53.687 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.155 * * * [progress]: [2/2] Setting up program.
0.163 * [progress]: [Phase 2 of 3] Improving.
0.164 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.164 * * [simplify]: iteration 0: 13 enodes
0.170 * * [simplify]: iteration 1: 29 enodes
0.182 * * [simplify]: iteration 2: 58 enodes
0.237 * * [simplify]: iteration 3: 114 enodes
0.291 * * [simplify]: iteration 4: 285 enodes
0.434 * * [simplify]: iteration 5: 816 enodes
1.451 * * [simplify]: iteration 6: 2792 enodes
2.514 * * [simplify]: iteration complete: 5003 enodes
2.514 * * [simplify]: Extracting #0: cost 1 inf + 0
2.515 * * [simplify]: Extracting #1: cost 108 inf + 0
2.517 * * [simplify]: Extracting #2: cost 443 inf + 1
2.520 * * [simplify]: Extracting #3: cost 1022 inf + 49
2.527 * * [simplify]: Extracting #4: cost 1321 inf + 10849
2.559 * * [simplify]: Extracting #5: cost 617 inf + 94525
2.636 * * [simplify]: Extracting #6: cost 187 inf + 373026
2.802 * * [simplify]: Extracting #7: cost 0 inf + 567203
2.968 * * [simplify]: Extracting #8: cost 0 inf + 562474
3.128 * * [simplify]: Extracting #9: cost 0 inf + 561804
3.255 * [simplify]: Simplified to:
  (/ (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
3.255 * * [progress]: iteration 1 / 4
3.255 * * * [progress]: picking best candidate
3.260 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
3.260 * * * [progress]: localizing error
3.296 * * * [progress]: generating rewritten candidates
3.296 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
3.305 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
3.333 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
3.376 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
3.410 * * * [progress]: generating series expansions
3.410 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
3.410 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
3.410 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
3.410 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
3.410 * [taylor]: Taking taylor expansion of 1.0 in k
3.410 * [backup-simplify]: Simplify 1.0 into 1.0
3.410 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.410 * [taylor]: Taking taylor expansion of k in k
3.410 * [backup-simplify]: Simplify 0 into 0
3.410 * [backup-simplify]: Simplify 1 into 1
3.411 * [backup-simplify]: Simplify (/ 1 1) into 1
3.411 * [backup-simplify]: Simplify (sqrt 0) into 0
3.413 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.413 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
3.413 * [taylor]: Taking taylor expansion of 1.0 in k
3.413 * [backup-simplify]: Simplify 1.0 into 1.0
3.413 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.413 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.413 * [taylor]: Taking taylor expansion of k in k
3.413 * [backup-simplify]: Simplify 0 into 0
3.413 * [backup-simplify]: Simplify 1 into 1
3.414 * [backup-simplify]: Simplify (/ 1 1) into 1
3.414 * [backup-simplify]: Simplify (sqrt 0) into 0
3.415 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.416 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.416 * [backup-simplify]: Simplify 0 into 0
3.417 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
3.418 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.419 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.422 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.424 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
3.424 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.425 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.429 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.432 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
3.432 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.434 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
3.434 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
3.434 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
3.434 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
3.434 * [taylor]: Taking taylor expansion of 1.0 in k
3.434 * [backup-simplify]: Simplify 1.0 into 1.0
3.434 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.434 * [taylor]: Taking taylor expansion of k in k
3.434 * [backup-simplify]: Simplify 0 into 0
3.435 * [backup-simplify]: Simplify 1 into 1
3.435 * [backup-simplify]: Simplify (sqrt 0) into 0
3.436 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.436 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
3.436 * [taylor]: Taking taylor expansion of 1.0 in k
3.436 * [backup-simplify]: Simplify 1.0 into 1.0
3.436 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.436 * [taylor]: Taking taylor expansion of k in k
3.436 * [backup-simplify]: Simplify 0 into 0
3.436 * [backup-simplify]: Simplify 1 into 1
3.437 * [backup-simplify]: Simplify (sqrt 0) into 0
3.438 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.439 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.439 * [backup-simplify]: Simplify 0 into 0
3.440 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
3.441 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.444 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.446 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
3.446 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.450 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.453 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
3.453 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.455 * [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))))))))
3.455 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
3.455 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
3.455 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
3.455 * [taylor]: Taking taylor expansion of 1.0 in k
3.455 * [backup-simplify]: Simplify 1.0 into 1.0
3.455 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.455 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.455 * [taylor]: Taking taylor expansion of -1 in k
3.455 * [backup-simplify]: Simplify -1 into -1
3.455 * [taylor]: Taking taylor expansion of k in k
3.455 * [backup-simplify]: Simplify 0 into 0
3.455 * [backup-simplify]: Simplify 1 into 1
3.456 * [backup-simplify]: Simplify (/ -1 1) into -1
3.456 * [backup-simplify]: Simplify (sqrt 0) into 0
3.457 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.458 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
3.458 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
3.458 * [taylor]: Taking taylor expansion of 1.0 in k
3.458 * [backup-simplify]: Simplify 1.0 into 1.0
3.458 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.458 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.458 * [taylor]: Taking taylor expansion of -1 in k
3.458 * [backup-simplify]: Simplify -1 into -1
3.458 * [taylor]: Taking taylor expansion of k in k
3.458 * [backup-simplify]: Simplify 0 into 0
3.458 * [backup-simplify]: Simplify 1 into 1
3.459 * [backup-simplify]: Simplify (/ -1 1) into -1
3.459 * [backup-simplify]: Simplify (sqrt 0) into 0
3.460 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.461 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
3.461 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.462 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
3.465 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.468 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
3.468 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.473 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.477 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
3.478 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
3.479 * [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)))))
3.479 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
3.480 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
3.480 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
3.480 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.480 * [taylor]: Taking taylor expansion of 2.0 in n
3.480 * [backup-simplify]: Simplify 2.0 into 2.0
3.480 * [taylor]: Taking taylor expansion of (* n PI) in n
3.480 * [taylor]: Taking taylor expansion of n in n
3.480 * [backup-simplify]: Simplify 0 into 0
3.480 * [backup-simplify]: Simplify 1 into 1
3.480 * [taylor]: Taking taylor expansion of PI in n
3.480 * [backup-simplify]: Simplify PI into PI
3.480 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.480 * [taylor]: Taking taylor expansion of 2.0 in n
3.480 * [backup-simplify]: Simplify 2.0 into 2.0
3.480 * [taylor]: Taking taylor expansion of (* n PI) in n
3.480 * [taylor]: Taking taylor expansion of n in n
3.480 * [backup-simplify]: Simplify 0 into 0
3.480 * [backup-simplify]: Simplify 1 into 1
3.480 * [taylor]: Taking taylor expansion of PI in n
3.480 * [backup-simplify]: Simplify PI into PI
3.481 * [backup-simplify]: Simplify (* 0 PI) into 0
3.481 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.481 * [backup-simplify]: Simplify 0 into 0
3.483 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.485 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.485 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.487 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.488 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
3.488 * [backup-simplify]: Simplify 0 into 0
3.489 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.490 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.490 * [backup-simplify]: Simplify 0 into 0
3.491 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.493 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.493 * [backup-simplify]: Simplify 0 into 0
3.493 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.494 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
3.494 * [backup-simplify]: Simplify 0 into 0
3.498 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.499 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
3.499 * [backup-simplify]: Simplify 0 into 0
3.501 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
3.502 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
3.502 * [backup-simplify]: Simplify 0 into 0
3.502 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
3.503 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
3.503 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
3.503 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.503 * [taylor]: Taking taylor expansion of 2.0 in n
3.503 * [backup-simplify]: Simplify 2.0 into 2.0
3.503 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.503 * [taylor]: Taking taylor expansion of PI in n
3.503 * [backup-simplify]: Simplify PI into PI
3.503 * [taylor]: Taking taylor expansion of n in n
3.503 * [backup-simplify]: Simplify 0 into 0
3.503 * [backup-simplify]: Simplify 1 into 1
3.503 * [backup-simplify]: Simplify (/ PI 1) into PI
3.503 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.503 * [taylor]: Taking taylor expansion of 2.0 in n
3.503 * [backup-simplify]: Simplify 2.0 into 2.0
3.503 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.503 * [taylor]: Taking taylor expansion of PI in n
3.503 * [backup-simplify]: Simplify PI into PI
3.503 * [taylor]: Taking taylor expansion of n in n
3.503 * [backup-simplify]: Simplify 0 into 0
3.503 * [backup-simplify]: Simplify 1 into 1
3.504 * [backup-simplify]: Simplify (/ PI 1) into PI
3.504 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.504 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.505 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
3.505 * [backup-simplify]: Simplify 0 into 0
3.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.507 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.507 * [backup-simplify]: Simplify 0 into 0
3.507 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.508 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.508 * [backup-simplify]: Simplify 0 into 0
3.509 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.509 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.509 * [backup-simplify]: Simplify 0 into 0
3.510 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.511 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.511 * [backup-simplify]: Simplify 0 into 0
3.512 * [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
3.513 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.513 * [backup-simplify]: Simplify 0 into 0
3.513 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
3.513 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
3.513 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
3.514 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.514 * [taylor]: Taking taylor expansion of -2.0 in n
3.514 * [backup-simplify]: Simplify -2.0 into -2.0
3.514 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.514 * [taylor]: Taking taylor expansion of PI in n
3.514 * [backup-simplify]: Simplify PI into PI
3.514 * [taylor]: Taking taylor expansion of n in n
3.514 * [backup-simplify]: Simplify 0 into 0
3.514 * [backup-simplify]: Simplify 1 into 1
3.514 * [backup-simplify]: Simplify (/ PI 1) into PI
3.514 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.514 * [taylor]: Taking taylor expansion of -2.0 in n
3.514 * [backup-simplify]: Simplify -2.0 into -2.0
3.514 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.514 * [taylor]: Taking taylor expansion of PI in n
3.514 * [backup-simplify]: Simplify PI into PI
3.514 * [taylor]: Taking taylor expansion of n in n
3.514 * [backup-simplify]: Simplify 0 into 0
3.514 * [backup-simplify]: Simplify 1 into 1
3.514 * [backup-simplify]: Simplify (/ PI 1) into PI
3.515 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.515 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.516 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.516 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
3.516 * [backup-simplify]: Simplify 0 into 0
3.517 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.517 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
3.517 * [backup-simplify]: Simplify 0 into 0
3.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.519 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.519 * [backup-simplify]: Simplify 0 into 0
3.519 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.520 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.520 * [backup-simplify]: Simplify 0 into 0
3.521 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.522 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.522 * [backup-simplify]: Simplify 0 into 0
3.522 * [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
3.523 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.523 * [backup-simplify]: Simplify 0 into 0
3.524 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
3.524 * * * * [progress]: [ 3 / 4 ] generating series at (2)
3.524 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
3.525 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0
3.525 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
3.525 * [taylor]: Taking taylor expansion of 1.0 in n
3.525 * [backup-simplify]: Simplify 1.0 into 1.0
3.525 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
3.525 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
3.525 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
3.525 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
3.525 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
3.525 * [taylor]: Taking taylor expansion of 0.5 in n
3.525 * [backup-simplify]: Simplify 0.5 into 0.5
3.525 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
3.525 * [taylor]: Taking taylor expansion of 1.0 in n
3.525 * [backup-simplify]: Simplify 1.0 into 1.0
3.525 * [taylor]: Taking taylor expansion of k in n
3.525 * [backup-simplify]: Simplify k into k
3.525 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.525 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.525 * [taylor]: Taking taylor expansion of 2.0 in n
3.525 * [backup-simplify]: Simplify 2.0 into 2.0
3.525 * [taylor]: Taking taylor expansion of (* n PI) in n
3.525 * [taylor]: Taking taylor expansion of n in n
3.525 * [backup-simplify]: Simplify 0 into 0
3.525 * [backup-simplify]: Simplify 1 into 1
3.525 * [taylor]: Taking taylor expansion of PI in n
3.525 * [backup-simplify]: Simplify PI into PI
3.525 * [backup-simplify]: Simplify (* 0 PI) into 0
3.525 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.526 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.527 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.528 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.528 * [backup-simplify]: Simplify (- k) into (- k)
3.528 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
3.528 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
3.530 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.531 * [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))))
3.532 * [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)))))
3.532 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.532 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.532 * [taylor]: Taking taylor expansion of k in n
3.532 * [backup-simplify]: Simplify k into k
3.532 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.532 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.533 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.533 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.533 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
3.533 * [taylor]: Taking taylor expansion of 1.0 in k
3.533 * [backup-simplify]: Simplify 1.0 into 1.0
3.533 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
3.533 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
3.533 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
3.533 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
3.533 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
3.533 * [taylor]: Taking taylor expansion of 0.5 in k
3.533 * [backup-simplify]: Simplify 0.5 into 0.5
3.533 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
3.533 * [taylor]: Taking taylor expansion of 1.0 in k
3.533 * [backup-simplify]: Simplify 1.0 into 1.0
3.533 * [taylor]: Taking taylor expansion of k in k
3.533 * [backup-simplify]: Simplify 0 into 0
3.533 * [backup-simplify]: Simplify 1 into 1
3.533 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
3.534 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
3.534 * [taylor]: Taking taylor expansion of 2.0 in k
3.534 * [backup-simplify]: Simplify 2.0 into 2.0
3.534 * [taylor]: Taking taylor expansion of (* n PI) in k
3.534 * [taylor]: Taking taylor expansion of n in k
3.534 * [backup-simplify]: Simplify n into n
3.534 * [taylor]: Taking taylor expansion of PI in k
3.534 * [backup-simplify]: Simplify PI into PI
3.534 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.534 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
3.534 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
3.534 * [backup-simplify]: Simplify (- 0) into 0
3.535 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
3.535 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
3.535 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
3.536 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
3.536 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.536 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.536 * [taylor]: Taking taylor expansion of k in k
3.536 * [backup-simplify]: Simplify 0 into 0
3.536 * [backup-simplify]: Simplify 1 into 1
3.536 * [backup-simplify]: Simplify (/ 1 1) into 1
3.537 * [backup-simplify]: Simplify (sqrt 0) into 0
3.538 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.538 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
3.538 * [taylor]: Taking taylor expansion of 1.0 in k
3.538 * [backup-simplify]: Simplify 1.0 into 1.0
3.538 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
3.538 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
3.538 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
3.538 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
3.538 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
3.538 * [taylor]: Taking taylor expansion of 0.5 in k
3.538 * [backup-simplify]: Simplify 0.5 into 0.5
3.539 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
3.539 * [taylor]: Taking taylor expansion of 1.0 in k
3.539 * [backup-simplify]: Simplify 1.0 into 1.0
3.539 * [taylor]: Taking taylor expansion of k in k
3.539 * [backup-simplify]: Simplify 0 into 0
3.539 * [backup-simplify]: Simplify 1 into 1
3.539 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
3.539 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
3.539 * [taylor]: Taking taylor expansion of 2.0 in k
3.539 * [backup-simplify]: Simplify 2.0 into 2.0
3.539 * [taylor]: Taking taylor expansion of (* n PI) in k
3.539 * [taylor]: Taking taylor expansion of n in k
3.539 * [backup-simplify]: Simplify n into n
3.539 * [taylor]: Taking taylor expansion of PI in k
3.539 * [backup-simplify]: Simplify PI into PI
3.539 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.539 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
3.539 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
3.540 * [backup-simplify]: Simplify (- 0) into 0
3.540 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
3.541 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
3.541 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
3.541 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
3.541 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.541 * [taylor]: Taking taylor expansion of k in k
3.541 * [backup-simplify]: Simplify 0 into 0
3.541 * [backup-simplify]: Simplify 1 into 1
3.541 * [backup-simplify]: Simplify (/ 1 1) into 1
3.542 * [backup-simplify]: Simplify (sqrt 0) into 0
3.543 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.543 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0
3.544 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.544 * [taylor]: Taking taylor expansion of 0 in n
3.544 * [backup-simplify]: Simplify 0 into 0
3.544 * [backup-simplify]: Simplify 0 into 0
3.545 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
3.545 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
3.546 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
3.546 * [backup-simplify]: Simplify (- 1) into -1
3.547 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.548 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
3.549 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
3.550 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))))
3.551 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
3.553 * [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)))
3.553 * [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
3.553 * [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
3.554 * [taylor]: Taking taylor expansion of +nan.0 in n
3.554 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.554 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.554 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.554 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.554 * [taylor]: Taking taylor expansion of 0.5 in n
3.554 * [backup-simplify]: Simplify 0.5 into 0.5
3.554 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.554 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.554 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.554 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.554 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.554 * [taylor]: Taking taylor expansion of 1.0 in n
3.554 * [backup-simplify]: Simplify 1.0 into 1.0
3.554 * [taylor]: Taking taylor expansion of (log PI) in n
3.554 * [taylor]: Taking taylor expansion of PI in n
3.554 * [backup-simplify]: Simplify PI into PI
3.554 * [backup-simplify]: Simplify (log PI) into (log PI)
3.555 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.557 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.557 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.557 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.557 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.557 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.557 * [taylor]: Taking taylor expansion of 1.0 in n
3.557 * [backup-simplify]: Simplify 1.0 into 1.0
3.557 * [taylor]: Taking taylor expansion of (log n) in n
3.557 * [taylor]: Taking taylor expansion of n in n
3.557 * [backup-simplify]: Simplify 0 into 0
3.557 * [backup-simplify]: Simplify 1 into 1
3.558 * [backup-simplify]: Simplify (log 1) into 0
3.558 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.558 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.559 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.559 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.559 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.559 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.559 * [taylor]: Taking taylor expansion of 1.0 in n
3.559 * [backup-simplify]: Simplify 1.0 into 1.0
3.559 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.559 * [taylor]: Taking taylor expansion of 2.0 in n
3.559 * [backup-simplify]: Simplify 2.0 into 2.0
3.559 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.560 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.562 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.562 * [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)
