 in n
5.534 * [backup-simplify]: Simplify 2.0 into 2.0
5.534 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.534 * [taylor]: Taking taylor expansion of PI in n
5.534 * [backup-simplify]: Simplify PI into PI
5.534 * [taylor]: Taking taylor expansion of n in n
5.534 * [backup-simplify]: Simplify 0 into 0
5.534 * [backup-simplify]: Simplify 1 into 1
5.535 * [backup-simplify]: Simplify (/ PI 1) into PI
5.535 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.537 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.537 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.537 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.537 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.539 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.540 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.541 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.541 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
5.541 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
5.542 * [taylor]: Taking taylor expansion of 0.5 in k
5.542 * [backup-simplify]: Simplify 0.5 into 0.5
5.542 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
5.542 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
5.542 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
5.542 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
5.542 * [taylor]: Taking taylor expansion of 2.0 in k
5.542 * [backup-simplify]: Simplify 2.0 into 2.0
5.542 * [taylor]: Taking taylor expansion of PI in k
5.542 * [backup-simplify]: Simplify PI into PI
5.542 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.544 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.544 * [taylor]: Taking taylor expansion of (log n) in k
5.544 * [taylor]: Taking taylor expansion of n in k
5.544 * [backup-simplify]: Simplify n into n
5.544 * [backup-simplify]: Simplify (log n) into (log n)
5.544 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.544 * [taylor]: Taking taylor expansion of 1.0 in k
5.544 * [backup-simplify]: Simplify 1.0 into 1.0
5.544 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.544 * [taylor]: Taking taylor expansion of k in k
5.544 * [backup-simplify]: Simplify 0 into 0
5.544 * [backup-simplify]: Simplify 1 into 1
5.545 * [backup-simplify]: Simplify (/ 1 1) into 1
5.545 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.546 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
5.547 * [backup-simplify]: Simplify (- 1) into -1
5.547 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.548 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
5.550 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
5.551 * [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)))))
5.553 * [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)))))
5.554 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.555 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.557 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.557 * [backup-simplify]: Simplify (- 0) into 0
5.558 * [backup-simplify]: Simplify (+ 0 0) into 0
5.558 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
5.560 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.561 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
5.564 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.564 * [taylor]: Taking taylor expansion of 0 in k
5.564 * [backup-simplify]: Simplify 0 into 0
5.564 * [backup-simplify]: Simplify 0 into 0
5.564 * [backup-simplify]: Simplify 0 into 0
5.565 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.567 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.571 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.571 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.572 * [backup-simplify]: Simplify (- 0) into 0
5.572 * [backup-simplify]: Simplify (+ 0 0) into 0
5.573 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
5.575 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.577 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
5.580 * [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
5.581 * [taylor]: Taking taylor expansion of 0 in k
5.581 * [backup-simplify]: Simplify 0 into 0
5.581 * [backup-simplify]: Simplify 0 into 0
5.581 * [backup-simplify]: Simplify 0 into 0
5.581 * [backup-simplify]: Simplify 0 into 0
5.582 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.583 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.590 * [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
5.591 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.591 * [backup-simplify]: Simplify (- 0) into 0
5.592 * [backup-simplify]: Simplify (+ 0 0) into 0
5.593 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
5.595 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.597 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
5.600 * [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
5.600 * [taylor]: Taking taylor expansion of 0 in k
5.600 * [backup-simplify]: Simplify 0 into 0
5.600 * [backup-simplify]: Simplify 0 into 0
5.602 * [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))))
5.603 * [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)))
5.603 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
5.603 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
5.603 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
5.603 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
5.603 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
5.603 * [taylor]: Taking taylor expansion of 0.5 in k
5.603 * [backup-simplify]: Simplify 0.5 into 0.5
5.603 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.603 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.603 * [taylor]: Taking taylor expansion of k in k
5.603 * [backup-simplify]: Simplify 0 into 0
5.603 * [backup-simplify]: Simplify 1 into 1
5.604 * [backup-simplify]: Simplify (/ 1 1) into 1
5.604 * [taylor]: Taking taylor expansion of 1.0 in k
5.604 * [backup-simplify]: Simplify 1.0 into 1.0
5.604 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
5.604 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
5.604 * [taylor]: Taking taylor expansion of -2.0 in k
5.604 * [backup-simplify]: Simplify -2.0 into -2.0
5.604 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.604 * [taylor]: Taking taylor expansion of PI in k
5.604 * [backup-simplify]: Simplify PI into PI
5.604 * [taylor]: Taking taylor expansion of n in k
5.604 * [backup-simplify]: Simplify n into n
5.604 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.604 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
5.604 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
5.605 * [backup-simplify]: Simplify (+ 1 0) into 1
5.605 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
5.605 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
5.606 * [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))))))
5.606 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
5.606 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
5.606 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
5.606 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
5.606 * [taylor]: Taking taylor expansion of 0.5 in n
5.606 * [backup-simplify]: Simplify 0.5 into 0.5
5.606 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.606 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.606 * [taylor]: Taking taylor expansion of k in n
5.606 * [backup-simplify]: Simplify k into k
5.606 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.606 * [taylor]: Taking taylor expansion of 1.0 in n
5.606 * [backup-simplify]: Simplify 1.0 into 1.0
5.606 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.606 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.606 * [taylor]: Taking taylor expansion of -2.0 in n
5.606 * [backup-simplify]: Simplify -2.0 into -2.0
5.606 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.606 * [taylor]: Taking taylor expansion of PI in n
5.606 * [backup-simplify]: Simplify PI into PI
5.606 * [taylor]: Taking taylor expansion of n in n
5.606 * [backup-simplify]: Simplify 0 into 0
5.606 * [backup-simplify]: Simplify 1 into 1
5.607 * [backup-simplify]: Simplify (/ PI 1) into PI
5.608 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.609 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.609 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.609 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
5.612 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.613 * [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))))
5.615 * [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)))))
5.615 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
5.615 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
5.615 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
5.615 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
5.615 * [taylor]: Taking taylor expansion of 0.5 in n
5.615 * [backup-simplify]: Simplify 0.5 into 0.5
5.615 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.615 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.615 * [taylor]: Taking taylor expansion of k in n
5.615 * [backup-simplify]: Simplify k into k
5.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.615 * [taylor]: Taking taylor expansion of 1.0 in n
5.615 * [backup-simplify]: Simplify 1.0 into 1.0
5.615 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.615 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.615 * [taylor]: Taking taylor expansion of -2.0 in n
5.615 * [backup-simplify]: Simplify -2.0 into -2.0
5.615 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.615 * [taylor]: Taking taylor expansion of PI in n
5.615 * [backup-simplify]: Simplify PI into PI
5.615 * [taylor]: Taking taylor expansion of n in n
5.615 * [backup-simplify]: Simplify 0 into 0
5.615 * [backup-simplify]: Simplify 1 into 1
5.616 * [backup-simplify]: Simplify (/ PI 1) into PI
5.617 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.618 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.618 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.618 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
5.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.621 * [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))))
5.623 * [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)))))
5.623 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
5.623 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
5.623 * [taylor]: Taking taylor expansion of 0.5 in k
5.623 * [backup-simplify]: Simplify 0.5 into 0.5
5.623 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
5.624 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.624 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.624 * [taylor]: Taking taylor expansion of k in k
5.624 * [backup-simplify]: Simplify 0 into 0
5.624 * [backup-simplify]: Simplify 1 into 1
5.624 * [backup-simplify]: Simplify (/ 1 1) into 1
5.624 * [taylor]: Taking taylor expansion of 1.0 in k
5.624 * [backup-simplify]: Simplify 1.0 into 1.0
5.624 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
5.624 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
5.624 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
5.624 * [taylor]: Taking taylor expansion of -2.0 in k
5.624 * [backup-simplify]: Simplify -2.0 into -2.0
5.624 * [taylor]: Taking taylor expansion of PI in k
5.625 * [backup-simplify]: Simplify PI into PI
5.625 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.626 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.626 * [taylor]: Taking taylor expansion of (log n) in k
5.626 * [taylor]: Taking taylor expansion of n in k
5.626 * [backup-simplify]: Simplify n into n
5.626 * [backup-simplify]: Simplify (log n) into (log n)
5.627 * [backup-simplify]: Simplify (+ 1 0) into 1
5.627 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.628 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
5.630 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
5.631 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
5.632 * [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)))))
5.634 * [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)))))
5.635 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.636 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
5.638 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
5.638 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.638 * [backup-simplify]: Simplify (+ 0 0) into 0
5.639 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
5.640 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.642 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
5.644 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.644 * [taylor]: Taking taylor expansion of 0 in k
5.644 * [backup-simplify]: Simplify 0 into 0
5.644 * [backup-simplify]: Simplify 0 into 0
5.645 * [backup-simplify]: Simplify 0 into 0
5.646 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.647 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.651 * [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
5.651 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.652 * [backup-simplify]: Simplify (+ 0 0) into 0
5.653 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
5.654 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.656 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
5.659 * [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
5.659 * [taylor]: Taking taylor expansion of 0 in k
5.659 * [backup-simplify]: Simplify 0 into 0
5.659 * [backup-simplify]: Simplify 0 into 0
5.659 * [backup-simplify]: Simplify 0 into 0
5.659 * [backup-simplify]: Simplify 0 into 0
5.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.662 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.669 * [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
5.670 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.670 * [backup-simplify]: Simplify (+ 0 0) into 0
5.671 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
5.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.687 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
5.690 * [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
5.690 * [taylor]: Taking taylor expansion of 0 in k
5.690 * [backup-simplify]: Simplify 0 into 0
5.690 * [backup-simplify]: Simplify 0 into 0
5.692 * [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))))))
5.692 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
5.692 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
5.692 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
5.692 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.692 * [taylor]: Taking taylor expansion of 2.0 in n
5.692 * [backup-simplify]: Simplify 2.0 into 2.0
5.692 * [taylor]: Taking taylor expansion of (* n PI) in n
5.692 * [taylor]: Taking taylor expansion of n in n
5.692 * [backup-simplify]: Simplify 0 into 0
5.692 * [backup-simplify]: Simplify 1 into 1
5.692 * [taylor]: Taking taylor expansion of PI in n
5.692 * [backup-simplify]: Simplify PI into PI
5.692 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.692 * [taylor]: Taking taylor expansion of 2.0 in n
5.692 * [backup-simplify]: Simplify 2.0 into 2.0
5.692 * [taylor]: Taking taylor expansion of (* n PI) in n
5.692 * [taylor]: Taking taylor expansion of n in n
5.692 * [backup-simplify]: Simplify 0 into 0
5.692 * [backup-simplify]: Simplify 1 into 1
5.692 * [taylor]: Taking taylor expansion of PI in n
5.692 * [backup-simplify]: Simplify PI into PI
5.693 * [backup-simplify]: Simplify (* 0 PI) into 0
5.693 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.693 * [backup-simplify]: Simplify 0 into 0
5.694 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.696 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.696 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
5.698 * [backup-simplify]: Simplify 0 into 0
5.698 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.699 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.699 * [backup-simplify]: Simplify 0 into 0
5.700 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.701 * [backup-simplify]: Simplify 0 into 0
5.702 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.703 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.703 * [backup-simplify]: Simplify 0 into 0
5.704 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.707 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.707 * [backup-simplify]: Simplify 0 into 0
5.709 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.712 * [backup-simplify]: Simplify 0 into 0
5.712 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
5.713 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
5.713 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
5.713 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.713 * [taylor]: Taking taylor expansion of 2.0 in n
5.713 * [backup-simplify]: Simplify 2.0 into 2.0
5.713 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.713 * [taylor]: Taking taylor expansion of PI in n
5.713 * [backup-simplify]: Simplify PI into PI
5.713 * [taylor]: Taking taylor expansion of n in n
5.713 * [backup-simplify]: Simplify 0 into 0
5.713 * [backup-simplify]: Simplify 1 into 1
5.714 * [backup-simplify]: Simplify (/ PI 1) into PI
5.714 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.714 * [taylor]: Taking taylor expansion of 2.0 in n
5.714 * [backup-simplify]: Simplify 2.0 into 2.0
5.714 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.714 * [taylor]: Taking taylor expansion of PI in n
5.714 * [backup-simplify]: Simplify PI into PI
5.714 * [taylor]: Taking taylor expansion of n in n
5.714 * [backup-simplify]: Simplify 0 into 0
5.714 * [backup-simplify]: Simplify 1 into 1
5.714 * [backup-simplify]: Simplify (/ PI 1) into PI
5.715 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.715 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.716 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.717 * [backup-simplify]: Simplify 0 into 0
5.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.719 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.719 * [backup-simplify]: Simplify 0 into 0
5.720 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.721 * [backup-simplify]: Simplify 0 into 0
5.722 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.724 * [backup-simplify]: Simplify 0 into 0
5.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.726 * [backup-simplify]: Simplify 0 into 0
5.727 * [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
5.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.729 * [backup-simplify]: Simplify 0 into 0
5.730 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
5.731 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
5.731 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
5.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.731 * [taylor]: Taking taylor expansion of -2.0 in n
5.731 * [backup-simplify]: Simplify -2.0 into -2.0
5.731 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.731 * [taylor]: Taking taylor expansion of PI in n
5.731 * [backup-simplify]: Simplify PI into PI
5.731 * [taylor]: Taking taylor expansion of n in n
5.731 * [backup-simplify]: Simplify 0 into 0
5.731 * [backup-simplify]: Simplify 1 into 1
5.732 * [backup-simplify]: Simplify (/ PI 1) into PI
5.732 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.732 * [taylor]: Taking taylor expansion of -2.0 in n
5.732 * [backup-simplify]: Simplify -2.0 into -2.0
5.732 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.732 * [taylor]: Taking taylor expansion of PI in n
5.732 * [backup-simplify]: Simplify PI into PI
5.732 * [taylor]: Taking taylor expansion of n in n
5.732 * [backup-simplify]: Simplify 0 into 0
5.732 * [backup-simplify]: Simplify 1 into 1
5.732 * [backup-simplify]: Simplify (/ PI 1) into PI
5.733 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.733 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.735 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
5.735 * [backup-simplify]: Simplify 0 into 0
5.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.737 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.737 * [backup-simplify]: Simplify 0 into 0
5.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.740 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.740 * [backup-simplify]: Simplify 0 into 0
5.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.742 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.742 * [backup-simplify]: Simplify 0 into 0
5.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.745 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.745 * [backup-simplify]: Simplify 0 into 0
5.746 * [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
5.748 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.748 * [backup-simplify]: Simplify 0 into 0
5.749 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
5.749 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
5.749 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
5.749 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
5.749 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
5.749 * [taylor]: Taking taylor expansion of 1.0 in k
5.749 * [backup-simplify]: Simplify 1.0 into 1.0
5.749 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.749 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.749 * [taylor]: Taking taylor expansion of k in k
5.749 * [backup-simplify]: Simplify 0 into 0
5.749 * [backup-simplify]: Simplify 1 into 1
5.750 * [backup-simplify]: Simplify (/ 1 1) into 1
5.750 * [backup-simplify]: Simplify (sqrt 0) into 0
5.752 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.752 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
5.752 * [taylor]: Taking taylor expansion of 1.0 in k
5.752 * [backup-simplify]: Simplify 1.0 into 1.0
5.752 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.752 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.752 * [taylor]: Taking taylor expansion of k in k
5.752 * [backup-simplify]: Simplify 0 into 0
5.752 * [backup-simplify]: Simplify 1 into 1
5.752 * [backup-simplify]: Simplify (/ 1 1) into 1
5.753 * [backup-simplify]: Simplify (sqrt 0) into 0
5.754 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.754 * [backup-simplify]: Simplify (* 1.0 0) into 0
5.754 * [backup-simplify]: Simplify 0 into 0
5.757 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
5.758 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.759 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.762 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.764 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
5.764 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.766 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.770 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.772 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
5.772 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.774 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
5.774 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
5.774 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
5.774 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
5.774 * [taylor]: Taking taylor expansion of 1.0 in k
5.774 * [backup-simplify]: Simplify 1.0 into 1.0
5.774 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.774 * [taylor]: Taking taylor expansion of k in k
5.774 * [backup-simplify]: Simplify 0 into 0
5.774 * [backup-simplify]: Simplify 1 into 1
5.775 * [backup-simplify]: Simplify (sqrt 0) into 0
5.776 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.776 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
5.776 * [taylor]: Taking taylor expansion of 1.0 in k
5.776 * [backup-simplify]: Simplify 1.0 into 1.0
5.776 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.776 * [taylor]: Taking taylor expansion of k in k
5.776 * [backup-simplify]: Simplify 0 into 0
5.776 * [backup-simplify]: Simplify 1 into 1
5.776 * [backup-simplify]: Simplify (sqrt 0) into 0
5.778 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.778 * [backup-simplify]: Simplify (* 1.0 0) into 0
5.778 * [backup-simplify]: Simplify 0 into 0
5.779 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
5.780 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.783 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.785 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
5.785 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.788 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.791 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
5.791 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.793 * [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))))))))
5.793 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
5.793 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
5.793 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
5.793 * [taylor]: Taking taylor expansion of 1.0 in k
5.794 * [backup-simplify]: Simplify 1.0 into 1.0
5.794 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.794 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.794 * [taylor]: Taking taylor expansion of -1 in k
5.794 * [backup-simplify]: Simplify -1 into -1
5.794 * [taylor]: Taking taylor expansion of k in k
5.794 * [backup-simplify]: Simplify 0 into 0
5.794 * [backup-simplify]: Simplify 1 into 1
5.795 * [backup-simplify]: Simplify (/ -1 1) into -1
5.795 * [backup-simplify]: Simplify (sqrt 0) into 0
5.796 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.797 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
5.797 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
5.797 * [taylor]: Taking taylor expansion of 1.0 in k
5.797 * [backup-simplify]: Simplify 1.0 into 1.0
5.797 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.797 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.797 * [taylor]: Taking taylor expansion of -1 in k
5.797 * [backup-simplify]: Simplify -1 into -1
5.797 * [taylor]: Taking taylor expansion of k in k
5.797 * [backup-simplify]: Simplify 0 into 0
5.797 * [backup-simplify]: Simplify 1 into 1
5.797 * [backup-simplify]: Simplify (/ -1 1) into -1
5.798 * [backup-simplify]: Simplify (sqrt 0) into 0
5.799 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.799 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
5.799 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.803 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.805 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
5.806 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.807 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.810 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.816 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
5.817 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.818 * [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)))))
5.818 * * * * [progress]: [ 4 / 4 ] generating series at (2)
5.819 * [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)))))
5.819 * [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
5.819 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
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 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
5.819 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) 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 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.819 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.819 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.819 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.819 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.820 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.820 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.820 * [taylor]: Taking taylor expansion of 0.5 in n
5.820 * [backup-simplify]: Simplify 0.5 into 0.5
5.820 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.820 * [taylor]: Taking taylor expansion of 1.0 in n
5.820 * [backup-simplify]: Simplify 1.0 into 1.0
5.820 * [taylor]: Taking taylor expansion of k in n
5.820 * [backup-simplify]: Simplify k into k
5.820 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.820 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.820 * [taylor]: Taking taylor expansion of 2.0 in n
5.820 * [backup-simplify]: Simplify 2.0 into 2.0
5.820 * [taylor]: Taking taylor expansion of (* n PI) in n
5.820 * [taylor]: Taking taylor expansion of n in n
5.820 * [backup-simplify]: Simplify 0 into 0
5.820 * [backup-simplify]: Simplify 1 into 1
5.820 * [taylor]: Taking taylor expansion of PI in n
5.820 * [backup-simplify]: Simplify PI into PI
5.821 * [backup-simplify]: Simplify (* 0 PI) into 0
5.821 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.822 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.824 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.825 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.825 * [backup-simplify]: Simplify (- k) into (- k)
5.825 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.825 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.827 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.828 * [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))))
5.829 * [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)))))
5.829 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
5.829 * [taylor]: Taking taylor expansion of 1.0 in k
5.829 * [backup-simplify]: Simplify 1.0 into 1.0
5.829 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
5.829 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.829 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.829 * [taylor]: Taking taylor expansion of k in k
5.829 * [backup-simplify]: Simplify 0 into 0
5.829 * [backup-simplify]: Simplify 1 into 1
5.838 * [backup-simplify]: Simplify (/ 1 1) into 1
5.839 * [backup-simplify]: Simplify (sqrt 0) into 0
5.840 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.840 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
5.840 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
5.840 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
5.840 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
5.840 * [taylor]: Taking taylor expansion of 0.5 in k
5.840 * [backup-simplify]: Simplify 0.5 into 0.5
5.840 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.840 * [taylor]: Taking taylor expansion of 1.0 in k
5.840 * [backup-simplify]: Simplify 1.0 into 1.0
5.840 * [taylor]: Taking taylor expansion of k in k
5.840 * [backup-simplify]: Simplify 0 into 0
5.840 * [backup-simplify]: Simplify 1 into 1
5.840 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
5.840 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
5.840 * [taylor]: Taking taylor expansion of 2.0 in k
5.840 * [backup-simplify]: Simplify 2.0 into 2.0
5.840 * [taylor]: Taking taylor expansion of (* n PI) in k
5.840 * [taylor]: Taking taylor expansion of n in k
5.841 * [backup-simplify]: Simplify n into n
5.841 * [taylor]: Taking taylor expansion of PI in k
5.841 * [backup-simplify]: Simplify PI into PI
5.841 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.841 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
5.841 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
5.841 * [backup-simplify]: Simplify (- 0) into 0
5.842 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.842 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
5.842 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
5.842 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
5.842 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
5.843 * [taylor]: Taking taylor expansion of 1.0 in k
5.843 * [backup-simplify]: Simplify 1.0 into 1.0
5.843 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
5.843 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.843 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.843 * [taylor]: Taking taylor expansion of k in k
5.843 * [backup-simplify]: Simplify 0 into 0
5.843 * [backup-simplify]: Simplify 1 into 1
5.843 * [backup-simplify]: Simplify (/ 1 1) into 1
5.843 * [backup-simplify]: Simplify (sqrt 0) into 0
5.845 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.845 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
5.845 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
5.845 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
5.845 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
5.845 * [taylor]: Taking taylor expansion of 0.5 in k
5.845 * [backup-simplify]: Simplify 0.5 into 0.5
5.845 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.845 * [taylor]: Taking taylor expansion of 1.0 in k
5.845 * [backup-simplify]: Simplify 1.0 into 1.0
5.845 * [taylor]: Taking taylor expansion of k in k
5.845 * [backup-simplify]: Simplify 0 into 0
5.845 * [backup-simplify]: Simplify 1 into 1
5.845 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
5.845 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
5.845 * [taylor]: Taking taylor expansion of 2.0 in k
5.845 * [backup-simplify]: Simplify 2.0 into 2.0
5.845 * [taylor]: Taking taylor expansion of (* n PI) in k
5.845 * [taylor]: Taking taylor expansion of n in k
5.845 * [backup-simplify]: Simplify n into n
5.845 * [taylor]: Taking taylor expansion of PI in k
5.845 * [backup-simplify]: Simplify PI into PI
5.845 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.846 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
5.846 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
5.846 * [backup-simplify]: Simplify (- 0) into 0
5.847 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.847 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
5.848 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
5.848 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
5.848 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
5.849 * [backup-simplify]: Simplify (* 1.0 0) into 0
5.849 * [taylor]: Taking taylor expansion of 0 in n
5.849 * [backup-simplify]: Simplify 0 into 0
5.849 * [backup-simplify]: Simplify 0 into 0
5.849 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
5.850 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
5.851 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
5.851 * [backup-simplify]: Simplify (- 1) into -1
5.851 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.853 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
5.854 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
5.854 * [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)))
5.856 * [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)))
5.858 * [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)))
5.858 * [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
5.858 * [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
5.858 * [taylor]: Taking taylor expansion of +nan.0 in n
5.858 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.858 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
5.858 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
5.858 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
5.858 * [taylor]: Taking taylor expansion of 0.5 in n
5.858 * [backup-simplify]: Simplify 0.5 into 0.5
5.859 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
5.859 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
5.859 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
5.859 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
5.859 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
5.859 * [taylor]: Taking taylor expansion of 1.0 in n
5.859 * [backup-simplify]: Simplify 1.0 into 1.0
5.859 * [taylor]: Taking taylor expansion of (log PI) in n
5.859 * [taylor]: Taking taylor expansion of PI in n
5.859 * [backup-simplify]: Simplify PI into PI
5.859 * [backup-simplify]: Simplify (log PI) into (log PI)
5.860 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
5.862 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
5.862 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
5.862 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
5.862 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
5.862 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
5.862 * [taylor]: Taking taylor expansion of 1.0 in n
5.862 * [backup-simplify]: Simplify 1.0 into 1.0
5.862 * [taylor]: Taking taylor expansion of (log n) in n
5.862 * [taylor]: Taking taylor expansion of n in n
5.862 * [backup-simplify]: Simplify 0 into 0
5.862 * [backup-simplify]: Simplify 1 into 1
5.863 * [backup-simplify]: Simplify (log 1) into 0
5.863 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
5.864 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
5.864 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
5.864 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
5.864 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
5.864 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
5.864 * [taylor]: Taking taylor expansion of 1.0 in n
5.864 * [backup-simplify]: Simplify 1.0 into 1.0
5.864 * [taylor]: Taking taylor expansion of (log 2.0) in n
5.864 * [taylor]: Taking taylor expansion of 2.0 in n
5.864 * [backup-simplify]: Simplify 2.0 into 2.0
5.864 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
5.865 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
5.867 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
5.867 * [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)
5.869 * [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)
5.870 * [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))
5.871 * [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)))
5.873 * [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)
5.875 * [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))
5.876 * [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)))
5.877 * [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)))
5.878 * [backup-simplify]: Simplify 0 into 0
5.878 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
5.879 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
5.881 * [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
5.882 * [backup-simplify]: Simplify (- 0) into 0
5.882 * [backup-simplify]: Simplify (+ 0 0) into 0
5.883 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
5.884 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
5.885 * [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)))
5.886 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.889 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.893 * [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))))))))
5.899 * [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))))))))
5.899 * [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
5.899 * [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
5.899 * [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
5.899 * [taylor]: Taking taylor expansion of +nan.0 in n
5.899 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.899 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
5.899 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
5.900 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
5.900 * [taylor]: Taking taylor expansion of 0.5 in n
5.900 * [backup-simplify]: Simplify 0.5 into 0.5
5.900 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
5.900 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
5.900 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
5.900 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
5.900 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
5.900 * [taylor]: Taking taylor expansion of 1.0 in n
5.900 * [backup-simplify]: Simplify 1.0 into 1.0
5.900 * [taylor]: Taking taylor expansion of (log PI) in n
5.900 * [taylor]: Taking taylor expansion of PI in n
5.900 * [backup-simplify]: Simplify PI into PI
5.900 * [backup-simplify]: Simplify (log PI) into (log PI)
5.901 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
5.903 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
5.903 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
5.903 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
5.903 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
5.903 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
5.903 * [taylor]: Taking taylor expansion of 1.0 in n
5.903 * [backup-simplify]: Simplify 1.0 into 1.0
5.903 * [taylor]: Taking taylor expansion of (log n) in n
5.903 * [taylor]: Taking taylor expansion of n in n
5.903 * [backup-simplify]: Simplify 0 into 0
5.904 * [backup-simplify]: Simplify 1 into 1
5.904 * [backup-simplify]: Simplify (log 1) into 0
5.904 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
5.904 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
5.905 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
5.905 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
5.905 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
5.905 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
5.905 * [taylor]: Taking taylor expansion of 1.0 in n
5.905 * [backup-simplify]: Simplify 1.0 into 1.0
5.905 * [taylor]: Taking taylor expansion of (log 2.0) in n
5.905 * [taylor]: Taking taylor expansion of 2.0 in n
5.905 * [backup-simplify]: Simplify 2.0 into 2.0
5.905 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
5.906 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
5.908 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
5.909 * [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)
5.910 * [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)
5.911 * [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))
5.913 * [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)))
5.914 * [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)
5.914 * [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
5.914 * [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
5.914 * [taylor]: Taking taylor expansion of +nan.0 in n
5.915 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.915 * [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
5.915 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
5.915 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
5.915 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
5.915 * [taylor]: Taking taylor expansion of 0.5 in n
5.915 * [backup-simplify]: Simplify 0.5 into 0.5
5.915 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
5.915 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
5.915 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
5.915 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
5.915 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
5.915 * [taylor]: Taking taylor expansion of 1.0 in n
5.915 * [backup-simplify]: Simplify 1.0 into 1.0
5.915 * [taylor]: Taking taylor expansion of (log 2.0) in n
5.915 * [taylor]: Taking taylor expansion of 2.0 in n
5.915 * [backup-simplify]: Simplify 2.0 into 2.0
5.916 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
5.917 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
5.918 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
5.918 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
5.918 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
5.918 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
5.918 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
5.918 * [taylor]: Taking taylor expansion of 1.0 in n
5.918 * [backup-simplify]: Simplify 1.0 into 1.0
5.918 * [taylor]: Taking taylor expansion of (log PI) in n
5.918 * [taylor]: Taking taylor expansion of PI in n
5.918 * [backup-simplify]: Simplify PI into PI
5.919 * [backup-simplify]: Simplify (log PI) into (log PI)
5.920 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
5.922 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
5.922 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
5.922 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
5.922 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
5.922 * [taylor]: Taking taylor expansion of 1.0 in n
5.922 * [backup-simplify]: Simplify 1.0 into 1.0
5.922 * [taylor]: Taking taylor expansion of (log n) in n
5.922 * [taylor]: Taking taylor expansion of n in n
5.923 * [backup-simplify]: Simplify 0 into 0
5.923 * [backup-simplify]: Simplify 1 into 1
5.923 * [backup-simplify]: Simplify (log 1) into 0
5.924 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
5.924 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
5.924 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
5.925 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
5.926 * [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)
5.927 * [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))
5.929 * [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)))
5.930 * [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)
5.930 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.930 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.930 * [taylor]: Taking taylor expansion of 2.0 in n
5.930 * [backup-simplify]: Simplify 2.0 into 2.0
5.930 * [taylor]: Taking taylor expansion of (* n PI) in n
5.930 * [taylor]: Taking taylor expansion of n in n
5.930 * [backup-simplify]: Simplify 0 into 0
5.930 * [backup-simplify]: Simplify 1 into 1
5.930 * [taylor]: Taking taylor expansion of PI in n
5.930 * [backup-simplify]: Simplify PI into PI
5.931 * [backup-simplify]: Simplify (* 0 PI) into 0
5.931 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.933 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.934 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.936 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.937 * [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))
5.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.941 * [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))
5.944 * [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)))
5.947 * [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))))))
5.953 * [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))))))))
5.959 * [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))))))))
5.966 * [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))))))))
5.968 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
5.969 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
5.970 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
5.971 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
5.972 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
5.973 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
5.974 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
5.974 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
5.976 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
5.977 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
5.979 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
5.980 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
5.982 * [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
5.984 * [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
5.986 * [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
5.988 * [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
5.989 * [backup-simplify]: Simplify (- 0) into 0
5.989 * [backup-simplify]: Simplify 0 into 0
5.989 * [backup-simplify]: Simplify 0 into 0
5.990 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.991 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
5.994 * [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
5.995 * [backup-simplify]: Simplify (- 0) into 0
5.996 * [backup-simplify]: Simplify (+ 0 0) into 0
6.005 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
6.007 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
6.009 * [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)))
6.010 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.014 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.020 * [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))))))))
6.031 * [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))))))))
6.031 * [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
6.031 * [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
6.031 * [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
6.031 * [taylor]: Taking taylor expansion of +nan.0 in n
6.031 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.031 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
6.031 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
6.031 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
6.031 * [taylor]: Taking taylor expansion of 0.5 in n
6.032 * [backup-simplify]: Simplify 0.5 into 0.5
6.032 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
6.032 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
6.032 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.032 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.032 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.032 * [taylor]: Taking taylor expansion of 1.0 in n
6.032 * [backup-simplify]: Simplify 1.0 into 1.0
6.032 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.032 * [taylor]: Taking taylor expansion of 2.0 in n
6.032 * [backup-simplify]: Simplify 2.0 into 2.0
6.033 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.034 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.035 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.035 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
6.035 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.035 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.035 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.036 * [taylor]: Taking taylor expansion of 1.0 in n
6.036 * [backup-simplify]: Simplify 1.0 into 1.0
6.036 * [taylor]: Taking taylor expansion of (log n) in n
6.036 * [taylor]: Taking taylor expansion of n in n
6.036 * [backup-simplify]: Simplify 0 into 0
6.036 * [backup-simplify]: Simplify 1 into 1
6.036 * [backup-simplify]: Simplify (log 1) into 0
6.037 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.037 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.037 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.037 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.037 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.037 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.037 * [taylor]: Taking taylor expansion of 1.0 in n
6.037 * [backup-simplify]: Simplify 1.0 into 1.0
6.037 * [taylor]: Taking taylor expansion of (log PI) in n
6.037 * [taylor]: Taking taylor expansion of PI in n
6.037 * [backup-simplify]: Simplify PI into PI
6.037 * [backup-simplify]: Simplify (log PI) into (log PI)
6.038 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.040 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.041 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.042 * [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)
6.043 * [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))
6.045 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
6.046 * [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)
6.046 * [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
6.047 * [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
6.047 * [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
6.047 * [taylor]: Taking taylor expansion of +nan.0 in n
6.047 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.047 * [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
6.047 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.047 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.047 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.047 * [taylor]: Taking taylor expansion of 0.5 in n
6.047 * [backup-simplify]: Simplify 0.5 into 0.5
6.047 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.047 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.047 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.047 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.047 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.047 * [taylor]: Taking taylor expansion of 1.0 in n
6.047 * [backup-simplify]: Simplify 1.0 into 1.0
6.047 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.047 * [taylor]: Taking taylor expansion of 2.0 in n
6.047 * [backup-simplify]: Simplify 2.0 into 2.0