3.564 * [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)
3.565 * [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))
3.567 * [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)))
3.568 * [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)
3.570 * [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))
3.572 * [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)))
3.573 * [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)))
3.573 * [backup-simplify]: Simplify 0 into 0
3.574 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.577 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.578 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
3.579 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
3.581 * [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
3.581 * [backup-simplify]: Simplify (- 0) into 0
3.582 * [backup-simplify]: Simplify (+ 0 0) into 0
3.583 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
3.585 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
3.586 * [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 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))
3.590 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))
3.596 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 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) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))
3.596 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n
3.596 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n
3.596 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
3.596 * [taylor]: Taking taylor expansion of +nan.0 in n
3.596 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.596 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
3.596 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.596 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.596 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.596 * [taylor]: Taking taylor expansion of 0.5 in n
3.596 * [backup-simplify]: Simplify 0.5 into 0.5
3.596 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.597 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.597 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.597 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.597 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.597 * [taylor]: Taking taylor expansion of 1.0 in n
3.597 * [backup-simplify]: Simplify 1.0 into 1.0
3.597 * [taylor]: Taking taylor expansion of (log PI) in n
3.597 * [taylor]: Taking taylor expansion of PI in n
3.597 * [backup-simplify]: Simplify PI into PI
3.597 * [backup-simplify]: Simplify (log PI) into (log PI)
3.598 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.600 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.600 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.600 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.600 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.600 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.600 * [taylor]: Taking taylor expansion of 1.0 in n
3.600 * [backup-simplify]: Simplify 1.0 into 1.0
3.600 * [taylor]: Taking taylor expansion of (log n) in n
3.600 * [taylor]: Taking taylor expansion of n in n
3.600 * [backup-simplify]: Simplify 0 into 0
3.600 * [backup-simplify]: Simplify 1 into 1
3.601 * [backup-simplify]: Simplify (log 1) into 0
3.601 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.601 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.601 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.601 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.601 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.601 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.602 * [taylor]: Taking taylor expansion of 1.0 in n
3.602 * [backup-simplify]: Simplify 1.0 into 1.0
3.602 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.602 * [taylor]: Taking taylor expansion of 2.0 in n
3.602 * [backup-simplify]: Simplify 2.0 into 2.0
3.602 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.603 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.604 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.605 * [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)
3.606 * [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)
3.608 * [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))
3.609 * [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)))
3.610 * [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)
3.611 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.611 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.611 * [taylor]: Taking taylor expansion of 2.0 in n
3.611 * [backup-simplify]: Simplify 2.0 into 2.0
3.611 * [taylor]: Taking taylor expansion of (* n PI) in n
3.611 * [taylor]: Taking taylor expansion of n in n
3.611 * [backup-simplify]: Simplify 0 into 0
3.611 * [backup-simplify]: Simplify 1 into 1
3.611 * [taylor]: Taking taylor expansion of PI in n
3.611 * [backup-simplify]: Simplify PI into PI
3.611 * [backup-simplify]: Simplify (* 0 PI) into 0
3.612 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.613 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.615 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.616 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.616 * [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
3.616 * [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
3.616 * [taylor]: Taking taylor expansion of +nan.0 in n
3.616 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.616 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.616 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.616 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.616 * [taylor]: Taking taylor expansion of 0.5 in n
3.616 * [backup-simplify]: Simplify 0.5 into 0.5
3.616 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.616 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.616 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.616 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.617 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.617 * [taylor]: Taking taylor expansion of 1.0 in n
3.617 * [backup-simplify]: Simplify 1.0 into 1.0
3.617 * [taylor]: Taking taylor expansion of (log PI) in n
3.617 * [taylor]: Taking taylor expansion of PI in n
3.617 * [backup-simplify]: Simplify PI into PI
3.617 * [backup-simplify]: Simplify (log PI) into (log PI)
3.618 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.620 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.620 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.620 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.620 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.620 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.620 * [taylor]: Taking taylor expansion of 1.0 in n
3.620 * [backup-simplify]: Simplify 1.0 into 1.0
3.620 * [taylor]: Taking taylor expansion of (log n) in n
3.620 * [taylor]: Taking taylor expansion of n in n
3.620 * [backup-simplify]: Simplify 0 into 0
3.620 * [backup-simplify]: Simplify 1 into 1
3.620 * [backup-simplify]: Simplify (log 1) into 0
3.621 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.621 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.621 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.621 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.621 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.621 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.621 * [taylor]: Taking taylor expansion of 1.0 in n
3.621 * [backup-simplify]: Simplify 1.0 into 1.0
3.621 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.621 * [taylor]: Taking taylor expansion of 2.0 in n
3.621 * [backup-simplify]: Simplify 2.0 into 2.0
3.622 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.623 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.624 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.625 * [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)
3.626 * [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)
3.627 * [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))
3.629 * [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)))
3.630 * [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)
3.632 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.637 * [backup-simplify]: Simplify (* (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) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))
3.639 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))))
3.640 * [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))
3.640 * [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)))
3.643 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +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) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))
3.646 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +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 n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))))))))
3.650 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +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 n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))
3.651 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
3.651 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
3.652 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
3.653 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
3.653 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.654 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
3.654 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
3.655 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
3.656 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
3.656 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
3.657 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
3.658 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
3.659 * [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
3.660 * [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
3.662 * [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
3.663 * [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
3.663 * [backup-simplify]: Simplify (- 0) into 0
3.663 * [backup-simplify]: Simplify 0 into 0
3.663 * [backup-simplify]: Simplify 0 into 0
3.664 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.666 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.667 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.668 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
3.670 * [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
3.671 * [backup-simplify]: Simplify (- 0) into 0
3.671 * [backup-simplify]: Simplify (+ 0 0) into 0
3.672 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
3.674 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
3.676 * [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 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))
3.681 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
3.693 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 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) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
3.693 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n
3.693 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n
3.693 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
3.693 * [taylor]: Taking taylor expansion of +nan.0 in n
3.693 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.693 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
3.693 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.693 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.693 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.693 * [taylor]: Taking taylor expansion of 0.5 in n
3.693 * [backup-simplify]: Simplify 0.5 into 0.5
3.693 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.693 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.693 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.693 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.693 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.693 * [taylor]: Taking taylor expansion of 1.0 in n
3.693 * [backup-simplify]: Simplify 1.0 into 1.0
3.693 * [taylor]: Taking taylor expansion of (log PI) in n
3.693 * [taylor]: Taking taylor expansion of PI in n
3.693 * [backup-simplify]: Simplify PI into PI
3.694 * [backup-simplify]: Simplify (log PI) into (log PI)
3.695 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.697 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.697 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.697 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.697 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.697 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.697 * [taylor]: Taking taylor expansion of 1.0 in n
3.697 * [backup-simplify]: Simplify 1.0 into 1.0
3.697 * [taylor]: Taking taylor expansion of (log n) in n
3.697 * [taylor]: Taking taylor expansion of n in n
3.697 * [backup-simplify]: Simplify 0 into 0
3.697 * [backup-simplify]: Simplify 1 into 1
3.697 * [backup-simplify]: Simplify (log 1) into 0
3.698 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.698 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.698 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.698 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.698 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.698 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.698 * [taylor]: Taking taylor expansion of 1.0 in n
3.698 * [backup-simplify]: Simplify 1.0 into 1.0
3.698 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.698 * [taylor]: Taking taylor expansion of 2.0 in n
3.698 * [backup-simplify]: Simplify 2.0 into 2.0
3.699 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.700 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.701 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.702 * [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)
3.703 * [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)
3.705 * [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))
3.706 * [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)))
3.707 * [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)
3.708 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.708 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.708 * [taylor]: Taking taylor expansion of 2.0 in n
3.708 * [backup-simplify]: Simplify 2.0 into 2.0
3.708 * [taylor]: Taking taylor expansion of (* n PI) in n
3.708 * [taylor]: Taking taylor expansion of n in n
3.708 * [backup-simplify]: Simplify 0 into 0
3.708 * [backup-simplify]: Simplify 1 into 1
3.708 * [taylor]: Taking taylor expansion of PI in n
3.708 * [backup-simplify]: Simplify PI into PI
3.708 * [backup-simplify]: Simplify (* 0 PI) into 0
3.709 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.710 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.712 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.713 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.713 * [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 PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n
3.713 * [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 PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n
3.713 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n
3.713 * [taylor]: Taking taylor expansion of +nan.0 in n
3.713 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.713 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
3.713 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
3.713 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
3.713 * [taylor]: Taking taylor expansion of 0.5 in n
3.713 * [backup-simplify]: Simplify 0.5 into 0.5
3.714 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
3.714 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
3.714 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.714 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.714 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.714 * [taylor]: Taking taylor expansion of 1.0 in n
3.714 * [backup-simplify]: Simplify 1.0 into 1.0
3.714 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.714 * [taylor]: Taking taylor expansion of 2.0 in n
3.714 * [backup-simplify]: Simplify 2.0 into 2.0
3.714 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.715 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.716 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.717 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
3.717 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.717 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.717 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.717 * [taylor]: Taking taylor expansion of 1.0 in n
3.717 * [backup-simplify]: Simplify 1.0 into 1.0
3.717 * [taylor]: Taking taylor expansion of (log n) in n
3.717 * [taylor]: Taking taylor expansion of n in n
3.717 * [backup-simplify]: Simplify 0 into 0
3.717 * [backup-simplify]: Simplify 1 into 1
3.717 * [backup-simplify]: Simplify (log 1) into 0
3.718 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.718 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.718 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.718 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.718 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.718 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.718 * [taylor]: Taking taylor expansion of 1.0 in n
3.718 * [backup-simplify]: Simplify 1.0 into 1.0
3.718 * [taylor]: Taking taylor expansion of (log PI) in n
3.718 * [taylor]: Taking taylor expansion of PI in n
3.718 * [backup-simplify]: Simplify PI into PI
3.719 * [backup-simplify]: Simplify (log PI) into (log PI)
3.720 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.721 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.722 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
3.723 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
3.725 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
3.726 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
3.728 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
3.728 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n
3.728 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
3.728 * [taylor]: Taking taylor expansion of +nan.0 in n
3.728 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.728 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
3.728 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
3.728 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
3.728 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
3.728 * [taylor]: Taking taylor expansion of 0.5 in n
3.728 * [backup-simplify]: Simplify 0.5 into 0.5
3.728 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
3.728 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
3.728 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
3.728 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
3.728 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
3.728 * [taylor]: Taking taylor expansion of 1.0 in n
3.728 * [backup-simplify]: Simplify 1.0 into 1.0
3.728 * [taylor]: Taking taylor expansion of (log PI) in n
3.728 * [taylor]: Taking taylor expansion of PI in n
3.728 * [backup-simplify]: Simplify PI into PI
3.729 * [backup-simplify]: Simplify (log PI) into (log PI)
3.730 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
3.731 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
3.732 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
3.732 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
3.732 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
3.732 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
3.732 * [taylor]: Taking taylor expansion of 1.0 in n
3.732 * [backup-simplify]: Simplify 1.0 into 1.0
3.732 * [taylor]: Taking taylor expansion of (log n) in n
3.732 * [taylor]: Taking taylor expansion of n in n
3.732 * [backup-simplify]: Simplify 0 into 0
3.732 * [backup-simplify]: Simplify 1 into 1
3.732 * [backup-simplify]: Simplify (log 1) into 0
3.733 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
3.733 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
3.733 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
3.733 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
3.733 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
3.733 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
3.733 * [taylor]: Taking taylor expansion of 1.0 in n
3.733 * [backup-simplify]: Simplify 1.0 into 1.0
3.733 * [taylor]: Taking taylor expansion of (log 2.0) in n
3.733 * [taylor]: Taking taylor expansion of 2.0 in n
3.733 * [backup-simplify]: Simplify 2.0 into 2.0
3.733 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
3.734 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
3.736 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
3.737 * [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)
3.738 * [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)
3.739 * [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))
3.741 * [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)))
3.742 * [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)
3.742 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
3.742 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
3.742 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
3.742 * [taylor]: Taking taylor expansion of 2.0 in n
3.742 * [backup-simplify]: Simplify 2.0 into 2.0
3.742 * [taylor]: Taking taylor expansion of (* n PI) in n
3.742 * [taylor]: Taking taylor expansion of n in n
3.742 * [backup-simplify]: Simplify 0 into 0
3.742 * [backup-simplify]: Simplify 1 into 1
3.742 * [taylor]: Taking taylor expansion of PI in n
3.742 * [backup-simplify]: Simplify PI into PI
3.743 * [backup-simplify]: Simplify (* 0 PI) into 0
3.743 * [backup-simplify]: Simplify (* 2.0 0) into 0
3.745 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.747 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
3.748 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.749 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.751 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.753 * [backup-simplify]: Simplify (* (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) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))
3.756 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))))
3.758 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
3.759 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.761 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
3.763 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
3.769 * [backup-simplify]: Simplify (* (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) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))
3.771 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))
3.775 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))
3.785 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))
3.793 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (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) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (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) (pow (log n) 2))))))))))
3.802 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (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) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
3.812 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
3.823 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +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 n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))))))))))))))
3.852 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +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 n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))))))))))))))))))))))
3.853 * [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 (- 1.0 (/ 1 k)))) (sqrt k)))
3.853 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0
3.853 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
3.853 * [taylor]: Taking taylor expansion of 1.0 in n
3.853 * [backup-simplify]: Simplify 1.0 into 1.0
3.853 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
3.853 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
3.853 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
3.853 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
3.854 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
3.854 * [taylor]: Taking taylor expansion of 0.5 in n
3.854 * [backup-simplify]: Simplify 0.5 into 0.5
3.854 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.854 * [taylor]: Taking taylor expansion of 1.0 in n
3.854 * [backup-simplify]: Simplify 1.0 into 1.0
3.854 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.854 * [taylor]: Taking taylor expansion of k in n
3.854 * [backup-simplify]: Simplify k into k
3.854 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.854 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.854 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.854 * [taylor]: Taking taylor expansion of 2.0 in n
3.854 * [backup-simplify]: Simplify 2.0 into 2.0
3.854 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.854 * [taylor]: Taking taylor expansion of PI in n
3.854 * [backup-simplify]: Simplify PI into PI
3.854 * [taylor]: Taking taylor expansion of n in n
3.854 * [backup-simplify]: Simplify 0 into 0
3.854 * [backup-simplify]: Simplify 1 into 1
3.855 * [backup-simplify]: Simplify (/ PI 1) into PI
3.856 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.857 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.857 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.857 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.857 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
3.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.860 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.861 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.861 * [taylor]: Taking taylor expansion of (sqrt k) in n
3.861 * [taylor]: Taking taylor expansion of k in n
3.862 * [backup-simplify]: Simplify k into k
3.862 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
3.862 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
3.862 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
3.862 * [taylor]: Taking taylor expansion of 1.0 in k
3.862 * [backup-simplify]: Simplify 1.0 into 1.0
3.862 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
3.862 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
3.862 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
3.862 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
3.862 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
3.862 * [taylor]: Taking taylor expansion of 0.5 in k
3.862 * [backup-simplify]: Simplify 0.5 into 0.5
3.862 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
3.862 * [taylor]: Taking taylor expansion of 1.0 in k
3.862 * [backup-simplify]: Simplify 1.0 into 1.0
3.862 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.862 * [taylor]: Taking taylor expansion of k in k
3.862 * [backup-simplify]: Simplify 0 into 0
3.862 * [backup-simplify]: Simplify 1 into 1
3.863 * [backup-simplify]: Simplify (/ 1 1) into 1
3.863 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
3.863 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
3.863 * [taylor]: Taking taylor expansion of 2.0 in k
3.863 * [backup-simplify]: Simplify 2.0 into 2.0
3.863 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.863 * [taylor]: Taking taylor expansion of PI in k
3.863 * [backup-simplify]: Simplify PI into PI
3.863 * [taylor]: Taking taylor expansion of n in k
3.863 * [backup-simplify]: Simplify n into n
3.863 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.863 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
3.863 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
3.863 * [backup-simplify]: Simplify (- 1) into -1
3.864 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.864 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
3.865 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
3.865 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
3.865 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.865 * [taylor]: Taking taylor expansion of k in k
3.865 * [backup-simplify]: Simplify 0 into 0
3.865 * [backup-simplify]: Simplify 1 into 1
3.865 * [backup-simplify]: Simplify (sqrt 0) into 0
3.867 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.867 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
3.867 * [taylor]: Taking taylor expansion of 1.0 in k
3.867 * [backup-simplify]: Simplify 1.0 into 1.0
3.867 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
3.867 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
3.867 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
3.867 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
3.867 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
3.867 * [taylor]: Taking taylor expansion of 0.5 in k
3.867 * [backup-simplify]: Simplify 0.5 into 0.5
3.867 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
3.867 * [taylor]: Taking taylor expansion of 1.0 in k
3.867 * [backup-simplify]: Simplify 1.0 into 1.0
3.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.867 * [taylor]: Taking taylor expansion of k in k
3.867 * [backup-simplify]: Simplify 0 into 0
3.867 * [backup-simplify]: Simplify 1 into 1
3.868 * [backup-simplify]: Simplify (/ 1 1) into 1
3.868 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
3.868 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
3.868 * [taylor]: Taking taylor expansion of 2.0 in k
3.868 * [backup-simplify]: Simplify 2.0 into 2.0
3.868 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.868 * [taylor]: Taking taylor expansion of PI in k
3.868 * [backup-simplify]: Simplify PI into PI
3.868 * [taylor]: Taking taylor expansion of n in k
3.868 * [backup-simplify]: Simplify n into n
3.868 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.868 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
3.868 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
3.869 * [backup-simplify]: Simplify (- 1) into -1
3.869 * [backup-simplify]: Simplify (+ 0 -1) into -1
3.869 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
3.869 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
3.870 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
3.870 * [taylor]: Taking taylor expansion of (sqrt k) in k
3.870 * [taylor]: Taking taylor expansion of k in k
3.870 * [backup-simplify]: Simplify 0 into 0
3.870 * [backup-simplify]: Simplify 1 into 1
3.870 * [backup-simplify]: Simplify (sqrt 0) into 0
3.871 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.872 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0
3.872 * [backup-simplify]: Simplify (* 1.0 0) into 0
3.872 * [taylor]: Taking taylor expansion of 0 in n
3.872 * [backup-simplify]: Simplify 0 into 0
3.872 * [backup-simplify]: Simplify 0 into 0
3.873 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.874 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.874 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
3.874 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
3.874 * [taylor]: Taking taylor expansion of +nan.0 in n
3.874 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.874 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
3.874 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
3.874 * [taylor]: Taking taylor expansion of 0.5 in n
3.874 * [backup-simplify]: Simplify 0.5 into 0.5
3.874 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
3.874 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.874 * [taylor]: Taking taylor expansion of 1.0 in n
3.874 * [backup-simplify]: Simplify 1.0 into 1.0
3.874 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.874 * [taylor]: Taking taylor expansion of k in n
3.875 * [backup-simplify]: Simplify k into k
3.875 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.875 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.875 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.875 * [taylor]: Taking taylor expansion of 2.0 in n
3.875 * [backup-simplify]: Simplify 2.0 into 2.0
3.875 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.875 * [taylor]: Taking taylor expansion of PI in n
3.875 * [backup-simplify]: Simplify PI into PI
3.875 * [taylor]: Taking taylor expansion of n in n
3.875 * [backup-simplify]: Simplify 0 into 0
3.875 * [backup-simplify]: Simplify 1 into 1
3.875 * [backup-simplify]: Simplify (/ PI 1) into PI
3.876 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.877 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.877 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.877 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.879 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.880 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
3.881 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.882 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.884 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
3.885 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.886 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.887 * [backup-simplify]: Simplify 0 into 0
3.890 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.891 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.892 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.892 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
3.892 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
3.892 * [taylor]: Taking taylor expansion of +nan.0 in n
3.892 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.892 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
3.892 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
3.892 * [taylor]: Taking taylor expansion of 0.5 in n
3.892 * [backup-simplify]: Simplify 0.5 into 0.5
3.892 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
3.892 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.892 * [taylor]: Taking taylor expansion of 1.0 in n
3.892 * [backup-simplify]: Simplify 1.0 into 1.0
3.892 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.892 * [taylor]: Taking taylor expansion of k in n
3.892 * [backup-simplify]: Simplify k into k
3.892 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.892 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.892 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.893 * [taylor]: Taking taylor expansion of 2.0 in n
3.893 * [backup-simplify]: Simplify 2.0 into 2.0
3.893 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.893 * [taylor]: Taking taylor expansion of PI in n
3.893 * [backup-simplify]: Simplify PI into PI
3.893 * [taylor]: Taking taylor expansion of n in n
3.893 * [backup-simplify]: Simplify 0 into 0
3.893 * [backup-simplify]: Simplify 1 into 1
3.893 * [backup-simplify]: Simplify (/ PI 1) into PI
3.894 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.895 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.895 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.895 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.897 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.898 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
3.902 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.904 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.905 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
3.906 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.907 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.907 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.908 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
3.909 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
3.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.909 * [backup-simplify]: Simplify (- 0) into 0
3.910 * [backup-simplify]: Simplify (+ 0 0) into 0
3.910 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.911 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
3.912 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0
3.913 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.914 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
3.915 * [backup-simplify]: Simplify (- 0) into 0
3.915 * [backup-simplify]: Simplify 0 into 0
3.915 * [backup-simplify]: Simplify 0 into 0
3.917 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.918 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.919 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
3.919 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
3.919 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
3.919 * [taylor]: Taking taylor expansion of +nan.0 in n
3.919 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.919 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
3.919 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
3.919 * [taylor]: Taking taylor expansion of 0.5 in n
3.919 * [backup-simplify]: Simplify 0.5 into 0.5
3.919 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
3.919 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
3.919 * [taylor]: Taking taylor expansion of 1.0 in n
3.919 * [backup-simplify]: Simplify 1.0 into 1.0
3.919 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.919 * [taylor]: Taking taylor expansion of k in n
3.919 * [backup-simplify]: Simplify k into k
3.919 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.919 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
3.919 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
3.919 * [taylor]: Taking taylor expansion of 2.0 in n
3.919 * [backup-simplify]: Simplify 2.0 into 2.0
3.919 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.919 * [taylor]: Taking taylor expansion of PI in n
3.919 * [backup-simplify]: Simplify PI into PI
3.919 * [taylor]: Taking taylor expansion of n in n
3.919 * [backup-simplify]: Simplify 0 into 0
3.919 * [backup-simplify]: Simplify 1 into 1
3.919 * [backup-simplify]: Simplify (/ PI 1) into PI
3.920 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
3.920 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
3.920 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
3.920 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
3.921 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
3.922 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
3.923 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
3.924 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
3.924 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
3.925 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.926 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
3.929 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +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)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
3.930 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
3.930 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0
3.930 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
3.930 * [taylor]: Taking taylor expansion of 1.0 in n
3.930 * [backup-simplify]: Simplify 1.0 into 1.0
3.930 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
3.930 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
3.930 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
3.930 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
3.930 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
3.930 * [taylor]: Taking taylor expansion of 0.5 in n
3.930 * [backup-simplify]: Simplify 0.5 into 0.5
3.930 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.930 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.930 * [taylor]: Taking taylor expansion of k in n
3.930 * [backup-simplify]: Simplify k into k
3.930 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.930 * [taylor]: Taking taylor expansion of 1.0 in n
3.930 * [backup-simplify]: Simplify 1.0 into 1.0
3.930 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.930 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.930 * [taylor]: Taking taylor expansion of -2.0 in n
3.930 * [backup-simplify]: Simplify -2.0 into -2.0
3.930 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.930 * [taylor]: Taking taylor expansion of PI in n
3.930 * [backup-simplify]: Simplify PI into PI
3.930 * [taylor]: Taking taylor expansion of n in n
3.930 * [backup-simplify]: Simplify 0 into 0
3.930 * [backup-simplify]: Simplify 1 into 1
3.930 * [backup-simplify]: Simplify (/ PI 1) into PI
3.931 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.931 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.932 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.932 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
3.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.933 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.934 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.934 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
3.934 * [taylor]: Taking taylor expansion of (/ -1 k) in n
3.934 * [taylor]: Taking taylor expansion of -1 in n
3.934 * [backup-simplify]: Simplify -1 into -1
3.934 * [taylor]: Taking taylor expansion of k in n
3.934 * [backup-simplify]: Simplify k into k
3.934 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
3.934 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
3.934 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
3.934 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
3.935 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
3.935 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
3.935 * [taylor]: Taking taylor expansion of 1.0 in k
3.935 * [backup-simplify]: Simplify 1.0 into 1.0
3.935 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
3.935 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
3.935 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
3.935 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
3.935 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
3.935 * [taylor]: Taking taylor expansion of 0.5 in k
3.935 * [backup-simplify]: Simplify 0.5 into 0.5
3.935 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
3.935 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.935 * [taylor]: Taking taylor expansion of k in k
3.935 * [backup-simplify]: Simplify 0 into 0
3.936 * [backup-simplify]: Simplify 1 into 1
3.936 * [backup-simplify]: Simplify (/ 1 1) into 1
3.936 * [taylor]: Taking taylor expansion of 1.0 in k
3.936 * [backup-simplify]: Simplify 1.0 into 1.0
3.936 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
3.936 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
3.936 * [taylor]: Taking taylor expansion of -2.0 in k
3.936 * [backup-simplify]: Simplify -2.0 into -2.0
3.936 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.936 * [taylor]: Taking taylor expansion of PI in k
3.936 * [backup-simplify]: Simplify PI into PI
3.936 * [taylor]: Taking taylor expansion of n in k
3.936 * [backup-simplify]: Simplify n into n
3.936 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.936 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
3.936 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
3.936 * [backup-simplify]: Simplify (+ 1 0) into 1
3.937 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
3.937 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
3.937 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
3.937 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.937 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.937 * [taylor]: Taking taylor expansion of -1 in k
3.937 * [backup-simplify]: Simplify -1 into -1
3.937 * [taylor]: Taking taylor expansion of k in k
3.937 * [backup-simplify]: Simplify 0 into 0
3.937 * [backup-simplify]: Simplify 1 into 1
3.937 * [backup-simplify]: Simplify (/ -1 1) into -1
3.937 * [backup-simplify]: Simplify (sqrt 0) into 0
3.938 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.938 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
3.938 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
3.938 * [taylor]: Taking taylor expansion of 1.0 in k
3.939 * [backup-simplify]: Simplify 1.0 into 1.0
3.939 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
3.939 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
3.939 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
3.939 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
3.939 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
3.939 * [taylor]: Taking taylor expansion of 0.5 in k
3.939 * [backup-simplify]: Simplify 0.5 into 0.5
3.939 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
3.939 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.939 * [taylor]: Taking taylor expansion of k in k
3.939 * [backup-simplify]: Simplify 0 into 0
3.939 * [backup-simplify]: Simplify 1 into 1
3.939 * [backup-simplify]: Simplify (/ 1 1) into 1
3.939 * [taylor]: Taking taylor expansion of 1.0 in k
3.939 * [backup-simplify]: Simplify 1.0 into 1.0
3.939 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
3.939 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
3.939 * [taylor]: Taking taylor expansion of -2.0 in k
3.939 * [backup-simplify]: Simplify -2.0 into -2.0
3.939 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.939 * [taylor]: Taking taylor expansion of PI in k
3.939 * [backup-simplify]: Simplify PI into PI
3.939 * [taylor]: Taking taylor expansion of n in k
3.939 * [backup-simplify]: Simplify n into n
3.939 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.939 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
3.939 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
3.940 * [backup-simplify]: Simplify (+ 1 0) into 1
3.940 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
3.940 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
3.940 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
3.940 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
3.940 * [taylor]: Taking taylor expansion of (/ -1 k) in k
3.940 * [taylor]: Taking taylor expansion of -1 in k
3.940 * [backup-simplify]: Simplify -1 into -1
3.940 * [taylor]: Taking taylor expansion of k in k
3.940 * [backup-simplify]: Simplify 0 into 0
3.940 * [backup-simplify]: Simplify 1 into 1
3.940 * [backup-simplify]: Simplify (/ -1 1) into -1
3.941 * [backup-simplify]: Simplify (sqrt 0) into 0
3.941 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
3.942 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
3.942 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
3.942 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
3.942 * [taylor]: Taking taylor expansion of +nan.0 in n
3.942 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.942 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
3.942 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
3.942 * [taylor]: Taking taylor expansion of 0.5 in n
3.942 * [backup-simplify]: Simplify 0.5 into 0.5
3.942 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
3.942 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.942 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.942 * [taylor]: Taking taylor expansion of -2.0 in n
3.942 * [backup-simplify]: Simplify -2.0 into -2.0
3.942 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.942 * [taylor]: Taking taylor expansion of PI in n
3.942 * [backup-simplify]: Simplify PI into PI
3.942 * [taylor]: Taking taylor expansion of n in n
3.942 * [backup-simplify]: Simplify 0 into 0
3.942 * [backup-simplify]: Simplify 1 into 1
3.943 * [backup-simplify]: Simplify (/ PI 1) into PI
3.943 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.944 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.944 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.944 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.944 * [taylor]: Taking taylor expansion of k in n
3.944 * [backup-simplify]: Simplify k into k
3.944 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.944 * [taylor]: Taking taylor expansion of 1.0 in n
3.944 * [backup-simplify]: Simplify 1.0 into 1.0
3.945 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.945 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.946 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
3.947 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.948 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.950 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.951 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
3.955 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.956 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.956 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.957 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
3.957 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
3.957 * [taylor]: Taking taylor expansion of +nan.0 in n
3.957 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.957 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
3.957 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
3.957 * [taylor]: Taking taylor expansion of 0.5 in n
3.957 * [backup-simplify]: Simplify 0.5 into 0.5
3.957 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
3.957 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.957 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.957 * [taylor]: Taking taylor expansion of -2.0 in n
3.957 * [backup-simplify]: Simplify -2.0 into -2.0
3.957 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.957 * [taylor]: Taking taylor expansion of PI in n
3.957 * [backup-simplify]: Simplify PI into PI
3.957 * [taylor]: Taking taylor expansion of n in n
3.957 * [backup-simplify]: Simplify 0 into 0
3.957 * [backup-simplify]: Simplify 1 into 1
3.957 * [backup-simplify]: Simplify (/ PI 1) into PI
3.958 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.959 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.959 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.959 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.959 * [taylor]: Taking taylor expansion of k in n
3.959 * [backup-simplify]: Simplify k into k
3.959 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.959 * [taylor]: Taking taylor expansion of 1.0 in n
3.959 * [backup-simplify]: Simplify 1.0 into 1.0
3.960 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.960 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.961 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
3.962 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.963 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.965 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.966 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.967 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.968 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.968 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.969 * [backup-simplify]: Simplify (+ 0 0) into 0