6.048 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.049 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.050 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.050 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.050 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.050 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.050 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.050 * [taylor]: Taking taylor expansion of 1.0 in n
6.050 * [backup-simplify]: Simplify 1.0 into 1.0
6.050 * [taylor]: Taking taylor expansion of (log PI) in n
6.050 * [taylor]: Taking taylor expansion of PI in n
6.050 * [backup-simplify]: Simplify PI into PI
6.051 * [backup-simplify]: Simplify (log PI) into (log PI)
6.052 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.053 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.053 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.054 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.054 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.054 * [taylor]: Taking taylor expansion of 1.0 in n
6.054 * [backup-simplify]: Simplify 1.0 into 1.0
6.054 * [taylor]: Taking taylor expansion of (log n) in n
6.054 * [taylor]: Taking taylor expansion of n in n
6.054 * [backup-simplify]: Simplify 0 into 0
6.054 * [backup-simplify]: Simplify 1 into 1
6.054 * [backup-simplify]: Simplify (log 1) into 0
6.054 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.055 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.055 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.055 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.057 * [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)
6.058 * [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))
6.059 * [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)))
6.060 * [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)
6.061 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.061 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.061 * [taylor]: Taking taylor expansion of 2.0 in n
6.061 * [backup-simplify]: Simplify 2.0 into 2.0
6.061 * [taylor]: Taking taylor expansion of (* n PI) in n
6.061 * [taylor]: Taking taylor expansion of n in n
6.061 * [backup-simplify]: Simplify 0 into 0
6.061 * [backup-simplify]: Simplify 1 into 1
6.061 * [taylor]: Taking taylor expansion of PI in n
6.061 * [backup-simplify]: Simplify PI into PI
6.061 * [backup-simplify]: Simplify (* 0 PI) into 0
6.062 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.063 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.065 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.066 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.066 * [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
6.066 * [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
6.066 * [taylor]: Taking taylor expansion of +nan.0 in n
6.066 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.066 * [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
6.066 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.066 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.066 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.066 * [taylor]: Taking taylor expansion of 0.5 in n
6.066 * [backup-simplify]: Simplify 0.5 into 0.5
6.066 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.066 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.066 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.066 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.066 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.066 * [taylor]: Taking taylor expansion of 1.0 in n
6.066 * [backup-simplify]: Simplify 1.0 into 1.0
6.066 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.066 * [taylor]: Taking taylor expansion of 2.0 in n
6.066 * [backup-simplify]: Simplify 2.0 into 2.0
6.067 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.068 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.069 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.069 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.069 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.069 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.069 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.069 * [taylor]: Taking taylor expansion of 1.0 in n
6.069 * [backup-simplify]: Simplify 1.0 into 1.0
6.069 * [taylor]: Taking taylor expansion of (log PI) in n
6.069 * [taylor]: Taking taylor expansion of PI in n
6.069 * [backup-simplify]: Simplify PI into PI
6.070 * [backup-simplify]: Simplify (log PI) into (log PI)
6.071 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.072 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.072 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.072 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.072 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.072 * [taylor]: Taking taylor expansion of 1.0 in n
6.072 * [backup-simplify]: Simplify 1.0 into 1.0
6.072 * [taylor]: Taking taylor expansion of (log n) in n
6.073 * [taylor]: Taking taylor expansion of n in n
6.073 * [backup-simplify]: Simplify 0 into 0
6.073 * [backup-simplify]: Simplify 1 into 1
6.073 * [backup-simplify]: Simplify (log 1) into 0
6.073 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.073 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.074 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.074 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.075 * [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)
6.077 * [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))
6.078 * [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)))
6.079 * [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)
6.079 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
6.079 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.080 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.080 * [taylor]: Taking taylor expansion of 2.0 in n
6.080 * [backup-simplify]: Simplify 2.0 into 2.0
6.080 * [taylor]: Taking taylor expansion of (* n PI) in n
6.080 * [taylor]: Taking taylor expansion of n in n
6.080 * [backup-simplify]: Simplify 0 into 0
6.080 * [backup-simplify]: Simplify 1 into 1
6.080 * [taylor]: Taking taylor expansion of PI in n
6.080 * [backup-simplify]: Simplify PI into PI
6.080 * [backup-simplify]: Simplify (* 0 PI) into 0
6.081 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.082 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.084 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.085 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.086 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.088 * [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))
6.089 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.093 * [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))
6.095 * [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)))
6.097 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.098 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.100 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
6.104 * [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))
6.106 * [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)))
6.109 * [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))))))))
6.123 * [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))))))))))))
6.137 * [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))))))))))))
6.156 * [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))))))))))))))
6.182 * [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))))))))))))))
6.199 * [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))))))))))))))
6.229 * [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))))))))))))))))))))))
6.230 * [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))))))
6.230 * [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
6.230 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
6.230 * [taylor]: Taking taylor expansion of 1.0 in n
6.230 * [backup-simplify]: Simplify 1.0 into 1.0
6.230 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
6.230 * [taylor]: Taking taylor expansion of (sqrt k) in n
6.230 * [taylor]: Taking taylor expansion of k in n
6.230 * [backup-simplify]: Simplify k into k
6.231 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
6.231 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.231 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
6.231 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
6.231 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
6.231 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
6.231 * [taylor]: Taking taylor expansion of 0.5 in n
6.231 * [backup-simplify]: Simplify 0.5 into 0.5
6.231 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.231 * [taylor]: Taking taylor expansion of 1.0 in n
6.231 * [backup-simplify]: Simplify 1.0 into 1.0
6.231 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.231 * [taylor]: Taking taylor expansion of k in n
6.231 * [backup-simplify]: Simplify k into k
6.231 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.231 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.231 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.231 * [taylor]: Taking taylor expansion of 2.0 in n
6.231 * [backup-simplify]: Simplify 2.0 into 2.0
6.231 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.231 * [taylor]: Taking taylor expansion of PI in n
6.231 * [backup-simplify]: Simplify PI into PI
6.231 * [taylor]: Taking taylor expansion of n in n
6.231 * [backup-simplify]: Simplify 0 into 0
6.231 * [backup-simplify]: Simplify 1 into 1
6.232 * [backup-simplify]: Simplify (/ PI 1) into PI
6.233 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.234 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.234 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.234 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.234 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
6.236 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.237 * [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))))
6.239 * [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)))))
6.239 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
6.239 * [taylor]: Taking taylor expansion of 1.0 in k
6.239 * [backup-simplify]: Simplify 1.0 into 1.0
6.239 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
6.239 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.239 * [taylor]: Taking taylor expansion of k in k
6.239 * [backup-simplify]: Simplify 0 into 0
6.239 * [backup-simplify]: Simplify 1 into 1
6.240 * [backup-simplify]: Simplify (sqrt 0) into 0
6.241 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.241 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
6.241 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
6.241 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
6.241 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
6.241 * [taylor]: Taking taylor expansion of 0.5 in k
6.241 * [backup-simplify]: Simplify 0.5 into 0.5
6.241 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
6.241 * [taylor]: Taking taylor expansion of 1.0 in k
6.241 * [backup-simplify]: Simplify 1.0 into 1.0
6.241 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.241 * [taylor]: Taking taylor expansion of k in k
6.242 * [backup-simplify]: Simplify 0 into 0
6.242 * [backup-simplify]: Simplify 1 into 1
6.242 * [backup-simplify]: Simplify (/ 1 1) into 1
6.242 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
6.242 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
6.242 * [taylor]: Taking taylor expansion of 2.0 in k
6.242 * [backup-simplify]: Simplify 2.0 into 2.0
6.242 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.242 * [taylor]: Taking taylor expansion of PI in k
6.242 * [backup-simplify]: Simplify PI into PI
6.242 * [taylor]: Taking taylor expansion of n in k
6.242 * [backup-simplify]: Simplify n into n
6.242 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.243 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
6.243 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
6.243 * [backup-simplify]: Simplify (- 1) into -1
6.244 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.244 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
6.244 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
6.244 * [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)))))
6.245 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
6.245 * [taylor]: Taking taylor expansion of 1.0 in k
6.245 * [backup-simplify]: Simplify 1.0 into 1.0
6.245 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
6.245 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.245 * [taylor]: Taking taylor expansion of k in k
6.245 * [backup-simplify]: Simplify 0 into 0
6.245 * [backup-simplify]: Simplify 1 into 1
6.245 * [backup-simplify]: Simplify (sqrt 0) into 0
6.247 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.247 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
6.247 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
6.247 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
6.247 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
6.247 * [taylor]: Taking taylor expansion of 0.5 in k
6.247 * [backup-simplify]: Simplify 0.5 into 0.5
6.247 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
6.247 * [taylor]: Taking taylor expansion of 1.0 in k
6.247 * [backup-simplify]: Simplify 1.0 into 1.0
6.247 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.247 * [taylor]: Taking taylor expansion of k in k
6.247 * [backup-simplify]: Simplify 0 into 0
6.247 * [backup-simplify]: Simplify 1 into 1
6.248 * [backup-simplify]: Simplify (/ 1 1) into 1
6.248 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
6.248 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
6.248 * [taylor]: Taking taylor expansion of 2.0 in k
6.248 * [backup-simplify]: Simplify 2.0 into 2.0
6.248 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.248 * [taylor]: Taking taylor expansion of PI in k
6.248 * [backup-simplify]: Simplify PI into PI
6.248 * [taylor]: Taking taylor expansion of n in k
6.248 * [backup-simplify]: Simplify n into n
6.249 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.249 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
6.249 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
6.250 * [backup-simplify]: Simplify (- 1) into -1
6.251 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.252 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
6.253 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
6.253 * [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)))))
6.254 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
6.254 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.254 * [taylor]: Taking taylor expansion of 0 in n
6.254 * [backup-simplify]: Simplify 0 into 0
6.254 * [backup-simplify]: Simplify 0 into 0
6.255 * [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)))))))
6.256 * [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)))))))
6.256 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.256 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.256 * [taylor]: Taking taylor expansion of +nan.0 in n
6.256 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.256 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.256 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.257 * [taylor]: Taking taylor expansion of 0.5 in n
6.257 * [backup-simplify]: Simplify 0.5 into 0.5
6.257 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.257 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.257 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.257 * [taylor]: Taking taylor expansion of 2.0 in n
6.257 * [backup-simplify]: Simplify 2.0 into 2.0
6.257 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.257 * [taylor]: Taking taylor expansion of PI in n
6.257 * [backup-simplify]: Simplify PI into PI
6.257 * [taylor]: Taking taylor expansion of n in n
6.257 * [backup-simplify]: Simplify 0 into 0
6.257 * [backup-simplify]: Simplify 1 into 1
6.258 * [backup-simplify]: Simplify (/ PI 1) into PI
6.258 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.260 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.260 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.260 * [taylor]: Taking taylor expansion of 1.0 in n
6.260 * [backup-simplify]: Simplify 1.0 into 1.0
6.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.260 * [taylor]: Taking taylor expansion of k in n
6.260 * [backup-simplify]: Simplify k into k
6.260 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.262 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.262 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.262 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.264 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.265 * [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))))
6.266 * [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)))))
6.268 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
6.269 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.270 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.271 * [backup-simplify]: Simplify 0 into 0
6.274 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.275 * [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)))))))
6.276 * [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)))))))
6.276 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.276 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.276 * [taylor]: Taking taylor expansion of +nan.0 in n
6.276 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.276 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.276 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.277 * [taylor]: Taking taylor expansion of 0.5 in n
6.277 * [backup-simplify]: Simplify 0.5 into 0.5
6.277 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.277 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.277 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.277 * [taylor]: Taking taylor expansion of 2.0 in n
6.277 * [backup-simplify]: Simplify 2.0 into 2.0
6.277 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.277 * [taylor]: Taking taylor expansion of PI in n
6.277 * [backup-simplify]: Simplify PI into PI
6.277 * [taylor]: Taking taylor expansion of n in n
6.277 * [backup-simplify]: Simplify 0 into 0
6.277 * [backup-simplify]: Simplify 1 into 1
6.277 * [backup-simplify]: Simplify (/ PI 1) into PI
6.278 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.279 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.279 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.279 * [taylor]: Taking taylor expansion of 1.0 in n
6.279 * [backup-simplify]: Simplify 1.0 into 1.0
6.279 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.279 * [taylor]: Taking taylor expansion of k in n
6.279 * [backup-simplify]: Simplify k into k
6.279 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.281 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.281 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.281 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.282 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.284 * [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))))
6.285 * [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)))))
6.286 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
6.287 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.289 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.290 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.291 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.291 * [backup-simplify]: Simplify (- 0) into 0
6.291 * [backup-simplify]: Simplify (+ 0 0) into 0
6.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.293 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
6.295 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
6.296 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
6.298 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
6.304 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.306 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
6.307 * [backup-simplify]: Simplify (- 0) into 0
6.307 * [backup-simplify]: Simplify 0 into 0
6.307 * [backup-simplify]: Simplify 0 into 0
6.311 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.321 * [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)))))))
6.323 * [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)))))))
6.323 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.323 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.323 * [taylor]: Taking taylor expansion of +nan.0 in n
6.323 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.323 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.323 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.323 * [taylor]: Taking taylor expansion of 0.5 in n
6.323 * [backup-simplify]: Simplify 0.5 into 0.5
6.323 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.323 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.323 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.324 * [taylor]: Taking taylor expansion of 2.0 in n
6.324 * [backup-simplify]: Simplify 2.0 into 2.0
6.324 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.324 * [taylor]: Taking taylor expansion of PI in n
6.324 * [backup-simplify]: Simplify PI into PI
6.324 * [taylor]: Taking taylor expansion of n in n
6.324 * [backup-simplify]: Simplify 0 into 0
6.324 * [backup-simplify]: Simplify 1 into 1
6.324 * [backup-simplify]: Simplify (/ PI 1) into PI
6.325 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.326 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.326 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.326 * [taylor]: Taking taylor expansion of 1.0 in n
6.326 * [backup-simplify]: Simplify 1.0 into 1.0
6.326 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.326 * [taylor]: Taking taylor expansion of k in n
6.326 * [backup-simplify]: Simplify k into k
6.326 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.333 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.333 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.334 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.335 * [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))))
6.336 * [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)))))
6.337 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
6.338 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.340 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.354 * [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))))))))
6.356 * [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))))
6.356 * [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
6.356 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 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 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
6.356 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
6.356 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
6.356 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
6.356 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
6.356 * [taylor]: Taking taylor expansion of 0.5 in n
6.356 * [backup-simplify]: Simplify 0.5 into 0.5
6.356 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.356 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.356 * [taylor]: Taking taylor expansion of k in n
6.356 * [backup-simplify]: Simplify k into k
6.356 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
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 (* -2.0 (/ PI n))) in n
6.356 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.357 * [taylor]: Taking taylor expansion of -2.0 in n
6.357 * [backup-simplify]: Simplify -2.0 into -2.0
6.357 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.357 * [taylor]: Taking taylor expansion of PI in n
6.357 * [backup-simplify]: Simplify PI into PI
6.357 * [taylor]: Taking taylor expansion of n in n
6.357 * [backup-simplify]: Simplify 0 into 0
6.357 * [backup-simplify]: Simplify 1 into 1
6.357 * [backup-simplify]: Simplify (/ PI 1) into PI
6.358 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.359 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.359 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.359 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
6.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.362 * [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))))
6.363 * [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)))))
6.363 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.363 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.363 * [taylor]: Taking taylor expansion of -1 in n
6.363 * [backup-simplify]: Simplify -1 into -1
6.363 * [taylor]: Taking taylor expansion of k in n
6.363 * [backup-simplify]: Simplify k into k
6.363 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.364 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.364 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.364 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.365 * [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)))
6.365 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
6.365 * [taylor]: Taking taylor expansion of 1.0 in k
6.365 * [backup-simplify]: Simplify 1.0 into 1.0
6.366 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
6.366 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
6.366 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
6.366 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
6.366 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
6.366 * [taylor]: Taking taylor expansion of 0.5 in k
6.366 * [backup-simplify]: Simplify 0.5 into 0.5
6.366 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.366 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.366 * [taylor]: Taking taylor expansion of k in k
6.366 * [backup-simplify]: Simplify 0 into 0
6.366 * [backup-simplify]: Simplify 1 into 1
6.367 * [backup-simplify]: Simplify (/ 1 1) into 1
6.367 * [taylor]: Taking taylor expansion of 1.0 in k
6.367 * [backup-simplify]: Simplify 1.0 into 1.0
6.367 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
6.367 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
6.367 * [taylor]: Taking taylor expansion of -2.0 in k
6.367 * [backup-simplify]: Simplify -2.0 into -2.0
6.367 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.367 * [taylor]: Taking taylor expansion of PI in k
6.367 * [backup-simplify]: Simplify PI into PI
6.367 * [taylor]: Taking taylor expansion of n in k
6.367 * [backup-simplify]: Simplify n into n
6.367 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.367 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
6.367 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
6.368 * [backup-simplify]: Simplify (+ 1 0) into 1
6.368 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
6.368 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
6.369 * [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))))))
6.369 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.369 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.369 * [taylor]: Taking taylor expansion of -1 in k
6.369 * [backup-simplify]: Simplify -1 into -1
6.369 * [taylor]: Taking taylor expansion of k in k
6.369 * [backup-simplify]: Simplify 0 into 0
6.369 * [backup-simplify]: Simplify 1 into 1
6.369 * [backup-simplify]: Simplify (/ -1 1) into -1
6.370 * [backup-simplify]: Simplify (sqrt 0) into 0
6.371 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.372 * [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)))))))
6.372 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
6.372 * [taylor]: Taking taylor expansion of 1.0 in k
6.372 * [backup-simplify]: Simplify 1.0 into 1.0
6.372 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
6.372 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
6.372 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
6.372 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
6.372 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
6.372 * [taylor]: Taking taylor expansion of 0.5 in k
6.372 * [backup-simplify]: Simplify 0.5 into 0.5
6.372 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.372 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.372 * [taylor]: Taking taylor expansion of k in k
6.372 * [backup-simplify]: Simplify 0 into 0
6.372 * [backup-simplify]: Simplify 1 into 1
6.373 * [backup-simplify]: Simplify (/ 1 1) into 1
6.373 * [taylor]: Taking taylor expansion of 1.0 in k
6.373 * [backup-simplify]: Simplify 1.0 into 1.0
6.373 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
6.373 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
6.373 * [taylor]: Taking taylor expansion of -2.0 in k
6.373 * [backup-simplify]: Simplify -2.0 into -2.0
6.373 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.373 * [taylor]: Taking taylor expansion of PI in k
6.373 * [backup-simplify]: Simplify PI into PI
6.373 * [taylor]: Taking taylor expansion of n in k
6.373 * [backup-simplify]: Simplify n into n
6.373 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.373 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
6.373 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
6.374 * [backup-simplify]: Simplify (+ 1 0) into 1
6.374 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
6.374 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
6.375 * [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))))))
6.375 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.375 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.375 * [taylor]: Taking taylor expansion of -1 in k
6.375 * [backup-simplify]: Simplify -1 into -1
6.375 * [taylor]: Taking taylor expansion of k in k
6.375 * [backup-simplify]: Simplify 0 into 0
6.375 * [backup-simplify]: Simplify 1 into 1
6.375 * [backup-simplify]: Simplify (/ -1 1) into -1
6.376 * [backup-simplify]: Simplify (sqrt 0) into 0
6.377 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.377 * [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)))))))
6.378 * [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)))))))
6.378 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.378 * [taylor]: Taking taylor expansion of +nan.0 in n
6.378 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.378 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.378 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.378 * [taylor]: Taking taylor expansion of 0.5 in n
6.378 * [backup-simplify]: Simplify 0.5 into 0.5
6.378 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.378 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.378 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.378 * [taylor]: Taking taylor expansion of k in n
6.378 * [backup-simplify]: Simplify k into k
6.378 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.378 * [taylor]: Taking taylor expansion of 1.0 in n
6.378 * [backup-simplify]: Simplify 1.0 into 1.0
6.378 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.378 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.379 * [taylor]: Taking taylor expansion of -2.0 in n
6.379 * [backup-simplify]: Simplify -2.0 into -2.0
6.379 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.379 * [taylor]: Taking taylor expansion of PI in n
6.379 * [backup-simplify]: Simplify PI into PI
6.379 * [taylor]: Taking taylor expansion of n in n
6.379 * [backup-simplify]: Simplify 0 into 0
6.379 * [backup-simplify]: Simplify 1 into 1
6.379 * [backup-simplify]: Simplify (/ PI 1) into PI
6.380 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.381 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.381 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.384 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.385 * [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))))
6.387 * [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)))))
6.388 * [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))))))
6.389 * [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))))))
6.390 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.393 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.395 * [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))))))))
6.395 * [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))))))))
6.395 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
6.395 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.395 * [taylor]: Taking taylor expansion of +nan.0 in n
6.395 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.396 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.396 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.396 * [taylor]: Taking taylor expansion of 0.5 in n
6.396 * [backup-simplify]: Simplify 0.5 into 0.5
6.396 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.396 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.396 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.396 * [taylor]: Taking taylor expansion of k in n
6.396 * [backup-simplify]: Simplify k into k
6.396 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.396 * [taylor]: Taking taylor expansion of 1.0 in n
6.396 * [backup-simplify]: Simplify 1.0 into 1.0
6.396 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.396 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.396 * [taylor]: Taking taylor expansion of -2.0 in n
6.396 * [backup-simplify]: Simplify -2.0 into -2.0
6.396 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.396 * [taylor]: Taking taylor expansion of PI in n
6.396 * [backup-simplify]: Simplify PI into PI
6.396 * [taylor]: Taking taylor expansion of n in n
6.396 * [backup-simplify]: Simplify 0 into 0
6.396 * [backup-simplify]: Simplify 1 into 1
6.397 * [backup-simplify]: Simplify (/ PI 1) into PI
6.397 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.399 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.399 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.400 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.401 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.403 * [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))))
6.404 * [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)))))
6.406 * [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))))))
6.407 * [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)))))))
6.408 * [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)))))))
6.409 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.410 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
6.412 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
6.413 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.413 * [backup-simplify]: Simplify (+ 0 0) into 0
6.415 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.416 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
6.418 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
6.420 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.422 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
6.422 * [backup-simplify]: Simplify 0 into 0
6.423 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.427 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.429 * [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))))))))
6.431 * [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))))))))
6.431 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
6.431 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.431 * [taylor]: Taking taylor expansion of +nan.0 in n
6.431 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.431 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.431 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.431 * [taylor]: Taking taylor expansion of 0.5 in n
6.431 * [backup-simplify]: Simplify 0.5 into 0.5
6.431 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.431 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.431 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.431 * [taylor]: Taking taylor expansion of k in n
6.431 * [backup-simplify]: Simplify k into k
6.431 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.431 * [taylor]: Taking taylor expansion of 1.0 in n
6.431 * [backup-simplify]: Simplify 1.0 into 1.0
6.431 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.431 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.431 * [taylor]: Taking taylor expansion of -2.0 in n
6.431 * [backup-simplify]: Simplify -2.0 into -2.0
6.431 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.431 * [taylor]: Taking taylor expansion of PI in n
6.431 * [backup-simplify]: Simplify PI into PI
6.431 * [taylor]: Taking taylor expansion of n in n
6.431 * [backup-simplify]: Simplify 0 into 0
6.431 * [backup-simplify]: Simplify 1 into 1
6.433 * [backup-simplify]: Simplify (/ PI 1) into PI
6.433 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.434 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.435 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.436 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.437 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.439 * [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))))
6.440 * [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)))))
6.441 * [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))))))
6.443 * [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)))))))
6.444 * [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)))))))
6.449 * [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))))))))))))
6.450 * * * [progress]: simplifying candidates
6.454 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) 1)
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 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))))))))))))
6.465 * * [simplify]: iteration 0: 369 enodes
6.717 * * [simplify]: iteration 1: 1028 enodes
7.691 * * [simplify]: iteration 2: 3472 enodes
10.071 * * [simplify]: iteration complete: 5001 enodes
10.071 * * [simplify]: Extracting #0: cost 125 inf + 0
10.074 * * [simplify]: Extracting #1: cost 638 inf + 43
10.082 * * [simplify]: Extracting #2: cost 1159 inf + 2395
10.112 * * [simplify]: Extracting #3: cost 1111 inf + 44265
10.170 * * [simplify]: Extracting #4: cost 745 inf + 188861
10.287 * * [simplify]: Extracting #5: cost 365 inf + 413031
10.494 * * [simplify]: Extracting #6: cost 115 inf + 617063
10.737 * * [simplify]: Extracting #7: cost 10 inf + 711172
11.009 * * [simplify]: Extracting #8: cost 0 inf + 719728
11.283 * * [simplify]: Extracting #9: cost 0 inf + 719393
11.530 * [simplify]: Simplified to:
  (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* 2.0 (* n PI)) (/ 1.0 2.0))
  (pow (* 2.0 (* n PI)) (/ k 2.0))
  (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k)))
  (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))
  (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))
  (expm1 (* 2.0 (* n PI)))
  (log1p (* 2.0 (* n PI)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))) n)
  (* (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))) n)
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))) n)
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* 2.0 (* (* PI (cbrt n)) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* 2.0 PI)
  (* n PI)
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* 1.0 (/ (* 1.0 1.0) k)) (sqrt k))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (/ (* 1.0 (/ (* 1.0 1.0) k)) (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (expm1 (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (exp (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (/ 1.0 k))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (/ 1.0 k))))
  (* (cbrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (/ 1.0 k))))
  (sqrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) 1.0)
  (* (sqrt k) (pow (* 2.0 (* n PI)) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (sqrt (/ 1.0 (sqrt k))))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt k) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (sqrt k))
  (* (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (/ 1.0 (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (cbrt k))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k))))
  (/ (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (cbrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (/ 1.0 (sqrt k)))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (- (fma (* 0.125 (* k k)) (fma (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (log (* 2.0 PI))) (log (* 2.0 PI)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) (log n)))) (fma 0.25 (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (log (* 2.0 PI))) (* (log n) (* k k))) (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* (fma (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (log (* 2.0 PI)) (* (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (log n))) 0.5))
  (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k)))
  (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (- (fma k +nan.0 +nan.0) (* (* k k) +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k)))))
  (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) +nan.0)))
  (fma (* +nan.0 (* (* k (log (* 2.0 PI))) (* k (log (* 2.0 PI))))) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (- (fma (* +nan.0 (* (* k k) (log (* 2.0 PI)))) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5) (* (* (* +nan.0 (* (* k k) (log (* 2.0 PI)))) (log n)) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)))) (fma (* (* (log n) (* k k)) +nan.0) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (fma k (* (* (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5) (log (* 2.0 PI))) +nan.0) (fma (* +nan.0 (* (* k (log n)) (* k (log n)))) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (fma +nan.0 (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (fma +nan.0 (fma (* k k) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5) (* (- k) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5))) (* (* +nan.0 (* k (log n))) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)))))))))
  (fma (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (* k (* k k))) (- +nan.0) (fma (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) k) +nan.0 (* (/ (- +nan.0) k) (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) k))))
  (fma +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k)) (- (* (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k) (/ +nan.0 k)) (* +nan.0 (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))))))
11.553 * * * [progress]: adding candidates to table
12.849 * * [progress]: iteration 2 / 4
12.849 * * * [progress]: picking best candidate
12.967 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
12.967 * * * [progress]: localizing error
13.019 * * * [progress]: generating rewritten candidates
13.019 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2)
13.066 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 2 1)
13.103 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
13.158 * * * [progress]: generating series expansions
13.158 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2)
13.159 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
13.159 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
13.159 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.159 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.159 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.159 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.159 * [taylor]: Taking taylor expansion of 0.5 in k
13.159 * [backup-simplify]: Simplify 0.5 into 0.5
13.159 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.159 * [taylor]: Taking taylor expansion of 1.0 in k
13.159 * [backup-simplify]: Simplify 1.0 into 1.0
13.159 * [taylor]: Taking taylor expansion of k in k
13.159 * [backup-simplify]: Simplify 0 into 0
13.159 * [backup-simplify]: Simplify 1 into 1
13.160 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.160 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.160 * [taylor]: Taking taylor expansion of 2.0 in k
13.160 * [backup-simplify]: Simplify 2.0 into 2.0
13.160 * [taylor]: Taking taylor expansion of (* n PI) in k
13.160 * [taylor]: Taking taylor expansion of n in k
13.160 * [backup-simplify]: Simplify n into n
13.160 * [taylor]: Taking taylor expansion of PI in k
13.160 * [backup-simplify]: Simplify PI into PI
13.160 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.160 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.160 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.161 * [backup-simplify]: Simplify (- 0) into 0
13.161 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.162 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.162 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.162 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.162 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.162 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.162 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.162 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.162 * [taylor]: Taking taylor expansion of 0.5 in n
13.162 * [backup-simplify]: Simplify 0.5 into 0.5
13.162 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.162 * [taylor]: Taking taylor expansion of 1.0 in n
13.162 * [backup-simplify]: Simplify 1.0 into 1.0
13.162 * [taylor]: Taking taylor expansion of k in n
13.162 * [backup-simplify]: Simplify k into k
13.162 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.162 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.162 * [taylor]: Taking taylor expansion of 2.0 in n
13.163 * [backup-simplify]: Simplify 2.0 into 2.0
13.163 * [taylor]: Taking taylor expansion of (* n PI) in n
13.163 * [taylor]: Taking taylor expansion of n in n
13.163 * [backup-simplify]: Simplify 0 into 0
13.163 * [backup-simplify]: Simplify 1 into 1
13.163 * [taylor]: Taking taylor expansion of PI in n
13.163 * [backup-simplify]: Simplify PI into PI
13.163 * [backup-simplify]: Simplify (* 0 PI) into 0
13.164 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.166 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.168 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.169 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.169 * [backup-simplify]: Simplify (- k) into (- k)
13.169 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.169 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.171 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.172 * [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))))
13.173 * [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)))))
13.173 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.173 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.173 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.174 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.174 * [taylor]: Taking taylor expansion of 0.5 in n
13.174 * [backup-simplify]: Simplify 0.5 into 0.5
13.174 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.174 * [taylor]: Taking taylor expansion of 1.0 in n
13.174 * [backup-simplify]: Simplify 1.0 into 1.0
13.174 * [taylor]: Taking taylor expansion of k in n
13.174 * [backup-simplify]: Simplify k into k
13.174 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.174 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.174 * [taylor]: Taking taylor expansion of 2.0 in n
13.174 * [backup-simplify]: Simplify 2.0 into 2.0
13.174 * [taylor]: Taking taylor expansion of (* n PI) in n
13.174 * [taylor]: Taking taylor expansion of n in n
13.174 * [backup-simplify]: Simplify 0 into 0
13.174 * [backup-simplify]: Simplify 1 into 1
13.174 * [taylor]: Taking taylor expansion of PI in n
13.174 * [backup-simplify]: Simplify PI into PI
13.175 * [backup-simplify]: Simplify (* 0 PI) into 0
13.175 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.177 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.178 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.180 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.180 * [backup-simplify]: Simplify (- k) into (- k)
13.180 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.180 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.181 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.183 * [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))))
13.184 * [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)))))
13.184 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.184 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.184 * [taylor]: Taking taylor expansion of 0.5 in k
13.184 * [backup-simplify]: Simplify 0.5 into 0.5
13.184 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.184 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.184 * [taylor]: Taking taylor expansion of 1.0 in k
13.184 * [backup-simplify]: Simplify 1.0 into 1.0
13.184 * [taylor]: Taking taylor expansion of k in k
13.184 * [backup-simplify]: Simplify 0 into 0
13.184 * [backup-simplify]: Simplify 1 into 1
13.184 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.184 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.185 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.185 * [taylor]: Taking taylor expansion of 2.0 in k
13.185 * [backup-simplify]: Simplify 2.0 into 2.0
13.185 * [taylor]: Taking taylor expansion of PI in k
13.185 * [backup-simplify]: Simplify PI into PI
13.185 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.186 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.186 * [taylor]: Taking taylor expansion of (log n) in k
13.186 * [taylor]: Taking taylor expansion of n in k
13.186 * [backup-simplify]: Simplify n into n
13.187 * [backup-simplify]: Simplify (log n) into (log n)
13.187 * [backup-simplify]: Simplify (- 0) into 0
13.187 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.189 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.190 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.191 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.192 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.193 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.195 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.196 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.198 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.199 * [backup-simplify]: Simplify (- 0) into 0
13.199 * [backup-simplify]: Simplify (+ 0 0) into 0
13.200 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.201 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.202 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.205 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.205 * [taylor]: Taking taylor expansion of 0 in k
13.205 * [backup-simplify]: Simplify 0 into 0
13.205 * [backup-simplify]: Simplify 0 into 0
13.206 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.207 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.209 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.209 * [backup-simplify]: Simplify (+ 0 0) into 0
13.209 * [backup-simplify]: Simplify (- 1) into -1
13.210 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.211 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.214 * [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))))
13.218 * [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))))))
13.221 * [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))))))
13.223 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.224 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.228 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.229 * [backup-simplify]: Simplify (- 0) into 0
13.229 * [backup-simplify]: Simplify (+ 0 0) into 0
13.230 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.231 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.233 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.235 * [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
13.235 * [taylor]: Taking taylor expansion of 0 in k
13.235 * [backup-simplify]: Simplify 0 into 0
13.235 * [backup-simplify]: Simplify 0 into 0
13.236 * [backup-simplify]: Simplify 0 into 0