3.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.970 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
3.972 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
3.973 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0
3.974 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0
3.976 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.978 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
3.978 * [backup-simplify]: Simplify 0 into 0
3.979 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.982 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
3.984 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.985 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
3.985 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
3.985 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
3.985 * [taylor]: Taking taylor expansion of +nan.0 in n
3.985 * [backup-simplify]: Simplify +nan.0 into +nan.0
3.985 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
3.985 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
3.985 * [taylor]: Taking taylor expansion of 0.5 in n
3.985 * [backup-simplify]: Simplify 0.5 into 0.5
3.985 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
3.985 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
3.985 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
3.985 * [taylor]: Taking taylor expansion of -2.0 in n
3.985 * [backup-simplify]: Simplify -2.0 into -2.0
3.985 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.985 * [taylor]: Taking taylor expansion of PI in n
3.985 * [backup-simplify]: Simplify PI into PI
3.985 * [taylor]: Taking taylor expansion of n in n
3.985 * [backup-simplify]: Simplify 0 into 0
3.985 * [backup-simplify]: Simplify 1 into 1
3.986 * [backup-simplify]: Simplify (/ PI 1) into PI
3.986 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
3.987 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
3.987 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
3.987 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.987 * [taylor]: Taking taylor expansion of k in n
3.987 * [backup-simplify]: Simplify k into k
3.987 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.987 * [taylor]: Taking taylor expansion of 1.0 in n
3.987 * [backup-simplify]: Simplify 1.0 into 1.0
3.989 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
3.989 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
3.990 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
3.991 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
3.992 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
3.993 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
3.995 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
3.996 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
4.000 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +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))))))))
4.000 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
4.001 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
4.001 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
4.001 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
4.001 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
4.001 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
4.001 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
4.001 * [taylor]: Taking taylor expansion of 0.5 in k
4.001 * [backup-simplify]: Simplify 0.5 into 0.5
4.001 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
4.001 * [taylor]: Taking taylor expansion of 1.0 in k
4.001 * [backup-simplify]: Simplify 1.0 into 1.0
4.001 * [taylor]: Taking taylor expansion of k in k
4.001 * [backup-simplify]: Simplify 0 into 0
4.001 * [backup-simplify]: Simplify 1 into 1
4.001 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
4.001 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
4.001 * [taylor]: Taking taylor expansion of 2.0 in k
4.001 * [backup-simplify]: Simplify 2.0 into 2.0
4.001 * [taylor]: Taking taylor expansion of (* n PI) in k
4.001 * [taylor]: Taking taylor expansion of n in k
4.001 * [backup-simplify]: Simplify n into n
4.001 * [taylor]: Taking taylor expansion of PI in k
4.001 * [backup-simplify]: Simplify PI into PI
4.001 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.001 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
4.001 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
4.001 * [backup-simplify]: Simplify (- 0) into 0
4.002 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
4.002 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
4.002 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
4.002 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
4.002 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
4.002 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
4.002 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
4.002 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
4.002 * [taylor]: Taking taylor expansion of 0.5 in n
4.002 * [backup-simplify]: Simplify 0.5 into 0.5
4.002 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
4.002 * [taylor]: Taking taylor expansion of 1.0 in n
4.002 * [backup-simplify]: Simplify 1.0 into 1.0
4.002 * [taylor]: Taking taylor expansion of k in n
4.002 * [backup-simplify]: Simplify k into k
4.002 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.002 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.002 * [taylor]: Taking taylor expansion of 2.0 in n
4.002 * [backup-simplify]: Simplify 2.0 into 2.0
4.002 * [taylor]: Taking taylor expansion of (* n PI) in n
4.002 * [taylor]: Taking taylor expansion of n in n
4.002 * [backup-simplify]: Simplify 0 into 0
4.002 * [backup-simplify]: Simplify 1 into 1
4.002 * [taylor]: Taking taylor expansion of PI in n
4.003 * [backup-simplify]: Simplify PI into PI
4.003 * [backup-simplify]: Simplify (* 0 PI) into 0
4.003 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.004 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.005 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.006 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.006 * [backup-simplify]: Simplify (- k) into (- k)
4.006 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
4.006 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
4.007 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.008 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
4.009 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
4.009 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
4.009 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
4.009 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
4.009 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
4.009 * [taylor]: Taking taylor expansion of 0.5 in n
4.009 * [backup-simplify]: Simplify 0.5 into 0.5
4.009 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
4.009 * [taylor]: Taking taylor expansion of 1.0 in n
4.009 * [backup-simplify]: Simplify 1.0 into 1.0
4.009 * [taylor]: Taking taylor expansion of k in n
4.009 * [backup-simplify]: Simplify k into k
4.009 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.009 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.009 * [taylor]: Taking taylor expansion of 2.0 in n
4.009 * [backup-simplify]: Simplify 2.0 into 2.0
4.009 * [taylor]: Taking taylor expansion of (* n PI) in n
4.009 * [taylor]: Taking taylor expansion of n in n
4.009 * [backup-simplify]: Simplify 0 into 0
4.009 * [backup-simplify]: Simplify 1 into 1
4.009 * [taylor]: Taking taylor expansion of PI in n
4.009 * [backup-simplify]: Simplify PI into PI
4.009 * [backup-simplify]: Simplify (* 0 PI) into 0
4.010 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.011 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.012 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.015 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.016 * [backup-simplify]: Simplify (- k) into (- k)
4.016 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
4.016 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
4.017 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.018 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
4.019 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
4.019 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
4.019 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
4.019 * [taylor]: Taking taylor expansion of 0.5 in k
4.019 * [backup-simplify]: Simplify 0.5 into 0.5
4.019 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
4.019 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
4.019 * [taylor]: Taking taylor expansion of 1.0 in k
4.019 * [backup-simplify]: Simplify 1.0 into 1.0
4.019 * [taylor]: Taking taylor expansion of k in k
4.019 * [backup-simplify]: Simplify 0 into 0
4.019 * [backup-simplify]: Simplify 1 into 1
4.019 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
4.019 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
4.019 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
4.019 * [taylor]: Taking taylor expansion of 2.0 in k
4.019 * [backup-simplify]: Simplify 2.0 into 2.0
4.019 * [taylor]: Taking taylor expansion of PI in k
4.019 * [backup-simplify]: Simplify PI into PI
4.020 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.020 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.020 * [taylor]: Taking taylor expansion of (log n) in k
4.020 * [taylor]: Taking taylor expansion of n in k
4.020 * [backup-simplify]: Simplify n into n
4.020 * [backup-simplify]: Simplify (log n) into (log n)
4.021 * [backup-simplify]: Simplify (- 0) into 0
4.021 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
4.022 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
4.022 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
4.023 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
4.024 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
4.024 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
4.025 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
4.026 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
4.027 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
4.027 * [backup-simplify]: Simplify (- 0) into 0
4.027 * [backup-simplify]: Simplify (+ 0 0) into 0
4.027 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
4.028 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.030 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
4.031 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.032 * [taylor]: Taking taylor expansion of 0 in k
4.032 * [backup-simplify]: Simplify 0 into 0
4.032 * [backup-simplify]: Simplify 0 into 0
4.032 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
4.033 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
4.034 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
4.034 * [backup-simplify]: Simplify (+ 0 0) into 0
4.034 * [backup-simplify]: Simplify (- 1) into -1
4.035 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.036 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
4.037 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
4.039 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
4.041 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
4.042 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
4.042 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
4.044 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
4.045 * [backup-simplify]: Simplify (- 0) into 0
4.045 * [backup-simplify]: Simplify (+ 0 0) into 0
4.046 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
4.046 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.047 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
4.049 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.049 * [taylor]: Taking taylor expansion of 0 in k
4.049 * [backup-simplify]: Simplify 0 into 0
4.049 * [backup-simplify]: Simplify 0 into 0
4.049 * [backup-simplify]: Simplify 0 into 0
4.050 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.052 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
4.053 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
4.053 * [backup-simplify]: Simplify (+ 0 0) into 0
4.053 * [backup-simplify]: Simplify (- 0) into 0
4.054 * [backup-simplify]: Simplify (+ 0 0) into 0
4.055 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
4.057 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
4.059 * [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 n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
4.063 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
4.070 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 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 (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
4.071 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
4.071 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
4.071 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
4.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
4.071 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
4.071 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
4.071 * [taylor]: Taking taylor expansion of 0.5 in k
4.071 * [backup-simplify]: Simplify 0.5 into 0.5
4.071 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
4.071 * [taylor]: Taking taylor expansion of 1.0 in k
4.071 * [backup-simplify]: Simplify 1.0 into 1.0
4.071 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.071 * [taylor]: Taking taylor expansion of k in k
4.071 * [backup-simplify]: Simplify 0 into 0
4.071 * [backup-simplify]: Simplify 1 into 1
4.072 * [backup-simplify]: Simplify (/ 1 1) into 1
4.072 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
4.072 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
4.072 * [taylor]: Taking taylor expansion of 2.0 in k
4.072 * [backup-simplify]: Simplify 2.0 into 2.0
4.072 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.072 * [taylor]: Taking taylor expansion of PI in k
4.072 * [backup-simplify]: Simplify PI into PI
4.072 * [taylor]: Taking taylor expansion of n in k
4.072 * [backup-simplify]: Simplify n into n
4.072 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.072 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
4.072 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
4.073 * [backup-simplify]: Simplify (- 1) into -1
4.073 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.073 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
4.074 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
4.074 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
4.074 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
4.074 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
4.074 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
4.074 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
4.074 * [taylor]: Taking taylor expansion of 0.5 in n
4.074 * [backup-simplify]: Simplify 0.5 into 0.5
4.074 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
4.074 * [taylor]: Taking taylor expansion of 1.0 in n
4.074 * [backup-simplify]: Simplify 1.0 into 1.0
4.074 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.074 * [taylor]: Taking taylor expansion of k in n
4.074 * [backup-simplify]: Simplify k into k
4.074 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.074 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
4.074 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
4.074 * [taylor]: Taking taylor expansion of 2.0 in n
4.074 * [backup-simplify]: Simplify 2.0 into 2.0
4.074 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.074 * [taylor]: Taking taylor expansion of PI in n
4.074 * [backup-simplify]: Simplify PI into PI
4.074 * [taylor]: Taking taylor expansion of n in n
4.074 * [backup-simplify]: Simplify 0 into 0
4.074 * [backup-simplify]: Simplify 1 into 1
4.075 * [backup-simplify]: Simplify (/ PI 1) into PI
4.075 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.076 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.076 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.077 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
4.077 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
4.078 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.079 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
4.081 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
4.081 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
4.081 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
4.081 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
4.081 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
4.081 * [taylor]: Taking taylor expansion of 0.5 in n
4.081 * [backup-simplify]: Simplify 0.5 into 0.5
4.081 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
4.081 * [taylor]: Taking taylor expansion of 1.0 in n
4.081 * [backup-simplify]: Simplify 1.0 into 1.0
4.081 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.081 * [taylor]: Taking taylor expansion of k in n
4.081 * [backup-simplify]: Simplify k into k
4.081 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.081 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
4.081 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
4.081 * [taylor]: Taking taylor expansion of 2.0 in n
4.081 * [backup-simplify]: Simplify 2.0 into 2.0
4.081 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.081 * [taylor]: Taking taylor expansion of PI in n
4.081 * [backup-simplify]: Simplify PI into PI
4.081 * [taylor]: Taking taylor expansion of n in n
4.082 * [backup-simplify]: Simplify 0 into 0
4.082 * [backup-simplify]: Simplify 1 into 1
4.082 * [backup-simplify]: Simplify (/ PI 1) into PI
4.083 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.084 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.084 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.084 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
4.084 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
4.086 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.087 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
4.088 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
4.088 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
4.088 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
4.088 * [taylor]: Taking taylor expansion of 0.5 in k
4.088 * [backup-simplify]: Simplify 0.5 into 0.5
4.088 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
4.088 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
4.089 * [taylor]: Taking taylor expansion of 1.0 in k
4.089 * [backup-simplify]: Simplify 1.0 into 1.0
4.089 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.089 * [taylor]: Taking taylor expansion of k in k
4.089 * [backup-simplify]: Simplify 0 into 0
4.089 * [backup-simplify]: Simplify 1 into 1
4.089 * [backup-simplify]: Simplify (/ 1 1) into 1
4.089 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
4.089 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
4.089 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
4.089 * [taylor]: Taking taylor expansion of 2.0 in k
4.089 * [backup-simplify]: Simplify 2.0 into 2.0
4.089 * [taylor]: Taking taylor expansion of PI in k
4.089 * [backup-simplify]: Simplify PI into PI
4.090 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.091 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.091 * [taylor]: Taking taylor expansion of (log n) in k
4.091 * [taylor]: Taking taylor expansion of n in k
4.091 * [backup-simplify]: Simplify n into n
4.091 * [backup-simplify]: Simplify (log n) into (log n)
4.091 * [backup-simplify]: Simplify (- 1) into -1
4.092 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.092 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.093 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
4.094 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
4.095 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
4.097 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
4.099 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
4.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.101 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
4.102 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
4.103 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.103 * [backup-simplify]: Simplify (- 0) into 0
4.103 * [backup-simplify]: Simplify (+ 0 0) into 0
4.104 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
4.105 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.107 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
4.109 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.109 * [taylor]: Taking taylor expansion of 0 in k
4.109 * [backup-simplify]: Simplify 0 into 0
4.109 * [backup-simplify]: Simplify 0 into 0
4.109 * [backup-simplify]: Simplify 0 into 0
4.110 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.111 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.115 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
4.115 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.116 * [backup-simplify]: Simplify (- 0) into 0
4.116 * [backup-simplify]: Simplify (+ 0 0) into 0
4.117 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
4.118 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.120 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
4.122 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.122 * [taylor]: Taking taylor expansion of 0 in k
4.122 * [backup-simplify]: Simplify 0 into 0
4.122 * [backup-simplify]: Simplify 0 into 0
4.122 * [backup-simplify]: Simplify 0 into 0
4.122 * [backup-simplify]: Simplify 0 into 0
4.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.125 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.128 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
4.128 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.131 * [backup-simplify]: Simplify (- 0) into 0
4.131 * [backup-simplify]: Simplify (+ 0 0) into 0
4.132 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
4.133 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.134 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
4.136 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 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
4.136 * [taylor]: Taking taylor expansion of 0 in k
4.136 * [backup-simplify]: Simplify 0 into 0
4.136 * [backup-simplify]: Simplify 0 into 0
4.137 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
4.137 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
4.137 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
4.137 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
4.137 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
4.137 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
4.137 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
4.137 * [taylor]: Taking taylor expansion of 0.5 in k
4.137 * [backup-simplify]: Simplify 0.5 into 0.5
4.137 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
4.137 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.137 * [taylor]: Taking taylor expansion of k in k
4.137 * [backup-simplify]: Simplify 0 into 0
4.137 * [backup-simplify]: Simplify 1 into 1
4.138 * [backup-simplify]: Simplify (/ 1 1) into 1
4.138 * [taylor]: Taking taylor expansion of 1.0 in k
4.138 * [backup-simplify]: Simplify 1.0 into 1.0
4.138 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
4.138 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
4.138 * [taylor]: Taking taylor expansion of -2.0 in k
4.138 * [backup-simplify]: Simplify -2.0 into -2.0
4.138 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.138 * [taylor]: Taking taylor expansion of PI in k
4.138 * [backup-simplify]: Simplify PI into PI
4.138 * [taylor]: Taking taylor expansion of n in k
4.138 * [backup-simplify]: Simplify n into n
4.138 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.138 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
4.138 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
4.138 * [backup-simplify]: Simplify (+ 1 0) into 1
4.138 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
4.139 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
4.139 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
4.139 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
4.139 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
4.139 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
4.139 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
4.139 * [taylor]: Taking taylor expansion of 0.5 in n
4.139 * [backup-simplify]: Simplify 0.5 into 0.5
4.139 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
4.139 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.139 * [taylor]: Taking taylor expansion of k in n
4.139 * [backup-simplify]: Simplify k into k
4.139 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.139 * [taylor]: Taking taylor expansion of 1.0 in n
4.139 * [backup-simplify]: Simplify 1.0 into 1.0
4.139 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
4.139 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
4.139 * [taylor]: Taking taylor expansion of -2.0 in n
4.139 * [backup-simplify]: Simplify -2.0 into -2.0
4.139 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.139 * [taylor]: Taking taylor expansion of PI in n
4.139 * [backup-simplify]: Simplify PI into PI
4.139 * [taylor]: Taking taylor expansion of n in n
4.139 * [backup-simplify]: Simplify 0 into 0
4.139 * [backup-simplify]: Simplify 1 into 1
4.140 * [backup-simplify]: Simplify (/ PI 1) into PI
4.140 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.141 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
4.141 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
4.141 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
4.142 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.143 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
4.143 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
4.143 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
4.143 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
4.143 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
4.143 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
4.143 * [taylor]: Taking taylor expansion of 0.5 in n
4.143 * [backup-simplify]: Simplify 0.5 into 0.5
4.143 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
4.144 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.144 * [taylor]: Taking taylor expansion of k in n
4.144 * [backup-simplify]: Simplify k into k
4.144 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.144 * [taylor]: Taking taylor expansion of 1.0 in n
4.144 * [backup-simplify]: Simplify 1.0 into 1.0
4.144 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
4.144 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
4.144 * [taylor]: Taking taylor expansion of -2.0 in n
4.144 * [backup-simplify]: Simplify -2.0 into -2.0
4.144 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.144 * [taylor]: Taking taylor expansion of PI in n
4.144 * [backup-simplify]: Simplify PI into PI
4.144 * [taylor]: Taking taylor expansion of n in n
4.144 * [backup-simplify]: Simplify 0 into 0
4.144 * [backup-simplify]: Simplify 1 into 1
4.144 * [backup-simplify]: Simplify (/ PI 1) into PI
4.144 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.145 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
4.145 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
4.145 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
4.146 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.147 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
4.148 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
4.148 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
4.148 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
4.148 * [taylor]: Taking taylor expansion of 0.5 in k
4.148 * [backup-simplify]: Simplify 0.5 into 0.5
4.148 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
4.148 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
4.148 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
4.148 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
4.148 * [taylor]: Taking taylor expansion of -2.0 in k
4.148 * [backup-simplify]: Simplify -2.0 into -2.0
4.148 * [taylor]: Taking taylor expansion of PI in k
4.148 * [backup-simplify]: Simplify PI into PI
4.148 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.149 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
4.149 * [taylor]: Taking taylor expansion of (log n) in k
4.149 * [taylor]: Taking taylor expansion of n in k
4.149 * [backup-simplify]: Simplify n into n
4.149 * [backup-simplify]: Simplify (log n) into (log n)
4.149 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
4.149 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.149 * [taylor]: Taking taylor expansion of k in k
4.149 * [backup-simplify]: Simplify 0 into 0
4.149 * [backup-simplify]: Simplify 1 into 1
4.149 * [backup-simplify]: Simplify (/ 1 1) into 1
4.149 * [taylor]: Taking taylor expansion of 1.0 in k
4.149 * [backup-simplify]: Simplify 1.0 into 1.0
4.149 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.150 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
4.150 * [backup-simplify]: Simplify (+ 1 0) into 1
4.151 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
4.152 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
4.152 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
4.153 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
4.154 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.154 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
4.155 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
4.155 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.156 * [backup-simplify]: Simplify (+ 0 0) into 0
4.156 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
4.157 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.158 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
4.159 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
4.159 * [taylor]: Taking taylor expansion of 0 in k
4.159 * [backup-simplify]: Simplify 0 into 0
4.159 * [backup-simplify]: Simplify 0 into 0
4.159 * [backup-simplify]: Simplify 0 into 0
4.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.160 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.162 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
4.162 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.163 * [backup-simplify]: Simplify (+ 0 0) into 0
4.163 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
4.164 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.165 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
4.167 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.167 * [taylor]: Taking taylor expansion of 0 in k
4.167 * [backup-simplify]: Simplify 0 into 0
4.167 * [backup-simplify]: Simplify 0 into 0
4.167 * [backup-simplify]: Simplify 0 into 0
4.167 * [backup-simplify]: Simplify 0 into 0
4.168 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.169 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.172 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
4.172 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.172 * [backup-simplify]: Simplify (+ 0 0) into 0
4.173 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
4.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.175 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
4.177 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
4.177 * [taylor]: Taking taylor expansion of 0 in k
4.177 * [backup-simplify]: Simplify 0 into 0
4.177 * [backup-simplify]: Simplify 0 into 0
4.178 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
4.178 * * * [progress]: simplifying candidates
4.180 * [simplify]: Simplifying:
  (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 (* (* 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)) (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)))
  (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))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +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))
  (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))))))))))))))))))))))
  (- (+ (* +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)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +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))))))))
  (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
4.184 * * [simplify]: iteration 0: 361 enodes
4.323 * * [simplify]: iteration 1: 1003 enodes
4.902 * * [simplify]: iteration 2: 3424 enodes
6.178 * * [simplify]: iteration complete: 5002 enodes
6.178 * * [simplify]: Extracting #0: cost 125 inf + 0
6.181 * * [simplify]: Extracting #1: cost 644 inf + 84
6.188 * * [simplify]: Extracting #2: cost 1158 inf + 1491
6.205 * * [simplify]: Extracting #3: cost 1125 inf + 30714
6.237 * * [simplify]: Extracting #4: cost 690 inf + 175644
6.314 * * [simplify]: Extracting #5: cost 416 inf + 329930
6.418 * * [simplify]: Extracting #6: cost 239 inf + 456919
6.551 * * [simplify]: Extracting #7: cost 66 inf + 627921
6.729 * * [simplify]: Extracting #8: cost 5 inf + 695481
6.925 * * [simplify]: Extracting #9: cost 0 inf + 697477
7.123 * * [simplify]: Extracting #10: cost 0 inf + 697127
7.288 * * [simplify]: Extracting #11: cost 0 inf + 697087
7.520 * [simplify]: Simplified to:
  (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 (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 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) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (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))
  (/ (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 (* 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)))
  (* n (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))))
  (* n (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))))
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* n (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))))
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* (* (cbrt n) (cbrt n)) (* 2.0 PI))
  (* 2.0 (* PI (sqrt n)))
  (* 2.0 PI)
  (* 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))))
  (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 (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))))
  (* (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) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0))) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (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 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (/ 1.0 (sqrt k))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0))) (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))))
  (/ (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (cbrt (sqrt k)))
  (* (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)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (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) (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ (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))) (cbrt (sqrt k)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (* (/ 1.0 (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 (sqrt k))))
  (* (/ 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)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ 1.0 2.0)))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (/ (- 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 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 (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (/ (log (* 2.0 (* n PI))) (/ 2.0 (- 1.0 k)))
  (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) 2.0))
  (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2) 2.0))
  (fma (- +nan.0) (* k k) (fma k (- +nan.0) +nan.0))
  (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) (/ +nan.0 (* k (* k k)))))
  (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) +nan.0))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (- k) (fma (* k k) (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (fma (- (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0)) (* (* k k) (log n)) (+ (fma (- (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0)) (* (* k (log (* 2.0 PI))) (* k (log (* 2.0 PI)))) (fma (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* (log n) (log (* 2.0 PI)))) (* k k) (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (- (* (log (* 2.0 PI)) k)) (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* (log n) k) (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* (* (log n) k) (* (log n) k)) (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (- (* (log (* 2.0 PI)) (* k k))))))))) (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0)))))
  (fma (- +nan.0) (/ (exp (* (log (* 2.0 (* n PI))) (* (- 1.0 k) 0.5))) (* k k)) (- (* +nan.0 (/ (exp (* (log (* 2.0 (* n PI))) (* (- 1.0 k) 0.5))) k)) (* (/ +nan.0 k) (/ (exp (* (log (* 2.0 (* n PI))) (* (- 1.0 k) 0.5))) (* k k)))))
  (fma (- (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) +nan.0 (* +nan.0 (+ (/ (- (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (* k k)) (/ (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k))))
  (fma (* 0.25 (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (log (* 2.0 PI)))) (* (* k k) (log n)) (fma (exp (* 0.5 (log (* 2.0 (* n PI))))) (* (* (* (log n) k) (* (log n) k)) 0.125) (- (fma (* (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* k k)) (exp (* 0.5 (log (* 2.0 (* n PI)))))) 0.125 (exp (* 0.5 (log (* 2.0 (* n PI)))))) (* 0.5 (* k (fma (exp (* 0.5 (log (* 2.0 (* n PI))))) (log n) (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (log (* 2.0 PI)))))))))
  (exp (* (log (* 2.0 (* n PI))) (* (- 1.0 k) 0.5)))
  (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))
7.532 * * * [progress]: adding candidates to table
8.532 * * [progress]: iteration 2 / 4
8.532 * * * [progress]: picking best candidate
8.598 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
8.599 * * * [progress]: localizing error
8.643 * * * [progress]: generating rewritten candidates
8.643 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2 1)
8.661 * * * * [progress]: [ 2 / 3 ] rewriting at (2)
8.678 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1 2)
8.706 * * * [progress]: generating series expansions
8.707 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2 1)
8.707 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
8.707 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
8.707 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.707 * [taylor]: Taking taylor expansion of 2.0 in n
8.707 * [backup-simplify]: Simplify 2.0 into 2.0
8.707 * [taylor]: Taking taylor expansion of (* n PI) in n
8.707 * [taylor]: Taking taylor expansion of n in n
8.707 * [backup-simplify]: Simplify 0 into 0
8.707 * [backup-simplify]: Simplify 1 into 1
8.707 * [taylor]: Taking taylor expansion of PI in n
8.707 * [backup-simplify]: Simplify PI into PI
8.707 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.707 * [taylor]: Taking taylor expansion of 2.0 in n
8.707 * [backup-simplify]: Simplify 2.0 into 2.0
8.707 * [taylor]: Taking taylor expansion of (* n PI) in n
8.707 * [taylor]: Taking taylor expansion of n in n
8.707 * [backup-simplify]: Simplify 0 into 0
8.708 * [backup-simplify]: Simplify 1 into 1
8.708 * [taylor]: Taking taylor expansion of PI in n
8.708 * [backup-simplify]: Simplify PI into PI
8.708 * [backup-simplify]: Simplify (* 0 PI) into 0
8.708 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.708 * [backup-simplify]: Simplify 0 into 0
8.709 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.710 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.715 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.715 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.716 * [backup-simplify]: Simplify 0 into 0
8.717 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.717 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.717 * [backup-simplify]: Simplify 0 into 0
8.718 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.719 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.719 * [backup-simplify]: Simplify 0 into 0
8.720 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
8.721 * [backup-simplify]: Simplify 0 into 0
8.722 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
8.723 * [backup-simplify]: Simplify 0 into 0
8.725 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
8.727 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
8.727 * [backup-simplify]: Simplify 0 into 0
8.727 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
8.728 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
8.728 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
8.728 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.728 * [taylor]: Taking taylor expansion of 2.0 in n
8.728 * [backup-simplify]: Simplify 2.0 into 2.0
8.728 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.728 * [taylor]: Taking taylor expansion of PI in n
8.728 * [backup-simplify]: Simplify PI into PI
8.728 * [taylor]: Taking taylor expansion of n in n
8.728 * [backup-simplify]: Simplify 0 into 0
8.728 * [backup-simplify]: Simplify 1 into 1
8.729 * [backup-simplify]: Simplify (/ PI 1) into PI
8.729 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.729 * [taylor]: Taking taylor expansion of 2.0 in n
8.729 * [backup-simplify]: Simplify 2.0 into 2.0
8.729 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.729 * [taylor]: Taking taylor expansion of PI in n
8.729 * [backup-simplify]: Simplify PI into PI
8.729 * [taylor]: Taking taylor expansion of n in n
8.729 * [backup-simplify]: Simplify 0 into 0
8.729 * [backup-simplify]: Simplify 1 into 1
8.730 * [backup-simplify]: Simplify (/ PI 1) into PI
8.730 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.731 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.732 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.732 * [backup-simplify]: Simplify 0 into 0
8.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.735 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.735 * [backup-simplify]: Simplify 0 into 0
8.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.737 * [backup-simplify]: Simplify 0 into 0
8.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.739 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.739 * [backup-simplify]: Simplify 0 into 0
8.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.741 * [backup-simplify]: Simplify 0 into 0
8.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.743 * [backup-simplify]: Simplify 0 into 0
8.743 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
8.744 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
8.744 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
8.744 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.744 * [taylor]: Taking taylor expansion of -2.0 in n
8.744 * [backup-simplify]: Simplify -2.0 into -2.0
8.744 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.744 * [taylor]: Taking taylor expansion of PI in n
8.744 * [backup-simplify]: Simplify PI into PI
8.744 * [taylor]: Taking taylor expansion of n in n
8.744 * [backup-simplify]: Simplify 0 into 0
8.744 * [backup-simplify]: Simplify 1 into 1
8.744 * [backup-simplify]: Simplify (/ PI 1) into PI
8.744 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.744 * [taylor]: Taking taylor expansion of -2.0 in n
8.744 * [backup-simplify]: Simplify -2.0 into -2.0
8.744 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.744 * [taylor]: Taking taylor expansion of PI in n
8.744 * [backup-simplify]: Simplify PI into PI
8.744 * [taylor]: Taking taylor expansion of n in n
8.744 * [backup-simplify]: Simplify 0 into 0
8.744 * [backup-simplify]: Simplify 1 into 1
8.745 * [backup-simplify]: Simplify (/ PI 1) into PI
8.745 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.745 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.746 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
8.746 * [backup-simplify]: Simplify 0 into 0
8.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.748 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.748 * [backup-simplify]: Simplify 0 into 0
8.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.749 * [backup-simplify]: Simplify 0 into 0
8.750 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.750 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.750 * [backup-simplify]: Simplify 0 into 0
8.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.752 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.752 * [backup-simplify]: Simplify 0 into 0
8.753 * [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
8.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.754 * [backup-simplify]: Simplify 0 into 0
8.754 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
8.754 * * * * [progress]: [ 2 / 3 ] generating series at (2)
8.755 * [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))))
8.755 * [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
8.755 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
8.755 * [taylor]: Taking taylor expansion of 1.0 in k
8.755 * [backup-simplify]: Simplify 1.0 into 1.0
8.755 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
8.755 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
8.755 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
8.755 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
8.755 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
8.755 * [taylor]: Taking taylor expansion of 0.5 in k
8.755 * [backup-simplify]: Simplify 0.5 into 0.5
8.755 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.755 * [taylor]: Taking taylor expansion of 1.0 in k
8.755 * [backup-simplify]: Simplify 1.0 into 1.0
8.755 * [taylor]: Taking taylor expansion of k in k
8.755 * [backup-simplify]: Simplify 0 into 0
8.755 * [backup-simplify]: Simplify 1 into 1
8.755 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
8.755 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
8.755 * [taylor]: Taking taylor expansion of 2.0 in k
8.755 * [backup-simplify]: Simplify 2.0 into 2.0
8.755 * [taylor]: Taking taylor expansion of (* n PI) in k
8.755 * [taylor]: Taking taylor expansion of n in k
8.755 * [backup-simplify]: Simplify n into n
8.755 * [taylor]: Taking taylor expansion of PI in k
8.755 * [backup-simplify]: Simplify PI into PI
8.755 * [backup-simplify]: Simplify (* n PI) into (* n PI)
8.755 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
8.755 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
8.756 * [backup-simplify]: Simplify (- 0) into 0
8.756 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.756 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
8.756 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
8.756 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
8.756 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
8.756 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.756 * [taylor]: Taking taylor expansion of k in k
8.757 * [backup-simplify]: Simplify 0 into 0
8.757 * [backup-simplify]: Simplify 1 into 1
8.757 * [backup-simplify]: Simplify (/ 1 1) into 1
8.757 * [backup-simplify]: Simplify (sqrt 0) into 0
8.758 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.758 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
8.758 * [taylor]: Taking taylor expansion of 1.0 in n
8.758 * [backup-simplify]: Simplify 1.0 into 1.0
8.758 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
8.758 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
8.758 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.758 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.758 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
8.758 * [taylor]: Taking taylor expansion of 0.5 in n
8.758 * [backup-simplify]: Simplify 0.5 into 0.5
8.758 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.758 * [taylor]: Taking taylor expansion of 1.0 in n
8.758 * [backup-simplify]: Simplify 1.0 into 1.0
8.758 * [taylor]: Taking taylor expansion of k in n
8.758 * [backup-simplify]: Simplify k into k
8.758 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.758 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.758 * [taylor]: Taking taylor expansion of 2.0 in n
8.758 * [backup-simplify]: Simplify 2.0 into 2.0
8.758 * [taylor]: Taking taylor expansion of (* n PI) in n
8.758 * [taylor]: Taking taylor expansion of n in n
8.758 * [backup-simplify]: Simplify 0 into 0
8.758 * [backup-simplify]: Simplify 1 into 1
8.758 * [taylor]: Taking taylor expansion of PI in n
8.758 * [backup-simplify]: Simplify PI into PI
8.759 * [backup-simplify]: Simplify (* 0 PI) into 0
8.759 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.760 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.761 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.761 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.761 * [backup-simplify]: Simplify (- k) into (- k)
8.762 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.762 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
8.762 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.763 * [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))))
8.764 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.764 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
8.764 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.764 * [taylor]: Taking taylor expansion of k in n
8.764 * [backup-simplify]: Simplify k into k
8.764 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.764 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
8.764 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.764 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
8.764 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
8.764 * [taylor]: Taking taylor expansion of 1.0 in n
8.764 * [backup-simplify]: Simplify 1.0 into 1.0
8.764 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
8.764 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
8.764 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.764 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.764 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
8.764 * [taylor]: Taking taylor expansion of 0.5 in n
8.764 * [backup-simplify]: Simplify 0.5 into 0.5
8.765 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.765 * [taylor]: Taking taylor expansion of 1.0 in n
8.765 * [backup-simplify]: Simplify 1.0 into 1.0
8.765 * [taylor]: Taking taylor expansion of k in n
8.765 * [backup-simplify]: Simplify k into k
8.765 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.765 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.765 * [taylor]: Taking taylor expansion of 2.0 in n