13.237 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.240 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.242 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.243 * [backup-simplify]: Simplify (+ 0 0) into 0
13.243 * [backup-simplify]: Simplify (- 0) into 0
13.244 * [backup-simplify]: Simplify (+ 0 0) into 0
13.246 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.248 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.253 * [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))))))
13.258 * [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))))))
13.270 * [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))))))
13.271 * [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))))
13.271 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
13.271 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.271 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.271 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.271 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.271 * [taylor]: Taking taylor expansion of 0.5 in k
13.271 * [backup-simplify]: Simplify 0.5 into 0.5
13.271 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.271 * [taylor]: Taking taylor expansion of 1.0 in k
13.271 * [backup-simplify]: Simplify 1.0 into 1.0
13.271 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.271 * [taylor]: Taking taylor expansion of k in k
13.271 * [backup-simplify]: Simplify 0 into 0
13.271 * [backup-simplify]: Simplify 1 into 1
13.272 * [backup-simplify]: Simplify (/ 1 1) into 1
13.272 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.272 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.272 * [taylor]: Taking taylor expansion of 2.0 in k
13.272 * [backup-simplify]: Simplify 2.0 into 2.0
13.272 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.272 * [taylor]: Taking taylor expansion of PI in k
13.272 * [backup-simplify]: Simplify PI into PI
13.272 * [taylor]: Taking taylor expansion of n in k
13.272 * [backup-simplify]: Simplify n into n
13.273 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.273 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.273 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.273 * [backup-simplify]: Simplify (- 1) into -1
13.274 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.274 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.274 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.274 * [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)))))
13.274 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.275 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.275 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.275 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.275 * [taylor]: Taking taylor expansion of 0.5 in n
13.275 * [backup-simplify]: Simplify 0.5 into 0.5
13.275 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.275 * [taylor]: Taking taylor expansion of 1.0 in n
13.275 * [backup-simplify]: Simplify 1.0 into 1.0
13.275 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.275 * [taylor]: Taking taylor expansion of k in n
13.275 * [backup-simplify]: Simplify k into k
13.275 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.275 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.275 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.275 * [taylor]: Taking taylor expansion of 2.0 in n
13.275 * [backup-simplify]: Simplify 2.0 into 2.0
13.275 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.275 * [taylor]: Taking taylor expansion of PI in n
13.275 * [backup-simplify]: Simplify PI into PI
13.275 * [taylor]: Taking taylor expansion of n in n
13.275 * [backup-simplify]: Simplify 0 into 0
13.275 * [backup-simplify]: Simplify 1 into 1
13.276 * [backup-simplify]: Simplify (/ PI 1) into PI
13.276 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.277 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.278 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.278 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.278 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.279 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.281 * [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))))
13.282 * [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)))))
13.282 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.282 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.282 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.282 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.282 * [taylor]: Taking taylor expansion of 0.5 in n
13.282 * [backup-simplify]: Simplify 0.5 into 0.5
13.282 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.282 * [taylor]: Taking taylor expansion of 1.0 in n
13.282 * [backup-simplify]: Simplify 1.0 into 1.0
13.282 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.282 * [taylor]: Taking taylor expansion of k in n
13.282 * [backup-simplify]: Simplify k into k
13.282 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.282 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.283 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.283 * [taylor]: Taking taylor expansion of 2.0 in n
13.283 * [backup-simplify]: Simplify 2.0 into 2.0
13.283 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.283 * [taylor]: Taking taylor expansion of PI in n
13.283 * [backup-simplify]: Simplify PI into PI
13.283 * [taylor]: Taking taylor expansion of n in n
13.283 * [backup-simplify]: Simplify 0 into 0
13.283 * [backup-simplify]: Simplify 1 into 1
13.283 * [backup-simplify]: Simplify (/ PI 1) into PI
13.284 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.285 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.285 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.285 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.285 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.288 * [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))))
13.289 * [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)))))
13.289 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
13.289 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
13.290 * [taylor]: Taking taylor expansion of 0.5 in k
13.290 * [backup-simplify]: Simplify 0.5 into 0.5
13.290 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
13.290 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.290 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.290 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.290 * [taylor]: Taking taylor expansion of 2.0 in k
13.290 * [backup-simplify]: Simplify 2.0 into 2.0
13.290 * [taylor]: Taking taylor expansion of PI in k
13.290 * [backup-simplify]: Simplify PI into PI
13.290 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.291 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.291 * [taylor]: Taking taylor expansion of (log n) in k
13.292 * [taylor]: Taking taylor expansion of n in k
13.292 * [backup-simplify]: Simplify n into n
13.292 * [backup-simplify]: Simplify (log n) into (log n)
13.292 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.292 * [taylor]: Taking taylor expansion of 1.0 in k
13.292 * [backup-simplify]: Simplify 1.0 into 1.0
13.292 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.292 * [taylor]: Taking taylor expansion of k in k
13.292 * [backup-simplify]: Simplify 0 into 0
13.292 * [backup-simplify]: Simplify 1 into 1
13.292 * [backup-simplify]: Simplify (/ 1 1) into 1
13.292 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.293 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.294 * [backup-simplify]: Simplify (- 1) into -1
13.294 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.296 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.297 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.298 * [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)))))
13.300 * [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)))))
13.301 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.302 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.304 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.304 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.304 * [backup-simplify]: Simplify (- 0) into 0
13.305 * [backup-simplify]: Simplify (+ 0 0) into 0
13.305 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.316 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.319 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.319 * [taylor]: Taking taylor expansion of 0 in k
13.319 * [backup-simplify]: Simplify 0 into 0
13.319 * [backup-simplify]: Simplify 0 into 0
13.319 * [backup-simplify]: Simplify 0 into 0
13.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.325 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.326 * [backup-simplify]: Simplify (- 0) into 0
13.326 * [backup-simplify]: Simplify (+ 0 0) into 0
13.327 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.328 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.330 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.333 * [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
13.333 * [taylor]: Taking taylor expansion of 0 in k
13.333 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify 0 into 0
13.334 * [backup-simplify]: Simplify 0 into 0
13.335 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.336 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.342 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.342 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.343 * [backup-simplify]: Simplify (- 0) into 0
13.344 * [backup-simplify]: Simplify (+ 0 0) into 0
13.345 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.348 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.351 * [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
13.351 * [taylor]: Taking taylor expansion of 0 in k
13.351 * [backup-simplify]: Simplify 0 into 0
13.351 * [backup-simplify]: Simplify 0 into 0
13.352 * [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))))
13.353 * [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)))
13.353 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
13.353 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.353 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.353 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.353 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.353 * [taylor]: Taking taylor expansion of 0.5 in k
13.353 * [backup-simplify]: Simplify 0.5 into 0.5
13.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.354 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.354 * [taylor]: Taking taylor expansion of k in k
13.354 * [backup-simplify]: Simplify 0 into 0
13.354 * [backup-simplify]: Simplify 1 into 1
13.354 * [backup-simplify]: Simplify (/ 1 1) into 1
13.354 * [taylor]: Taking taylor expansion of 1.0 in k
13.354 * [backup-simplify]: Simplify 1.0 into 1.0
13.354 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.354 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.354 * [taylor]: Taking taylor expansion of -2.0 in k
13.354 * [backup-simplify]: Simplify -2.0 into -2.0
13.354 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.354 * [taylor]: Taking taylor expansion of PI in k
13.354 * [backup-simplify]: Simplify PI into PI
13.354 * [taylor]: Taking taylor expansion of n in k
13.354 * [backup-simplify]: Simplify n into n
13.354 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.355 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.355 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.355 * [backup-simplify]: Simplify (+ 1 0) into 1
13.356 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.356 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.356 * [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))))))
13.356 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.356 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.356 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.356 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.356 * [taylor]: Taking taylor expansion of 0.5 in n
13.356 * [backup-simplify]: Simplify 0.5 into 0.5
13.356 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.356 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.356 * [taylor]: Taking taylor expansion of k in n
13.356 * [backup-simplify]: Simplify k into k
13.356 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.356 * [taylor]: Taking taylor expansion of 1.0 in n
13.357 * [backup-simplify]: Simplify 1.0 into 1.0
13.357 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.357 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.357 * [taylor]: Taking taylor expansion of -2.0 in n
13.357 * [backup-simplify]: Simplify -2.0 into -2.0
13.357 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.357 * [taylor]: Taking taylor expansion of PI in n
13.357 * [backup-simplify]: Simplify PI into PI
13.357 * [taylor]: Taking taylor expansion of n in n
13.357 * [backup-simplify]: Simplify 0 into 0
13.357 * [backup-simplify]: Simplify 1 into 1
13.357 * [backup-simplify]: Simplify (/ PI 1) into PI
13.358 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.359 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.359 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.359 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.362 * [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))))
13.364 * [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)))))
13.364 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.364 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.364 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.364 * [taylor]: Taking taylor expansion of 0.5 in n
13.364 * [backup-simplify]: Simplify 0.5 into 0.5
13.364 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.364 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.364 * [taylor]: Taking taylor expansion of k in n
13.364 * [backup-simplify]: Simplify k into k
13.364 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.364 * [taylor]: Taking taylor expansion of 1.0 in n
13.364 * [backup-simplify]: Simplify 1.0 into 1.0
13.364 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.364 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.364 * [taylor]: Taking taylor expansion of -2.0 in n
13.364 * [backup-simplify]: Simplify -2.0 into -2.0
13.364 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.364 * [taylor]: Taking taylor expansion of PI in n
13.364 * [backup-simplify]: Simplify PI into PI
13.364 * [taylor]: Taking taylor expansion of n in n
13.364 * [backup-simplify]: Simplify 0 into 0
13.364 * [backup-simplify]: Simplify 1 into 1
13.365 * [backup-simplify]: Simplify (/ PI 1) into PI
13.366 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.367 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.367 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.367 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.368 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.370 * [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))))
13.371 * [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)))))
13.371 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
13.371 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
13.371 * [taylor]: Taking taylor expansion of 0.5 in k
13.371 * [backup-simplify]: Simplify 0.5 into 0.5
13.371 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
13.371 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.371 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.371 * [taylor]: Taking taylor expansion of k in k
13.371 * [backup-simplify]: Simplify 0 into 0
13.371 * [backup-simplify]: Simplify 1 into 1
13.372 * [backup-simplify]: Simplify (/ 1 1) into 1
13.372 * [taylor]: Taking taylor expansion of 1.0 in k
13.372 * [backup-simplify]: Simplify 1.0 into 1.0
13.372 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
13.372 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
13.372 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
13.372 * [taylor]: Taking taylor expansion of -2.0 in k
13.372 * [backup-simplify]: Simplify -2.0 into -2.0
13.372 * [taylor]: Taking taylor expansion of PI in k
13.372 * [backup-simplify]: Simplify PI into PI
13.373 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.374 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.374 * [taylor]: Taking taylor expansion of (log n) in k
13.374 * [taylor]: Taking taylor expansion of n in k
13.374 * [backup-simplify]: Simplify n into n
13.374 * [backup-simplify]: Simplify (log n) into (log n)
13.374 * [backup-simplify]: Simplify (+ 1 0) into 1
13.374 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.376 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
13.377 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
13.378 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
13.379 * [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)))))
13.381 * [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)))))
13.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.382 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.384 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
13.384 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.385 * [backup-simplify]: Simplify (+ 0 0) into 0
13.385 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
13.387 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.388 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
13.390 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.391 * [taylor]: Taking taylor expansion of 0 in k
13.391 * [backup-simplify]: Simplify 0 into 0
13.391 * [backup-simplify]: Simplify 0 into 0
13.391 * [backup-simplify]: Simplify 0 into 0
13.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.393 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.396 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
13.397 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.397 * [backup-simplify]: Simplify (+ 0 0) into 0
13.398 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
13.400 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.401 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
13.404 * [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
13.404 * [taylor]: Taking taylor expansion of 0 in k
13.404 * [backup-simplify]: Simplify 0 into 0
13.404 * [backup-simplify]: Simplify 0 into 0
13.404 * [backup-simplify]: Simplify 0 into 0
13.404 * [backup-simplify]: Simplify 0 into 0
13.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.406 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.413 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
13.413 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.414 * [backup-simplify]: Simplify (+ 0 0) into 0
13.415 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
13.417 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.419 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
13.422 * [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
13.423 * [taylor]: Taking taylor expansion of 0 in k
13.423 * [backup-simplify]: Simplify 0 into 0
13.423 * [backup-simplify]: Simplify 0 into 0
13.424 * [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))))))
13.424 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 2 1)
13.425 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.425 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
13.425 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.425 * [taylor]: Taking taylor expansion of 2.0 in n
13.425 * [backup-simplify]: Simplify 2.0 into 2.0
13.425 * [taylor]: Taking taylor expansion of (* n PI) in n
13.425 * [taylor]: Taking taylor expansion of n in n
13.425 * [backup-simplify]: Simplify 0 into 0
13.425 * [backup-simplify]: Simplify 1 into 1
13.425 * [taylor]: Taking taylor expansion of PI in n
13.425 * [backup-simplify]: Simplify PI into PI
13.425 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.425 * [taylor]: Taking taylor expansion of 2.0 in n
13.425 * [backup-simplify]: Simplify 2.0 into 2.0
13.425 * [taylor]: Taking taylor expansion of (* n PI) in n
13.425 * [taylor]: Taking taylor expansion of n in n
13.425 * [backup-simplify]: Simplify 0 into 0
13.425 * [backup-simplify]: Simplify 1 into 1
13.425 * [taylor]: Taking taylor expansion of PI in n
13.425 * [backup-simplify]: Simplify PI into PI
13.426 * [backup-simplify]: Simplify (* 0 PI) into 0
13.426 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.426 * [backup-simplify]: Simplify 0 into 0
13.428 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.429 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.430 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.431 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.432 * [backup-simplify]: Simplify 0 into 0
13.433 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.435 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.435 * [backup-simplify]: Simplify 0 into 0
13.436 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.437 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.438 * [backup-simplify]: Simplify 0 into 0
13.439 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.441 * [backup-simplify]: Simplify 0 into 0
13.443 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.445 * [backup-simplify]: Simplify 0 into 0
13.447 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.449 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.449 * [backup-simplify]: Simplify 0 into 0
13.450 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.450 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
13.450 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
13.450 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.450 * [taylor]: Taking taylor expansion of 2.0 in n
13.450 * [backup-simplify]: Simplify 2.0 into 2.0
13.451 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.451 * [taylor]: Taking taylor expansion of PI in n
13.451 * [backup-simplify]: Simplify PI into PI
13.451 * [taylor]: Taking taylor expansion of n in n
13.451 * [backup-simplify]: Simplify 0 into 0
13.451 * [backup-simplify]: Simplify 1 into 1
13.451 * [backup-simplify]: Simplify (/ PI 1) into PI
13.451 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.451 * [taylor]: Taking taylor expansion of 2.0 in n
13.451 * [backup-simplify]: Simplify 2.0 into 2.0
13.451 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.451 * [taylor]: Taking taylor expansion of PI in n
13.451 * [backup-simplify]: Simplify PI into PI
13.451 * [taylor]: Taking taylor expansion of n in n
13.451 * [backup-simplify]: Simplify 0 into 0
13.452 * [backup-simplify]: Simplify 1 into 1
13.452 * [backup-simplify]: Simplify (/ PI 1) into PI
13.453 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.453 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.454 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.455 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.455 * [backup-simplify]: Simplify 0 into 0
13.457 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.458 * [backup-simplify]: Simplify 0 into 0
13.459 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.460 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.460 * [backup-simplify]: Simplify 0 into 0
13.462 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.463 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.463 * [backup-simplify]: Simplify 0 into 0
13.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.466 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.466 * [backup-simplify]: Simplify 0 into 0
13.467 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.469 * [backup-simplify]: Simplify 0 into 0
13.470 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
13.470 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
13.470 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
13.470 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.470 * [taylor]: Taking taylor expansion of -2.0 in n
13.470 * [backup-simplify]: Simplify -2.0 into -2.0
13.470 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.471 * [taylor]: Taking taylor expansion of PI in n
13.471 * [backup-simplify]: Simplify PI into PI
13.471 * [taylor]: Taking taylor expansion of n in n
13.471 * [backup-simplify]: Simplify 0 into 0
13.471 * [backup-simplify]: Simplify 1 into 1
13.471 * [backup-simplify]: Simplify (/ PI 1) into PI
13.471 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.471 * [taylor]: Taking taylor expansion of -2.0 in n
13.471 * [backup-simplify]: Simplify -2.0 into -2.0
13.471 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.471 * [taylor]: Taking taylor expansion of PI in n
13.471 * [backup-simplify]: Simplify PI into PI
13.471 * [taylor]: Taking taylor expansion of n in n
13.471 * [backup-simplify]: Simplify 0 into 0
13.471 * [backup-simplify]: Simplify 1 into 1
13.472 * [backup-simplify]: Simplify (/ PI 1) into PI
13.473 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.473 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.475 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.475 * [backup-simplify]: Simplify 0 into 0
13.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.485 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.485 * [backup-simplify]: Simplify 0 into 0
13.487 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.488 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.488 * [backup-simplify]: Simplify 0 into 0
13.489 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.490 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.491 * [backup-simplify]: Simplify 0 into 0
13.492 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.493 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.493 * [backup-simplify]: Simplify 0 into 0
13.495 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.497 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.497 * [backup-simplify]: Simplify 0 into 0
13.497 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
13.497 * * * * [progress]: [ 3 / 3 ] generating series at (2)
13.499 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
13.499 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
13.499 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
13.499 * [taylor]: Taking taylor expansion of 1.0 in k
13.499 * [backup-simplify]: Simplify 1.0 into 1.0
13.499 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
13.499 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.499 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.499 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.499 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.499 * [taylor]: Taking taylor expansion of 0.5 in k
13.499 * [backup-simplify]: Simplify 0.5 into 0.5
13.499 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.499 * [taylor]: Taking taylor expansion of 1.0 in k
13.499 * [backup-simplify]: Simplify 1.0 into 1.0
13.499 * [taylor]: Taking taylor expansion of k in k
13.499 * [backup-simplify]: Simplify 0 into 0
13.499 * [backup-simplify]: Simplify 1 into 1
13.499 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.499 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.500 * [taylor]: Taking taylor expansion of 2.0 in k
13.500 * [backup-simplify]: Simplify 2.0 into 2.0
13.500 * [taylor]: Taking taylor expansion of (* n PI) in k
13.500 * [taylor]: Taking taylor expansion of n in k
13.500 * [backup-simplify]: Simplify n into n
13.500 * [taylor]: Taking taylor expansion of PI in k
13.500 * [backup-simplify]: Simplify PI into PI
13.500 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.500 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.500 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.500 * [backup-simplify]: Simplify (- 0) into 0
13.501 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.501 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.502 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.502 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.502 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.502 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.502 * [taylor]: Taking taylor expansion of k in k
13.502 * [backup-simplify]: Simplify 0 into 0
13.502 * [backup-simplify]: Simplify 1 into 1
13.502 * [backup-simplify]: Simplify (/ 1 1) into 1
13.503 * [backup-simplify]: Simplify (sqrt 0) into 0
13.504 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.504 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.504 * [taylor]: Taking taylor expansion of 1.0 in n
13.504 * [backup-simplify]: Simplify 1.0 into 1.0
13.504 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.504 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.504 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.504 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.504 * [taylor]: Taking taylor expansion of 0.5 in n
13.504 * [backup-simplify]: Simplify 0.5 into 0.5
13.504 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.505 * [taylor]: Taking taylor expansion of 1.0 in n
13.505 * [backup-simplify]: Simplify 1.0 into 1.0
13.505 * [taylor]: Taking taylor expansion of k in n
13.505 * [backup-simplify]: Simplify k into k
13.505 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.505 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.505 * [taylor]: Taking taylor expansion of 2.0 in n
13.505 * [backup-simplify]: Simplify 2.0 into 2.0
13.505 * [taylor]: Taking taylor expansion of (* n PI) in n
13.505 * [taylor]: Taking taylor expansion of n in n
13.505 * [backup-simplify]: Simplify 0 into 0
13.505 * [backup-simplify]: Simplify 1 into 1
13.505 * [taylor]: Taking taylor expansion of PI in n
13.505 * [backup-simplify]: Simplify PI into PI
13.505 * [backup-simplify]: Simplify (* 0 PI) into 0
13.506 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.507 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.509 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.510 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.510 * [backup-simplify]: Simplify (- k) into (- k)
13.510 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.511 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.512 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.513 * [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))))
13.515 * [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)))))
13.515 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.515 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.515 * [taylor]: Taking taylor expansion of k in n
13.515 * [backup-simplify]: Simplify k into k
13.515 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.515 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.515 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.515 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.515 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.515 * [taylor]: Taking taylor expansion of 1.0 in n
13.515 * [backup-simplify]: Simplify 1.0 into 1.0
13.515 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.515 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.515 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.515 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.515 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.516 * [taylor]: Taking taylor expansion of 0.5 in n
13.516 * [backup-simplify]: Simplify 0.5 into 0.5
13.516 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.516 * [taylor]: Taking taylor expansion of 1.0 in n
13.516 * [backup-simplify]: Simplify 1.0 into 1.0
13.516 * [taylor]: Taking taylor expansion of k in n
13.516 * [backup-simplify]: Simplify k into k
13.516 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.516 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.516 * [taylor]: Taking taylor expansion of 2.0 in n
13.516 * [backup-simplify]: Simplify 2.0 into 2.0
13.516 * [taylor]: Taking taylor expansion of (* n PI) in n
13.516 * [taylor]: Taking taylor expansion of n in n
13.516 * [backup-simplify]: Simplify 0 into 0
13.516 * [backup-simplify]: Simplify 1 into 1
13.516 * [taylor]: Taking taylor expansion of PI in n
13.516 * [backup-simplify]: Simplify PI into PI
13.517 * [backup-simplify]: Simplify (* 0 PI) into 0
13.517 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.519 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.520 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.521 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.521 * [backup-simplify]: Simplify (- k) into (- k)
13.522 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.522 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.523 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.524 * [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))))
13.526 * [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)))))
13.526 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.526 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.526 * [taylor]: Taking taylor expansion of k in n
13.526 * [backup-simplify]: Simplify k into k
13.526 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.526 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.526 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.526 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.528 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
13.529 * [backup-simplify]: Simplify (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))
13.529 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) in k
13.529 * [taylor]: Taking taylor expansion of 1.0 in k
13.529 * [backup-simplify]: Simplify 1.0 into 1.0
13.529 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
13.529 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.529 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.529 * [taylor]: Taking taylor expansion of k in k
13.529 * [backup-simplify]: Simplify 0 into 0
13.529 * [backup-simplify]: Simplify 1 into 1
13.530 * [backup-simplify]: Simplify (/ 1 1) into 1
13.530 * [backup-simplify]: Simplify (sqrt 0) into 0
13.532 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.532 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.532 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.532 * [taylor]: Taking taylor expansion of 0.5 in k
13.532 * [backup-simplify]: Simplify 0.5 into 0.5
13.532 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.532 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.532 * [taylor]: Taking taylor expansion of 1.0 in k
13.532 * [backup-simplify]: Simplify 1.0 into 1.0
13.532 * [taylor]: Taking taylor expansion of k in k
13.532 * [backup-simplify]: Simplify 0 into 0
13.532 * [backup-simplify]: Simplify 1 into 1
13.532 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.532 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.532 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.532 * [taylor]: Taking taylor expansion of 2.0 in k
13.532 * [backup-simplify]: Simplify 2.0 into 2.0
13.532 * [taylor]: Taking taylor expansion of PI in k
13.532 * [backup-simplify]: Simplify PI into PI
13.533 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.534 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.534 * [taylor]: Taking taylor expansion of (log n) in k
13.534 * [taylor]: Taking taylor expansion of n in k
13.534 * [backup-simplify]: Simplify n into n
13.534 * [backup-simplify]: Simplify (log n) into (log n)
13.534 * [backup-simplify]: Simplify (- 0) into 0
13.535 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.536 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.537 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.539 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.540 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.541 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0
13.542 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.542 * [backup-simplify]: Simplify 0 into 0
13.543 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.544 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.546 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.547 * [backup-simplify]: Simplify (- 0) into 0
13.547 * [backup-simplify]: Simplify (+ 0 0) into 0
13.548 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.549 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.551 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.553 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.554 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
13.556 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0
13.556 * [taylor]: Taking taylor expansion of 0 in k
13.556 * [backup-simplify]: Simplify 0 into 0
13.557 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.559 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.560 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.561 * [backup-simplify]: Simplify (+ 0 0) into 0
13.561 * [backup-simplify]: Simplify (- 1) into -1
13.561 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.563 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.566 * [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))))
13.570 * [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))))))
13.574 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.576 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.578 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.579 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
13.580 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.582 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.586 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.587 * [backup-simplify]: Simplify (- 0) into 0
13.587 * [backup-simplify]: Simplify (+ 0 0) into 0
13.588 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.591 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.594 * [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
13.596 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
13.598 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))))) into 0
13.598 * [taylor]: Taking taylor expansion of 0 in k
13.598 * [backup-simplify]: Simplify 0 into 0
13.599 * [backup-simplify]: Simplify 0 into 0
13.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.604 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.606 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.606 * [backup-simplify]: Simplify (+ 0 0) into 0
13.607 * [backup-simplify]: Simplify (- 0) into 0
13.607 * [backup-simplify]: Simplify (+ 0 0) into 0
13.609 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.612 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.617 * [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))))))
13.617 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.621 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.631 * [backup-simplify]: Simplify (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))
13.639 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))
13.644 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))
13.645 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.654 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
13.656 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.657 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.664 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.665 * [backup-simplify]: Simplify (- 0) into 0
13.665 * [backup-simplify]: Simplify (+ 0 0) into 0
13.666 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
13.668 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.670 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.673 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.675 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
13.679 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))))) into 0
13.679 * [taylor]: Taking taylor expansion of 0 in k
13.679 * [backup-simplify]: Simplify 0 into 0
13.679 * [backup-simplify]: Simplify 0 into 0
13.679 * [backup-simplify]: Simplify 0 into 0
13.696 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.708 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.727 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
13.727 * [backup-simplify]: Simplify (+ 0 0) into 0
13.728 * [backup-simplify]: Simplify (- 0) into 0
13.728 * [backup-simplify]: Simplify (+ 0 0) into 0
13.731 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.755 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
13.767 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))
13.768 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.772 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.792 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))) (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))
13.816 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))))))))
13.832 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))))))))
13.855 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))))))))))
13.856 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
13.857 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (n k) around 0
13.857 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
13.857 * [taylor]: Taking taylor expansion of 1.0 in k
13.857 * [backup-simplify]: Simplify 1.0 into 1.0
13.857 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
13.857 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.857 * [taylor]: Taking taylor expansion of k in k
13.857 * [backup-simplify]: Simplify 0 into 0
13.857 * [backup-simplify]: Simplify 1 into 1
13.857 * [backup-simplify]: Simplify (sqrt 0) into 0
13.859 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.859 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.859 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.859 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.859 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.859 * [taylor]: Taking taylor expansion of 0.5 in k
13.859 * [backup-simplify]: Simplify 0.5 into 0.5
13.859 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.859 * [taylor]: Taking taylor expansion of 1.0 in k
13.859 * [backup-simplify]: Simplify 1.0 into 1.0
13.859 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.859 * [taylor]: Taking taylor expansion of k in k
13.859 * [backup-simplify]: Simplify 0 into 0
13.859 * [backup-simplify]: Simplify 1 into 1
13.860 * [backup-simplify]: Simplify (/ 1 1) into 1
13.860 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.860 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.860 * [taylor]: Taking taylor expansion of 2.0 in k
13.860 * [backup-simplify]: Simplify 2.0 into 2.0
13.860 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.860 * [taylor]: Taking taylor expansion of PI in k
13.860 * [backup-simplify]: Simplify PI into PI
13.860 * [taylor]: Taking taylor expansion of n in k
13.860 * [backup-simplify]: Simplify n into n
13.860 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.860 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.860 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.861 * [backup-simplify]: Simplify (- 1) into -1
13.861 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.862 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.862 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.862 * [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)))))
13.862 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
13.862 * [taylor]: Taking taylor expansion of 1.0 in n
13.862 * [backup-simplify]: Simplify 1.0 into 1.0
13.862 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.862 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.862 * [taylor]: Taking taylor expansion of k in n
13.862 * [backup-simplify]: Simplify k into k
13.862 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.862 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.863 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.863 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.863 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.863 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.863 * [taylor]: Taking taylor expansion of 0.5 in n
13.863 * [backup-simplify]: Simplify 0.5 into 0.5
13.863 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.863 * [taylor]: Taking taylor expansion of 1.0 in n
13.863 * [backup-simplify]: Simplify 1.0 into 1.0
13.863 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.863 * [taylor]: Taking taylor expansion of k in n
13.863 * [backup-simplify]: Simplify k into k
13.863 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.863 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.863 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.863 * [taylor]: Taking taylor expansion of 2.0 in n
13.863 * [backup-simplify]: Simplify 2.0 into 2.0
13.863 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.863 * [taylor]: Taking taylor expansion of PI in n
13.863 * [backup-simplify]: Simplify PI into PI
13.863 * [taylor]: Taking taylor expansion of n in n
13.863 * [backup-simplify]: Simplify 0 into 0
13.863 * [backup-simplify]: Simplify 1 into 1
13.864 * [backup-simplify]: Simplify (/ PI 1) into PI
13.865 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.866 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.866 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.866 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.866 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.868 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.869 * [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))))
13.871 * [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)))))
13.871 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
13.871 * [taylor]: Taking taylor expansion of 1.0 in n
13.871 * [backup-simplify]: Simplify 1.0 into 1.0
13.871 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.871 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.871 * [taylor]: Taking taylor expansion of k in n
13.871 * [backup-simplify]: Simplify k into k
13.871 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.871 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.871 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.871 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.871 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.871 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.872 * [taylor]: Taking taylor expansion of 0.5 in n
13.872 * [backup-simplify]: Simplify 0.5 into 0.5
13.872 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.872 * [taylor]: Taking taylor expansion of 1.0 in n
13.872 * [backup-simplify]: Simplify 1.0 into 1.0
13.872 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.872 * [taylor]: Taking taylor expansion of k in n
13.872 * [backup-simplify]: Simplify k into k
13.872 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.872 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.872 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.872 * [taylor]: Taking taylor expansion of 2.0 in n
13.872 * [backup-simplify]: Simplify 2.0 into 2.0
13.872 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.872 * [taylor]: Taking taylor expansion of PI in n
13.872 * [backup-simplify]: Simplify PI into PI
13.872 * [taylor]: Taking taylor expansion of n in n
13.872 * [backup-simplify]: Simplify 0 into 0
13.872 * [backup-simplify]: Simplify 1 into 1
13.873 * [backup-simplify]: Simplify (/ PI 1) into PI
13.873 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.874 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.875 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.875 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.875 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.890 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.891 * [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))))
13.892 * [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)))))
13.893 * [backup-simplify]: Simplify (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
13.894 * [backup-simplify]: Simplify (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.894 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) in k
13.894 * [taylor]: Taking taylor expansion of 1.0 in k
13.895 * [backup-simplify]: Simplify 1.0 into 1.0
13.895 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k
13.895 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.895 * [taylor]: Taking taylor expansion of k in k
13.895 * [backup-simplify]: Simplify 0 into 0
13.895 * [backup-simplify]: Simplify 1 into 1
13.895 * [backup-simplify]: Simplify (sqrt 0) into 0
13.897 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.897 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
13.897 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
13.897 * [taylor]: Taking taylor expansion of 0.5 in k
13.897 * [backup-simplify]: Simplify 0.5 into 0.5
13.897 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
13.897 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.897 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.897 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.897 * [taylor]: Taking taylor expansion of 2.0 in k
13.897 * [backup-simplify]: Simplify 2.0 into 2.0
13.897 * [taylor]: Taking taylor expansion of PI in k
13.897 * [backup-simplify]: Simplify PI into PI
13.898 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.899 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.899 * [taylor]: Taking taylor expansion of (log n) in k
13.899 * [taylor]: Taking taylor expansion of n in k
13.899 * [backup-simplify]: Simplify n into n
13.899 * [backup-simplify]: Simplify (log n) into (log n)
13.899 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.899 * [taylor]: Taking taylor expansion of 1.0 in k
13.899 * [backup-simplify]: Simplify 1.0 into 1.0
13.899 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.900 * [taylor]: Taking taylor expansion of k in k
13.900 * [backup-simplify]: Simplify 0 into 0
13.900 * [backup-simplify]: Simplify 1 into 1
13.900 * [backup-simplify]: Simplify (/ 1 1) into 1
13.900 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.901 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.901 * [backup-simplify]: Simplify (- 1) into -1
13.902 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.903 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.904 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.905 * [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)))))
13.906 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0
13.906 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.906 * [backup-simplify]: Simplify 0 into 0
13.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.908 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.910 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.910 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.910 * [backup-simplify]: Simplify (- 0) into 0
13.911 * [backup-simplify]: Simplify (+ 0 0) into 0
13.911 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.912 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.913 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.914 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.915 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
13.916 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
13.916 * [taylor]: Taking taylor expansion of 0 in k
13.916 * [backup-simplify]: Simplify 0 into 0
13.916 * [backup-simplify]: Simplify 0 into 0
13.918 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.919 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.921 * [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)))))))
13.922 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.923 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.926 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.926 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.927 * [backup-simplify]: Simplify (- 0) into 0
13.927 * [backup-simplify]: Simplify (+ 0 0) into 0
13.928 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.929 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.931 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.933 * [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