8.765 * [backup-simplify]: Simplify 2.0 into 2.0
8.765 * [taylor]: Taking taylor expansion of (* n PI) in n
8.765 * [taylor]: Taking taylor expansion of n in n
8.765 * [backup-simplify]: Simplify 0 into 0
8.765 * [backup-simplify]: Simplify 1 into 1
8.765 * [taylor]: Taking taylor expansion of PI in n
8.765 * [backup-simplify]: Simplify PI into PI
8.765 * [backup-simplify]: Simplify (* 0 PI) into 0
8.765 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.766 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.767 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.768 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.768 * [backup-simplify]: Simplify (- k) into (- k)
8.768 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.768 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
8.769 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.770 * [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))))
8.772 * [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)))))
8.772 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
8.772 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.772 * [taylor]: Taking taylor expansion of k in n
8.772 * [backup-simplify]: Simplify k into k
8.772 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.772 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
8.772 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.772 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
8.774 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
8.775 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
8.775 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
8.775 * [taylor]: Taking taylor expansion of 1.0 in k
8.775 * [backup-simplify]: Simplify 1.0 into 1.0
8.775 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
8.775 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
8.775 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
8.775 * [taylor]: Taking taylor expansion of 0.5 in k
8.775 * [backup-simplify]: Simplify 0.5 into 0.5
8.775 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
8.776 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.776 * [taylor]: Taking taylor expansion of 1.0 in k
8.776 * [backup-simplify]: Simplify 1.0 into 1.0
8.776 * [taylor]: Taking taylor expansion of k in k
8.776 * [backup-simplify]: Simplify 0 into 0
8.776 * [backup-simplify]: Simplify 1 into 1
8.776 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
8.776 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.776 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.776 * [taylor]: Taking taylor expansion of 2.0 in k
8.776 * [backup-simplify]: Simplify 2.0 into 2.0
8.776 * [taylor]: Taking taylor expansion of PI in k
8.776 * [backup-simplify]: Simplify PI into PI
8.776 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.777 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.778 * [taylor]: Taking taylor expansion of (log n) in k
8.778 * [taylor]: Taking taylor expansion of n in k
8.778 * [backup-simplify]: Simplify n into n
8.778 * [backup-simplify]: Simplify (log n) into (log n)
8.778 * [backup-simplify]: Simplify (- 0) into 0
8.779 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.780 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
8.781 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
8.782 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
8.783 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
8.783 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
8.783 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.783 * [taylor]: Taking taylor expansion of k in k
8.783 * [backup-simplify]: Simplify 0 into 0
8.783 * [backup-simplify]: Simplify 1 into 1
8.784 * [backup-simplify]: Simplify (/ 1 1) into 1
8.784 * [backup-simplify]: Simplify (sqrt 0) into 0
8.785 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.787 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
8.787 * [backup-simplify]: Simplify (* 1.0 0) into 0
8.787 * [backup-simplify]: Simplify 0 into 0
8.788 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.791 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.791 * [backup-simplify]: Simplify (- 0) into 0
8.792 * [backup-simplify]: Simplify (+ 0 0) into 0
8.792 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
8.794 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.795 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
8.797 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.798 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
8.800 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
8.800 * [taylor]: Taking taylor expansion of 0 in k
8.800 * [backup-simplify]: Simplify 0 into 0
8.801 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.803 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
8.804 * [backup-simplify]: Simplify (+ 0 0) into 0
8.805 * [backup-simplify]: Simplify (- 1) into -1
8.805 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.807 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
8.809 * [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))))
8.813 * [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))))))
8.817 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (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)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
8.819 * [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))))))
8.820 * [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))))))
8.820 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.821 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
8.822 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.823 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.827 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
8.827 * [backup-simplify]: Simplify (- 0) into 0
8.828 * [backup-simplify]: Simplify (+ 0 0) into 0
8.828 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
8.830 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.831 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.834 * [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
8.836 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
8.838 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
8.838 * [taylor]: Taking taylor expansion of 0 in k
8.838 * [backup-simplify]: Simplify 0 into 0
8.838 * [backup-simplify]: Simplify 0 into 0
8.841 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
8.845 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.846 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.849 * [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
8.851 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
8.852 * [backup-simplify]: Simplify (+ 0 0) into 0
8.852 * [backup-simplify]: Simplify (- 0) into 0
8.852 * [backup-simplify]: Simplify (+ 0 0) into 0
8.854 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.857 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
8.861 * [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 n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
8.870 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (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)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
8.877 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 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)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
8.881 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
8.881 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.881 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
8.882 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.883 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.886 * [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
8.887 * [backup-simplify]: Simplify (- 0) into 0
8.887 * [backup-simplify]: Simplify (+ 0 0) into 0
8.887 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
8.888 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.890 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
8.891 * [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
8.892 * [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
8.894 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
8.894 * [taylor]: Taking taylor expansion of 0 in k
8.894 * [backup-simplify]: Simplify 0 into 0
8.894 * [backup-simplify]: Simplify 0 into 0
8.894 * [backup-simplify]: Simplify 0 into 0
8.895 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.897 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.898 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.901 * [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
8.903 * [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
8.903 * [backup-simplify]: Simplify (+ 0 0) into 0
8.903 * [backup-simplify]: Simplify (- 0) into 0
8.904 * [backup-simplify]: Simplify (+ 0 0) into 0
8.905 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
8.907 * [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
8.911 * [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 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
8.923 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (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)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
8.944 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 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)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +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)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
8.961 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +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)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)))) (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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
8.982 * [backup-simplify]: Simplify (+ (* (- (+ (* +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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +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)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (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)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
8.984 * [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 (- 1.0 (/ 1 k)))) (sqrt k)))
8.984 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
8.984 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
8.984 * [taylor]: Taking taylor expansion of 1.0 in k
8.984 * [backup-simplify]: Simplify 1.0 into 1.0
8.984 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
8.984 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
8.984 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
8.984 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
8.984 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
8.984 * [taylor]: Taking taylor expansion of 0.5 in k
8.984 * [backup-simplify]: Simplify 0.5 into 0.5
8.984 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.984 * [taylor]: Taking taylor expansion of 1.0 in k
8.984 * [backup-simplify]: Simplify 1.0 into 1.0
8.984 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.984 * [taylor]: Taking taylor expansion of k in k
8.984 * [backup-simplify]: Simplify 0 into 0
8.984 * [backup-simplify]: Simplify 1 into 1
8.985 * [backup-simplify]: Simplify (/ 1 1) into 1
8.985 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
8.985 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
8.985 * [taylor]: Taking taylor expansion of 2.0 in k
8.985 * [backup-simplify]: Simplify 2.0 into 2.0
8.985 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.985 * [taylor]: Taking taylor expansion of PI in k
8.985 * [backup-simplify]: Simplify PI into PI
8.985 * [taylor]: Taking taylor expansion of n in k
8.985 * [backup-simplify]: Simplify n into n
8.985 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.985 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
8.985 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
8.985 * [backup-simplify]: Simplify (- 1) into -1
8.986 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.987 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
8.987 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
8.987 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
8.987 * [taylor]: Taking taylor expansion of (sqrt k) in k
8.987 * [taylor]: Taking taylor expansion of k in k
8.987 * [backup-simplify]: Simplify 0 into 0
8.987 * [backup-simplify]: Simplify 1 into 1
8.988 * [backup-simplify]: Simplify (sqrt 0) into 0
8.989 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.989 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
8.989 * [taylor]: Taking taylor expansion of 1.0 in n
8.989 * [backup-simplify]: Simplify 1.0 into 1.0
8.989 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
8.990 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
8.990 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.990 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.990 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
8.990 * [taylor]: Taking taylor expansion of 0.5 in n
8.990 * [backup-simplify]: Simplify 0.5 into 0.5
8.990 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.990 * [taylor]: Taking taylor expansion of 1.0 in n
8.990 * [backup-simplify]: Simplify 1.0 into 1.0
8.990 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.990 * [taylor]: Taking taylor expansion of k in n
8.990 * [backup-simplify]: Simplify k into k
8.990 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.990 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.990 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.990 * [taylor]: Taking taylor expansion of 2.0 in n
8.990 * [backup-simplify]: Simplify 2.0 into 2.0
8.990 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.990 * [taylor]: Taking taylor expansion of PI in n
8.990 * [backup-simplify]: Simplify PI into PI
8.990 * [taylor]: Taking taylor expansion of n in n
8.990 * [backup-simplify]: Simplify 0 into 0
8.990 * [backup-simplify]: Simplify 1 into 1
8.991 * [backup-simplify]: Simplify (/ PI 1) into PI
8.992 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.993 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.993 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.993 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.993 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
8.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.996 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
8.997 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
8.997 * [taylor]: Taking taylor expansion of (sqrt k) in n
8.997 * [taylor]: Taking taylor expansion of k in n
8.997 * [backup-simplify]: Simplify k into k
8.997 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
8.997 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
8.997 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
8.997 * [taylor]: Taking taylor expansion of 1.0 in n
8.997 * [backup-simplify]: Simplify 1.0 into 1.0
8.997 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
8.997 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
8.997 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.997 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.997 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
8.997 * [taylor]: Taking taylor expansion of 0.5 in n
8.997 * [backup-simplify]: Simplify 0.5 into 0.5
8.997 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.997 * [taylor]: Taking taylor expansion of 1.0 in n
8.997 * [backup-simplify]: Simplify 1.0 into 1.0
8.997 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.997 * [taylor]: Taking taylor expansion of k in n
8.997 * [backup-simplify]: Simplify k into k
8.997 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.997 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.997 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.997 * [taylor]: Taking taylor expansion of 2.0 in n
8.997 * [backup-simplify]: Simplify 2.0 into 2.0
8.997 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.997 * [taylor]: Taking taylor expansion of PI in n
8.997 * [backup-simplify]: Simplify PI into PI
8.997 * [taylor]: Taking taylor expansion of n in n
8.997 * [backup-simplify]: Simplify 0 into 0
8.997 * [backup-simplify]: Simplify 1 into 1
8.998 * [backup-simplify]: Simplify (/ PI 1) into PI
8.998 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.999 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.999 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.999 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.999 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
9.000 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.000 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
9.001 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
9.001 * [taylor]: Taking taylor expansion of (sqrt k) in n
9.001 * [taylor]: Taking taylor expansion of k in n
9.001 * [backup-simplify]: Simplify k into k
9.001 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
9.001 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
9.002 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
9.003 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
9.003 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
9.003 * [taylor]: Taking taylor expansion of 1.0 in k
9.003 * [backup-simplify]: Simplify 1.0 into 1.0
9.003 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
9.003 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
9.003 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
9.003 * [taylor]: Taking taylor expansion of 0.5 in k
9.003 * [backup-simplify]: Simplify 0.5 into 0.5
9.003 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
9.003 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
9.003 * [taylor]: Taking taylor expansion of 1.0 in k
9.003 * [backup-simplify]: Simplify 1.0 into 1.0
9.003 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.003 * [taylor]: Taking taylor expansion of k in k
9.003 * [backup-simplify]: Simplify 0 into 0
9.003 * [backup-simplify]: Simplify 1 into 1
9.004 * [backup-simplify]: Simplify (/ 1 1) into 1
9.004 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
9.004 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
9.004 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
9.004 * [taylor]: Taking taylor expansion of 2.0 in k
9.004 * [backup-simplify]: Simplify 2.0 into 2.0
9.004 * [taylor]: Taking taylor expansion of PI in k
9.004 * [backup-simplify]: Simplify PI into PI
9.004 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
9.005 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.005 * [taylor]: Taking taylor expansion of (log n) in k
9.005 * [taylor]: Taking taylor expansion of n in k
9.005 * [backup-simplify]: Simplify n into n
9.005 * [backup-simplify]: Simplify (log n) into (log n)
9.005 * [backup-simplify]: Simplify (- 1) into -1
9.005 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.005 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.006 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
9.007 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
9.007 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
9.008 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
9.008 * [taylor]: Taking taylor expansion of (sqrt k) in k
9.008 * [taylor]: Taking taylor expansion of k in k
9.008 * [backup-simplify]: Simplify 0 into 0
9.008 * [backup-simplify]: Simplify 1 into 1
9.008 * [backup-simplify]: Simplify (sqrt 0) into 0
9.009 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
9.010 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
9.010 * [backup-simplify]: Simplify (* 1.0 0) into 0
9.010 * [backup-simplify]: Simplify 0 into 0
9.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.011 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
9.012 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
9.012 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.013 * [backup-simplify]: Simplify (- 0) into 0
9.013 * [backup-simplify]: Simplify (+ 0 0) into 0
9.013 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
9.014 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.015 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
9.016 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.017 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
9.018 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
9.018 * [taylor]: Taking taylor expansion of 0 in k
9.018 * [backup-simplify]: Simplify 0 into 0
9.018 * [backup-simplify]: Simplify 0 into 0
9.019 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.020 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.021 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.021 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
9.022 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.022 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
9.024 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
9.024 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.025 * [backup-simplify]: Simplify (- 0) into 0
9.025 * [backup-simplify]: Simplify (+ 0 0) into 0
9.025 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
9.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.027 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
9.029 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.030 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
9.031 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
9.031 * [taylor]: Taking taylor expansion of 0 in k
9.031 * [backup-simplify]: Simplify 0 into 0
9.031 * [backup-simplify]: Simplify 0 into 0
9.031 * [backup-simplify]: Simplify 0 into 0
9.033 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.034 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.036 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.037 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.037 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
9.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.039 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.042 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
9.042 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.042 * [backup-simplify]: Simplify (- 0) into 0
9.043 * [backup-simplify]: Simplify (+ 0 0) into 0
9.043 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
9.044 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.045 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
9.047 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 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
9.048 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
9.050 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
9.050 * [taylor]: Taking taylor expansion of 0 in k
9.050 * [backup-simplify]: Simplify 0 into 0
9.050 * [backup-simplify]: Simplify 0 into 0
9.050 * [backup-simplify]: Simplify 0 into 0
9.050 * [backup-simplify]: Simplify 0 into 0
9.053 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.054 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.056 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.060 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
9.063 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +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)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
9.063 * [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))))
9.063 * [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
9.063 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
9.063 * [taylor]: Taking taylor expansion of 1.0 in k
9.063 * [backup-simplify]: Simplify 1.0 into 1.0
9.064 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
9.064 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
9.064 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
9.064 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
9.064 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
9.064 * [taylor]: Taking taylor expansion of 0.5 in k
9.064 * [backup-simplify]: Simplify 0.5 into 0.5
9.064 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
9.064 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.064 * [taylor]: Taking taylor expansion of k in k
9.064 * [backup-simplify]: Simplify 0 into 0
9.064 * [backup-simplify]: Simplify 1 into 1
9.064 * [backup-simplify]: Simplify (/ 1 1) into 1
9.064 * [taylor]: Taking taylor expansion of 1.0 in k
9.064 * [backup-simplify]: Simplify 1.0 into 1.0
9.064 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
9.064 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
9.064 * [taylor]: Taking taylor expansion of -2.0 in k
9.064 * [backup-simplify]: Simplify -2.0 into -2.0
9.064 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.064 * [taylor]: Taking taylor expansion of PI in k
9.064 * [backup-simplify]: Simplify PI into PI
9.064 * [taylor]: Taking taylor expansion of n in k
9.064 * [backup-simplify]: Simplify n into n
9.064 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.064 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
9.064 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
9.065 * [backup-simplify]: Simplify (+ 1 0) into 1
9.065 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
9.065 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