13.934 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
13.935 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
13.937 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
13.937 * [taylor]: Taking taylor expansion of 0 in k
13.937 * [backup-simplify]: Simplify 0 into 0
13.937 * [backup-simplify]: Simplify 0 into 0
13.937 * [backup-simplify]: Simplify 0 into 0
13.940 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.942 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.945 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.946 * [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)))))))
13.947 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.948 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.954 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.954 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.955 * [backup-simplify]: Simplify (- 0) into 0
13.955 * [backup-simplify]: Simplify (+ 0 0) into 0
13.956 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.957 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.959 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.962 * [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
13.963 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
13.965 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
13.967 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))))) into 0
13.967 * [taylor]: Taking taylor expansion of 0 in k
13.967 * [backup-simplify]: Simplify 0 into 0
13.967 * [backup-simplify]: Simplify 0 into 0
13.968 * [backup-simplify]: Simplify 0 into 0
13.968 * [backup-simplify]: Simplify 0 into 0
13.971 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.973 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.977 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.978 * [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)))))))
13.983 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
13.984 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
13.984 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
13.984 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
13.984 * [taylor]: Taking taylor expansion of 1.0 in k
13.984 * [backup-simplify]: Simplify 1.0 into 1.0
13.984 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
13.984 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.984 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.984 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.984 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.984 * [taylor]: Taking taylor expansion of 0.5 in k
13.984 * [backup-simplify]: Simplify 0.5 into 0.5
13.984 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.984 * [taylor]: Taking taylor expansion of k in k
13.984 * [backup-simplify]: Simplify 0 into 0
13.985 * [backup-simplify]: Simplify 1 into 1
13.985 * [backup-simplify]: Simplify (/ 1 1) into 1
13.985 * [taylor]: Taking taylor expansion of 1.0 in k
13.985 * [backup-simplify]: Simplify 1.0 into 1.0
13.985 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.985 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.985 * [taylor]: Taking taylor expansion of -2.0 in k
13.985 * [backup-simplify]: Simplify -2.0 into -2.0
13.985 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.985 * [taylor]: Taking taylor expansion of PI in k
13.985 * [backup-simplify]: Simplify PI into PI
13.985 * [taylor]: Taking taylor expansion of n in k
13.985 * [backup-simplify]: Simplify n into n
13.985 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.985 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.985 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.986 * [backup-simplify]: Simplify (+ 1 0) into 1
13.986 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.986 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.987 * [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))))))
13.987 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.987 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.987 * [taylor]: Taking taylor expansion of -1 in k
13.987 * [backup-simplify]: Simplify -1 into -1
13.987 * [taylor]: Taking taylor expansion of k in k
13.987 * [backup-simplify]: Simplify 0 into 0
13.987 * [backup-simplify]: Simplify 1 into 1
13.987 * [backup-simplify]: Simplify (/ -1 1) into -1
13.988 * [backup-simplify]: Simplify (sqrt 0) into 0
13.989 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.989 * [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)))))))
13.989 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.989 * [taylor]: Taking taylor expansion of 1.0 in n
13.989 * [backup-simplify]: Simplify 1.0 into 1.0
13.989 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.989 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.990 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.990 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.990 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.990 * [taylor]: Taking taylor expansion of 0.5 in n
13.990 * [backup-simplify]: Simplify 0.5 into 0.5
13.990 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.990 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.990 * [taylor]: Taking taylor expansion of k in n
13.990 * [backup-simplify]: Simplify k into k
13.990 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.990 * [taylor]: Taking taylor expansion of 1.0 in n
13.990 * [backup-simplify]: Simplify 1.0 into 1.0
13.990 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.990 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.990 * [taylor]: Taking taylor expansion of -2.0 in n
13.990 * [backup-simplify]: Simplify -2.0 into -2.0
13.990 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.990 * [taylor]: Taking taylor expansion of PI in n
13.990 * [backup-simplify]: Simplify PI into PI
13.990 * [taylor]: Taking taylor expansion of n in n
13.990 * [backup-simplify]: Simplify 0 into 0
13.990 * [backup-simplify]: Simplify 1 into 1
13.991 * [backup-simplify]: Simplify (/ PI 1) into PI
13.991 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.993 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.993 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.993 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.995 * [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))))
13.997 * [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)))))
13.997 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.997 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.997 * [taylor]: Taking taylor expansion of -1 in n
13.997 * [backup-simplify]: Simplify -1 into -1
13.997 * [taylor]: Taking taylor expansion of k in n
13.997 * [backup-simplify]: Simplify k into k
13.997 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.997 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.997 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.997 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.998 * [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)))
13.999 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.999 * [taylor]: Taking taylor expansion of 1.0 in n
13.999 * [backup-simplify]: Simplify 1.0 into 1.0
13.999 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.999 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.999 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.999 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.999 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.999 * [taylor]: Taking taylor expansion of 0.5 in n
13.999 * [backup-simplify]: Simplify 0.5 into 0.5
13.999 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.999 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.999 * [taylor]: Taking taylor expansion of k in n
13.999 * [backup-simplify]: Simplify k into k
13.999 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.999 * [taylor]: Taking taylor expansion of 1.0 in n
13.999 * [backup-simplify]: Simplify 1.0 into 1.0
13.999 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.999 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.999 * [taylor]: Taking taylor expansion of -2.0 in n
13.999 * [backup-simplify]: Simplify -2.0 into -2.0
13.999 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.999 * [taylor]: Taking taylor expansion of PI in n
13.999 * [backup-simplify]: Simplify PI into PI
13.999 * [taylor]: Taking taylor expansion of n in n
13.999 * [backup-simplify]: Simplify 0 into 0
13.999 * [backup-simplify]: Simplify 1 into 1
14.000 * [backup-simplify]: Simplify (/ PI 1) into PI
14.000 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.001 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.002 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
14.002 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
14.003 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.004 * [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))))
14.005 * [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)))))
14.005 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
14.006 * [taylor]: Taking taylor expansion of (/ -1 k) in n
14.006 * [taylor]: Taking taylor expansion of -1 in n
14.006 * [backup-simplify]: Simplify -1 into -1
14.006 * [taylor]: Taking taylor expansion of k in n
14.006 * [backup-simplify]: Simplify k into k
14.006 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
14.006 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
14.006 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
14.006 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
14.008 * [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)))
14.009 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))))
14.009 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) in k
14.009 * [taylor]: Taking taylor expansion of 1.0 in k
14.009 * [backup-simplify]: Simplify 1.0 into 1.0
14.009 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k
14.009 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
14.009 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
14.009 * [taylor]: Taking taylor expansion of 0.5 in k
14.009 * [backup-simplify]: Simplify 0.5 into 0.5
14.009 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
14.009 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
14.009 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.009 * [taylor]: Taking taylor expansion of k in k
14.009 * [backup-simplify]: Simplify 0 into 0
14.009 * [backup-simplify]: Simplify 1 into 1
14.010 * [backup-simplify]: Simplify (/ 1 1) into 1
14.010 * [taylor]: Taking taylor expansion of 1.0 in k
14.010 * [backup-simplify]: Simplify 1.0 into 1.0
14.010 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
14.010 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
14.010 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
14.010 * [taylor]: Taking taylor expansion of -2.0 in k
14.010 * [backup-simplify]: Simplify -2.0 into -2.0
14.010 * [taylor]: Taking taylor expansion of PI in k
14.010 * [backup-simplify]: Simplify PI into PI
14.011 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.012 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.012 * [taylor]: Taking taylor expansion of (log n) in k
14.012 * [taylor]: Taking taylor expansion of n in k
14.012 * [backup-simplify]: Simplify n into n
14.012 * [backup-simplify]: Simplify (log n) into (log n)
14.012 * [backup-simplify]: Simplify (+ 1 0) into 1
14.012 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.014 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
14.015 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
14.016 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
14.017 * [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)))))
14.018 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.018 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.018 * [taylor]: Taking taylor expansion of -1 in k
14.018 * [backup-simplify]: Simplify -1 into -1
14.018 * [taylor]: Taking taylor expansion of k in k
14.018 * [backup-simplify]: Simplify 0 into 0
14.018 * [backup-simplify]: Simplify 1 into 1
14.018 * [backup-simplify]: Simplify (/ -1 1) into -1
14.019 * [backup-simplify]: Simplify (sqrt 0) into 0
14.020 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.021 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
14.022 * [backup-simplify]: Simplify (* 1.0 (* +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))))))
14.024 * [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))))))
14.025 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.025 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
14.027 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
14.028 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.028 * [backup-simplify]: Simplify (+ 0 0) into 0
14.029 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
14.039 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.040 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
14.042 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.044 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
14.045 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))))) into 0
14.045 * [taylor]: Taking taylor expansion of 0 in k
14.045 * [backup-simplify]: Simplify 0 into 0
14.046 * [backup-simplify]: Simplify 0 into 0
14.047 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.049 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.052 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
14.055 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +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)))))))
14.056 * [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)))))))
14.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.058 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.062 * [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
14.062 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.063 * [backup-simplify]: Simplify (+ 0 0) into 0
14.063 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
14.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.066 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
14.069 * [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
14.069 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.070 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
14.071 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
14.074 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
14.074 * [taylor]: Taking taylor expansion of 0 in k
14.074 * [backup-simplify]: Simplify 0 into 0
14.074 * [backup-simplify]: Simplify 0 into 0
14.074 * [backup-simplify]: Simplify 0 into 0
14.075 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.078 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.082 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
14.087 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +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)))))))
14.089 * [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)))))))
14.094 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
14.094 * * * [progress]: simplifying candidates
14.097 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (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 k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
14.104 * * [simplify]: iteration 0: 270 enodes
14.284 * * [simplify]: iteration 1: 765 enodes
14.899 * * [simplify]: iteration 2: 2571 enodes
16.731 * * [simplify]: iteration complete: 5000 enodes
16.732 * * [simplify]: Extracting #0: cost 73 inf + 0
16.734 * * [simplify]: Extracting #1: cost 614 inf + 1
16.741 * * [simplify]: Extracting #2: cost 1151 inf + 2162
16.761 * * [simplify]: Extracting #3: cost 1159 inf + 39680
16.815 * * [simplify]: Extracting #4: cost 715 inf + 204222
16.921 * * [simplify]: Extracting #5: cost 281 inf + 417211
17.092 * * [simplify]: Extracting #6: cost 130 inf + 493304
17.306 * * [simplify]: Extracting #7: cost 58 inf + 529930
17.580 * * [simplify]: Extracting #8: cost 13 inf + 563879
17.866 * * [simplify]: Extracting #9: cost 0 inf + 568587
18.154 * * [simplify]: Extracting #10: cost 0 inf + 565737
18.453 * * [simplify]: Extracting #11: cost 0 inf + 565407
18.735 * [simplify]: Simplified to:
  (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* 2.0 (* n PI)) (/ 1.0 2.0))
  (pow (* 2.0 (* n PI)) (/ k 2.0))
  (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k)))
  (pow (* 2.0 (* n PI)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k)))
  (pow (* 2.0 (* n PI)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* 1/2 (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* 1/2 (/ (- 1.0 k) 2.0)))
  (expm1 (* 2.0 (* n PI)))
  (log1p (* 2.0 (* n PI)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* (cbrt n) (* (* PI 2.0) (cbrt n)))
  (* (* (sqrt n) 2.0) PI)
  (* PI 2.0)
  (* n PI)
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (- 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (/ (sqrt k) 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* 2.0 (* n PI)) (/ k 2.0)))
  (fma (* (* k k) 0.125) (fma (* (log (* PI 2.0)) (exp (* (log (* 2.0 (* n PI))) 0.5))) (log (* PI 2.0)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) (log n)))) (- (fma (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (log n))) (log (* PI 2.0))) 0.25 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* 0.5 (* k (fma (log (* PI 2.0)) (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (log n)))))))
  (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k))))
  (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (fma (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* k k) (fma (- +nan.0) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (log n))) (fma (* (log (* PI 2.0)) (* k k)) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (fma (- +nan.0) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) k)) (- (- (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0))))) +nan.0) (* k (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))))) (fma (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (log n))) (log (* PI 2.0))) (- +nan.0) (- (fma (* k (log (* PI 2.0))) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* +nan.0 (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* (log n) k) (* (log n) k))))))))))))
  (- (- (* (/ +nan.0 (* k k)) (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k)) (* (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k) (/ +nan.0 k)))))
  (fma +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) k)) (* +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (* k k)) (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))))))
18.748 * * * [progress]: adding candidates to table
19.630 * * [progress]: iteration 3 / 4
19.630 * * * [progress]: picking best candidate
19.722 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>
19.722 * * * [progress]: localizing error
19.769 * * * [progress]: generating rewritten candidates
19.769 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
19.814 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
19.849 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
19.876 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
19.957 * * * [progress]: generating series expansions
19.957 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
19.958 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
19.958 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
19.958 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
19.958 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
19.958 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
19.959 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
19.959 * [taylor]: Taking taylor expansion of 0.5 in k
19.959 * [backup-simplify]: Simplify 0.5 into 0.5
19.959 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.959 * [taylor]: Taking taylor expansion of 1.0 in k
19.959 * [backup-simplify]: Simplify 1.0 into 1.0
19.959 * [taylor]: Taking taylor expansion of k in k
19.959 * [backup-simplify]: Simplify 0 into 0
19.959 * [backup-simplify]: Simplify 1 into 1
19.959 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
19.959 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
19.959 * [taylor]: Taking taylor expansion of 2.0 in k
19.959 * [backup-simplify]: Simplify 2.0 into 2.0
19.959 * [taylor]: Taking taylor expansion of (* n PI) in k
19.959 * [taylor]: Taking taylor expansion of n in k
19.959 * [backup-simplify]: Simplify n into n
19.959 * [taylor]: Taking taylor expansion of PI in k
19.959 * [backup-simplify]: Simplify PI into PI
19.959 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.959 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
19.959 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
19.960 * [backup-simplify]: Simplify (- 0) into 0
19.960 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.961 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
19.961 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
19.961 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
19.961 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.961 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.961 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.961 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.961 * [taylor]: Taking taylor expansion of 0.5 in n
19.961 * [backup-simplify]: Simplify 0.5 into 0.5
19.961 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.961 * [taylor]: Taking taylor expansion of 1.0 in n
19.962 * [backup-simplify]: Simplify 1.0 into 1.0
19.962 * [taylor]: Taking taylor expansion of k in n
19.962 * [backup-simplify]: Simplify k into k
19.962 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.962 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.962 * [taylor]: Taking taylor expansion of 2.0 in n
19.962 * [backup-simplify]: Simplify 2.0 into 2.0
19.962 * [taylor]: Taking taylor expansion of (* n PI) in n
19.962 * [taylor]: Taking taylor expansion of n in n
19.962 * [backup-simplify]: Simplify 0 into 0
19.962 * [backup-simplify]: Simplify 1 into 1
19.962 * [taylor]: Taking taylor expansion of PI in n
19.962 * [backup-simplify]: Simplify PI into PI
19.962 * [backup-simplify]: Simplify (* 0 PI) into 0
19.963 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.965 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.966 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.968 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.968 * [backup-simplify]: Simplify (- k) into (- k)
19.968 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.968 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.969 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.971 * [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))))
19.973 * [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)))))
19.973 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.973 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.973 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.973 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.973 * [taylor]: Taking taylor expansion of 0.5 in n
19.973 * [backup-simplify]: Simplify 0.5 into 0.5
19.973 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.973 * [taylor]: Taking taylor expansion of 1.0 in n
19.973 * [backup-simplify]: Simplify 1.0 into 1.0
19.973 * [taylor]: Taking taylor expansion of k in n
19.973 * [backup-simplify]: Simplify k into k
19.973 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.973 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.973 * [taylor]: Taking taylor expansion of 2.0 in n
19.973 * [backup-simplify]: Simplify 2.0 into 2.0
19.973 * [taylor]: Taking taylor expansion of (* n PI) in n
19.973 * [taylor]: Taking taylor expansion of n in n
19.973 * [backup-simplify]: Simplify 0 into 0
19.973 * [backup-simplify]: Simplify 1 into 1
19.973 * [taylor]: Taking taylor expansion of PI in n
19.973 * [backup-simplify]: Simplify PI into PI
19.974 * [backup-simplify]: Simplify (* 0 PI) into 0
19.974 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.976 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.978 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.979 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.979 * [backup-simplify]: Simplify (- k) into (- k)
19.979 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.979 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.981 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.982 * [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))))
19.984 * [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)))))
19.988 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
19.988 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
19.988 * [taylor]: Taking taylor expansion of 0.5 in k
19.989 * [backup-simplify]: Simplify 0.5 into 0.5
19.989 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
19.989 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.989 * [taylor]: Taking taylor expansion of 1.0 in k
19.989 * [backup-simplify]: Simplify 1.0 into 1.0
19.989 * [taylor]: Taking taylor expansion of k in k
19.989 * [backup-simplify]: Simplify 0 into 0
19.989 * [backup-simplify]: Simplify 1 into 1
19.989 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
19.989 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
19.989 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
19.989 * [taylor]: Taking taylor expansion of 2.0 in k
19.989 * [backup-simplify]: Simplify 2.0 into 2.0
19.989 * [taylor]: Taking taylor expansion of PI in k
19.989 * [backup-simplify]: Simplify PI into PI
19.990 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.991 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.991 * [taylor]: Taking taylor expansion of (log n) in k
19.991 * [taylor]: Taking taylor expansion of n in k
19.991 * [backup-simplify]: Simplify n into n
19.991 * [backup-simplify]: Simplify (log n) into (log n)
19.992 * [backup-simplify]: Simplify (- 0) into 0
19.992 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.994 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
19.995 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
19.996 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
19.997 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
19.999 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
20.000 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.001 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
20.003 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.004 * [backup-simplify]: Simplify (- 0) into 0
20.004 * [backup-simplify]: Simplify (+ 0 0) into 0
20.005 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
20.006 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.008 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
20.010 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.010 * [taylor]: Taking taylor expansion of 0 in k
20.010 * [backup-simplify]: Simplify 0 into 0
20.010 * [backup-simplify]: Simplify 0 into 0
20.011 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.013 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.014 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
20.015 * [backup-simplify]: Simplify (+ 0 0) into 0
20.015 * [backup-simplify]: Simplify (- 1) into -1
20.016 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.019 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
20.022 * [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))))
20.026 * [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))))))
20.029 * [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))))))
20.030 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.032 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.036 * [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
20.036 * [backup-simplify]: Simplify (- 0) into 0
20.037 * [backup-simplify]: Simplify (+ 0 0) into 0
20.038 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
20.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.042 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
20.055 * [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
20.055 * [taylor]: Taking taylor expansion of 0 in k
20.055 * [backup-simplify]: Simplify 0 into 0
20.055 * [backup-simplify]: Simplify 0 into 0
20.055 * [backup-simplify]: Simplify 0 into 0
20.056 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.060 * [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
20.062 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
20.063 * [backup-simplify]: Simplify (+ 0 0) into 0
20.063 * [backup-simplify]: Simplify (- 0) into 0
20.063 * [backup-simplify]: Simplify (+ 0 0) into 0
20.065 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
20.068 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
20.074 * [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))))))
20.080 * [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))))))
20.093 * [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))))))
20.094 * [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))))
20.094 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
20.094 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.095 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.095 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.095 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.095 * [taylor]: Taking taylor expansion of 0.5 in k
20.095 * [backup-simplify]: Simplify 0.5 into 0.5
20.095 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.095 * [taylor]: Taking taylor expansion of 1.0 in k
20.095 * [backup-simplify]: Simplify 1.0 into 1.0
20.095 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.095 * [taylor]: Taking taylor expansion of k in k
20.095 * [backup-simplify]: Simplify 0 into 0
20.095 * [backup-simplify]: Simplify 1 into 1
20.095 * [backup-simplify]: Simplify (/ 1 1) into 1
20.096 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.096 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.096 * [taylor]: Taking taylor expansion of 2.0 in k
20.096 * [backup-simplify]: Simplify 2.0 into 2.0
20.096 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.096 * [taylor]: Taking taylor expansion of PI in k
20.096 * [backup-simplify]: Simplify PI into PI
20.096 * [taylor]: Taking taylor expansion of n in k
20.096 * [backup-simplify]: Simplify n into n
20.096 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.096 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.096 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.097 * [backup-simplify]: Simplify (- 1) into -1
20.097 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.098 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.098 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.098 * [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)))))
20.098 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.098 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.098 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.098 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.098 * [taylor]: Taking taylor expansion of 0.5 in n
20.098 * [backup-simplify]: Simplify 0.5 into 0.5
20.098 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.098 * [taylor]: Taking taylor expansion of 1.0 in n
20.098 * [backup-simplify]: Simplify 1.0 into 1.0
20.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.098 * [taylor]: Taking taylor expansion of k in n
20.098 * [backup-simplify]: Simplify k into k
20.098 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.099 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.099 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.099 * [taylor]: Taking taylor expansion of 2.0 in n
20.099 * [backup-simplify]: Simplify 2.0 into 2.0
20.099 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.099 * [taylor]: Taking taylor expansion of PI in n
20.099 * [backup-simplify]: Simplify PI into PI
20.099 * [taylor]: Taking taylor expansion of n in n
20.099 * [backup-simplify]: Simplify 0 into 0
20.099 * [backup-simplify]: Simplify 1 into 1
20.100 * [backup-simplify]: Simplify (/ PI 1) into PI
20.100 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.101 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.102 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.102 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.102 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.105 * [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))))
20.106 * [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)))))
20.106 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.106 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.106 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.106 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.106 * [taylor]: Taking taylor expansion of 0.5 in n
20.106 * [backup-simplify]: Simplify 0.5 into 0.5
20.106 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.106 * [taylor]: Taking taylor expansion of 1.0 in n
20.106 * [backup-simplify]: Simplify 1.0 into 1.0
20.106 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.106 * [taylor]: Taking taylor expansion of k in n
20.106 * [backup-simplify]: Simplify k into k
20.106 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.106 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.107 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.107 * [taylor]: Taking taylor expansion of 2.0 in n
20.107 * [backup-simplify]: Simplify 2.0 into 2.0
20.107 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.107 * [taylor]: Taking taylor expansion of PI in n
20.107 * [backup-simplify]: Simplify PI into PI
20.107 * [taylor]: Taking taylor expansion of n in n
20.107 * [backup-simplify]: Simplify 0 into 0
20.107 * [backup-simplify]: Simplify 1 into 1
20.107 * [backup-simplify]: Simplify (/ PI 1) into PI
20.108 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.109 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.109 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.109 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.109 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.112 * [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))))
20.113 * [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)))))
20.113 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
20.114 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
20.114 * [taylor]: Taking taylor expansion of 0.5 in k
20.114 * [backup-simplify]: Simplify 0.5 into 0.5
20.114 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
20.114 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
20.114 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
20.114 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
20.114 * [taylor]: Taking taylor expansion of 2.0 in k
20.114 * [backup-simplify]: Simplify 2.0 into 2.0
20.114 * [taylor]: Taking taylor expansion of PI in k
20.114 * [backup-simplify]: Simplify PI into PI
20.114 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.115 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.115 * [taylor]: Taking taylor expansion of (log n) in k
20.115 * [taylor]: Taking taylor expansion of n in k
20.115 * [backup-simplify]: Simplify n into n
20.116 * [backup-simplify]: Simplify (log n) into (log n)
20.116 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.116 * [taylor]: Taking taylor expansion of 1.0 in k
20.116 * [backup-simplify]: Simplify 1.0 into 1.0
20.116 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.116 * [taylor]: Taking taylor expansion of k in k
20.116 * [backup-simplify]: Simplify 0 into 0
20.116 * [backup-simplify]: Simplify 1 into 1
20.116 * [backup-simplify]: Simplify (/ 1 1) into 1
20.116 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.117 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
20.118 * [backup-simplify]: Simplify (- 1) into -1
20.118 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.119 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
20.120 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
20.122 * [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)))))
20.123 * [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)))))
20.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.125 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.127 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.127 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.127 * [backup-simplify]: Simplify (- 0) into 0
20.128 * [backup-simplify]: Simplify (+ 0 0) into 0
20.128 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
20.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.132 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
20.134 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.134 * [taylor]: Taking taylor expansion of 0 in k
20.134 * [backup-simplify]: Simplify 0 into 0
20.134 * [backup-simplify]: Simplify 0 into 0
20.134 * [backup-simplify]: Simplify 0 into 0
20.136 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.137 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.141 * [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
20.142 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.142 * [backup-simplify]: Simplify (- 0) into 0
20.142 * [backup-simplify]: Simplify (+ 0 0) into 0
20.143 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
20.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.146 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
20.149 * [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
20.149 * [taylor]: Taking taylor expansion of 0 in k
20.149 * [backup-simplify]: Simplify 0 into 0
20.149 * [backup-simplify]: Simplify 0 into 0
20.149 * [backup-simplify]: Simplify 0 into 0
20.149 * [backup-simplify]: Simplify 0 into 0
20.150 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.151 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.157 * [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
20.158 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.158 * [backup-simplify]: Simplify (- 0) into 0
20.158 * [backup-simplify]: Simplify (+ 0 0) into 0
20.160 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
20.161 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.163 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
20.165 * [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
20.166 * [taylor]: Taking taylor expansion of 0 in k
20.166 * [backup-simplify]: Simplify 0 into 0
20.166 * [backup-simplify]: Simplify 0 into 0
20.167 * [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))))
20.168 * [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)))
20.168 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
20.168 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
20.168 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
20.168 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
20.168 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
20.168 * [taylor]: Taking taylor expansion of 0.5 in k
20.168 * [backup-simplify]: Simplify 0.5 into 0.5
20.168 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
20.168 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.168 * [taylor]: Taking taylor expansion of k in k
20.168 * [backup-simplify]: Simplify 0 into 0
20.168 * [backup-simplify]: Simplify 1 into 1
20.168 * [backup-simplify]: Simplify (/ 1 1) into 1
20.168 * [taylor]: Taking taylor expansion of 1.0 in k
20.168 * [backup-simplify]: Simplify 1.0 into 1.0
20.168 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
20.169 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
20.169 * [taylor]: Taking taylor expansion of -2.0 in k
20.169 * [backup-simplify]: Simplify -2.0 into -2.0
20.169 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.169 * [taylor]: Taking taylor expansion of PI in k
20.169 * [backup-simplify]: Simplify PI into PI
20.169 * [taylor]: Taking taylor expansion of n in k
20.169 * [backup-simplify]: Simplify n into n
20.169 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.169 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
20.169 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
20.169 * [backup-simplify]: Simplify (+ 1 0) into 1
20.170 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
20.170 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
20.170 * [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))))))
20.170 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
20.170 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
20.170 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
20.170 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
20.170 * [taylor]: Taking taylor expansion of 0.5 in n
20.170 * [backup-simplify]: Simplify 0.5 into 0.5
20.170 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.170 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.170 * [taylor]: Taking taylor expansion of k in n
20.170 * [backup-simplify]: Simplify k into k
20.171 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.171 * [taylor]: Taking taylor expansion of 1.0 in n
20.171 * [backup-simplify]: Simplify 1.0 into 1.0
20.171 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.171 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.171 * [taylor]: Taking taylor expansion of -2.0 in n
20.171 * [backup-simplify]: Simplify -2.0 into -2.0
20.171 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.171 * [taylor]: Taking taylor expansion of PI in n
20.171 * [backup-simplify]: Simplify PI into PI
20.171 * [taylor]: Taking taylor expansion of n in n
20.171 * [backup-simplify]: Simplify 0 into 0
20.171 * [backup-simplify]: Simplify 1 into 1
20.171 * [backup-simplify]: Simplify (/ PI 1) into PI
20.172 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.173 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.173 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.173 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
20.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.176 * [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))))
20.177 * [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)))))
20.177 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
20.177 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
20.177 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
20.177 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
20.177 * [taylor]: Taking taylor expansion of 0.5 in n
20.177 * [backup-simplify]: Simplify 0.5 into 0.5
20.177 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.177 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.177 * [taylor]: Taking taylor expansion of k in n
20.177 * [backup-simplify]: Simplify k into k
20.177 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.177 * [taylor]: Taking taylor expansion of 1.0 in n
20.177 * [backup-simplify]: Simplify 1.0 into 1.0
20.177 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.177 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.177 * [taylor]: Taking taylor expansion of -2.0 in n
20.177 * [backup-simplify]: Simplify -2.0 into -2.0
20.177 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.177 * [taylor]: Taking taylor expansion of PI in n
20.177 * [backup-simplify]: Simplify PI into PI
20.178 * [taylor]: Taking taylor expansion of n in n
20.178 * [backup-simplify]: Simplify 0 into 0
20.178 * [backup-simplify]: Simplify 1 into 1
20.178 * [backup-simplify]: Simplify (/ PI 1) into PI
20.179 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.179 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.180 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.180 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
20.181 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.182 * [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))))
20.183 * [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)))))
20.184 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
20.184 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
20.184 * [taylor]: Taking taylor expansion of 0.5 in k
20.184 * [backup-simplify]: Simplify 0.5 into 0.5
20.184 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
20.184 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
20.184 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.184 * [taylor]: Taking taylor expansion of k in k
20.184 * [backup-simplify]: Simplify 0 into 0
20.184 * [backup-simplify]: Simplify 1 into 1
20.185 * [backup-simplify]: Simplify (/ 1 1) into 1
20.185 * [taylor]: Taking taylor expansion of 1.0 in k
20.185 * [backup-simplify]: Simplify 1.0 into 1.0
20.185 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
20.185 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
20.185 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
20.185 * [taylor]: Taking taylor expansion of -2.0 in k
20.185 * [backup-simplify]: Simplify -2.0 into -2.0
20.185 * [taylor]: Taking taylor expansion of PI in k
20.185 * [backup-simplify]: Simplify PI into PI
20.185 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.186 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.186 * [taylor]: Taking taylor expansion of (log n) in k
20.186 * [taylor]: Taking taylor expansion of n in k
20.186 * [backup-simplify]: Simplify n into n
20.186 * [backup-simplify]: Simplify (log n) into (log n)
20.187 * [backup-simplify]: Simplify (+ 1 0) into 1
20.187 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.188 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
20.189 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
20.190 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
20.191 * [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)))))
20.192 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
20.193 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.194 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
20.196 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
20.196 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.196 * [backup-simplify]: Simplify (+ 0 0) into 0
20.197 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
20.198 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.199 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
20.201 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.201 * [taylor]: Taking taylor expansion of 0 in k
20.201 * [backup-simplify]: Simplify 0 into 0
20.202 * [backup-simplify]: Simplify 0 into 0
20.202 * [backup-simplify]: Simplify 0 into 0
20.203 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.204 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.208 * [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
20.208 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.208 * [backup-simplify]: Simplify (+ 0 0) into 0
20.209 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
20.219 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.221 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
20.223 * [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
20.223 * [taylor]: Taking taylor expansion of 0 in k
20.223 * [backup-simplify]: Simplify 0 into 0
20.223 * [backup-simplify]: Simplify 0 into 0
20.223 * [backup-simplify]: Simplify 0 into 0
20.224 * [backup-simplify]: Simplify 0 into 0
20.225 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.226 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.232 * [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
20.233 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.233 * [backup-simplify]: Simplify (+ 0 0) into 0
20.235 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
20.237 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.238 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
20.241 * [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
20.241 * [taylor]: Taking taylor expansion of 0 in k
20.241 * [backup-simplify]: Simplify 0 into 0
20.241 * [backup-simplify]: Simplify 0 into 0
20.243 * [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))))))
20.243 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
20.243 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
20.244 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
20.244 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.244 * [taylor]: Taking taylor expansion of 2.0 in n
20.244 * [backup-simplify]: Simplify 2.0 into 2.0
20.244 * [taylor]: Taking taylor expansion of (* n PI) in n
20.244 * [taylor]: Taking taylor expansion of n in n
20.244 * [backup-simplify]: Simplify 0 into 0
20.244 * [backup-simplify]: Simplify 1 into 1
20.244 * [taylor]: Taking taylor expansion of PI in n
20.244 * [backup-simplify]: Simplify PI into PI
20.244 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.244 * [taylor]: Taking taylor expansion of 2.0 in n
20.244 * [backup-simplify]: Simplify 2.0 into 2.0
20.244 * [taylor]: Taking taylor expansion of (* n PI) in n
20.244 * [taylor]: Taking taylor expansion of n in n
20.244 * [backup-simplify]: Simplify 0 into 0
20.244 * [backup-simplify]: Simplify 1 into 1
20.244 * [taylor]: Taking taylor expansion of PI in n
20.244 * [backup-simplify]: Simplify PI into PI
20.245 * [backup-simplify]: Simplify (* 0 PI) into 0
20.245 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.245 * [backup-simplify]: Simplify 0 into 0
20.247 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.248 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.249 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.250 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.251 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
20.251 * [backup-simplify]: Simplify 0 into 0
20.252 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.254 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.254 * [backup-simplify]: Simplify 0 into 0
20.255 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
20.257 * [backup-simplify]: Simplify 0 into 0
20.259 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.261 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
20.261 * [backup-simplify]: Simplify 0 into 0
20.263 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.265 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
20.265 * [backup-simplify]: Simplify 0 into 0
20.267 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
20.269 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
20.269 * [backup-simplify]: Simplify 0 into 0
20.270 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
20.271 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
20.271 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
20.271 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.271 * [taylor]: Taking taylor expansion of 2.0 in n
20.271 * [backup-simplify]: Simplify 2.0 into 2.0
20.271 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.271 * [taylor]: Taking taylor expansion of PI in n
20.271 * [backup-simplify]: Simplify PI into PI
20.271 * [taylor]: Taking taylor expansion of n in n
20.271 * [backup-simplify]: Simplify 0 into 0
20.271 * [backup-simplify]: Simplify 1 into 1
20.272 * [backup-simplify]: Simplify (/ PI 1) into PI
20.272 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.272 * [taylor]: Taking taylor expansion of 2.0 in n
20.272 * [backup-simplify]: Simplify 2.0 into 2.0
20.272 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.272 * [taylor]: Taking taylor expansion of PI in n
20.272 * [backup-simplify]: Simplify PI into PI
20.272 * [taylor]: Taking taylor expansion of n in n
20.272 * [backup-simplify]: Simplify 0 into 0
20.272 * [backup-simplify]: Simplify 1 into 1
20.272 * [backup-simplify]: Simplify (/ PI 1) into PI
20.273 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.274 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.274 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.275 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.275 * [backup-simplify]: Simplify 0 into 0