9.065 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
9.065 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.065 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.065 * [taylor]: Taking taylor expansion of -1 in k
9.065 * [backup-simplify]: Simplify -1 into -1
9.065 * [taylor]: Taking taylor expansion of k in k
9.065 * [backup-simplify]: Simplify 0 into 0
9.065 * [backup-simplify]: Simplify 1 into 1
9.065 * [backup-simplify]: Simplify (/ -1 1) into -1
9.066 * [backup-simplify]: Simplify (sqrt 0) into 0
9.066 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.067 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
9.067 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
9.067 * [taylor]: Taking taylor expansion of 1.0 in n
9.067 * [backup-simplify]: Simplify 1.0 into 1.0
9.067 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
9.067 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
9.067 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
9.067 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
9.067 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
9.067 * [taylor]: Taking taylor expansion of 0.5 in n
9.067 * [backup-simplify]: Simplify 0.5 into 0.5
9.067 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
9.067 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.067 * [taylor]: Taking taylor expansion of k in n
9.067 * [backup-simplify]: Simplify k into k
9.067 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.067 * [taylor]: Taking taylor expansion of 1.0 in n
9.067 * [backup-simplify]: Simplify 1.0 into 1.0
9.067 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
9.067 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
9.067 * [taylor]: Taking taylor expansion of -2.0 in n
9.067 * [backup-simplify]: Simplify -2.0 into -2.0
9.067 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.067 * [taylor]: Taking taylor expansion of PI in n
9.067 * [backup-simplify]: Simplify PI into PI
9.067 * [taylor]: Taking taylor expansion of n in n
9.067 * [backup-simplify]: Simplify 0 into 0
9.067 * [backup-simplify]: Simplify 1 into 1
9.067 * [backup-simplify]: Simplify (/ PI 1) into PI
9.068 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
9.068 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
9.068 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
9.069 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
9.069 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.070 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
9.071 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.071 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.071 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.071 * [taylor]: Taking taylor expansion of -1 in n
9.071 * [backup-simplify]: Simplify -1 into -1
9.071 * [taylor]: Taking taylor expansion of k in n
9.071 * [backup-simplify]: Simplify k into k
9.071 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.071 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.071 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.071 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.072 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
9.072 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
9.072 * [taylor]: Taking taylor expansion of 1.0 in n
9.072 * [backup-simplify]: Simplify 1.0 into 1.0
9.072 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
9.072 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
9.072 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
9.072 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
9.072 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
9.072 * [taylor]: Taking taylor expansion of 0.5 in n
9.072 * [backup-simplify]: Simplify 0.5 into 0.5
9.072 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
9.072 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.072 * [taylor]: Taking taylor expansion of k in n
9.072 * [backup-simplify]: Simplify k into k
9.072 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.072 * [taylor]: Taking taylor expansion of 1.0 in n
9.072 * [backup-simplify]: Simplify 1.0 into 1.0
9.073 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
9.073 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
9.073 * [taylor]: Taking taylor expansion of -2.0 in n
9.073 * [backup-simplify]: Simplify -2.0 into -2.0
9.073 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.073 * [taylor]: Taking taylor expansion of PI in n
9.073 * [backup-simplify]: Simplify PI into PI
9.073 * [taylor]: Taking taylor expansion of n in n
9.073 * [backup-simplify]: Simplify 0 into 0
9.073 * [backup-simplify]: Simplify 1 into 1
9.073 * [backup-simplify]: Simplify (/ PI 1) into PI
9.074 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
9.075 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
9.075 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
9.075 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
9.077 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.078 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
9.079 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.079 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
9.079 * [taylor]: Taking taylor expansion of (/ -1 k) in n
9.079 * [taylor]: Taking taylor expansion of -1 in n
9.080 * [backup-simplify]: Simplify -1 into -1
9.080 * [taylor]: Taking taylor expansion of k in n
9.080 * [backup-simplify]: Simplify k into k
9.080 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
9.080 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
9.080 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
9.080 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
9.081 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
9.083 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
9.083 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
9.083 * [taylor]: Taking taylor expansion of 1.0 in k
9.083 * [backup-simplify]: Simplify 1.0 into 1.0
9.083 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
9.083 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
9.083 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
9.083 * [taylor]: Taking taylor expansion of 0.5 in k
9.083 * [backup-simplify]: Simplify 0.5 into 0.5
9.083 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
9.083 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
9.083 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
9.083 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
9.083 * [taylor]: Taking taylor expansion of -2.0 in k
9.083 * [backup-simplify]: Simplify -2.0 into -2.0
9.083 * [taylor]: Taking taylor expansion of PI in k
9.083 * [backup-simplify]: Simplify PI into PI
9.084 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
9.085 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
9.085 * [taylor]: Taking taylor expansion of (log n) in k
9.085 * [taylor]: Taking taylor expansion of n in k
9.085 * [backup-simplify]: Simplify n into n
9.085 * [backup-simplify]: Simplify (log n) into (log n)
9.085 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
9.085 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.085 * [taylor]: Taking taylor expansion of k in k
9.085 * [backup-simplify]: Simplify 0 into 0
9.085 * [backup-simplify]: Simplify 1 into 1
9.086 * [backup-simplify]: Simplify (/ 1 1) into 1
9.086 * [taylor]: Taking taylor expansion of 1.0 in k
9.086 * [backup-simplify]: Simplify 1.0 into 1.0
9.086 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.087 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
9.087 * [backup-simplify]: Simplify (+ 1 0) into 1
9.089 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
9.090 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
9.091 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.092 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
9.092 * [taylor]: Taking taylor expansion of (/ -1 k) in k
9.092 * [taylor]: Taking taylor expansion of -1 in k
9.092 * [backup-simplify]: Simplify -1 into -1
9.092 * [taylor]: Taking taylor expansion of k in k
9.092 * [backup-simplify]: Simplify 0 into 0
9.092 * [backup-simplify]: Simplify 1 into 1
9.092 * [backup-simplify]: Simplify (/ -1 1) into -1
9.093 * [backup-simplify]: Simplify (sqrt 0) into 0
9.094 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
9.095 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
9.097 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
9.098 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
9.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.100 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
9.101 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
9.101 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.101 * [backup-simplify]: Simplify (+ 0 0) into 0
9.102 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
9.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.103 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
9.105 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.106 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
9.107 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
9.107 * [taylor]: Taking taylor expansion of 0 in k
9.107 * [backup-simplify]: Simplify 0 into 0
9.107 * [backup-simplify]: Simplify 0 into 0
9.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
9.109 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
9.110 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
9.112 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
9.113 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
9.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.114 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
9.116 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
9.116 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.116 * [backup-simplify]: Simplify (+ 0 0) into 0
9.117 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
9.118 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.119 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
9.120 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.120 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.121 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
9.122 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
9.123 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
9.123 * [taylor]: Taking taylor expansion of 0 in k
9.123 * [backup-simplify]: Simplify 0 into 0
9.123 * [backup-simplify]: Simplify 0 into 0
9.123 * [backup-simplify]: Simplify 0 into 0
9.124 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.126 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
9.129 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
9.131 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
9.132 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
9.136 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +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))))))))
9.136 * * * * [progress]: [ 3 / 3 ] generating series at (2 1 2)
9.137 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
9.137 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
9.137 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
9.137 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
9.137 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
9.137 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
9.137 * [taylor]: Taking taylor expansion of 0.5 in k
9.137 * [backup-simplify]: Simplify 0.5 into 0.5
9.137 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
9.137 * [taylor]: Taking taylor expansion of 1.0 in k
9.137 * [backup-simplify]: Simplify 1.0 into 1.0
9.137 * [taylor]: Taking taylor expansion of k in k
9.137 * [backup-simplify]: Simplify 0 into 0
9.137 * [backup-simplify]: Simplify 1 into 1
9.137 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
9.138 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
9.138 * [taylor]: Taking taylor expansion of 2.0 in k
9.138 * [backup-simplify]: Simplify 2.0 into 2.0
9.138 * [taylor]: Taking taylor expansion of (* n PI) in k
9.138 * [taylor]: Taking taylor expansion of n in k
9.138 * [backup-simplify]: Simplify n into n
9.138 * [taylor]: Taking taylor expansion of PI in k
9.138 * [backup-simplify]: Simplify PI into PI
9.138 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.138 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
9.138 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
9.138 * [backup-simplify]: Simplify (- 0) into 0
9.139 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
9.139 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
9.139 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
9.139 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
9.139 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
9.139 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
9.140 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
9.140 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
9.140 * [taylor]: Taking taylor expansion of 0.5 in n
9.140 * [backup-simplify]: Simplify 0.5 into 0.5
9.140 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
9.140 * [taylor]: Taking taylor expansion of 1.0 in n
9.140 * [backup-simplify]: Simplify 1.0 into 1.0
9.140 * [taylor]: Taking taylor expansion of k in n
9.140 * [backup-simplify]: Simplify k into k
9.140 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
9.140 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
9.140 * [taylor]: Taking taylor expansion of 2.0 in n
9.140 * [backup-simplify]: Simplify 2.0 into 2.0
9.140 * [taylor]: Taking taylor expansion of (* n PI) in n
9.140 * [taylor]: Taking taylor expansion of n in n
9.140 * [backup-simplify]: Simplify 0 into 0
9.140 * [backup-simplify]: Simplify 1 into 1
9.140 * [taylor]: Taking taylor expansion of PI in n
9.140 * [backup-simplify]: Simplify PI into PI
9.140 * [backup-simplify]: Simplify (* 0 PI) into 0
9.141 * [backup-simplify]: Simplify (* 2.0 0) into 0
9.142 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.144 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
9.145 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.145 * [backup-simplify]: Simplify (- k) into (- k)
9.145 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
9.145 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
9.147 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
9.148 * [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))))
9.149 * [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)))))
9.149 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
9.149 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
9.149 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
9.149 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
9.149 * [taylor]: Taking taylor expansion of 0.5 in n
9.149 * [backup-simplify]: Simplify 0.5 into 0.5
9.149 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
9.149 * [taylor]: Taking taylor expansion of 1.0 in n
9.149 * [backup-simplify]: Simplify 1.0 into 1.0
9.149 * [taylor]: Taking taylor expansion of k in n
9.149 * [backup-simplify]: Simplify k into k
9.149 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
9.149 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
9.149 * [taylor]: Taking taylor expansion of 2.0 in n
9.149 * [backup-simplify]: Simplify 2.0 into 2.0
9.149 * [taylor]: Taking taylor expansion of (* n PI) in n
9.149 * [taylor]: Taking taylor expansion of n in n
9.149 * [backup-simplify]: Simplify 0 into 0
9.150 * [backup-simplify]: Simplify 1 into 1
9.150 * [taylor]: Taking taylor expansion of PI in n
9.150 * [backup-simplify]: Simplify PI into PI
9.150 * [backup-simplify]: Simplify (* 0 PI) into 0
9.150 * [backup-simplify]: Simplify (* 2.0 0) into 0
9.152 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.154 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
9.155 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.155 * [backup-simplify]: Simplify (- k) into (- k)
9.155 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
9.155 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
9.157 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
9.158 * [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))))
9.159 * [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)))))
9.159 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
9.159 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
9.159 * [taylor]: Taking taylor expansion of 0.5 in k
9.159 * [backup-simplify]: Simplify 0.5 into 0.5
9.160 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
9.160 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
9.160 * [taylor]: Taking taylor expansion of 1.0 in k
9.160 * [backup-simplify]: Simplify 1.0 into 1.0
9.160 * [taylor]: Taking taylor expansion of k in k
9.160 * [backup-simplify]: Simplify 0 into 0
9.160 * [backup-simplify]: Simplify 1 into 1
9.160 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
9.160 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
9.160 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
9.160 * [taylor]: Taking taylor expansion of 2.0 in k
9.160 * [backup-simplify]: Simplify 2.0 into 2.0
9.160 * [taylor]: Taking taylor expansion of PI in k
9.160 * [backup-simplify]: Simplify PI into PI
9.160 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
9.162 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.162 * [taylor]: Taking taylor expansion of (log n) in k
9.162 * [taylor]: Taking taylor expansion of n in k
9.162 * [backup-simplify]: Simplify n into n
9.162 * [backup-simplify]: Simplify (log n) into (log n)
9.162 * [backup-simplify]: Simplify (- 0) into 0
9.163 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
9.164 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
9.165 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
9.166 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
9.167 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
9.168 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
9.170 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.171 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
9.172 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
9.173 * [backup-simplify]: Simplify (- 0) into 0
9.173 * [backup-simplify]: Simplify (+ 0 0) into 0
9.174 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
9.175 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
9.177 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
9.182 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.182 * [taylor]: Taking taylor expansion of 0 in k
9.182 * [backup-simplify]: Simplify 0 into 0
9.182 * [backup-simplify]: Simplify 0 into 0
9.183 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
9.184 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
9.185 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.186 * [backup-simplify]: Simplify (+ 0 0) into 0
9.186 * [backup-simplify]: Simplify (- 1) into -1
9.186 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.188 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
9.190 * [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))))
9.192 * [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))))))
9.194 * [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))))))
9.195 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.196 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.198 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
9.198 * [backup-simplify]: Simplify (- 0) into 0
9.198 * [backup-simplify]: Simplify (+ 0 0) into 0
9.199 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
9.200 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
9.201 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
9.203 * [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
9.203 * [taylor]: Taking taylor expansion of 0 in k
9.203 * [backup-simplify]: Simplify 0 into 0
9.203 * [backup-simplify]: Simplify 0 into 0
9.203 * [backup-simplify]: Simplify 0 into 0
9.203 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
9.205 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
9.206 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.207 * [backup-simplify]: Simplify (+ 0 0) into 0
9.207 * [backup-simplify]: Simplify (- 0) into 0
9.207 * [backup-simplify]: Simplify (+ 0 0) into 0
9.208 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
9.210 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
9.212 * [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 n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
9.216 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
9.222 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 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 (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
9.223 * [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))))
9.223 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
9.223 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
9.223 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
9.223 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
9.223 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
9.223 * [taylor]: Taking taylor expansion of 0.5 in k
9.223 * [backup-simplify]: Simplify 0.5 into 0.5
9.223 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
9.223 * [taylor]: Taking taylor expansion of 1.0 in k
9.223 * [backup-simplify]: Simplify 1.0 into 1.0
9.223 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.223 * [taylor]: Taking taylor expansion of k in k
9.223 * [backup-simplify]: Simplify 0 into 0
9.223 * [backup-simplify]: Simplify 1 into 1
9.223 * [backup-simplify]: Simplify (/ 1 1) into 1
9.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
9.223 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
9.223 * [taylor]: Taking taylor expansion of 2.0 in k
9.223 * [backup-simplify]: Simplify 2.0 into 2.0
9.223 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.223 * [taylor]: Taking taylor expansion of PI in k
9.223 * [backup-simplify]: Simplify PI into PI
9.223 * [taylor]: Taking taylor expansion of n in k
9.223 * [backup-simplify]: Simplify n into n
9.223 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.223 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
9.223 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
9.224 * [backup-simplify]: Simplify (- 1) into -1
9.224 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.224 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
9.224 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
9.224 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
9.224 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
9.225 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
9.225 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
9.225 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
9.225 * [taylor]: Taking taylor expansion of 0.5 in n
9.225 * [backup-simplify]: Simplify 0.5 into 0.5
9.225 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
9.225 * [taylor]: Taking taylor expansion of 1.0 in n
9.225 * [backup-simplify]: Simplify 1.0 into 1.0
9.225 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.225 * [taylor]: Taking taylor expansion of k in n
9.225 * [backup-simplify]: Simplify k into k
9.225 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.225 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
9.225 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
9.225 * [taylor]: Taking taylor expansion of 2.0 in n
9.225 * [backup-simplify]: Simplify 2.0 into 2.0
9.225 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.225 * [taylor]: Taking taylor expansion of PI in n
9.225 * [backup-simplify]: Simplify PI into PI
9.225 * [taylor]: Taking taylor expansion of n in n
9.225 * [backup-simplify]: Simplify 0 into 0
9.225 * [backup-simplify]: Simplify 1 into 1
9.225 * [backup-simplify]: Simplify (/ PI 1) into PI
9.226 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
9.226 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.226 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.226 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
9.227 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
9.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.228 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
9.229 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
9.229 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
9.229 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
9.229 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
9.229 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
9.229 * [taylor]: Taking taylor expansion of 0.5 in n
9.229 * [backup-simplify]: Simplify 0.5 into 0.5
9.229 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
9.229 * [taylor]: Taking taylor expansion of 1.0 in n
9.229 * [backup-simplify]: Simplify 1.0 into 1.0
9.229 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.229 * [taylor]: Taking taylor expansion of k in n
9.229 * [backup-simplify]: Simplify k into k
9.229 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.229 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
9.229 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
9.229 * [taylor]: Taking taylor expansion of 2.0 in n