20.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.278 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.278 * [backup-simplify]: Simplify 0 into 0
20.279 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.280 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.280 * [backup-simplify]: Simplify 0 into 0
20.281 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.283 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.283 * [backup-simplify]: Simplify 0 into 0
20.284 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.286 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.286 * [backup-simplify]: Simplify 0 into 0
20.287 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.289 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.289 * [backup-simplify]: Simplify 0 into 0
20.290 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
20.290 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
20.290 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
20.290 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.290 * [taylor]: Taking taylor expansion of -2.0 in n
20.290 * [backup-simplify]: Simplify -2.0 into -2.0
20.290 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.290 * [taylor]: Taking taylor expansion of PI in n
20.290 * [backup-simplify]: Simplify PI into PI
20.290 * [taylor]: Taking taylor expansion of n in n
20.290 * [backup-simplify]: Simplify 0 into 0
20.290 * [backup-simplify]: Simplify 1 into 1
20.291 * [backup-simplify]: Simplify (/ PI 1) into PI
20.291 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.291 * [taylor]: Taking taylor expansion of -2.0 in n
20.291 * [backup-simplify]: Simplify -2.0 into -2.0
20.291 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.291 * [taylor]: Taking taylor expansion of PI in n
20.291 * [backup-simplify]: Simplify PI into PI
20.291 * [taylor]: Taking taylor expansion of n in n
20.291 * [backup-simplify]: Simplify 0 into 0
20.291 * [backup-simplify]: Simplify 1 into 1
20.292 * [backup-simplify]: Simplify (/ PI 1) into PI
20.292 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.293 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.295 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
20.295 * [backup-simplify]: Simplify 0 into 0
20.296 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.297 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.297 * [backup-simplify]: Simplify 0 into 0
20.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.299 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.299 * [backup-simplify]: Simplify 0 into 0
20.301 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.302 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.302 * [backup-simplify]: Simplify 0 into 0
20.304 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.305 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.306 * [backup-simplify]: Simplify 0 into 0
20.307 * [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
20.309 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.309 * [backup-simplify]: Simplify 0 into 0
20.310 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
20.310 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
20.311 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))))
20.311 * [approximate]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0
20.311 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
20.311 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.311 * [taylor]: Taking taylor expansion of k in n
20.311 * [backup-simplify]: Simplify k into k
20.311 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.311 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.311 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
20.311 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
20.311 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
20.312 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
20.312 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
20.312 * [taylor]: Taking taylor expansion of 0.5 in n
20.312 * [backup-simplify]: Simplify 0.5 into 0.5
20.312 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
20.312 * [taylor]: Taking taylor expansion of 1.0 in n
20.312 * [backup-simplify]: Simplify 1.0 into 1.0
20.312 * [taylor]: Taking taylor expansion of k in n
20.312 * [backup-simplify]: Simplify k into k
20.312 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.312 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.312 * [taylor]: Taking taylor expansion of 2.0 in n
20.312 * [backup-simplify]: Simplify 2.0 into 2.0
20.312 * [taylor]: Taking taylor expansion of (* n PI) in n
20.312 * [taylor]: Taking taylor expansion of n in n
20.312 * [backup-simplify]: Simplify 0 into 0
20.312 * [backup-simplify]: Simplify 1 into 1
20.312 * [taylor]: Taking taylor expansion of PI in n
20.312 * [backup-simplify]: Simplify PI into PI
20.313 * [backup-simplify]: Simplify (* 0 PI) into 0
20.313 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.315 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.316 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.317 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.317 * [backup-simplify]: Simplify (- k) into (- k)
20.317 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
20.317 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
20.319 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.320 * [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))))
20.321 * [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)))))
20.323 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
20.323 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
20.323 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.323 * [taylor]: Taking taylor expansion of k in k
20.323 * [backup-simplify]: Simplify 0 into 0
20.323 * [backup-simplify]: Simplify 1 into 1
20.323 * [backup-simplify]: Simplify (sqrt 0) into 0
20.325 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.325 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
20.325 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
20.325 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
20.325 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
20.325 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
20.325 * [taylor]: Taking taylor expansion of 0.5 in k
20.325 * [backup-simplify]: Simplify 0.5 into 0.5
20.325 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
20.325 * [taylor]: Taking taylor expansion of 1.0 in k
20.325 * [backup-simplify]: Simplify 1.0 into 1.0
20.325 * [taylor]: Taking taylor expansion of k in k
20.325 * [backup-simplify]: Simplify 0 into 0
20.325 * [backup-simplify]: Simplify 1 into 1
20.325 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
20.325 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
20.325 * [taylor]: Taking taylor expansion of 2.0 in k
20.325 * [backup-simplify]: Simplify 2.0 into 2.0
20.325 * [taylor]: Taking taylor expansion of (* n PI) in k
20.326 * [taylor]: Taking taylor expansion of n in k
20.326 * [backup-simplify]: Simplify n into n
20.326 * [taylor]: Taking taylor expansion of PI in k
20.326 * [backup-simplify]: Simplify PI into PI
20.326 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.326 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
20.326 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
20.326 * [backup-simplify]: Simplify (- 0) into 0
20.327 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
20.327 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
20.327 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
20.327 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
20.328 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)
20.328 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
20.328 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.328 * [taylor]: Taking taylor expansion of k in k
20.328 * [backup-simplify]: Simplify 0 into 0
20.328 * [backup-simplify]: Simplify 1 into 1
20.328 * [backup-simplify]: Simplify (sqrt 0) into 0
20.330 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.330 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
20.330 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
20.330 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
20.330 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
20.330 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
20.330 * [taylor]: Taking taylor expansion of 0.5 in k
20.330 * [backup-simplify]: Simplify 0.5 into 0.5
20.330 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
20.330 * [taylor]: Taking taylor expansion of 1.0 in k
20.330 * [backup-simplify]: Simplify 1.0 into 1.0
20.330 * [taylor]: Taking taylor expansion of k in k
20.330 * [backup-simplify]: Simplify 0 into 0
20.330 * [backup-simplify]: Simplify 1 into 1
20.330 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
20.330 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
20.330 * [taylor]: Taking taylor expansion of 2.0 in k
20.330 * [backup-simplify]: Simplify 2.0 into 2.0
20.330 * [taylor]: Taking taylor expansion of (* n PI) in k
20.330 * [taylor]: Taking taylor expansion of n in k
20.331 * [backup-simplify]: Simplify n into n
20.331 * [taylor]: Taking taylor expansion of PI in k
20.331 * [backup-simplify]: Simplify PI into PI
20.331 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.331 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
20.331 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
20.331 * [backup-simplify]: Simplify (- 0) into 0
20.332 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
20.332 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
20.332 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
20.333 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
20.333 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)
20.341 * [backup-simplify]: Simplify (* 0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) into 0
20.342 * [taylor]: Taking taylor expansion of 0 in n
20.342 * [backup-simplify]: Simplify 0 into 0
20.342 * [backup-simplify]: Simplify 0 into 0
20.342 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
20.343 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
20.344 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
20.344 * [backup-simplify]: Simplify (- 1) into -1
20.345 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.346 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
20.347 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
20.348 * [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)))
20.351 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))
20.355 * [backup-simplify]: Simplify (+ (* 0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.355 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.355 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.355 * [taylor]: Taking taylor expansion of +nan.0 in n
20.355 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.355 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.355 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.355 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.355 * [taylor]: Taking taylor expansion of 0.5 in n
20.355 * [backup-simplify]: Simplify 0.5 into 0.5
20.355 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.355 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.355 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.355 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.355 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.355 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.355 * [taylor]: Taking taylor expansion of 1.0 in n
20.355 * [backup-simplify]: Simplify 1.0 into 1.0
20.355 * [taylor]: Taking taylor expansion of (log PI) in n
20.355 * [taylor]: Taking taylor expansion of PI in n
20.355 * [backup-simplify]: Simplify PI into PI
20.356 * [backup-simplify]: Simplify (log PI) into (log PI)
20.358 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.360 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.360 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.360 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.360 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.360 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.360 * [taylor]: Taking taylor expansion of 1.0 in n
20.360 * [backup-simplify]: Simplify 1.0 into 1.0
20.360 * [taylor]: Taking taylor expansion of (log n) in n
20.360 * [taylor]: Taking taylor expansion of n in n
20.360 * [backup-simplify]: Simplify 0 into 0
20.360 * [backup-simplify]: Simplify 1 into 1
20.361 * [backup-simplify]: Simplify (log 1) into 0
20.361 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.361 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.361 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.362 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.362 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.362 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.362 * [taylor]: Taking taylor expansion of 1.0 in n
20.362 * [backup-simplify]: Simplify 1.0 into 1.0
20.362 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.362 * [taylor]: Taking taylor expansion of 2.0 in n
20.362 * [backup-simplify]: Simplify 2.0 into 2.0
20.362 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.363 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.365 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.366 * [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)
20.367 * [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)
20.368 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.370 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.371 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.373 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.375 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.377 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.378 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.378 * [backup-simplify]: Simplify 0 into 0
20.379 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
20.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
20.382 * [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
20.383 * [backup-simplify]: Simplify (- 0) into 0
20.383 * [backup-simplify]: Simplify (+ 0 0) into 0
20.384 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
20.385 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
20.387 * [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)))
20.395 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* 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 (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))
20.412 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.420 * [backup-simplify]: Simplify (+ (* 0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))
20.420 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n
20.420 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n
20.420 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) in n
20.420 * [taylor]: Taking taylor expansion of +nan.0 in n
20.420 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.420 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5) in n
20.420 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))))) in n
20.420 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
20.420 * [taylor]: Taking taylor expansion of 0.5 in n
20.420 * [backup-simplify]: Simplify 0.5 into 0.5
20.420 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
20.420 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
20.421 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
20.421 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.421 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.421 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.421 * [taylor]: Taking taylor expansion of 1.0 in n
20.421 * [backup-simplify]: Simplify 1.0 into 1.0
20.421 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.421 * [taylor]: Taking taylor expansion of 2.0 in n
20.421 * [backup-simplify]: Simplify 2.0 into 2.0
20.422 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.423 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.424 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.424 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
20.424 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.424 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.424 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.424 * [taylor]: Taking taylor expansion of 1.0 in n
20.424 * [backup-simplify]: Simplify 1.0 into 1.0
20.425 * [taylor]: Taking taylor expansion of (log n) in n
20.425 * [taylor]: Taking taylor expansion of n in n
20.425 * [backup-simplify]: Simplify 0 into 0
20.425 * [backup-simplify]: Simplify 1 into 1
20.425 * [backup-simplify]: Simplify (log 1) into 0
20.425 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.426 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.426 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.426 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.426 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.426 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.426 * [taylor]: Taking taylor expansion of 1.0 in n
20.426 * [backup-simplify]: Simplify 1.0 into 1.0
20.426 * [taylor]: Taking taylor expansion of (log PI) in n
20.426 * [taylor]: Taking taylor expansion of PI in n
20.426 * [backup-simplify]: Simplify PI into PI
20.426 * [backup-simplify]: Simplify (log PI) into (log PI)
20.427 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.429 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.430 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.431 * [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)
20.432 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)
20.434 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))
20.435 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))
20.437 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.437 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n
20.437 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.437 * [taylor]: Taking taylor expansion of +nan.0 in n
20.437 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.437 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.437 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.437 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.437 * [taylor]: Taking taylor expansion of 2.0 in n
20.437 * [backup-simplify]: Simplify 2.0 into 2.0
20.437 * [taylor]: Taking taylor expansion of (* n PI) in n
20.437 * [taylor]: Taking taylor expansion of n in n
20.437 * [backup-simplify]: Simplify 0 into 0
20.437 * [backup-simplify]: Simplify 1 into 1
20.437 * [taylor]: Taking taylor expansion of PI in n
20.437 * [backup-simplify]: Simplify PI into PI
20.438 * [backup-simplify]: Simplify (* 0 PI) into 0
20.438 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.440 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.441 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.443 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.443 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.443 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.443 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.443 * [taylor]: Taking taylor expansion of 0.5 in n
20.443 * [backup-simplify]: Simplify 0.5 into 0.5
20.443 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.443 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.443 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.443 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.443 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.443 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.443 * [taylor]: Taking taylor expansion of 1.0 in n
20.443 * [backup-simplify]: Simplify 1.0 into 1.0
20.443 * [taylor]: Taking taylor expansion of (log PI) in n
20.443 * [taylor]: Taking taylor expansion of PI in n
20.443 * [backup-simplify]: Simplify PI into PI
20.444 * [backup-simplify]: Simplify (log PI) into (log PI)
20.445 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.446 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.446 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.446 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.446 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.446 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.446 * [taylor]: Taking taylor expansion of 1.0 in n
20.447 * [backup-simplify]: Simplify 1.0 into 1.0
20.447 * [taylor]: Taking taylor expansion of (log n) in n
20.447 * [taylor]: Taking taylor expansion of n in n
20.447 * [backup-simplify]: Simplify 0 into 0
20.447 * [backup-simplify]: Simplify 1 into 1
20.447 * [backup-simplify]: Simplify (log 1) into 0
20.447 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.448 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.448 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.448 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.448 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.448 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.448 * [taylor]: Taking taylor expansion of 1.0 in n
20.448 * [backup-simplify]: Simplify 1.0 into 1.0
20.448 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.448 * [taylor]: Taking taylor expansion of 2.0 in n
20.448 * [backup-simplify]: Simplify 2.0 into 2.0
20.448 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.449 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.451 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.452 * [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)
20.453 * [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)
20.454 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.456 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.457 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.459 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.461 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))
20.463 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.466 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.469 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.472 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))
20.479 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.486 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.494 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.496 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
20.497 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
20.498 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
20.499 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.500 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.500 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
20.501 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
20.502 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
20.504 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
20.505 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
20.506 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
20.508 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
20.510 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) (/ 0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0))))) into 0
20.513 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1)))) 1) into 0
20.515 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)))) into 0
20.517 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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
20.519 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
20.520 * [backup-simplify]: Simplify (- 0) into 0
20.520 * [backup-simplify]: Simplify 0 into 0
20.520 * [backup-simplify]: Simplify 0 into 0
20.521 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
20.525 * [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
20.525 * [backup-simplify]: Simplify (- 0) into 0
20.526 * [backup-simplify]: Simplify (+ 0 0) into 0
20.527 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
20.529 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
20.531 * [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)))
20.544 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -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 (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* 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 (* 2.0 (* n PI)) 0.5))) (* (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))
20.548 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.558 * [backup-simplify]: Simplify (+ (* 0 (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))) (+ (* +nan.0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))
20.558 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))) in n
20.558 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) in n
20.558 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.558 * [taylor]: Taking taylor expansion of +nan.0 in n
20.558 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.558 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.558 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.558 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.558 * [taylor]: Taking taylor expansion of 0.5 in n
20.558 * [backup-simplify]: Simplify 0.5 into 0.5
20.558 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.558 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.558 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.558 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.558 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.558 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.558 * [taylor]: Taking taylor expansion of 1.0 in n
20.558 * [backup-simplify]: Simplify 1.0 into 1.0
20.558 * [taylor]: Taking taylor expansion of (log PI) in n
20.558 * [taylor]: Taking taylor expansion of PI in n
20.558 * [backup-simplify]: Simplify PI into PI
20.559 * [backup-simplify]: Simplify (log PI) into (log PI)
20.560 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.562 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.562 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.562 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.562 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.562 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.562 * [taylor]: Taking taylor expansion of 1.0 in n
20.562 * [backup-simplify]: Simplify 1.0 into 1.0
20.562 * [taylor]: Taking taylor expansion of (log n) in n
20.562 * [taylor]: Taking taylor expansion of n in n
20.562 * [backup-simplify]: Simplify 0 into 0
20.562 * [backup-simplify]: Simplify 1 into 1
20.562 * [backup-simplify]: Simplify (log 1) into 0
20.563 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.563 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.563 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.563 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.563 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.563 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.564 * [taylor]: Taking taylor expansion of 1.0 in n
20.564 * [backup-simplify]: Simplify 1.0 into 1.0
20.564 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.564 * [taylor]: Taking taylor expansion of 2.0 in n
20.564 * [backup-simplify]: Simplify 2.0 into 2.0
20.564 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.565 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.566 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.567 * [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)
20.581 * [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)
20.583 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.584 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.586 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.587 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.587 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) in n
20.588 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) in n
20.588 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
20.588 * [taylor]: Taking taylor expansion of +nan.0 in n
20.588 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.588 * [taylor]: Taking taylor expansion of (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
20.588 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) in n
20.588 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))))) in n
20.588 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
20.588 * [taylor]: Taking taylor expansion of 0.5 in n
20.588 * [backup-simplify]: Simplify 0.5 into 0.5
20.588 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
20.588 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
20.588 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
20.588 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.588 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.588 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.588 * [taylor]: Taking taylor expansion of 1.0 in n
20.588 * [backup-simplify]: Simplify 1.0 into 1.0
20.588 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.588 * [taylor]: Taking taylor expansion of 2.0 in n
20.588 * [backup-simplify]: Simplify 2.0 into 2.0
20.589 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.590 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.592 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.592 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
20.592 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.593 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.593 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.593 * [taylor]: Taking taylor expansion of 1.0 in n
20.593 * [backup-simplify]: Simplify 1.0 into 1.0
20.593 * [taylor]: Taking taylor expansion of (log PI) in n
20.593 * [taylor]: Taking taylor expansion of PI in n
20.593 * [backup-simplify]: Simplify PI into PI
20.593 * [backup-simplify]: Simplify (log PI) into (log PI)
20.595 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.598 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.598 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.598 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.598 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.598 * [taylor]: Taking taylor expansion of 1.0 in n
20.598 * [backup-simplify]: Simplify 1.0 into 1.0
20.598 * [taylor]: Taking taylor expansion of (log n) in n
20.598 * [taylor]: Taking taylor expansion of n in n
20.598 * [backup-simplify]: Simplify 0 into 0
20.598 * [backup-simplify]: Simplify 1 into 1
20.598 * [backup-simplify]: Simplify (log 1) into 0
20.599 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.599 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.599 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.600 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.602 * [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)
20.603 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)
20.604 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))
20.606 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))
20.608 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.608 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
20.608 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.608 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.608 * [taylor]: Taking taylor expansion of 2.0 in n
20.608 * [backup-simplify]: Simplify 2.0 into 2.0
20.608 * [taylor]: Taking taylor expansion of (* n PI) in n
20.608 * [taylor]: Taking taylor expansion of n in n
20.608 * [backup-simplify]: Simplify 0 into 0
20.608 * [backup-simplify]: Simplify 1 into 1
20.608 * [taylor]: Taking taylor expansion of PI in n
20.609 * [backup-simplify]: Simplify PI into PI
20.609 * [backup-simplify]: Simplify (* 0 PI) into 0
20.609 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.611 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.613 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.614 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.616 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.616 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n
20.616 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n
20.616 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.616 * [taylor]: Taking taylor expansion of +nan.0 in n
20.616 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.616 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.616 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.616 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.616 * [taylor]: Taking taylor expansion of 2.0 in n
20.616 * [backup-simplify]: Simplify 2.0 into 2.0
20.616 * [taylor]: Taking taylor expansion of (* n PI) in n
20.616 * [taylor]: Taking taylor expansion of n in n
20.617 * [backup-simplify]: Simplify 0 into 0
20.617 * [backup-simplify]: Simplify 1 into 1
20.617 * [taylor]: Taking taylor expansion of PI in n
20.617 * [backup-simplify]: Simplify PI into PI
20.618 * [backup-simplify]: Simplify (* 0 PI) into 0
20.619 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.620 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.622 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.624 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.624 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.624 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.624 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.624 * [taylor]: Taking taylor expansion of 0.5 in n
20.624 * [backup-simplify]: Simplify 0.5 into 0.5
20.624 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.624 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.624 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.624 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.624 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.624 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.624 * [taylor]: Taking taylor expansion of 1.0 in n
20.624 * [backup-simplify]: Simplify 1.0 into 1.0
20.624 * [taylor]: Taking taylor expansion of (log PI) in n
20.624 * [taylor]: Taking taylor expansion of PI in n
20.624 * [backup-simplify]: Simplify PI into PI
20.625 * [backup-simplify]: Simplify (log PI) into (log PI)
20.627 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.628 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.629 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.629 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.629 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.629 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.629 * [taylor]: Taking taylor expansion of 1.0 in n
20.629 * [backup-simplify]: Simplify 1.0 into 1.0
20.629 * [taylor]: Taking taylor expansion of (log n) in n
20.629 * [taylor]: Taking taylor expansion of n in n
20.629 * [backup-simplify]: Simplify 0 into 0
20.629 * [backup-simplify]: Simplify 1 into 1
20.629 * [backup-simplify]: Simplify (log 1) into 0
20.630 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.630 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.630 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.630 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.630 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.630 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.630 * [taylor]: Taking taylor expansion of 1.0 in n
20.630 * [backup-simplify]: Simplify 1.0 into 1.0
20.630 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.630 * [taylor]: Taking taylor expansion of 2.0 in n
20.630 * [backup-simplify]: Simplify 2.0 into 2.0
20.631 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.632 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.633 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.634 * [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)
20.635 * [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)
20.637 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.639 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.641 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.643 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.643 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n
20.643 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.643 * [taylor]: Taking taylor expansion of +nan.0 in n
20.643 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.643 * [taylor]: Taking taylor expansion of (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.643 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
20.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.643 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.643 * [taylor]: Taking taylor expansion of 2.0 in n
20.643 * [backup-simplify]: Simplify 2.0 into 2.0
20.644 * [taylor]: Taking taylor expansion of (* n PI) in n
20.644 * [taylor]: Taking taylor expansion of n in n
20.644 * [backup-simplify]: Simplify 0 into 0
20.644 * [backup-simplify]: Simplify 1 into 1
20.644 * [taylor]: Taking taylor expansion of PI in n
20.644 * [backup-simplify]: Simplify PI into PI
20.645 * [backup-simplify]: Simplify (* 0 PI) into 0
20.645 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.647 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.648 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.649 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.651 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.651 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.651 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.651 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.651 * [taylor]: Taking taylor expansion of 0.5 in n
20.651 * [backup-simplify]: Simplify 0.5 into 0.5
20.651 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.651 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.651 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.651 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.651 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.651 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.652 * [taylor]: Taking taylor expansion of 1.0 in n
20.652 * [backup-simplify]: Simplify 1.0 into 1.0
20.652 * [taylor]: Taking taylor expansion of (log PI) in n
20.652 * [taylor]: Taking taylor expansion of PI in n
20.652 * [backup-simplify]: Simplify PI into PI
20.652 * [backup-simplify]: Simplify (log PI) into (log PI)
20.653 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.655 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.655 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.655 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.655 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.655 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.655 * [taylor]: Taking taylor expansion of 1.0 in n
20.655 * [backup-simplify]: Simplify 1.0 into 1.0
20.655 * [taylor]: Taking taylor expansion of (log n) in n
20.655 * [taylor]: Taking taylor expansion of n in n
20.655 * [backup-simplify]: Simplify 0 into 0
20.655 * [backup-simplify]: Simplify 1 into 1
20.656 * [backup-simplify]: Simplify (log 1) into 0
20.656 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.656 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.657 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.657 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.657 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.657 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.657 * [taylor]: Taking taylor expansion of 1.0 in n
20.657 * [backup-simplify]: Simplify 1.0 into 1.0
20.657 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.657 * [taylor]: Taking taylor expansion of 2.0 in n
20.657 * [backup-simplify]: Simplify 2.0 into 2.0
20.657 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.658 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.661 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.662 * [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)
20.664 * [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)
20.665 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.667 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.669 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.671 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.672 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.674 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.675 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.678 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.681 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))
20.684 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)))
20.685 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.688 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.691 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.693 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.694 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.697 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.700 * [backup-simplify]: Simplify (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.703 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.706 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.720 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))
20.737 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))
20.757 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))
20.789 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))
20.815 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.840 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.863 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.898 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) (pow (* 1 k) 3)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 1 k)))) into (- (+ (* +nan.0 (* (pow k 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))))))))))))))))))))))))
20.900 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
20.900 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0
20.900 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
20.900 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
20.900 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.900 * [taylor]: Taking taylor expansion of k in n
20.900 * [backup-simplify]: Simplify k into k
20.900 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.900 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
20.900 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.900 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
20.901 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
20.901 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.901 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.901 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.901 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.901 * [taylor]: Taking taylor expansion of 0.5 in n
20.901 * [backup-simplify]: Simplify 0.5 into 0.5
20.901 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.901 * [taylor]: Taking taylor expansion of 1.0 in n
20.901 * [backup-simplify]: Simplify 1.0 into 1.0
20.901 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.901 * [taylor]: Taking taylor expansion of k in n
20.901 * [backup-simplify]: Simplify k into k
20.901 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.901 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.901 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.901 * [taylor]: Taking taylor expansion of 2.0 in n
20.901 * [backup-simplify]: Simplify 2.0 into 2.0
20.901 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.901 * [taylor]: Taking taylor expansion of PI in n
20.901 * [backup-simplify]: Simplify PI into PI
20.901 * [taylor]: Taking taylor expansion of n in n
20.901 * [backup-simplify]: Simplify 0 into 0
20.901 * [backup-simplify]: Simplify 1 into 1
20.902 * [backup-simplify]: Simplify (/ PI 1) into PI
20.902 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.903 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.904 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.904 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.904 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.906 * [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))))
20.908 * [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)))))
20.909 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.909 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.909 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.909 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.909 * [taylor]: Taking taylor expansion of k in k
20.909 * [backup-simplify]: Simplify 0 into 0
20.909 * [backup-simplify]: Simplify 1 into 1
20.909 * [backup-simplify]: Simplify (/ 1 1) into 1
20.910 * [backup-simplify]: Simplify (sqrt 0) into 0
20.911 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.911 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.911 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.911 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.911 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.911 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.911 * [taylor]: Taking taylor expansion of 0.5 in k
20.911 * [backup-simplify]: Simplify 0.5 into 0.5
20.911 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.911 * [taylor]: Taking taylor expansion of 1.0 in k
20.912 * [backup-simplify]: Simplify 1.0 into 1.0
20.912 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.912 * [taylor]: Taking taylor expansion of k in k
20.912 * [backup-simplify]: Simplify 0 into 0
20.912 * [backup-simplify]: Simplify 1 into 1
20.912 * [backup-simplify]: Simplify (/ 1 1) into 1
20.912 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.912 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.912 * [taylor]: Taking taylor expansion of 2.0 in k
20.912 * [backup-simplify]: Simplify 2.0 into 2.0
20.912 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.912 * [taylor]: Taking taylor expansion of PI in k
20.912 * [backup-simplify]: Simplify PI into PI
20.912 * [taylor]: Taking taylor expansion of n in k
20.912 * [backup-simplify]: Simplify n into n
20.912 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.912 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.913 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.913 * [backup-simplify]: Simplify (- 1) into -1
20.913 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.914 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.914 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.914 * [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)))))
20.914 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))
20.915 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.915 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.915 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.915 * [taylor]: Taking taylor expansion of k in k
20.915 * [backup-simplify]: Simplify 0 into 0
20.915 * [backup-simplify]: Simplify 1 into 1
20.928 * [backup-simplify]: Simplify (/ 1 1) into 1
20.928 * [backup-simplify]: Simplify (sqrt 0) into 0
20.930 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.930 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.930 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.930 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.930 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.930 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.930 * [taylor]: Taking taylor expansion of 0.5 in k
20.930 * [backup-simplify]: Simplify 0.5 into 0.5
20.930 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.930 * [taylor]: Taking taylor expansion of 1.0 in k
20.930 * [backup-simplify]: Simplify 1.0 into 1.0
20.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.930 * [taylor]: Taking taylor expansion of k in k
20.930 * [backup-simplify]: Simplify 0 into 0
20.930 * [backup-simplify]: Simplify 1 into 1
20.931 * [backup-simplify]: Simplify (/ 1 1) into 1
20.931 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.931 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.931 * [taylor]: Taking taylor expansion of 2.0 in k
20.931 * [backup-simplify]: Simplify 2.0 into 2.0
20.931 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.931 * [taylor]: Taking taylor expansion of PI in k
20.931 * [backup-simplify]: Simplify PI into PI
20.931 * [taylor]: Taking taylor expansion of n in k
20.931 * [backup-simplify]: Simplify n into n
20.931 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.931 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.931 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.932 * [backup-simplify]: Simplify (- 1) into -1
20.932 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.933 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.933 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.933 * [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)))))
20.933 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))
20.934 * [backup-simplify]: Simplify (* 0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into 0
20.934 * [taylor]: Taking taylor expansion of 0 in n
20.934 * [backup-simplify]: Simplify 0 into 0
20.934 * [backup-simplify]: Simplify 0 into 0
20.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.936 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.936 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.936 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.936 * [taylor]: Taking taylor expansion of +nan.0 in n
20.936 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.936 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.936 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.936 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.936 * [taylor]: Taking taylor expansion of 0.5 in n
20.936 * [backup-simplify]: Simplify 0.5 into 0.5
20.936 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.936 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.936 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.936 * [taylor]: Taking taylor expansion of 2.0 in n
20.937 * [backup-simplify]: Simplify 2.0 into 2.0
20.937 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.937 * [taylor]: Taking taylor expansion of PI in n
20.937 * [backup-simplify]: Simplify PI into PI
20.937 * [taylor]: Taking taylor expansion of n in n
20.937 * [backup-simplify]: Simplify 0 into 0
20.937 * [backup-simplify]: Simplify 1 into 1
20.937 * [backup-simplify]: Simplify (/ PI 1) into PI
20.938 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.939 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.939 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.939 * [taylor]: Taking taylor expansion of 1.0 in n
20.939 * [backup-simplify]: Simplify 1.0 into 1.0
20.939 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.939 * [taylor]: Taking taylor expansion of k in n
20.939 * [backup-simplify]: Simplify k into k
20.939 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.941 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.941 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.943 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.944 * [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))))
20.945 * [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)))))
20.947 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.948 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
20.950 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.951 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.951 * [backup-simplify]: Simplify 0 into 0
20.952 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.953 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.957 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.958 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.958 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.958 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.958 * [taylor]: Taking taylor expansion of +nan.0 in n
20.958 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.958 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.958 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.958 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.958 * [taylor]: Taking taylor expansion of 0.5 in n
20.958 * [backup-simplify]: Simplify 0.5 into 0.5
20.958 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.958 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.958 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.958 * [taylor]: Taking taylor expansion of 2.0 in n
20.959 * [backup-simplify]: Simplify 2.0 into 2.0
20.959 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.959 * [taylor]: Taking taylor expansion of PI in n
20.959 * [backup-simplify]: Simplify PI into PI
20.959 * [taylor]: Taking taylor expansion of n in n
20.959 * [backup-simplify]: Simplify 0 into 0
20.959 * [backup-simplify]: Simplify 1 into 1
20.959 * [backup-simplify]: Simplify (/ PI 1) into PI
20.960 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.961 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.961 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.961 * [taylor]: Taking taylor expansion of 1.0 in n
20.961 * [backup-simplify]: Simplify 1.0 into 1.0
20.961 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.961 * [taylor]: Taking taylor expansion of k in n
20.961 * [backup-simplify]: Simplify k into k
20.961 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.963 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.963 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.964 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.965 * [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))))
20.967 * [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)))))
20.968 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.970 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
20.971 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.972 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.974 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.975 * [backup-simplify]: Simplify (- 0) into 0
20.975 * [backup-simplify]: Simplify (+ 0 0) into 0
20.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.977 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.979 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.980 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
20.982 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
20.984 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.987 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
20.989 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
20.989 * [backup-simplify]: Simplify (- 0) into 0
20.989 * [backup-simplify]: Simplify 0 into 0
20.990 * [backup-simplify]: Simplify 0 into 0
20.991 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.992 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.997 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.999 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.999 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.999 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.999 * [taylor]: Taking taylor expansion of +nan.0 in n
20.999 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.999 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.999 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.999 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.999 * [taylor]: Taking taylor expansion of 0.5 in n
20.999 * [backup-simplify]: Simplify 0.5 into 0.5
20.999 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.000 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.000 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.000 * [taylor]: Taking taylor expansion of 2.0 in n
21.000 * [backup-simplify]: Simplify 2.0 into 2.0
21.000 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.000 * [taylor]: Taking taylor expansion of PI in n
21.000 * [backup-simplify]: Simplify PI into PI
21.000 * [taylor]: Taking taylor expansion of n in n
21.000 * [backup-simplify]: Simplify 0 into 0
21.000 * [backup-simplify]: Simplify 1 into 1
21.000 * [backup-simplify]: Simplify (/ PI 1) into PI
21.001 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.002 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.002 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.002 * [taylor]: Taking taylor expansion of 1.0 in n
21.002 * [backup-simplify]: Simplify 1.0 into 1.0
21.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.002 * [taylor]: Taking taylor expansion of k in n
21.002 * [backup-simplify]: Simplify k into k
21.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.004 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.004 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.004 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.006 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.007 * [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))))
21.008 * [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)))))
21.010 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
21.011 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
21.012 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
21.014 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
21.019 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))))) into (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))))))))))
21.020 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))))
21.020 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in (k n) around 0
21.020 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
21.020 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.020 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.020 * [taylor]: Taking taylor expansion of -1 in n
21.020 * [backup-simplify]: Simplify -1 into -1
21.020 * [taylor]: Taking taylor expansion of k in n
21.020 * [backup-simplify]: Simplify k into k
21.020 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.020 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.021 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.021 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.021 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
21.021 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
21.021 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
21.021 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
21.021 * [taylor]: Taking taylor expansion of 0.5 in n
21.021 * [backup-simplify]: Simplify 0.5 into 0.5
21.021 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.021 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.021 * [taylor]: Taking taylor expansion of k in n
21.021 * [backup-simplify]: Simplify k into k
21.021 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.021 * [taylor]: Taking taylor expansion of 1.0 in n
21.021 * [backup-simplify]: Simplify 1.0 into 1.0
21.021 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.021 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.021 * [taylor]: Taking taylor expansion of -2.0 in n
21.021 * [backup-simplify]: Simplify -2.0 into -2.0
21.021 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.021 * [taylor]: Taking taylor expansion of PI in n
21.021 * [backup-simplify]: Simplify PI into PI
21.021 * [taylor]: Taking taylor expansion of n in n
21.021 * [backup-simplify]: Simplify 0 into 0
21.021 * [backup-simplify]: Simplify 1 into 1
21.022 * [backup-simplify]: Simplify (/ PI 1) into PI
21.023 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.024 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.024 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.025 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
21.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.027 * [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))))
21.029 * [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)))))
21.030 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.030 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
21.030 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.030 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.030 * [taylor]: Taking taylor expansion of -1 in k
21.030 * [backup-simplify]: Simplify -1 into -1
21.030 * [taylor]: Taking taylor expansion of k in k
21.030 * [backup-simplify]: Simplify 0 into 0
21.030 * [backup-simplify]: Simplify 1 into 1
21.031 * [backup-simplify]: Simplify (/ -1 1) into -1
21.031 * [backup-simplify]: Simplify (sqrt 0) into 0
21.033 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.033 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.033 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.033 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.033 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.033 * [taylor]: Taking taylor expansion of 0.5 in k
21.033 * [backup-simplify]: Simplify 0.5 into 0.5
21.033 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.033 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.033 * [taylor]: Taking taylor expansion of k in k
21.033 * [backup-simplify]: Simplify 0 into 0
21.033 * [backup-simplify]: Simplify 1 into 1
21.033 * [backup-simplify]: Simplify (/ 1 1) into 1
21.033 * [taylor]: Taking taylor expansion of 1.0 in k
21.033 * [backup-simplify]: Simplify 1.0 into 1.0
21.033 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.034 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.034 * [taylor]: Taking taylor expansion of -2.0 in k
21.034 * [backup-simplify]: Simplify -2.0 into -2.0
21.034 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.034 * [taylor]: Taking taylor expansion of PI in k
21.034 * [backup-simplify]: Simplify PI into PI
21.034 * [taylor]: Taking taylor expansion of n in k
21.034 * [backup-simplify]: Simplify n into n
21.034 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.034 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.034 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.034 * [backup-simplify]: Simplify (+ 1 0) into 1
21.035 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.035 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.035 * [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))))))
21.036 * [backup-simplify]: Simplify (/ +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)))))))
21.036 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
21.036 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.036 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.036 * [taylor]: Taking taylor expansion of -1 in k
21.036 * [backup-simplify]: Simplify -1 into -1
21.036 * [taylor]: Taking taylor expansion of k in k
21.036 * [backup-simplify]: Simplify 0 into 0
21.036 * [backup-simplify]: Simplify 1 into 1
21.037 * [backup-simplify]: Simplify (/ -1 1) into -1
21.037 * [backup-simplify]: Simplify (sqrt 0) into 0
21.039 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.039 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.039 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.039 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.039 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.039 * [taylor]: Taking taylor expansion of 0.5 in k
21.039 * [backup-simplify]: Simplify 0.5 into 0.5
21.039 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.039 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.039 * [taylor]: Taking taylor expansion of k in k
21.039 * [backup-simplify]: Simplify 0 into 0
21.039 * [backup-simplify]: Simplify 1 into 1
21.040 * [backup-simplify]: Simplify (/ 1 1) into 1
21.040 * [taylor]: Taking taylor expansion of 1.0 in k
21.040 * [backup-simplify]: Simplify 1.0 into 1.0
21.040 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.040 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.040 * [taylor]: Taking taylor expansion of -2.0 in k
21.040 * [backup-simplify]: Simplify -2.0 into -2.0
21.040 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.040 * [taylor]: Taking taylor expansion of PI in k
21.040 * [backup-simplify]: Simplify PI into PI
21.040 * [taylor]: Taking taylor expansion of n in k
21.040 * [backup-simplify]: Simplify n into n
21.040 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.040 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.040 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.041 * [backup-simplify]: Simplify (+ 1 0) into 1
21.041 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.041 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.042 * [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))))))
21.042 * [backup-simplify]: Simplify (/ +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)))))))
21.042 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.042 * [taylor]: Taking taylor expansion of +nan.0 in n
21.042 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.042 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.042 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.042 * [taylor]: Taking taylor expansion of 0.5 in n
21.042 * [backup-simplify]: Simplify 0.5 into 0.5
21.042 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.042 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.042 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.042 * [taylor]: Taking taylor expansion of k in n
21.042 * [backup-simplify]: Simplify k into k
21.042 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.043 * [taylor]: Taking taylor expansion of 1.0 in n
21.043 * [backup-simplify]: Simplify 1.0 into 1.0
21.043 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.043 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.043 * [taylor]: Taking taylor expansion of -2.0 in n
21.043 * [backup-simplify]: Simplify -2.0 into -2.0
21.043 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.043 * [taylor]: Taking taylor expansion of PI in n
21.043 * [backup-simplify]: Simplify PI into PI
21.043 * [taylor]: Taking taylor expansion of n in n
21.043 * [backup-simplify]: Simplify 0 into 0
21.043 * [backup-simplify]: Simplify 1 into 1
21.044 * [backup-simplify]: Simplify (/ PI 1) into PI
21.044 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.045 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.045 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.047 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.049 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.050 * [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))))
21.051 * [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)))))
21.053 * [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))))))
21.054 * [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))))))
21.055 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
21.058 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.059 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))
21.059 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n
21.059 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.059 * [taylor]: Taking taylor expansion of +nan.0 in n
21.059 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.060 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.060 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.060 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.060 * [taylor]: Taking taylor expansion of 0.5 in n
21.060 * [backup-simplify]: Simplify 0.5 into 0.5
21.060 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.060 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.060 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.060 * [taylor]: Taking taylor expansion of k in n
21.060 * [backup-simplify]: Simplify k into k
21.060 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.060 * [taylor]: Taking taylor expansion of 1.0 in n
21.060 * [backup-simplify]: Simplify 1.0 into 1.0
21.060 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.060 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.060 * [taylor]: Taking taylor expansion of -2.0 in n
21.060 * [backup-simplify]: Simplify -2.0 into -2.0
21.060 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.060 * [taylor]: Taking taylor expansion of PI in n
21.060 * [backup-simplify]: Simplify PI into PI
21.060 * [taylor]: Taking taylor expansion of n in n
21.060 * [backup-simplify]: Simplify 0 into 0
21.060 * [backup-simplify]: Simplify 1 into 1
21.061 * [backup-simplify]: Simplify (/ PI 1) into PI
21.061 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.063 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.063 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.066 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.068 * [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))))
21.069 * [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)))))
21.070 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.072 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
21.073 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.074 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.076 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.076 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
21.078 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
21.079 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.079 * [backup-simplify]: Simplify (+ 0 0) into 0
21.081 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.082 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
21.085 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
21.087 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.091 * [backup-simplify]: Simplify (- (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0
21.091 * [backup-simplify]: Simplify 0 into 0
21.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.106 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.107 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))
21.108 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n
21.108 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.108 * [taylor]: Taking taylor expansion of +nan.0 in n
21.108 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.108 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.108 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.108 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.108 * [taylor]: Taking taylor expansion of 0.5 in n
21.108 * [backup-simplify]: Simplify 0.5 into 0.5
21.108 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.108 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.108 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.108 * [taylor]: Taking taylor expansion of k in n
21.108 * [backup-simplify]: Simplify k into k
21.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.108 * [taylor]: Taking taylor expansion of 1.0 in n
21.108 * [backup-simplify]: Simplify 1.0 into 1.0
21.108 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.108 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.108 * [taylor]: Taking taylor expansion of -2.0 in n
21.108 * [backup-simplify]: Simplify -2.0 into -2.0
21.108 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.108 * [taylor]: Taking taylor expansion of PI in n
21.108 * [backup-simplify]: Simplify PI into PI
21.108 * [taylor]: Taking taylor expansion of n in n
21.108 * [backup-simplify]: Simplify 0 into 0
21.108 * [backup-simplify]: Simplify 1 into 1
21.109 * [backup-simplify]: Simplify (/ PI 1) into PI
21.110 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.111 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.111 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.112 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.114 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.115 * [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))))
21.116 * [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)))))
21.118 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.119 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
21.120 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.122 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.127 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (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 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))))
21.127 * * * * [progress]: [ 4 / 4 ] generating series at (2)
21.128 * [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)))))
21.128 * [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
21.129 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
21.129 * [taylor]: Taking taylor expansion of 1.0 in n
21.129 * [backup-simplify]: Simplify 1.0 into 1.0
21.129 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
21.129 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
21.129 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.129 * [taylor]: Taking taylor expansion of k in n
21.129 * [backup-simplify]: Simplify k into k
21.129 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.129 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
21.129 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.129 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
21.129 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
21.129 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
21.129 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
21.129 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
21.129 * [taylor]: Taking taylor expansion of 0.5 in n
21.129 * [backup-simplify]: Simplify 0.5 into 0.5
21.129 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
21.129 * [taylor]: Taking taylor expansion of 1.0 in n
21.129 * [backup-simplify]: Simplify 1.0 into 1.0
21.129 * [taylor]: Taking taylor expansion of k in n
21.130 * [backup-simplify]: Simplify k into k
21.130 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.130 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.130 * [taylor]: Taking taylor expansion of 2.0 in n
21.130 * [backup-simplify]: Simplify 2.0 into 2.0
21.130 * [taylor]: Taking taylor expansion of (* n PI) in n
21.130 * [taylor]: Taking taylor expansion of n in n
21.130 * [backup-simplify]: Simplify 0 into 0
21.130 * [backup-simplify]: Simplify 1 into 1
21.130 * [taylor]: Taking taylor expansion of PI in n
21.130 * [backup-simplify]: Simplify PI into PI
21.130 * [backup-simplify]: Simplify (* 0 PI) into 0
21.131 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.133 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.134 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.135 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.135 * [backup-simplify]: Simplify (- k) into (- k)
21.136 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
21.136 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
21.137 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.138 * [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))))
21.140 * [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)))))
21.140 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
21.140 * [taylor]: Taking taylor expansion of 1.0 in k
21.140 * [backup-simplify]: Simplify 1.0 into 1.0
21.140 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
21.140 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
21.140 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.140 * [taylor]: Taking taylor expansion of k in k
21.140 * [backup-simplify]: Simplify 0 into 0
21.140 * [backup-simplify]: Simplify 1 into 1
21.140 * [backup-simplify]: Simplify (/ 1 1) into 1
21.141 * [backup-simplify]: Simplify (sqrt 0) into 0
21.142 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.142 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
21.142 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
21.142 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
21.142 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
21.142 * [taylor]: Taking taylor expansion of 0.5 in k
21.142 * [backup-simplify]: Simplify 0.5 into 0.5
21.143 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
21.143 * [taylor]: Taking taylor expansion of 1.0 in k
21.143 * [backup-simplify]: Simplify 1.0 into 1.0
21.143 * [taylor]: Taking taylor expansion of k in k
21.143 * [backup-simplify]: Simplify 0 into 0
21.143 * [backup-simplify]: Simplify 1 into 1
21.143 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
21.143 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
21.143 * [taylor]: Taking taylor expansion of 2.0 in k
21.143 * [backup-simplify]: Simplify 2.0 into 2.0
21.143 * [taylor]: Taking taylor expansion of (* n PI) in k
21.143 * [taylor]: Taking taylor expansion of n in k
21.143 * [backup-simplify]: Simplify n into n
21.143 * [taylor]: Taking taylor expansion of PI in k
21.143 * [backup-simplify]: Simplify PI into PI
21.143 * [backup-simplify]: Simplify (* n PI) into (* n PI)
21.143 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
21.143 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
21.144 * [backup-simplify]: Simplify (- 0) into 0
21.144 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
21.145 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
21.145 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
21.145 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
21.145 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
21.145 * [taylor]: Taking taylor expansion of 1.0 in k
21.145 * [backup-simplify]: Simplify 1.0 into 1.0
21.145 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
21.145 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
21.145 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.145 * [taylor]: Taking taylor expansion of k in k
21.145 * [backup-simplify]: Simplify 0 into 0
21.145 * [backup-simplify]: Simplify 1 into 1
21.146 * [backup-simplify]: Simplify (/ 1 1) into 1
21.146 * [backup-simplify]: Simplify (sqrt 0) into 0
21.148 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.148 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
21.148 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
21.148 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
21.148 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
21.148 * [taylor]: Taking taylor expansion of 0.5 in k
21.148 * [backup-simplify]: Simplify 0.5 into 0.5
21.148 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
21.148 * [taylor]: Taking taylor expansion of 1.0 in k
21.148 * [backup-simplify]: Simplify 1.0 into 1.0
21.148 * [taylor]: Taking taylor expansion of k in k
21.148 * [backup-simplify]: Simplify 0 into 0
21.148 * [backup-simplify]: Simplify 1 into 1
21.148 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
21.148 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
21.148 * [taylor]: Taking taylor expansion of 2.0 in k
21.148 * [backup-simplify]: Simplify 2.0 into 2.0
21.148 * [taylor]: Taking taylor expansion of (* n PI) in k
21.148 * [taylor]: Taking taylor expansion of n in k
21.148 * [backup-simplify]: Simplify n into n
21.148 * [taylor]: Taking taylor expansion of PI in k
21.148 * [backup-simplify]: Simplify PI into PI
21.148 * [backup-simplify]: Simplify (* n PI) into (* n PI)
21.148 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
21.149 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
21.149 * [backup-simplify]: Simplify (- 0) into 0
21.150 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
21.150 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
21.150 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
21.150 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
21.151 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
21.151 * [backup-simplify]: Simplify (* 1.0 0) into 0
21.151 * [taylor]: Taking taylor expansion of 0 in n
21.151 * [backup-simplify]: Simplify 0 into 0
21.151 * [backup-simplify]: Simplify 0 into 0
21.152 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
21.153 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
21.154 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
21.154 * [backup-simplify]: Simplify (- 1) into -1
21.155 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.157 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
21.158 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
21.158 * [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)))
21.161 * [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)))
21.163 * [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)))
21.163 * [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
21.163 * [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
21.163 * [taylor]: Taking taylor expansion of +nan.0 in n
21.163 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.163 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
21.163 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
21.163 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
21.163 * [taylor]: Taking taylor expansion of 0.5 in n
21.163 * [backup-simplify]: Simplify 0.5 into 0.5
21.163 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
21.164 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
21.164 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.164 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.164 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.164 * [taylor]: Taking taylor expansion of 1.0 in n
21.164 * [backup-simplify]: Simplify 1.0 into 1.0
21.164 * [taylor]: Taking taylor expansion of (log PI) in n
21.164 * [taylor]: Taking taylor expansion of PI in n
21.164 * [backup-simplify]: Simplify PI into PI
21.164 * [backup-simplify]: Simplify (log PI) into (log PI)
21.165 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.167 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.167 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
21.167 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.167 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.167 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.167 * [taylor]: Taking taylor expansion of 1.0 in n
21.167 * [backup-simplify]: Simplify 1.0 into 1.0
21.167 * [taylor]: Taking taylor expansion of (log n) in n
21.167 * [taylor]: Taking taylor expansion of n in n
21.167 * [backup-simplify]: Simplify 0 into 0
21.167 * [backup-simplify]: Simplify 1 into 1
21.168 * [backup-simplify]: Simplify (log 1) into 0
21.168 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.168 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.168 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.169 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.169 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.169 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.169 * [taylor]: Taking taylor expansion of 1.0 in n
21.169 * [backup-simplify]: Simplify 1.0 into 1.0
21.169 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.169 * [taylor]: Taking taylor expansion of 2.0 in n
21.169 * [backup-simplify]: Simplify 2.0 into 2.0
21.169 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.170 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.172 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.172 * [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)
21.174 * [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)
21.175 * [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))
21.176 * [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)))
21.178 * [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)
21.180 * [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))
21.181 * [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)))
21.183 * [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)))
21.183 * [backup-simplify]: Simplify 0 into 0
21.184 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
21.185 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
21.187 * [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
21.188 * [backup-simplify]: Simplify (- 0) into 0
21.188 * [backup-simplify]: Simplify (+ 0 0) into 0
21.191 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
21.192 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
21.194 * [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)))
21.194 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
21.198 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.202 * [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))))))))
21.208 * [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))))))))
21.208 * [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
21.208 * [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
21.208 * [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
21.208 * [taylor]: Taking taylor expansion of +nan.0 in n
21.208 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.208 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
21.208 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
21.208 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
21.208 * [taylor]: Taking taylor expansion of 0.5 in n
21.208 * [backup-simplify]: Simplify 0.5 into 0.5
21.208 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
21.208 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
21.208 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.208 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.208 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.209 * [taylor]: Taking taylor expansion of 1.0 in n
21.209 * [backup-simplify]: Simplify 1.0 into 1.0
21.209 * [taylor]: Taking taylor expansion of (log PI) in n
21.209 * [taylor]: Taking taylor expansion of PI in n
21.209 * [backup-simplify]: Simplify PI into PI
21.209 * [backup-simplify]: Simplify (log PI) into (log PI)
21.210 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.212 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.212 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
21.212 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.212 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.212 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.212 * [taylor]: Taking taylor expansion of 1.0 in n
21.212 * [backup-simplify]: Simplify 1.0 into 1.0
21.212 * [taylor]: Taking taylor expansion of (log n) in n
21.212 * [taylor]: Taking taylor expansion of n in n
21.212 * [backup-simplify]: Simplify 0 into 0
21.212 * [backup-simplify]: Simplify 1 into 1
21.212 * [backup-simplify]: Simplify (log 1) into 0
21.213 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.213 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.213 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.213 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.213 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.213 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.213 * [taylor]: Taking taylor expansion of 1.0 in n
21.213 * [backup-simplify]: Simplify 1.0 into 1.0
21.213 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.213 * [taylor]: Taking taylor expansion of 2.0 in n
21.213 * [backup-simplify]: Simplify 2.0 into 2.0
21.214 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.215 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.217 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.217 * [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)
21.219 * [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)
21.220 * [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))
21.222 * [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)))
21.223 * [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)
21.223 * [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
21.223 * [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
21.223 * [taylor]: Taking taylor expansion of +nan.0 in n
21.223 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.223 * [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
21.223 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
21.224 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
21.224 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
21.224 * [taylor]: Taking taylor expansion of 0.5 in n
21.224 * [backup-simplify]: Simplify 0.5 into 0.5
21.224 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
21.224 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
21.224 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.224 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.224 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.224 * [taylor]: Taking taylor expansion of 1.0 in n
21.224 * [backup-simplify]: Simplify 1.0 into 1.0
21.224 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.224 * [taylor]: Taking taylor expansion of 2.0 in n
21.224 * [backup-simplify]: Simplify 2.0 into 2.0
21.224 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.225 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.227 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.227 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
21.227 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.227 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.227 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.227 * [taylor]: Taking taylor expansion of 1.0 in n
21.227 * [backup-simplify]: Simplify 1.0 into 1.0
21.227 * [taylor]: Taking taylor expansion of (log PI) in n
21.227 * [taylor]: Taking taylor expansion of PI in n
21.227 * [backup-simplify]: Simplify PI into PI
21.228 * [backup-simplify]: Simplify (log PI) into (log PI)
21.229 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.230 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.230 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.230 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.230 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.230 * [taylor]: Taking taylor expansion of 1.0 in n
21.230 * [backup-simplify]: Simplify 1.0 into 1.0
21.230 * [taylor]: Taking taylor expansion of (log n) in n
21.230 * [taylor]: Taking taylor expansion of n in n
21.230 * [backup-simplify]: Simplify 0 into 0
21.231 * [backup-simplify]: Simplify 1 into 1
21.231 * [backup-simplify]: Simplify (log 1) into 0
21.231 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.231 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.232 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.232 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.234 * [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)
21.235 * [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))
21.236 * [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)))
21.238 * [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)
21.238 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.238 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.238 * [taylor]: Taking taylor expansion of 2.0 in n
21.238 * [backup-simplify]: Simplify 2.0 into 2.0
21.238 * [taylor]: Taking taylor expansion of (* n PI) in n
21.238 * [taylor]: Taking taylor expansion of n in n
21.238 * [backup-simplify]: Simplify 0 into 0
21.238 * [backup-simplify]: Simplify 1 into 1
21.238 * [taylor]: Taking taylor expansion of PI in n
21.238 * [backup-simplify]: Simplify PI into PI
21.239 * [backup-simplify]: Simplify (* 0 PI) into 0
21.239 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.241 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.242 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.243 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.245 * [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))
21.247 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.249 * [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))
21.252 * [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)))
21.255 * [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))))))
21.261 * [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))))))))
21.267 * [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))))))))
21.284 * [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))))))))
21.286 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
21.287 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
21.289 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
21.290 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
21.291 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.291 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
21.292 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
21.294 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
21.296 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
21.297 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
21.301 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
21.303 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
21.306 * [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
21.308 * [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
21.311 * [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
21.313 * [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
21.313 * [backup-simplify]: Simplify (- 0) into 0
21.313 * [backup-simplify]: Simplify 0 into 0
21.313 * [backup-simplify]: Simplify 0 into 0
21.315 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
21.316 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
21.320 * [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
21.321 * [backup-simplify]: Simplify (- 0) into 0
21.321 * [backup-simplify]: Simplify (+ 0 0) into 0
21.323 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
21.324 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
21.327 * [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)))
21.329 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.333 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.340 * [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))))))))
21.353 * [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))))))))
21.354 * [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
21.354 * [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
21.354 * [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
21.354 * [taylor]: Taking taylor expansion of +nan.0 in n
21.354 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.354 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
21.354 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
21.354 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
21.354 * [taylor]: Taking taylor expansion of 0.5 in n
21.354 * [backup-simplify]: Simplify 0.5 into 0.5
21.354 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
21.354 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
21.354 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.354 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.354 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.354 * [taylor]: Taking taylor expansion of 1.0 in n
21.354 * [backup-simplify]: Simplify 1.0 into 1.0
21.354 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.354 * [taylor]: Taking taylor expansion of 2.0 in n
21.354 * [backup-simplify]: Simplify 2.0 into 2.0
21.355 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.356 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.358 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.358 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
21.358 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.358 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.358 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.358 * [taylor]: Taking taylor expansion of 1.0 in n
21.358 * [backup-simplify]: Simplify 1.0 into 1.0
21.359 * [taylor]: Taking taylor expansion of (log n) in n
21.359 * [taylor]: Taking taylor expansion of n in n
21.359 * [backup-simplify]: Simplify 0 into 0
21.359 * [backup-simplify]: Simplify 1 into 1
21.359 * [backup-simplify]: Simplify (log 1) into 0
21.360 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.360 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.360 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.360 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.360 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.360 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.360 * [taylor]: Taking taylor expansion of 1.0 in n
21.360 * [backup-simplify]: Simplify 1.0 into 1.0
21.360 * [taylor]: Taking taylor expansion of (log PI) in n
21.360 * [taylor]: Taking taylor expansion of PI in n
21.360 * [backup-simplify]: Simplify PI into PI
21.361 * [backup-simplify]: Simplify (log PI) into (log PI)
21.362 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.364 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.365 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.366 * [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)
21.368 * [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))
21.369 * [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)))
21.371 * [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)
21.371 * [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
21.371 * [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
21.371 * [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
21.371 * [taylor]: Taking taylor expansion of +nan.0 in n
21.371 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.371 * [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
21.371 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
21.371 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
21.371 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
21.371 * [taylor]: Taking taylor expansion of 0.5 in n
21.371 * [backup-simplify]: Simplify 0.5 into 0.5
21.371 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
21.371 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
21.371 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.371 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.372 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.372 * [taylor]: Taking taylor expansion of 1.0 in n
21.372 * [backup-simplify]: Simplify 1.0 into 1.0
21.372 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.372 * [taylor]: Taking taylor expansion of 2.0 in n
21.372 * [backup-simplify]: Simplify 2.0 into 2.0
21.372 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.373 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.375 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.375 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
21.375 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.375 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.375 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.375 * [taylor]: Taking taylor expansion of 1.0 in n
21.375 * [backup-simplify]: Simplify 1.0 into 1.0
21.375 * [taylor]: Taking taylor expansion of (log PI) in n
21.375 * [taylor]: Taking taylor expansion of PI in n
21.375 * [backup-simplify]: Simplify PI into PI
21.376 * [backup-simplify]: Simplify (log PI) into (log PI)
21.378 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.380 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.380 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.381 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.381 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.381 * [taylor]: Taking taylor expansion of 1.0 in n
21.381 * [backup-simplify]: Simplify 1.0 into 1.0
21.381 * [taylor]: Taking taylor expansion of (log n) in n
21.381 * [taylor]: Taking taylor expansion of n in n
21.381 * [backup-simplify]: Simplify 0 into 0
21.381 * [backup-simplify]: Simplify 1 into 1
21.381 * [backup-simplify]: Simplify (log 1) into 0
21.382 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.382 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.382 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.383 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.384 * [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)
21.386 * [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))
21.387 * [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)))
21.389 * [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)
21.389 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.389 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.389 * [taylor]: Taking taylor expansion of 2.0 in n
21.389 * [backup-simplify]: Simplify 2.0 into 2.0
21.389 * [taylor]: Taking taylor expansion of (* n PI) in n
21.389 * [taylor]: Taking taylor expansion of n in n
21.389 * [backup-simplify]: Simplify 0 into 0
21.389 * [backup-simplify]: Simplify 1 into 1
21.389 * [taylor]: Taking taylor expansion of PI in n
21.389 * [backup-simplify]: Simplify PI into PI
21.389 * [backup-simplify]: Simplify (* 0 PI) into 0
21.390 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.391 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.392 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.393 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.393 * [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
21.393 * [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
21.393 * [taylor]: Taking taylor expansion of +nan.0 in n
21.393 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.393 * [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
21.393 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
21.393 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
21.393 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
21.393 * [taylor]: Taking taylor expansion of 0.5 in n
21.393 * [backup-simplify]: Simplify 0.5 into 0.5
21.393 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
21.393 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
21.393 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.393 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.393 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.393 * [taylor]: Taking taylor expansion of 1.0 in n
21.394 * [backup-simplify]: Simplify 1.0 into 1.0
21.394 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.394 * [taylor]: Taking taylor expansion of 2.0 in n
21.394 * [backup-simplify]: Simplify 2.0 into 2.0
21.394 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.395 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.396 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.396 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
21.396 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.396 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.397 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.397 * [taylor]: Taking taylor expansion of 1.0 in n
21.397 * [backup-simplify]: Simplify 1.0 into 1.0
21.397 * [taylor]: Taking taylor expansion of (log PI) in n
21.397 * [taylor]: Taking taylor expansion of PI in n
21.397 * [backup-simplify]: Simplify PI into PI
21.397 * [backup-simplify]: Simplify (log PI) into (log PI)
21.398 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.400 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.400 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.400 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.400 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.400 * [taylor]: Taking taylor expansion of 1.0 in n
21.400 * [backup-simplify]: Simplify 1.0 into 1.0
21.400 * [taylor]: Taking taylor expansion of (log n) in n
21.400 * [taylor]: Taking taylor expansion of n in n
21.400 * [backup-simplify]: Simplify 0 into 0
21.400 * [backup-simplify]: Simplify 1 into 1
21.400 * [backup-simplify]: Simplify (log 1) into 0
21.401 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.401 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.401 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.402 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.403 * [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)
21.404 * [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))
21.405 * [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)))
21.407 * [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)
21.407 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
21.407 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.407 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.407 * [taylor]: Taking taylor expansion of 2.0 in n
21.407 * [backup-simplify]: Simplify 2.0 into 2.0
21.407 * [taylor]: Taking taylor expansion of (* n PI) in n
21.407 * [taylor]: Taking taylor expansion of n in n
21.407 * [backup-simplify]: Simplify 0 into 0
21.407 * [backup-simplify]: Simplify 1 into 1
21.407 * [taylor]: Taking taylor expansion of PI in n
21.407 * [backup-simplify]: Simplify PI into PI
21.408 * [backup-simplify]: Simplify (* 0 PI) into 0
21.408 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.410 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.412 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.413 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.414 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.416 * [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))
21.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.420 * [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))
21.422 * [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)))
21.424 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.426 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.429 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
21.433 * [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))
21.436 * [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)))
21.439 * [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))))))))
21.452 * [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))))))))))))
21.490 * [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))))))))))))
21.507 * [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))))))))))))))
21.525 * [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))))))))))))))
21.543 * [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))))))))))))))
21.571 * [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))))))))))))))))))))))
21.573 * [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))))))
21.573 * [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
21.573 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
21.573 * [taylor]: Taking taylor expansion of 1.0 in n
21.573 * [backup-simplify]: Simplify 1.0 into 1.0
21.573 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
21.573 * [taylor]: Taking taylor expansion of (sqrt k) in n
21.573 * [taylor]: Taking taylor expansion of k in n
21.573 * [backup-simplify]: Simplify k into k
21.573 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
21.573 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
21.574 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
21.574 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
21.574 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
21.574 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
21.574 * [taylor]: Taking taylor expansion of 0.5 in n
21.574 * [backup-simplify]: Simplify 0.5 into 0.5
21.574 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.574 * [taylor]: Taking taylor expansion of 1.0 in n
21.574 * [backup-simplify]: Simplify 1.0 into 1.0
21.574 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.574 * [taylor]: Taking taylor expansion of k in n
21.574 * [backup-simplify]: Simplify k into k
21.574 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.574 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.574 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.574 * [taylor]: Taking taylor expansion of 2.0 in n
21.574 * [backup-simplify]: Simplify 2.0 into 2.0
21.574 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.574 * [taylor]: Taking taylor expansion of PI in n
21.574 * [backup-simplify]: Simplify PI into PI
21.574 * [taylor]: Taking taylor expansion of n in n
21.574 * [backup-simplify]: Simplify 0 into 0
21.574 * [backup-simplify]: Simplify 1 into 1
21.575 * [backup-simplify]: Simplify (/ PI 1) into PI
21.575 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.577 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.577 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.577 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.577 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
21.579 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.580 * [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))))
21.581 * [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)))))
21.581 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
21.581 * [taylor]: Taking taylor expansion of 1.0 in k
21.581 * [backup-simplify]: Simplify 1.0 into 1.0
21.581 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
21.581 * [taylor]: Taking taylor expansion of (sqrt k) in k
21.581 * [taylor]: Taking taylor expansion of k in k
21.581 * [backup-simplify]: Simplify 0 into 0
21.581 * [backup-simplify]: Simplify 1 into 1
21.582 * [backup-simplify]: Simplify (sqrt 0) into 0
21.583 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.583 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
21.583 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
21.583 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
21.583 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
21.583 * [taylor]: Taking taylor expansion of 0.5 in k
21.583 * [backup-simplify]: Simplify 0.5 into 0.5
21.583 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
21.583 * [taylor]: Taking taylor expansion of 1.0 in k
21.583 * [backup-simplify]: Simplify 1.0 into 1.0
21.583 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.583 * [taylor]: Taking taylor expansion of k in k
21.583 * [backup-simplify]: Simplify 0 into 0
21.583 * [backup-simplify]: Simplify 1 into 1
21.584 * [backup-simplify]: Simplify (/ 1 1) into 1
21.584 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
21.584 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
21.584 * [taylor]: Taking taylor expansion of 2.0 in k
21.584 * [backup-simplify]: Simplify 2.0 into 2.0
21.584 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.584 * [taylor]: Taking taylor expansion of PI in k
21.584 * [backup-simplify]: Simplify PI into PI
21.584 * [taylor]: Taking taylor expansion of n in k
21.584 * [backup-simplify]: Simplify n into n
21.584 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.584 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
21.584 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
21.585 * [backup-simplify]: Simplify (- 1) into -1
21.585 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.586 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
21.586 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
21.586 * [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)))))
21.586 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
21.586 * [taylor]: Taking taylor expansion of 1.0 in k
21.586 * [backup-simplify]: Simplify 1.0 into 1.0
21.586 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
21.586 * [taylor]: Taking taylor expansion of (sqrt k) in k
21.587 * [taylor]: Taking taylor expansion of k in k
21.587 * [backup-simplify]: Simplify 0 into 0
21.587 * [backup-simplify]: Simplify 1 into 1
21.587 * [backup-simplify]: Simplify (sqrt 0) into 0
21.589 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.589 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
21.589 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
21.589 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
21.589 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
21.589 * [taylor]: Taking taylor expansion of 0.5 in k
21.589 * [backup-simplify]: Simplify 0.5 into 0.5
21.589 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
21.589 * [taylor]: Taking taylor expansion of 1.0 in k
21.589 * [backup-simplify]: Simplify 1.0 into 1.0
21.589 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.589 * [taylor]: Taking taylor expansion of k in k
21.589 * [backup-simplify]: Simplify 0 into 0
21.589 * [backup-simplify]: Simplify 1 into 1
21.589 * [backup-simplify]: Simplify (/ 1 1) into 1
21.590 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
21.590 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
21.590 * [taylor]: Taking taylor expansion of 2.0 in k
21.590 * [backup-simplify]: Simplify 2.0 into 2.0
21.590 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.590 * [taylor]: Taking taylor expansion of PI in k
21.590 * [backup-simplify]: Simplify PI into PI
21.590 * [taylor]: Taking taylor expansion of n in k
21.590 * [backup-simplify]: Simplify n into n
21.590 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.590 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
21.590 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
21.590 * [backup-simplify]: Simplify (- 1) into -1
21.591 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.591 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
21.591 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
21.592 * [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)))))
21.592 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
21.593 * [backup-simplify]: Simplify (* 1.0 0) into 0
21.593 * [taylor]: Taking taylor expansion of 0 in n
21.593 * [backup-simplify]: Simplify 0 into 0
21.593 * [backup-simplify]: Simplify 0 into 0
21.594 * [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)))))))
21.595 * [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)))))))
21.595 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.595 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.595 * [taylor]: Taking taylor expansion of +nan.0 in n
21.595 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.595 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.595 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.595 * [taylor]: Taking taylor expansion of 0.5 in n
21.595 * [backup-simplify]: Simplify 0.5 into 0.5
21.595 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.595 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.595 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.595 * [taylor]: Taking taylor expansion of 2.0 in n
21.595 * [backup-simplify]: Simplify 2.0 into 2.0
21.595 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.595 * [taylor]: Taking taylor expansion of PI in n
21.595 * [backup-simplify]: Simplify PI into PI
21.595 * [taylor]: Taking taylor expansion of n in n
21.595 * [backup-simplify]: Simplify 0 into 0
21.595 * [backup-simplify]: Simplify 1 into 1
21.596 * [backup-simplify]: Simplify (/ PI 1) into PI
21.597 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.598 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.598 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.598 * [taylor]: Taking taylor expansion of 1.0 in n
21.598 * [backup-simplify]: Simplify 1.0 into 1.0
21.598 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.598 * [taylor]: Taking taylor expansion of k in n
21.598 * [backup-simplify]: Simplify k into k
21.598 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.600 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.600 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.600 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.601 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.602 * [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))))
21.604 * [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)))))
21.605 * [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))))))
21.606 * [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)))))))
21.608 * [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)))))))
21.608 * [backup-simplify]: Simplify 0 into 0
21.611 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.612 * [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)))))))
21.613 * [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)))))))
21.613 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.613 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.613 * [taylor]: Taking taylor expansion of +nan.0 in n
21.614 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.614 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.614 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.614 * [taylor]: Taking taylor expansion of 0.5 in n
21.614 * [backup-simplify]: Simplify 0.5 into 0.5
21.614 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.614 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.614 * [taylor]: Taking taylor expansion of 2.0 in n
21.614 * [backup-simplify]: Simplify 2.0 into 2.0
21.614 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.614 * [taylor]: Taking taylor expansion of PI in n
21.614 * [backup-simplify]: Simplify PI into PI
21.614 * [taylor]: Taking taylor expansion of n in n
21.614 * [backup-simplify]: Simplify 0 into 0
21.614 * [backup-simplify]: Simplify 1 into 1
21.614 * [backup-simplify]: Simplify (/ PI 1) into PI
21.615 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.616 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.616 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.616 * [taylor]: Taking taylor expansion of 1.0 in n
21.616 * [backup-simplify]: Simplify 1.0 into 1.0
21.616 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.616 * [taylor]: Taking taylor expansion of k in n
21.616 * [backup-simplify]: Simplify k into k
21.616 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.618 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.618 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.619 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.620 * [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))))
21.622 * [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)))))
21.623 * [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))))))
21.625 * [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)))))))
21.626 * [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)))))))
21.628 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.628 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.629 * [backup-simplify]: Simplify (- 0) into 0
21.629 * [backup-simplify]: Simplify (+ 0 0) into 0
21.630 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.631 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
21.633 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
21.634 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
21.665 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
21.668 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.670 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
21.670 * [backup-simplify]: Simplify (- 0) into 0
21.670 * [backup-simplify]: Simplify 0 into 0
21.670 * [backup-simplify]: Simplify 0 into 0
21.674 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.676 * [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)))))))
21.678 * [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)))))))
21.678 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.678 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.678 * [taylor]: Taking taylor expansion of +nan.0 in n
21.678 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.678 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.678 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.678 * [taylor]: Taking taylor expansion of 0.5 in n
21.678 * [backup-simplify]: Simplify 0.5 into 0.5
21.678 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.678 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.678 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.678 * [taylor]: Taking taylor expansion of 2.0 in n
21.678 * [backup-simplify]: Simplify 2.0 into 2.0
21.678 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.678 * [taylor]: Taking taylor expansion of PI in n
21.678 * [backup-simplify]: Simplify PI into PI
21.678 * [taylor]: Taking taylor expansion of n in n
21.678 * [backup-simplify]: Simplify 0 into 0
21.678 * [backup-simplify]: Simplify 1 into 1
21.679 * [backup-simplify]: Simplify (/ PI 1) into PI
21.679 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.681 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.681 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.681 * [taylor]: Taking taylor expansion of 1.0 in n
21.681 * [backup-simplify]: Simplify 1.0 into 1.0
21.681 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.681 * [taylor]: Taking taylor expansion of k in n
21.681 * [backup-simplify]: Simplify k into k
21.681 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.682 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.683 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.684 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.685 * [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))))
21.687 * [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)))))
21.688 * [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))))))
21.689 * [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)))))))
21.691 * [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)))))))
21.696 * [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))))))))
21.697 * [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))))
21.697 * [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
21.697 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
21.697 * [taylor]: Taking taylor expansion of 1.0 in n
21.697 * [backup-simplify]: Simplify 1.0 into 1.0
21.697 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
21.698 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
21.698 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
21.698 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
21.698 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
21.698 * [taylor]: Taking taylor expansion of 0.5 in n
21.698 * [backup-simplify]: Simplify 0.5 into 0.5
21.698 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.698 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.698 * [taylor]: Taking taylor expansion of k in n
21.698 * [backup-simplify]: Simplify k into k
21.698 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.698 * [taylor]: Taking taylor expansion of 1.0 in n
21.698 * [backup-simplify]: Simplify 1.0 into 1.0
21.698 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.698 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.698 * [taylor]: Taking taylor expansion of -2.0 in n
21.698 * [backup-simplify]: Simplify -2.0 into -2.0
21.698 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.698 * [taylor]: Taking taylor expansion of PI in n
21.698 * [backup-simplify]: Simplify PI into PI
21.698 * [taylor]: Taking taylor expansion of n in n
21.698 * [backup-simplify]: Simplify 0 into 0
21.698 * [backup-simplify]: Simplify 1 into 1
21.699 * [backup-simplify]: Simplify (/ PI 1) into PI
21.699 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.701 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.701 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.701 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
21.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.704 * [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))))
21.705 * [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)))))
21.705 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.705 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.705 * [taylor]: Taking taylor expansion of -1 in n
21.705 * [backup-simplify]: Simplify -1 into -1
21.705 * [taylor]: Taking taylor expansion of k in n
21.705 * [backup-simplify]: Simplify k into k
21.705 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.705 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.706 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.706 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.707 * [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)))
21.707 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
21.707 * [taylor]: Taking taylor expansion of 1.0 in k
21.707 * [backup-simplify]: Simplify 1.0 into 1.0
21.707 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
21.707 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.707 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.707 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.707 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.708 * [taylor]: Taking taylor expansion of 0.5 in k
21.708 * [backup-simplify]: Simplify 0.5 into 0.5
21.708 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.708 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.708 * [taylor]: Taking taylor expansion of k in k
21.708 * [backup-simplify]: Simplify 0 into 0
21.708 * [backup-simplify]: Simplify 1 into 1
21.708 * [backup-simplify]: Simplify (/ 1 1) into 1
21.708 * [taylor]: Taking taylor expansion of 1.0 in k
21.708 * [backup-simplify]: Simplify 1.0 into 1.0
21.708 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.708 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.708 * [taylor]: Taking taylor expansion of -2.0 in k
21.708 * [backup-simplify]: Simplify -2.0 into -2.0
21.708 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.708 * [taylor]: Taking taylor expansion of PI in k
21.709 * [backup-simplify]: Simplify PI into PI
21.709 * [taylor]: Taking taylor expansion of n in k
21.709 * [backup-simplify]: Simplify n into n
21.709 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.709 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.709 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.709 * [backup-simplify]: Simplify (+ 1 0) into 1
21.710 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.710 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.710 * [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))))))
21.710 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.710 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.710 * [taylor]: Taking taylor expansion of -1 in k
21.710 * [backup-simplify]: Simplify -1 into -1
21.710 * [taylor]: Taking taylor expansion of k in k
21.710 * [backup-simplify]: Simplify 0 into 0
21.711 * [backup-simplify]: Simplify 1 into 1
21.711 * [backup-simplify]: Simplify (/ -1 1) into -1
21.711 * [backup-simplify]: Simplify (sqrt 0) into 0
21.713 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.713 * [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)))))))
21.713 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
21.713 * [taylor]: Taking taylor expansion of 1.0 in k
21.713 * [backup-simplify]: Simplify 1.0 into 1.0
21.713 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
21.713 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.713 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.713 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.713 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.713 * [taylor]: Taking taylor expansion of 0.5 in k
21.714 * [backup-simplify]: Simplify 0.5 into 0.5
21.714 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.714 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.714 * [taylor]: Taking taylor expansion of k in k
21.714 * [backup-simplify]: Simplify 0 into 0
21.714 * [backup-simplify]: Simplify 1 into 1
21.714 * [backup-simplify]: Simplify (/ 1 1) into 1
21.714 * [taylor]: Taking taylor expansion of 1.0 in k
21.714 * [backup-simplify]: Simplify 1.0 into 1.0
21.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.714 * [taylor]: Taking taylor expansion of -2.0 in k
21.714 * [backup-simplify]: Simplify -2.0 into -2.0
21.714 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.714 * [taylor]: Taking taylor expansion of PI in k
21.714 * [backup-simplify]: Simplify PI into PI
21.714 * [taylor]: Taking taylor expansion of n in k
21.714 * [backup-simplify]: Simplify n into n
21.715 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.715 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.715 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.715 * [backup-simplify]: Simplify (+ 1 0) into 1
21.716 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.716 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.716 * [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))))))
21.716 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.716 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.716 * [taylor]: Taking taylor expansion of -1 in k
21.716 * [backup-simplify]: Simplify -1 into -1
21.716 * [taylor]: Taking taylor expansion of k in k
21.716 * [backup-simplify]: Simplify 0 into 0
21.716 * [backup-simplify]: Simplify 1 into 1
21.717 * [backup-simplify]: Simplify (/ -1 1) into -1
21.717 * [backup-simplify]: Simplify (sqrt 0) into 0
21.719 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.719 * [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)))))))
21.719 * [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)))))))
21.719 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.719 * [taylor]: Taking taylor expansion of +nan.0 in n
21.720 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.720 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.720 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.720 * [taylor]: Taking taylor expansion of 0.5 in n
21.720 * [backup-simplify]: Simplify 0.5 into 0.5
21.720 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.720 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.720 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.720 * [taylor]: Taking taylor expansion of k in n
21.720 * [backup-simplify]: Simplify k into k
21.720 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.720 * [taylor]: Taking taylor expansion of 1.0 in n
21.720 * [backup-simplify]: Simplify 1.0 into 1.0
21.720 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.720 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.720 * [taylor]: Taking taylor expansion of -2.0 in n
21.720 * [backup-simplify]: Simplify -2.0 into -2.0
21.720 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.720 * [taylor]: Taking taylor expansion of PI in n
21.720 * [backup-simplify]: Simplify PI into PI
21.720 * [taylor]: Taking taylor expansion of n in n
21.720 * [backup-simplify]: Simplify 0 into 0
21.720 * [backup-simplify]: Simplify 1 into 1
21.721 * [backup-simplify]: Simplify (/ PI 1) into PI
21.722 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.723 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.723 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.725 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.726 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.727 * [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))))
21.728 * [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)))))
21.729 * [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))))))
21.731 * [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))))))
21.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
21.734 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.736 * [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))))))))
21.736 * [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))))))))
21.736 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.736 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.736 * [taylor]: Taking taylor expansion of +nan.0 in n
21.736 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.736 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.736 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.737 * [taylor]: Taking taylor expansion of 0.5 in n
21.737 * [backup-simplify]: Simplify 0.5 into 0.5
21.737 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.737 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.737 * [taylor]: Taking taylor expansion of k in n
21.737 * [backup-simplify]: Simplify k into k
21.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.737 * [taylor]: Taking taylor expansion of 1.0 in n
21.737 * [backup-simplify]: Simplify 1.0 into 1.0
21.737 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.737 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.737 * [taylor]: Taking taylor expansion of -2.0 in n
21.737 * [backup-simplify]: Simplify -2.0 into -2.0
21.737 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.737 * [taylor]: Taking taylor expansion of PI in n
21.737 * [backup-simplify]: Simplify PI into PI
21.737 * [taylor]: Taking taylor expansion of n in n
21.737 * [backup-simplify]: Simplify 0 into 0
21.737 * [backup-simplify]: Simplify 1 into 1
21.738 * [backup-simplify]: Simplify (/ PI 1) into PI
21.738 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.739 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.739 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.741 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.741 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.742 * [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))))
21.743 * [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)))))
21.744 * [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))))))
21.745 * [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)))))))
21.746 * [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)))))))
21.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.748 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
21.750 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
21.750 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.751 * [backup-simplify]: Simplify (+ 0 0) into 0
21.752 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.753 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
21.755 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
21.757 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.759 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
21.759 * [backup-simplify]: Simplify 0 into 0
21.760 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.764 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.766 * [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))))))))
21.767 * [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))))))))
21.767 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.767 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.767 * [taylor]: Taking taylor expansion of +nan.0 in n
21.767 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.767 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.767 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.767 * [taylor]: Taking taylor expansion of 0.5 in n
21.767 * [backup-simplify]: Simplify 0.5 into 0.5
21.767 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.767 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.767 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.767 * [taylor]: Taking taylor expansion of k in n
21.767 * [backup-simplify]: Simplify k into k
21.767 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.767 * [taylor]: Taking taylor expansion of 1.0 in n
21.767 * [backup-simplify]: Simplify 1.0 into 1.0
21.767 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.767 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.767 * [taylor]: Taking taylor expansion of -2.0 in n
21.768 * [backup-simplify]: Simplify -2.0 into -2.0
21.768 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.768 * [taylor]: Taking taylor expansion of PI in n
21.768 * [backup-simplify]: Simplify PI into PI
21.768 * [taylor]: Taking taylor expansion of n in n
21.768 * [backup-simplify]: Simplify 0 into 0
21.768 * [backup-simplify]: Simplify 1 into 1
21.769 * [backup-simplify]: Simplify (/ PI 1) into PI
21.769 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.771 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.771 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.773 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.774 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.775 * [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))))
21.776 * [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)))))
21.778 * [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))))))
21.779 * [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)))))))
21.781 * [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)))))))
21.786 * [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))))))))))))
21.786 * * * [progress]: simplifying candidates
21.797 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (log (sqrt k)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (* (cbrt k) (cbrt k))) 1)
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
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  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) 1))
  (/ (sqrt 1.0) (/ (sqrt (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) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ 1 1))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (/ 1 (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) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (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 (sqrt (/ (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 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt 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 (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt 1) (* (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) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt 1) (sqrt (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 (/ (sqrt 1) 1))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt 1) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ 1 (* (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) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ 1 (sqrt (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 (/ 1 1))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 1)
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt k))
  (/ 1.0 (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ 1.0 (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (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 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt 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 (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt 1) (* (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 1) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt 1) 1))
  (/ 1.0 (/ (sqrt 1) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ 1 1))
  (/ 1.0 (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 1)
  (/ 1.0 (sqrt k))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt 1.0))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1.0))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (sqrt k))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow k 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))))))))))
  (- (+ (* +nan.0 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))))
  (- (+ (* +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))))))))))))
21.821 * * [simplify]: iteration 0: 610 enodes
22.300 * * [simplify]: iteration 1: 1732 enodes
23.728 * * [simplify]: iteration complete: 5000 enodes
23.728 * * [simplify]: Extracting #0: cost 283 inf + 0
23.732 * * [simplify]: Extracting #1: cost 982 inf + 2
23.742 * * [simplify]: Extracting #2: cost 1343 inf + 10203
23.773 * * [simplify]: Extracting #3: cost 1177 inf + 116116
23.875 * * [simplify]: Extracting #4: cost 769 inf + 360437
23.997 * * [simplify]: Extracting #5: cost 533 inf + 537043
24.148 * * [simplify]: Extracting #6: cost 491 inf + 624286
24.348 * * [simplify]: Extracting #7: cost 330 inf + 828927
24.586 * * [simplify]: Extracting #8: cost 131 inf + 1045318
24.874 * * [simplify]: Extracting #9: cost 25 inf + 1164798
25.225 * * [simplify]: Extracting #10: cost 6 inf + 1208109
25.567 * * [simplify]: Extracting #11: cost 0 inf + 1222817
25.951 * * [simplify]: Extracting #12: cost 0 inf + 1222572
26.292 * * [simplify]: Extracting #13: cost 0 inf + 1222522
26.642 * [simplify]: Simplified to:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (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 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 (* (* 2.0 PI) (* 2.0 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)))
  (* (sqrt n) (* 2.0 PI))
  (* 2.0 PI)
  (* n PI)
  (expm1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (exp (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (/ (* (sqrt k) k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (fabs (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ (fabs (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (fabs (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (sqrt k) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt k)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (/ (/ (* (sqrt k) k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 1.0)))
  (* (* (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- 1.0)
  (- (/ (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) (cbrt (/ (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) (cbrt 1.0)) (sqrt (/ (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) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (fabs (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (fabs (cbrt k)))
  (/ (cbrt 1.0) (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (fabs (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (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) 2)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (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) 2)))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt 1.0)))
  (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ (/ (sqrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ (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 (/ (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) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (sqrt k)))
  (* (/ (sqrt 1.0) (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (sqrt 1.0) (fabs (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (cbrt k)))
  (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (fabs (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (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) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (sqrt 1.0)
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
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  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (sqrt 1.0)
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (sqrt 1.0)
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  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
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  (/ 1.0 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
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  (* (/ 1.0 (cbrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
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  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
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  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
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  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
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  (* (/ 1.0 (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (/ (* 1.0 (pow n (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
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  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (/ (* 1.0 (pow n (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (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
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  1
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (sqrt k))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ 1.0 (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) 1.0) (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)))) (cbrt (/ (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 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (/ 1.0 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (* (/ 1.0 (fabs (cbrt 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 (fabs (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (* (/ 1.0 (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* 1.0 (* (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1.0
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (* (/ 1.0 (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* 1.0 (* (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1.0
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  1.0
  (/ 1.0 (sqrt k))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt k))
  (/ (/ (sqrt k) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) (sqrt 1.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (sqrt k))
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  (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n))))))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (- (fma +nan.0 (* (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5) (* k k)) (+ (* (- (* (* +nan.0 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* k (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (* +nan.0 (* k (* k k))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5) (+ (* (- (* (* +nan.0 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* k (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (* +nan.0 (* k (* (log (* 2.0 PI)) (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5) (+ (* (* +nan.0 k) (- (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (+ (- (* (* +nan.0 (* (log (* 2.0 PI)) (* k k))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (* (* +nan.0 (* (log n) (* k (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (* (* +nan.0 (* k (* k k))) (* (* (log n) (log n)) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (+ (* (log n) (* (* k k) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* (* (* k (* (log (* 2.0 PI)) (* k k))) (log n)) (- (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))))))))))))))
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  (+ (- (/ +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))))) (- (/ (/ +nan.0 k) (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n))))))) (/ (/ +nan.0 (* k k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))))))
  (+ (* (- (* (* +nan.0 (* k k)) (* (log (* 2.0 PI)) (log (* 2.0 PI))))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (+ (- (* +nan.0 (* (* (log (* 2.0 PI)) (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (* +nan.0 (* (* (* (log (* 2.0 PI)) (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (log n)))) (+ (- (* (* (* +nan.0 (log n)) (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* (* +nan.0 (* k (log (* 2.0 PI)))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (+ (- (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (* (* (log n) (log n)) (* k k)) +nan.0)) (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (log n)))) (+ (- (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) +nan.0) (* (* +nan.0 (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (* k (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) +nan.0)))))))
  (+ (* (- +nan.0) (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))) (* k (* k k)))) (* +nan.0 (- (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))) k) (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))) (* k k)))))
  (+ (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))) k))) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))) (* k k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))))))
26.702 * * * [progress]: adding candidates to table
29.471 * * [progress]: iteration 4 / 4
29.471 * * * [progress]: picking best candidate
29.561 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
29.561 * * * [progress]: localizing error
29.625 * * * [progress]: generating rewritten candidates
29.625 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
29.678 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
29.732 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
29.768 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
29.845 * * * [progress]: generating series expansions
29.845 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
29.847 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
29.847 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
29.847 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
29.847 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
29.847 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
29.847 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
29.847 * [taylor]: Taking taylor expansion of 0.5 in k
29.847 * [backup-simplify]: Simplify 0.5 into 0.5
29.847 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
29.847 * [taylor]: Taking taylor expansion of 1.0 in k
29.847 * [backup-simplify]: Simplify 1.0 into 1.0
29.847 * [taylor]: Taking taylor expansion of k in k
29.847 * [backup-simplify]: Simplify 0 into 0
29.848 * [backup-simplify]: Simplify 1 into 1
29.848 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
29.848 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
29.848 * [taylor]: Taking taylor expansion of 2.0 in k
29.848 * [backup-simplify]: Simplify 2.0 into 2.0
29.848 * [taylor]: Taking taylor expansion of (* n PI) in k
29.848 * [taylor]: Taking taylor expansion of n in k
29.848 * [backup-simplify]: Simplify n into n
29.848 * [taylor]: Taking taylor expansion of PI in k
29.848 * [backup-simplify]: Simplify PI into PI
29.848 * [backup-simplify]: Simplify (* n PI) into (* n PI)
29.848 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
29.848 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
29.849 * [backup-simplify]: Simplify (- 0) into 0
29.849 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
29.850 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
29.850 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
29.850 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
29.850 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
29.850 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
29.850 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
29.850 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
29.850 * [taylor]: Taking taylor expansion of 0.5 in n
29.850 * [backup-simplify]: Simplify 0.5 into 0.5
29.850 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
29.850 * [taylor]: Taking taylor expansion of 1.0 in n
29.850 * [backup-simplify]: Simplify 1.0 into 1.0
29.850 * [taylor]: Taking taylor expansion of k in n
29.850 * [backup-simplify]: Simplify k into k
29.850 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
29.850 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
29.850 * [taylor]: Taking taylor expansion of 2.0 in n
29.850 * [backup-simplify]: Simplify 2.0 into 2.0
29.850 * [taylor]: Taking taylor expansion of (* n PI) in n
29.850 * [taylor]: Taking taylor expansion of n in n
29.850 * [backup-simplify]: Simplify 0 into 0
29.850 * [backup-simplify]: Simplify 1 into 1
29.850 * [taylor]: Taking taylor expansion of PI in n
29.850 * [backup-simplify]: Simplify PI into PI
29.851 * [backup-simplify]: Simplify (* 0 PI) into 0
29.851 * [backup-simplify]: Simplify (* 2.0 0) into 0
29.853 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
29.855 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
29.856 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.856 * [backup-simplify]: Simplify (- k) into (- k)
29.856 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
29.856 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
29.858 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.859 * [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))))
29.860 * [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)))))
29.860 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
29.860 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
29.860 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
29.860 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
29.860 * [taylor]: Taking taylor expansion of 0.5 in n
29.860 * [backup-simplify]: Simplify 0.5 into 0.5
29.860 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
29.860 * [taylor]: Taking taylor expansion of 1.0 in n
29.860 * [backup-simplify]: Simplify 1.0 into 1.0
29.861 * [taylor]: Taking taylor expansion of k in n
29.861 * [backup-simplify]: Simplify k into k
29.861 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
29.861 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
29.861 * [taylor]: Taking taylor expansion of 2.0 in n
29.861 * [backup-simplify]: Simplify 2.0 into 2.0
29.861 * [taylor]: Taking taylor expansion of (* n PI) in n
29.861 * [taylor]: Taking taylor expansion of n in n
29.861 * [backup-simplify]: Simplify 0 into 0
29.861 * [backup-simplify]: Simplify 1 into 1
29.861 * [taylor]: Taking taylor expansion of PI in n
29.861 * [backup-simplify]: Simplify PI into PI
29.861 * [backup-simplify]: Simplify (* 0 PI) into 0
29.862 * [backup-simplify]: Simplify (* 2.0 0) into 0
29.863 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
29.865 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
29.866 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.866 * [backup-simplify]: Simplify (- k) into (- k)
29.866 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
29.866 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
29.868 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.869 * [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))))
29.870 * [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)))))
29.870 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
29.870 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
29.871 * [taylor]: Taking taylor expansion of 0.5 in k
29.871 * [backup-simplify]: Simplify 0.5 into 0.5
29.871 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
29.871 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
29.871 * [taylor]: Taking taylor expansion of 1.0 in k
29.871 * [backup-simplify]: Simplify 1.0 into 1.0
29.871 * [taylor]: Taking taylor expansion of k in k
29.871 * [backup-simplify]: Simplify 0 into 0
29.871 * [backup-simplify]: Simplify 1 into 1
29.871 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
29.871 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
29.871 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
29.871 * [taylor]: Taking taylor expansion of 2.0 in k
29.871 * [backup-simplify]: Simplify 2.0 into 2.0
29.871 * [taylor]: Taking taylor expansion of PI in k
29.871 * [backup-simplify]: Simplify PI into PI
29.872 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.873 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.873 * [taylor]: Taking taylor expansion of (log n) in k
29.873 * [taylor]: Taking taylor expansion of n in k
29.873 * [backup-simplify]: Simplify n into n
29.873 * [backup-simplify]: Simplify (log n) into (log n)
29.873 * [backup-simplify]: Simplify (- 0) into 0
29.874 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
29.875 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
29.876 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
29.877 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
29.879 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
29.880 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
29.881 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
29.883 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
29.885 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
29.885 * [backup-simplify]: Simplify (- 0) into 0
29.885 * [backup-simplify]: Simplify (+ 0 0) into 0
29.886 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
29.887 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.889 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
29.891 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.891 * [taylor]: Taking taylor expansion of 0 in k
29.891 * [backup-simplify]: Simplify 0 into 0
29.891 * [backup-simplify]: Simplify 0 into 0
29.892 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
29.894 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
29.895 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
29.895 * [backup-simplify]: Simplify (+ 0 0) into 0
29.895 * [backup-simplify]: Simplify (- 1) into -1
29.896 * [backup-simplify]: Simplify (+ 0 -1) into -1
29.898 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
29.900 * [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))))
29.903 * [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))))))
29.907 * [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))))))
29.908 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
29.910 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
29.913 * [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
29.914 * [backup-simplify]: Simplify (- 0) into 0
29.914 * [backup-simplify]: Simplify (+ 0 0) into 0
29.915 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
29.917 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.919 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
29.921 * [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
29.921 * [taylor]: Taking taylor expansion of 0 in k
29.921 * [backup-simplify]: Simplify 0 into 0
29.921 * [backup-simplify]: Simplify 0 into 0
29.921 * [backup-simplify]: Simplify 0 into 0
29.922 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
29.953 * [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
29.955 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
29.956 * [backup-simplify]: Simplify (+ 0 0) into 0
29.956 * [backup-simplify]: Simplify (- 0) into 0
29.957 * [backup-simplify]: Simplify (+ 0 0) into 0
29.958 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
29.960 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
29.963 * [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))))))
29.967 * [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))))))
29.978 * [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))))))
29.979 * [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))))
29.979 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
29.979 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
29.979 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
29.979 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
29.979 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
29.979 * [taylor]: Taking taylor expansion of 0.5 in k
29.979 * [backup-simplify]: Simplify 0.5 into 0.5
29.979 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
29.980 * [taylor]: Taking taylor expansion of 1.0 in k
29.980 * [backup-simplify]: Simplify 1.0 into 1.0
29.980 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.980 * [taylor]: Taking taylor expansion of k in k
29.980 * [backup-simplify]: Simplify 0 into 0
29.980 * [backup-simplify]: Simplify 1 into 1
29.980 * [backup-simplify]: Simplify (/ 1 1) into 1
29.980 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
29.980 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
29.980 * [taylor]: Taking taylor expansion of 2.0 in k
29.980 * [backup-simplify]: Simplify 2.0 into 2.0
29.980 * [taylor]: Taking taylor expansion of (/ PI n) in k
29.980 * [taylor]: Taking taylor expansion of PI in k
29.980 * [backup-simplify]: Simplify PI into PI
29.980 * [taylor]: Taking taylor expansion of n in k
29.980 * [backup-simplify]: Simplify n into n
29.980 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
29.981 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
29.981 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
29.981 * [backup-simplify]: Simplify (- 1) into -1
29.982 * [backup-simplify]: Simplify (+ 0 -1) into -1
29.982 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
29.982 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
29.983 * [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)))))
29.983 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
29.983 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
29.983 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
29.983 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
29.983 * [taylor]: Taking taylor expansion of 0.5 in n
29.983 * [backup-simplify]: Simplify 0.5 into 0.5
29.983 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
29.983 * [taylor]: Taking taylor expansion of 1.0 in n
29.983 * [backup-simplify]: Simplify 1.0 into 1.0
29.983 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.983 * [taylor]: Taking taylor expansion of k in n
29.983 * [backup-simplify]: Simplify k into k
29.983 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.983 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
29.983 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
29.983 * [taylor]: Taking taylor expansion of 2.0 in n
29.983 * [backup-simplify]: Simplify 2.0 into 2.0
29.983 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.983 * [taylor]: Taking taylor expansion of PI in n
29.983 * [backup-simplify]: Simplify PI into PI
29.983 * [taylor]: Taking taylor expansion of n in n
29.983 * [backup-simplify]: Simplify 0 into 0
29.983 * [backup-simplify]: Simplify 1 into 1
29.984 * [backup-simplify]: Simplify (/ PI 1) into PI
29.985 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.986 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.986 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
29.986 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
29.986 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
29.987 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.989 * [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))))
29.990 * [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)))))
29.990 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
29.990 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
29.990 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
29.990 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
29.990 * [taylor]: Taking taylor expansion of 0.5 in n
29.990 * [backup-simplify]: Simplify 0.5 into 0.5
29.990 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
29.990 * [taylor]: Taking taylor expansion of 1.0 in n
29.990 * [backup-simplify]: Simplify 1.0 into 1.0
29.990 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.990 * [taylor]: Taking taylor expansion of k in n
29.990 * [backup-simplify]: Simplify k into k
29.990 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.990 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
29.990 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
29.990 * [taylor]: Taking taylor expansion of 2.0 in n
29.990 * [backup-simplify]: Simplify 2.0 into 2.0
29.990 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.990 * [taylor]: Taking taylor expansion of PI in n
29.990 * [backup-simplify]: Simplify PI into PI
29.990 * [taylor]: Taking taylor expansion of n in n
29.990 * [backup-simplify]: Simplify 0 into 0
29.990 * [backup-simplify]: Simplify 1 into 1
29.991 * [backup-simplify]: Simplify (/ PI 1) into PI
29.991 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.992 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.993 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
29.993 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
29.993 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
29.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.996 * [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))))
29.997 * [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)))))
29.997 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
29.997 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
29.997 * [taylor]: Taking taylor expansion of 0.5 in k
29.997 * [backup-simplify]: Simplify 0.5 into 0.5
29.997 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
29.997 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
29.997 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
29.997 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
29.997 * [taylor]: Taking taylor expansion of 2.0 in k
29.997 * [backup-simplify]: Simplify 2.0 into 2.0
29.997 * [taylor]: Taking taylor expansion of PI in k
29.997 * [backup-simplify]: Simplify PI into PI
29.998 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.999 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.999 * [taylor]: Taking taylor expansion of (log n) in k
29.999 * [taylor]: Taking taylor expansion of n in k
29.999 * [backup-simplify]: Simplify n into n
29.999 * [backup-simplify]: Simplify (log n) into (log n)
29.999 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
29.999 * [taylor]: Taking taylor expansion of 1.0 in k
29.999 * [backup-simplify]: Simplify 1.0 into 1.0
29.999 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.999 * [taylor]: Taking taylor expansion of k in k
29.999 * [backup-simplify]: Simplify 0 into 0
29.999 * [backup-simplify]: Simplify 1 into 1
29.999 * [backup-simplify]: Simplify (/ 1 1) into 1
30.000 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
30.001 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
30.001 * [backup-simplify]: Simplify (- 1) into -1
30.001 * [backup-simplify]: Simplify (+ 0 -1) into -1
30.002 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
30.004 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
30.005 * [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)))))
30.006 * [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)))))
30.007 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
30.008 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
30.010 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
30.010 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
30.010 * [backup-simplify]: Simplify (- 0) into 0
30.011 * [backup-simplify]: Simplify (+ 0 0) into 0
30.011 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
30.013 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
30.014 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
30.016 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
30.017 * [taylor]: Taking taylor expansion of 0 in k
30.017 * [backup-simplify]: Simplify 0 into 0
30.017 * [backup-simplify]: Simplify 0 into 0
30.017 * [backup-simplify]: Simplify 0 into 0
30.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.018 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
30.021 * [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
30.021 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
30.021 * [backup-simplify]: Simplify (- 0) into 0
30.021 * [backup-simplify]: Simplify (+ 0 0) into 0
30.022 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
30.023 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
30.024 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
30.025 * [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
30.025 * [taylor]: Taking taylor expansion of 0 in k
30.025 * [backup-simplify]: Simplify 0 into 0
30.025 * [backup-simplify]: Simplify 0 into 0
30.025 * [backup-simplify]: Simplify 0 into 0
30.025 * [backup-simplify]: Simplify 0 into 0
30.027 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.028 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
30.034 * [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
30.034 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
30.035 * [backup-simplify]: Simplify (- 0) into 0
30.035 * [backup-simplify]: Simplify (+ 0 0) into 0
30.037 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
30.038 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
30.040 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
30.043 * [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
30.044 * [taylor]: Taking taylor expansion of 0 in k
30.044 * [backup-simplify]: Simplify 0 into 0
30.044 * [backup-simplify]: Simplify 0 into 0
30.047 * [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))))
30.048 * [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)))
30.048 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
30.048 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
30.049 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
30.049 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
30.049 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
30.049 * [taylor]: Taking taylor expansion of 0.5 in k
30.049 * [backup-simplify]: Simplify 0.5 into 0.5
30.049 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
30.049 * [taylor]: Taking taylor expansion of (/ 1 k) in k
30.049 * [taylor]: Taking taylor expansion of k in k
30.049 * [backup-simplify]: Simplify 0 into 0
30.049 * [backup-simplify]: Simplify 1 into 1
30.049 * [backup-simplify]: Simplify (/ 1 1) into 1
30.049 * [taylor]: Taking taylor expansion of 1.0 in k
30.049 * [backup-simplify]: Simplify 1.0 into 1.0
30.049 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
30.049 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
30.049 * [taylor]: Taking taylor expansion of -2.0 in k
30.050 * [backup-simplify]: Simplify -2.0 into -2.0
30.050 * [taylor]: Taking taylor expansion of (/ PI n) in k
30.050 * [taylor]: Taking taylor expansion of PI in k
30.050 * [backup-simplify]: Simplify PI into PI
30.050 * [taylor]: Taking taylor expansion of n in k
30.050 * [backup-simplify]: Simplify n into n
30.050 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
30.050 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
30.050 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
30.050 * [backup-simplify]: Simplify (+ 1 0) into 1
30.051 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
30.051 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
30.051 * [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))))))
30.051 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
30.051 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
30.051 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
30.051 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
30.051 * [taylor]: Taking taylor expansion of 0.5 in n
30.051 * [backup-simplify]: Simplify 0.5 into 0.5
30.051 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
30.051 * [taylor]: Taking taylor expansion of (/ 1 k) in n
30.051 * [taylor]: Taking taylor expansion of k in n
30.052 * [backup-simplify]: Simplify k into k
30.052 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
30.052 * [taylor]: Taking taylor expansion of 1.0 in n
30.052 * [backup-simplify]: Simplify 1.0 into 1.0
30.052 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
30.052 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
30.052 * [taylor]: Taking taylor expansion of -2.0 in n
30.052 * [backup-simplify]: Simplify -2.0 into -2.0
30.052 * [taylor]: Taking taylor expansion of (/ PI n) in n
30.052 * [taylor]: Taking taylor expansion of PI in n
30.052 * [backup-simplify]: Simplify PI into PI
30.052 * [taylor]: Taking taylor expansion of n in n
30.052 * [backup-simplify]: Simplify 0 into 0
30.052 * [backup-simplify]: Simplify 1 into 1
30.052 * [backup-simplify]: Simplify (/ PI 1) into PI
30.053 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
30.054 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
30.054 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
30.055 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
30.057 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
30.059 * [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))))
30.060 * [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)))))
30.060 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
30.060 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
30.061 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
30.061 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
30.061 * [taylor]: Taking taylor expansion of 0.5 in n
30.061 * [backup-simplify]: Simplify 0.5 into 0.5
30.061 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
30.061 * [taylor]: Taking taylor expansion of (/ 1 k) in n
30.061 * [taylor]: Taking taylor expansion of k in n
30.061 * [backup-simplify]: Simplify k into k
30.061 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
30.061 * [taylor]: Taking taylor expansion of 1.0 in n
30.061 * [backup-simplify]: Simplify 1.0 into 1.0
30.061 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
30.061 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
30.061 * [taylor]: Taking taylor expansion of -2.0 in n
30.061 * [backup-simplify]: Simplify -2.0 into -2.0
30.061 * [taylor]: Taking taylor expansion of (/ PI n) in n
30.061 * [taylor]: Taking taylor expansion of PI in n
30.061 * [backup-simplify]: Simplify PI into PI
30.061 * [taylor]: Taking taylor expansion of n in n
30.061 * [backup-simplify]: Simplify 0 into 0
30.061 * [backup-simplify]: Simplify 1 into 1
30.062 * [backup-simplify]: Simplify (/ PI 1) into PI
30.062 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
30.063 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
30.064 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
30.064 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
30.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
30.066 * [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))))
30.067 * [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)))))
30.068 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
30.068 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
30.068 * [taylor]: Taking taylor expansion of 0.5 in k
30.068 * [backup-simplify]: Simplify 0.5 into 0.5
30.068 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
30.068 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
30.068 * [taylor]: Taking taylor expansion of (/ 1 k) in k
30.068 * [taylor]: Taking taylor expansion of k in k
30.068 * [backup-simplify]: Simplify 0 into 0
30.068 * [backup-simplify]: Simplify 1 into 1
30.068 * [backup-simplify]: Simplify (/ 1 1) into 1
30.068 * [taylor]: Taking taylor expansion of 1.0 in k
30.068 * [backup-simplify]: Simplify 1.0 into 1.0
30.068 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
30.068 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
30.068 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
30.068 * [taylor]: Taking taylor expansion of -2.0 in k
30.068 * [backup-simplify]: Simplify -2.0 into -2.0
30.068 * [taylor]: Taking taylor expansion of PI in k
30.068 * [backup-simplify]: Simplify PI into PI
30.069 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
30.069 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
30.069 * [taylor]: Taking taylor expansion of (log n) in k
30.069 * [taylor]: Taking taylor expansion of n in k
30.069 * [backup-simplify]: Simplify n into n
30.069 * [backup-simplify]: Simplify (log n) into (log n)
30.070 * [backup-simplify]: Simplify (+ 1 0) into 1
30.070 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
30.070 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
30.071 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
30.072 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
30.073 * [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)))))
30.073 * [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)))))
30.074 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
30.074 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
30.075 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
30.075 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
30.076 * [backup-simplify]: Simplify (+ 0 0) into 0
30.076 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
30.077 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
30.078 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
30.079 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
30.079 * [taylor]: Taking taylor expansion of 0 in k
30.079 * [backup-simplify]: Simplify 0 into 0
30.079 * [backup-simplify]: Simplify 0 into 0
30.079 * [backup-simplify]: Simplify 0 into 0
30.080 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.081 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
30.085 * [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
30.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
30.085 * [backup-simplify]: Simplify (+ 0 0) into 0
30.086 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
30.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
30.089 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
30.092 * [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
30.092 * [taylor]: Taking taylor expansion of 0 in k
30.092 * [backup-simplify]: Simplify 0 into 0
30.092 * [backup-simplify]: Simplify 0 into 0
30.092 * [backup-simplify]: Simplify 0 into 0
30.092 * [backup-simplify]: Simplify 0 into 0
30.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.098 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
30.104 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
30.105 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
30.105 * [backup-simplify]: Simplify (+ 0 0) into 0
30.106 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
30.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
30.110 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
30.113 * [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
30.113 * [taylor]: Taking taylor expansion of 0 in k
30.113 * [backup-simplify]: Simplify 0 into 0
30.113 * [backup-simplify]: Simplify 0 into 0
30.114 * [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))))))
30.114 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
30.115 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k)))
30.115 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
30.115 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
30.115 * [taylor]: Taking taylor expansion of 1.0 in k
30.115 * [backup-simplify]: Simplify 1.0 into 1.0
30.115 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
30.115 * [taylor]: Taking taylor expansion of (/ 1 k) in k
30.115 * [taylor]: Taking taylor expansion of k in k
30.115 * [backup-simplify]: Simplify 0 into 0
30.115 * [backup-simplify]: Simplify 1 into 1
30.115 * [backup-simplify]: Simplify (/ 1 1) into 1
30.116 * [backup-simplify]: Simplify (sqrt 0) into 0
30.117 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
30.117 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
30.117 * [taylor]: Taking taylor expansion of 1.0 in k
30.117 * [backup-simplify]: Simplify 1.0 into 1.0
30.117 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
30.117 * [taylor]: Taking taylor expansion of (/ 1 k) in k
30.117 * [taylor]: Taking taylor expansion of k in k
30.117 * [backup-simplify]: Simplify 0 into 0
30.118 * [backup-simplify]: Simplify 1 into 1
30.118 * [backup-simplify]: Simplify (/ 1 1) into 1
30.119 * [backup-simplify]: Simplify (sqrt 0) into 0
30.120 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
30.120 * [backup-simplify]: Simplify (* 1.0 0) into 0
30.120 * [backup-simplify]: Simplify 0 into 0
30.121 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
30.121 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.122 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
30.124 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.125 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
30.125 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.126 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.129 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
30.131 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
30.131 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.132 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
30.132 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k))
30.132 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
30.132 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
30.132 * [taylor]: Taking taylor expansion of 1.0 in k
30.132 * [backup-simplify]: Simplify 1.0 into 1.0
30.132 * [taylor]: Taking taylor expansion of (sqrt k) in k
30.132 * [taylor]: Taking taylor expansion of k in k
30.132 * [backup-simplify]: Simplify 0 into 0
30.132 * [backup-simplify]: Simplify 1 into 1
30.133 * [backup-simplify]: Simplify (sqrt 0) into 0
30.133 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
30.133 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
30.133 * [taylor]: Taking taylor expansion of 1.0 in k
30.133 * [backup-simplify]: Simplify 1.0 into 1.0
30.133 * [taylor]: Taking taylor expansion of (sqrt k) in k
30.133 * [taylor]: Taking taylor expansion of k in k
30.133 * [backup-simplify]: Simplify 0 into 0
30.133 * [backup-simplify]: Simplify 1 into 1
30.134 * [backup-simplify]: Simplify (sqrt 0) into 0
30.134 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
30.135 * [backup-simplify]: Simplify (* 1.0 0) into 0
30.135 * [backup-simplify]: Simplify 0 into 0
30.136 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
30.136 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.138 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.139 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
30.139 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.141 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
30.143 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
30.143 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.144 * [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))))))))
30.144 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k)))
30.144 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
30.144 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
30.144 * [taylor]: Taking taylor expansion of 1.0 in k
30.145 * [backup-simplify]: Simplify 1.0 into 1.0
30.145 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
30.145 * [taylor]: Taking taylor expansion of (/ -1 k) in k
30.145 * [taylor]: Taking taylor expansion of -1 in k
30.145 * [backup-simplify]: Simplify -1 into -1
30.145 * [taylor]: Taking taylor expansion of k in k
30.145 * [backup-simplify]: Simplify 0 into 0
30.145 * [backup-simplify]: Simplify 1 into 1
30.145 * [backup-simplify]: Simplify (/ -1 1) into -1
30.145 * [backup-simplify]: Simplify (sqrt 0) into 0
30.146 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
30.146 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
30.146 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
30.146 * [taylor]: Taking taylor expansion of 1.0 in k
30.146 * [backup-simplify]: Simplify 1.0 into 1.0
30.146 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
30.146 * [taylor]: Taking taylor expansion of (/ -1 k) in k
30.146 * [taylor]: Taking taylor expansion of -1 in k
30.146 * [backup-simplify]: Simplify -1 into -1
30.146 * [taylor]: Taking taylor expansion of k in k
30.146 * [backup-simplify]: Simplify 0 into 0
30.146 * [backup-simplify]: Simplify 1 into 1
30.147 * [backup-simplify]: Simplify (/ -1 1) into -1
30.147 * [backup-simplify]: Simplify (sqrt 0) into 0
30.148 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
30.148 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
30.148 * [backup-simplify]: Simplify +nan.0 into +nan.0
30.149 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
30.152 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.155 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
30.155 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.156 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.160 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
30.165 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
30.165 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
30.167 * [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)))))
30.167 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
30.168 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
30.168 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
30.168 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
30.168 * [taylor]: Taking taylor expansion of 2.0 in n
30.168 * [backup-simplify]: Simplify 2.0 into 2.0
30.168 * [taylor]: Taking taylor expansion of (* n PI) in n
30.168 * [taylor]: Taking taylor expansion of n in n
30.168 * [backup-simplify]: Simplify 0 into 0
30.168 * [backup-simplify]: Simplify 1 into 1
30.168 * [taylor]: Taking taylor expansion of PI in n
30.168 * [backup-simplify]: Simplify PI into PI
30.168 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
30.168 * [taylor]: Taking taylor expansion of 2.0 in n
30.168 * [backup-simplify]: Simplify 2.0 into 2.0
30.168 * [taylor]: Taking taylor expansion of (* n PI) in n
30.168 * [taylor]: Taking taylor expansion of n in n
30.168 * [backup-simplify]: Simplify 0 into 0
30.168 * [backup-simplify]: Simplify 1 into 1
30.168 * [taylor]: Taking taylor expansion of PI in n
30.168 * [backup-simplify]: Simplify PI into PI
30.169 * [backup-simplify]: Simplify (* 0 PI) into 0
30.169 * [backup-simplify]: Simplify (* 2.0 0) into 0
30.169 * [backup-simplify]: Simplify 0 into 0
30.171 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
30.173 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
30.173 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
30.174 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
30.175 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
30.175 * [backup-simplify]: Simplify 0 into 0
30.176 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
30.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
30.178 * [backup-simplify]: Simplify 0 into 0
30.179 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
30.180 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
30.180 * [backup-simplify]: Simplify 0 into 0
30.182 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
30.183 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
30.183 * [backup-simplify]: Simplify 0 into 0
30.185 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
30.186 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
30.186 * [backup-simplify]: Simplify 0 into 0
30.188 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
30.190 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
30.190 * [backup-simplify]: Simplify 0 into 0
30.191 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
30.191 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
30.191 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
30.191 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
30.191 * [taylor]: Taking taylor expansion of 2.0 in n
30.191 * [backup-simplify]: Simplify 2.0 into 2.0
30.191 * [taylor]: Taking taylor expansion of (/ PI n) in n
30.191 * [taylor]: Taking taylor expansion of PI in n
30.191 * [backup-simplify]: Simplify PI into PI
30.191 * [taylor]: Taking taylor expansion of n in n
30.191 * [backup-simplify]: Simplify 0 into 0
30.191 * [backup-simplify]: Simplify 1 into 1
30.192 * [backup-simplify]: Simplify (/ PI 1) into PI
30.192 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
30.192 * [taylor]: Taking taylor expansion of 2.0 in n
30.192 * [backup-simplify]: Simplify 2.0 into 2.0
30.192 * [taylor]: Taking taylor expansion of (/ PI n) in n
30.192 * [taylor]: Taking taylor expansion of PI in n
30.192 * [backup-simplify]: Simplify PI into PI
30.192 * [taylor]: Taking taylor expansion of n in n
30.192 * [backup-simplify]: Simplify 0 into 0
30.192 * [backup-simplify]: Simplify 1 into 1
30.193 * [backup-simplify]: Simplify (/ PI 1) into PI
30.193 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
30.193 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
30.194 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
30.195 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
30.195 * [backup-simplify]: Simplify 0 into 0
30.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.198 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
30.198 * [backup-simplify]: Simplify 0 into 0
30.199 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.201 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
30.201 * [backup-simplify]: Simplify 0 into 0
30.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.203 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
30.203 * [backup-simplify]: Simplify 0 into 0
30.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.206 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
30.206 * [backup-simplify]: Simplify 0 into 0
30.207 * [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
30.209 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
30.209 * [backup-simplify]: Simplify 0 into 0
30.210 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
30.210 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
30.210 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
30.210 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
30.210 * [taylor]: Taking taylor expansion of -2.0 in n
30.210 * [backup-simplify]: Simplify -2.0 into -2.0
30.210 * [taylor]: Taking taylor expansion of (/ PI n) in n
30.210 * [taylor]: Taking taylor expansion of PI in n
30.211 * [backup-simplify]: Simplify PI into PI
30.211 * [taylor]: Taking taylor expansion of n in n
30.211 * [backup-simplify]: Simplify 0 into 0
30.211 * [backup-simplify]: Simplify 1 into 1
30.211 * [backup-simplify]: Simplify (/ PI 1) into PI
30.211 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
30.211 * [taylor]: Taking taylor expansion of -2.0 in n
30.211 * [backup-simplify]: Simplify -2.0 into -2.0
30.211 * [taylor]: Taking taylor expansion of (/ PI n) in n
30.211 * [taylor]: Taking taylor expansion of PI in n
30.211 * [backup-simplify]: Simplify PI into PI
30.211 * [taylor]: Taking taylor expansion of n in n
30.211 * [backup-simplify]: Simplify 0 into 0
30.211 * [backup-simplify]: Simplify 1 into 1
30.212 * [backup-simplify]: Simplify (/ PI 1) into PI
30.212 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
30.213 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
30.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
30.215 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
30.215 * [backup-simplify]: Simplify 0 into 0
30.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.217 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
30.217 * [backup-simplify]: Simplify 0 into 0
30.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.219 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
30.219 * [backup-simplify]: Simplify 0 into 0
30.220 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.221 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
30.221 * [backup-simplify]: Simplify 0 into 0
30.223 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.224 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
30.224 * [backup-simplify]: Simplify 0 into 0
30.226 * [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
30.227 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
30.227 * [backup-simplify]: Simplify 0 into 0
30.228 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
30.228 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
30.228 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4))
30.228 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0
30.228 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
30.228 * [taylor]: Taking taylor expansion of 1.0 in k
30.228 * [backup-simplify]: Simplify 1.0 into 1.0
30.228 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
30.228 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
30.228 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
30.228 * [taylor]: Taking taylor expansion of 1/4 in k
30.229 * [backup-simplify]: Simplify 1/4 into 1/4
30.229 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
30.229 * [taylor]: Taking taylor expansion of (/ 1 k) in k
30.229 * [taylor]: Taking taylor expansion of k in k
30.229 * [backup-simplify]: Simplify 0 into 0
30.229 * [backup-simplify]: Simplify 1 into 1
30.235 * [backup-simplify]: Simplify (/ 1 1) into 1
30.235 * [backup-simplify]: Simplify (log 1) into 0
30.236 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.236 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
30.236 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
30.236 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
30.236 * [taylor]: Taking taylor expansion of 1.0 in k
30.236 * [backup-simplify]: Simplify 1.0 into 1.0
30.236 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
30.236 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
30.236 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
30.236 * [taylor]: Taking taylor expansion of 1/4 in k
30.236 * [backup-simplify]: Simplify 1/4 into 1/4
30.237 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
30.237 * [taylor]: Taking taylor expansion of (/ 1 k) in k
30.237 * [taylor]: Taking taylor expansion of k in k
30.237 * [backup-simplify]: Simplify 0 into 0
30.237 * [backup-simplify]: Simplify 1 into 1
30.237 * [backup-simplify]: Simplify (/ 1 1) into 1
30.237 * [backup-simplify]: Simplify (log 1) into 0
30.238 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.238 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
30.238 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
30.238 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
30.239 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
30.239 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
30.241 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
30.241 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.242 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
30.243 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
30.243 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0
30.243 * [backup-simplify]: Simplify 0 into 0
30.244 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.247 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
30.248 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.248 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
30.250 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
30.251 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0
30.251 * [backup-simplify]: Simplify 0 into 0
30.252 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.257 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
30.258 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.259 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
30.261 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
30.263 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0
30.263 * [backup-simplify]: Simplify 0 into 0
30.265 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.277 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
30.277 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.279 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
30.282 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
30.284 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0
30.284 * [backup-simplify]: Simplify 0 into 0
30.285 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.303 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
30.304 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.306 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
30.310 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
30.312 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0
30.312 * [backup-simplify]: Simplify 0 into 0
30.313 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.346 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
30.347 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
30.368 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
30.389 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
30.392 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0
30.392 * [backup-simplify]: Simplify 0 into 0
30.392 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
30.392 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4))
30.392 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0
30.392 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
30.392 * [taylor]: Taking taylor expansion of 1.0 in k
30.392 * [backup-simplify]: Simplify 1.0 into 1.0
30.392 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
30.392 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
30.392 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
30.392 * [taylor]: Taking taylor expansion of 1/4 in k
30.392 * [backup-simplify]: Simplify 1/4 into 1/4
30.392 * [taylor]: Taking taylor expansion of (log k) in k
30.392 * [taylor]: Taking taylor expansion of k in k
30.392 * [backup-simplify]: Simplify 0 into 0
30.392 * [backup-simplify]: Simplify 1 into 1
30.393 * [backup-simplify]: Simplify (log 1) into 0
30.393 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.393 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
30.393 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
30.393 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
30.394 * [taylor]: Taking taylor expansion of 1.0 in k
30.394 * [backup-simplify]: Simplify 1.0 into 1.0
30.394 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
30.394 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
30.394 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
30.394 * [taylor]: Taking taylor expansion of 1/4 in k
30.394 * [backup-simplify]: Simplify 1/4 into 1/4
30.394 * [taylor]: Taking taylor expansion of (log k) in k
30.394 * [taylor]: Taking taylor expansion of k in k
30.394 * [backup-simplify]: Simplify 0 into 0
30.394 * [backup-simplify]: Simplify 1 into 1
30.394 * [backup-simplify]: Simplify (log 1) into 0
30.395 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.395 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
30.395 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
30.395 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
30.395 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
30.398 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
30.399 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.399 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
30.400 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
30.401 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0
30.401 * [backup-simplify]: Simplify 0 into 0
30.404 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
30.404 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.405 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
30.407 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
30.408 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0
30.408 * [backup-simplify]: Simplify 0 into 0
30.413 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
30.414 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.415 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
30.417 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
30.418 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0
30.418 * [backup-simplify]: Simplify 0 into 0
30.433 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
30.433 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.435 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
30.438 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
30.439 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0
30.439 * [backup-simplify]: Simplify 0 into 0
30.458 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
30.459 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.461 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
30.464 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
30.467 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0
30.467 * [backup-simplify]: Simplify 0 into 0
30.498 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
30.499 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
30.501 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
30.507 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
30.510 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0
30.510 * [backup-simplify]: Simplify 0 into 0
30.511 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
30.511 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k)))))
30.511 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0
30.511 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
30.511 * [taylor]: Taking taylor expansion of 1.0 in k
30.511 * [backup-simplify]: Simplify 1.0 into 1.0
30.511 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
30.511 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
30.511 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
30.511 * [taylor]: Taking taylor expansion of (/ -1 k) in k
30.511 * [taylor]: Taking taylor expansion of -1 in k
30.511 * [backup-simplify]: Simplify -1 into -1
30.511 * [taylor]: Taking taylor expansion of k in k
30.511 * [backup-simplify]: Simplify 0 into 0
30.511 * [backup-simplify]: Simplify 1 into 1
30.512 * [backup-simplify]: Simplify (/ -1 1) into -1
30.512 * [backup-simplify]: Simplify (sqrt 0) into 0
30.514 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
30.514 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
30.515 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
30.515 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
30.518 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.520 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
30.522 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
30.522 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
30.522 * [taylor]: Taking taylor expansion of 1.0 in k
30.522 * [backup-simplify]: Simplify 1.0 into 1.0
30.522 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
30.522 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
30.522 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
30.522 * [taylor]: Taking taylor expansion of (/ -1 k) in k
30.522 * [taylor]: Taking taylor expansion of -1 in k
30.523 * [backup-simplify]: Simplify -1 into -1
30.523 * [taylor]: Taking taylor expansion of k in k
30.523 * [backup-simplify]: Simplify 0 into 0
30.523 * [backup-simplify]: Simplify 1 into 1
30.523 * [backup-simplify]: Simplify (/ -1 1) into -1
30.523 * [backup-simplify]: Simplify (sqrt 0) into 0
30.525 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
30.525 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
30.526 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
30.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
30.530 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.532 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
30.534 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
30.535 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
30.536 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
30.539 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
30.541 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
30.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.546 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
30.550 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
30.555 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
30.570 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
30.578 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
30.595 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
30.596 * * * [progress]: simplifying candidates
30.611 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
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  (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k))))
  (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
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  (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (- (/ 1.0 (sqrt (sqrt k))))
  (- (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1)
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1)
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1)
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1)
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt 1)))
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt 1))
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) 1)
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
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  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
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  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) 1)
  (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ 1.0 (sqrt (sqrt k))))
  (log1p (/ 1.0 (sqrt (sqrt k))))
  (- (log 1.0) (log (sqrt (sqrt k))))
  (log (/ 1.0 (sqrt (sqrt k))))
  (exp (/ 1.0 (sqrt (sqrt k))))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (cbrt (/ 1.0 (sqrt (sqrt k))))
  (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (- 1.0)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt 1)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1.0)
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (sqrt (sqrt k)) (cbrt 1.0))
  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (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))))))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 1.0 (pow (/ 1 k) 1/4))
  (* 1.0 (pow (/ 1 k) 1/4))
  (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
30.638 * * [simplify]: iteration 0: 566 enodes
31.057 * * [simplify]: iteration 1: 1372 enodes
32.009 * * [simplify]: iteration 2: 3578 enodes
33.889 * * [simplify]: iteration complete: 5023 enodes
33.890 * * [simplify]: Extracting #0: cost 252 inf + 0
33.895 * * [simplify]: Extracting #1: cost 1163 inf + 2
33.908 * * [simplify]: Extracting #2: cost 1692 inf + 4697
33.946 * * [simplify]: Extracting #3: cost 1338 inf + 96806
34.041 * * [simplify]: Extracting #4: cost 393 inf + 352603
34.196 * * [simplify]: Extracting #5: cost 56 inf + 475820
34.366 * * [simplify]: Extracting #6: cost 12 inf + 489658
34.536 * * [simplify]: Extracting #7: cost 0 inf + 493293
34.697 * * [simplify]: Extracting #8: cost 0 inf + 493238
34.874 * [simplify]: Simplified to:
  (expm1 (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* PI (* n 2.0)) (/ 1.0 2.0))
  (pow (* PI (* n 2.0)) (/ k 2.0))
  (pow (* PI (* n 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* PI (* n 2.0)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* PI (* n 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* PI (* n 2.0)) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (pow (* PI (* n 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* PI (* n 2.0)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* n 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* PI (* n 2.0)) (sqrt (- 1.0 k)))
  (pow (* PI (* n 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* n 2.0)) (/ 1 (sqrt 2.0)))
  (* PI (* n 2.0))
  (pow (* PI (* n 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* PI (* n 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* PI (* n 2.0)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* PI (* n 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* n 2.0)) (/ 1 (sqrt 2.0)))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (pow (* PI (* n 2.0)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (exp (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (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 (sqrt k))))
  (- (sqrt (sqrt k)))
  (* (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (* (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (fabs (cbrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
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  1.0
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34.986 * * * [progress]: adding candidates to table
37.587 * [progress]: [Phase 3 of 3] Extracting.
37.588 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
37.595 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
37.595 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
37.754 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
37.902 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
38.037 * * * [regime]: Found split indices: #<option (#s(si 7 255))>
38.037 * [simplify]: Simplifying:
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
38.037 * * [simplify]: iteration 0: 13 enodes
38.040 * * [simplify]: iteration 1: 15 enodes
38.042 * * [simplify]: iteration complete: 15 enodes
38.042 * * [simplify]: Extracting #0: cost 1 inf + 0
38.042 * * [simplify]: Extracting #1: cost 3 inf + 0
38.042 * * [simplify]: Extracting #2: cost 4 inf + 1
38.042 * * [simplify]: Extracting #3: cost 7 inf + 1
38.042 * * [simplify]: Extracting #4: cost 9 inf + 43
38.042 * * [simplify]: Extracting #5: cost 6 inf + 170
38.042 * * [simplify]: Extracting #6: cost 3 inf + 296
38.043 * * [simplify]: Extracting #7: cost 1 inf + 1126
38.043 * * [simplify]: Extracting #8: cost 0 inf + 1621
38.043 * [simplify]: Simplified to:
  (/ 1.0 (/ (sqrt k) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))))
48.192 * [regime-testing]: Baseline error score: 0.36206858809282094
48.208 * [regime-testing]: Oracle error score: 0.03604698712375105
48.250 * [regime-testing]: End program error score: 0.36206858809282094