9.229 * [backup-simplify]: Simplify 2.0 into 2.0
9.229 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.229 * [taylor]: Taking taylor expansion of PI in n
9.229 * [backup-simplify]: Simplify PI into PI
9.229 * [taylor]: Taking taylor expansion of n in n
9.229 * [backup-simplify]: Simplify 0 into 0
9.229 * [backup-simplify]: Simplify 1 into 1
9.230 * [backup-simplify]: Simplify (/ PI 1) into PI
9.230 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
9.231 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.231 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
9.231 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
9.231 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
9.232 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.232 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
9.233 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
9.233 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
9.233 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
9.233 * [taylor]: Taking taylor expansion of 0.5 in k
9.233 * [backup-simplify]: Simplify 0.5 into 0.5
9.233 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
9.233 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
9.233 * [taylor]: Taking taylor expansion of 1.0 in k
9.233 * [backup-simplify]: Simplify 1.0 into 1.0
9.233 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.233 * [taylor]: Taking taylor expansion of k in k
9.233 * [backup-simplify]: Simplify 0 into 0
9.234 * [backup-simplify]: Simplify 1 into 1
9.234 * [backup-simplify]: Simplify (/ 1 1) into 1
9.234 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
9.234 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
9.234 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
9.234 * [taylor]: Taking taylor expansion of 2.0 in k
9.234 * [backup-simplify]: Simplify 2.0 into 2.0
9.234 * [taylor]: Taking taylor expansion of PI in k
9.234 * [backup-simplify]: Simplify PI into PI
9.234 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
9.235 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
9.235 * [taylor]: Taking taylor expansion of (log n) in k
9.235 * [taylor]: Taking taylor expansion of n in k
9.235 * [backup-simplify]: Simplify n into n
9.235 * [backup-simplify]: Simplify (log n) into (log n)
9.235 * [backup-simplify]: Simplify (- 1) into -1
9.235 * [backup-simplify]: Simplify (+ 0 -1) into -1
9.235 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.236 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
9.237 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
9.238 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
9.239 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
9.240 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
9.241 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.242 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
9.244 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
9.244 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.244 * [backup-simplify]: Simplify (- 0) into 0
9.244 * [backup-simplify]: Simplify (+ 0 0) into 0
9.245 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
9.246 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.247 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
9.249 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.249 * [taylor]: Taking taylor expansion of 0 in k
9.249 * [backup-simplify]: Simplify 0 into 0
9.249 * [backup-simplify]: Simplify 0 into 0
9.249 * [backup-simplify]: Simplify 0 into 0
9.250 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.251 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
9.254 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
9.255 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.255 * [backup-simplify]: Simplify (- 0) into 0
9.255 * [backup-simplify]: Simplify (+ 0 0) into 0
9.256 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
9.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.259 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
9.261 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.261 * [taylor]: Taking taylor expansion of 0 in k
9.261 * [backup-simplify]: Simplify 0 into 0
9.261 * [backup-simplify]: Simplify 0 into 0
9.262 * [backup-simplify]: Simplify 0 into 0
9.262 * [backup-simplify]: Simplify 0 into 0
9.263 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.264 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.269 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
9.270 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.270 * [backup-simplify]: Simplify (- 0) into 0
9.270 * [backup-simplify]: Simplify (+ 0 0) into 0
9.271 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
9.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
9.275 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
9.277 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 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
9.277 * [taylor]: Taking taylor expansion of 0 in k
9.277 * [backup-simplify]: Simplify 0 into 0
9.277 * [backup-simplify]: Simplify 0 into 0
9.279 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
9.280 * [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)))
9.280 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
9.280 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
9.280 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
9.280 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
9.280 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
9.280 * [taylor]: Taking taylor expansion of 0.5 in k
9.280 * [backup-simplify]: Simplify 0.5 into 0.5
9.280 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
9.280 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.280 * [taylor]: Taking taylor expansion of k in k
9.280 * [backup-simplify]: Simplify 0 into 0
9.280 * [backup-simplify]: Simplify 1 into 1
9.280 * [backup-simplify]: Simplify (/ 1 1) into 1
9.280 * [taylor]: Taking taylor expansion of 1.0 in k
9.280 * [backup-simplify]: Simplify 1.0 into 1.0
9.280 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
9.280 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
9.280 * [taylor]: Taking taylor expansion of -2.0 in k
9.280 * [backup-simplify]: Simplify -2.0 into -2.0
9.280 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.280 * [taylor]: Taking taylor expansion of PI in k
9.280 * [backup-simplify]: Simplify PI into PI
9.280 * [taylor]: Taking taylor expansion of n in k
9.280 * [backup-simplify]: Simplify n into n
9.281 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.281 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
9.281 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
9.281 * [backup-simplify]: Simplify (+ 1 0) into 1
9.282 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
9.282 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
9.282 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
9.282 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
9.282 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
9.282 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
9.282 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
9.282 * [taylor]: Taking taylor expansion of 0.5 in n
9.282 * [backup-simplify]: Simplify 0.5 into 0.5
9.282 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
9.282 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.282 * [taylor]: Taking taylor expansion of k in n
9.282 * [backup-simplify]: Simplify k into k
9.282 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.282 * [taylor]: Taking taylor expansion of 1.0 in n
9.282 * [backup-simplify]: Simplify 1.0 into 1.0
9.282 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
9.282 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
9.282 * [taylor]: Taking taylor expansion of -2.0 in n
9.282 * [backup-simplify]: Simplify -2.0 into -2.0
9.282 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.283 * [taylor]: Taking taylor expansion of PI in n
9.283 * [backup-simplify]: Simplify PI into PI
9.283 * [taylor]: Taking taylor expansion of n in n
9.283 * [backup-simplify]: Simplify 0 into 0
9.283 * [backup-simplify]: Simplify 1 into 1
9.283 * [backup-simplify]: Simplify (/ PI 1) into PI
9.284 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
9.284 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
9.285 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
9.285 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
9.286 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.287 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
9.288 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.288 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
9.288 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
9.288 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
9.288 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
9.288 * [taylor]: Taking taylor expansion of 0.5 in n
9.288 * [backup-simplify]: Simplify 0.5 into 0.5
9.288 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
9.289 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.289 * [taylor]: Taking taylor expansion of k in n
9.289 * [backup-simplify]: Simplify k into k
9.289 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.289 * [taylor]: Taking taylor expansion of 1.0 in n
9.289 * [backup-simplify]: Simplify 1.0 into 1.0
9.289 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
9.289 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
9.289 * [taylor]: Taking taylor expansion of -2.0 in n
9.289 * [backup-simplify]: Simplify -2.0 into -2.0
9.289 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.289 * [taylor]: Taking taylor expansion of PI in n
9.289 * [backup-simplify]: Simplify PI into PI
9.289 * [taylor]: Taking taylor expansion of n in n
9.289 * [backup-simplify]: Simplify 0 into 0
9.289 * [backup-simplify]: Simplify 1 into 1
9.289 * [backup-simplify]: Simplify (/ PI 1) into PI
9.290 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
9.291 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
9.291 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
9.291 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
9.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.296 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
9.298 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.298 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
9.298 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
9.298 * [taylor]: Taking taylor expansion of 0.5 in k
9.298 * [backup-simplify]: Simplify 0.5 into 0.5
9.298 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
9.298 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
9.298 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
9.298 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
9.298 * [taylor]: Taking taylor expansion of -2.0 in k
9.298 * [backup-simplify]: Simplify -2.0 into -2.0
9.298 * [taylor]: Taking taylor expansion of PI in k
9.298 * [backup-simplify]: Simplify PI into PI
9.298 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
9.299 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
9.299 * [taylor]: Taking taylor expansion of (log n) in k
9.299 * [taylor]: Taking taylor expansion of n in k
9.299 * [backup-simplify]: Simplify n into n
9.300 * [backup-simplify]: Simplify (log n) into (log n)
9.300 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
9.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.300 * [taylor]: Taking taylor expansion of k in k
9.300 * [backup-simplify]: Simplify 0 into 0
9.300 * [backup-simplify]: Simplify 1 into 1
9.300 * [backup-simplify]: Simplify (/ 1 1) into 1
9.300 * [taylor]: Taking taylor expansion of 1.0 in k
9.300 * [backup-simplify]: Simplify 1.0 into 1.0
9.300 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.301 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
9.302 * [backup-simplify]: Simplify (+ 1 0) into 1
9.303 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
9.303 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
9.305 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.306 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
9.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.307 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
9.309 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
9.309 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.310 * [backup-simplify]: Simplify (+ 0 0) into 0
9.310 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
9.311 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.313 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
9.314 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.314 * [taylor]: Taking taylor expansion of 0 in k
9.314 * [backup-simplify]: Simplify 0 into 0
9.314 * [backup-simplify]: Simplify 0 into 0
9.314 * [backup-simplify]: Simplify 0 into 0
9.315 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.316 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
9.319 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
9.320 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.320 * [backup-simplify]: Simplify (+ 0 0) into 0
9.321 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
9.322 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.324 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
9.326 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.326 * [taylor]: Taking taylor expansion of 0 in k
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.326 * [backup-simplify]: Simplify 0 into 0
9.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.328 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.331 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
9.332 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.332 * [backup-simplify]: Simplify (+ 0 0) into 0
9.333 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
9.334 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
9.335 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
9.337 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.337 * [taylor]: Taking taylor expansion of 0 in k
9.337 * [backup-simplify]: Simplify 0 into 0
9.337 * [backup-simplify]: Simplify 0 into 0
9.338 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
9.338 * * * [progress]: simplifying candidates
9.339 * [simplify]: Simplifying:
  (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)))
  (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))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (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)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log 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)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +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))))))))
  (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
9.342 * * [simplify]: iteration 0: 268 enodes
9.444 * * [simplify]: iteration 1: 761 enodes
9.785 * * [simplify]: iteration 2: 2480 enodes
10.806 * * [simplify]: iteration complete: 5000 enodes
10.807 * * [simplify]: Extracting #0: cost 73 inf + 0
10.809 * * [simplify]: Extracting #1: cost 614 inf + 1
10.816 * * [simplify]: Extracting #2: cost 1139 inf + 1214
10.835 * * [simplify]: Extracting #3: cost 1224 inf + 35312
10.907 * * [simplify]: Extracting #4: cost 637 inf + 264300
11.003 * * [simplify]: Extracting #5: cost 244 inf + 456655
11.135 * * [simplify]: Extracting #6: cost 141 inf + 519457
11.321 * * [simplify]: Extracting #7: cost 29 inf + 585012
11.532 * * [simplify]: Extracting #8: cost 1 inf + 593010
11.739 * * [simplify]: Extracting #9: cost 0 inf + 588173
11.951 * * [simplify]: Extracting #10: cost 0 inf + 587148
12.170 * * [simplify]: Extracting #11: cost 0 inf + 587103
12.381 * [simplify]: Simplified to:
  (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)))
  (* (* PI 2.0) (* (cbrt n) (cbrt n)))
  (* (sqrt n) (* PI 2.0))
  (* PI 2.0)
  (* n PI)
  (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)))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (+ (log (/ 1.0 (sqrt k))) (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0))
  (exp (/ (* 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)) (* (/ (* 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))))
  (* (/ (* 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)) (/ (* 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))))
  (cbrt (/ (* 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)) (* (/ (* 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))))
  (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 k) 2.0))) 1.0)
  (- (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 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (fabs (cbrt k)))
  (* (/ 1.0 (sqrt (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 (sqrt (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) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ k 2.0)) (sqrt k))
  (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) (log (* 2.0 (* n PI)))) 2.0)
  (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0)
  (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0)
  (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0)
  (/ (- 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 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 (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (/ (* (- 1.0 k) (log (* 2.0 (* n PI)))) 2.0)
  (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) 2))
  (pow (* 2.0 (* n PI)) (/ (/ (- 1.0 k) 2.0) 2))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (fma (* (- +nan.0) (log (* PI 2.0))) (* (log n) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* k k))) (+ (fma (* (* (- +nan.0) (log (* PI 2.0))) (log (* PI 2.0))) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* k k)) (- (fma (* k k) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (- (fma (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (* k k) (log n)) (- (fma (* k (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) (log n) (* k (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))))) (* (* k (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) (log (* PI 2.0))))) (* +nan.0 (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* k k)) (log (* PI 2.0)))))) (* (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (* k (log n)) (* k (log n)))))) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))))
  (fma (- (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) (* k k))) +nan.0 (* +nan.0 (- (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) k) (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) (* (* k k) k)))))
  (fma (exp (* (- 1.0 k) (* (- (log (* PI -2.0)) (log (/ -1 n))) 0.5))) (- +nan.0) (* +nan.0 (- (/ (exp (* (- 1.0 k) (* (- (log (* PI -2.0)) (log (/ -1 n))) 0.5))) k) (/ (exp (* (- 1.0 k) (* (- (log (* PI -2.0)) (log (/ -1 n))) 0.5))) (* k k)))))
  (fma (* (log (* PI 2.0)) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (* (* k k) (log n)) 0.25) (fma (* (* k (log n)) (* k (log n))) (* 0.125 (exp (* (log (* 2.0 (* n PI))) 0.5))) (- (fma (* (* (* (log (* PI 2.0)) k) (* (log (* PI 2.0)) k)) (exp (* (log (* 2.0 (* n PI))) 0.5))) 0.125 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* 0.5 (* k (fma (exp (* (log (* 2.0 (* n PI))) 0.5)) (log n) (* (log (* PI 2.0)) (exp (* (log (* 2.0 (* n PI))) 0.5)))))))))
  (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5))
  (exp (* (- 1.0 k) (* (- (log (* PI -2.0)) (log (/ -1 n))) 0.5)))
12.395 * * * [progress]: adding candidates to table
13.050 * * [progress]: iteration 3 / 4
13.051 * * * [progress]: picking best candidate
13.109 * * * * [pick]: Picked  #<alt (λ (k n) (* (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)))))>
13.109 * * * [progress]: localizing error
13.176 * * * [progress]: generating rewritten candidates
13.176 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 2 1)
13.191 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
13.211 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
13.253 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
13.275 * * * [progress]: generating series expansions
13.275 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 2 1)
13.275 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.275 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
13.275 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) 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 (* n PI) in n
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
13.275 * [taylor]: Taking taylor expansion of PI in n
13.276 * [backup-simplify]: Simplify PI into PI
13.276 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.276 * [taylor]: Taking taylor expansion of 2.0 in n
13.276 * [backup-simplify]: Simplify 2.0 into 2.0
13.276 * [taylor]: Taking taylor expansion of (* n PI) in n
13.276 * [taylor]: Taking taylor expansion of n in n
13.276 * [backup-simplify]: Simplify 0 into 0
13.276 * [backup-simplify]: Simplify 1 into 1
13.276 * [taylor]: Taking taylor expansion of PI in n
13.276 * [backup-simplify]: Simplify PI into PI
13.276 * [backup-simplify]: Simplify (* 0 PI) into 0
13.277 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.277 * [backup-simplify]: Simplify 0 into 0
13.279 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.280 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.281 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.283 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.284 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.284 * [backup-simplify]: Simplify 0 into 0
13.285 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.286 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.286 * [backup-simplify]: Simplify 0 into 0
13.288 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.289 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.289 * [backup-simplify]: Simplify 0 into 0
13.291 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.293 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.293 * [backup-simplify]: Simplify 0 into 0
13.295 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.297 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.297 * [backup-simplify]: Simplify 0 into 0
13.299 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.301 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.301 * [backup-simplify]: Simplify 0 into 0
13.302 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.302 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
13.302 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
13.302 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.302 * [taylor]: Taking taylor expansion of 2.0 in n
13.302 * [backup-simplify]: Simplify 2.0 into 2.0
13.302 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.303 * [taylor]: Taking taylor expansion of PI in n
13.303 * [backup-simplify]: Simplify PI into PI
13.303 * [taylor]: Taking taylor expansion of n in n
13.303 * [backup-simplify]: Simplify 0 into 0
13.303 * [backup-simplify]: Simplify 1 into 1
13.303 * [backup-simplify]: Simplify (/ PI 1) into PI
13.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.303 * [taylor]: Taking taylor expansion of 2.0 in n
13.303 * [backup-simplify]: Simplify 2.0 into 2.0
13.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.303 * [taylor]: Taking taylor expansion of PI in n
13.303 * [backup-simplify]: Simplify PI into PI
13.303 * [taylor]: Taking taylor expansion of n in n
13.303 * [backup-simplify]: Simplify 0 into 0
13.303 * [backup-simplify]: Simplify 1 into 1
13.304 * [backup-simplify]: Simplify (/ PI 1) into PI
13.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.306 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.307 * [backup-simplify]: Simplify 0 into 0
13.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.309 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.309 * [backup-simplify]: Simplify 0 into 0
13.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.312 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.312 * [backup-simplify]: Simplify 0 into 0
13.313 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.315 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.315 * [backup-simplify]: Simplify 0 into 0
13.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.318 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.318 * [backup-simplify]: Simplify 0 into 0
13.319 * [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
13.321 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.321 * [backup-simplify]: Simplify 0 into 0
13.321 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
13.322 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
13.322 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
13.322 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.322 * [taylor]: Taking taylor expansion of -2.0 in n
13.322 * [backup-simplify]: Simplify -2.0 into -2.0
13.322 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.322 * [taylor]: Taking taylor expansion of PI in n
13.322 * [backup-simplify]: Simplify PI into PI
13.322 * [taylor]: Taking taylor expansion of n in n
13.322 * [backup-simplify]: Simplify 0 into 0
13.323 * [backup-simplify]: Simplify 1 into 1
13.323 * [backup-simplify]: Simplify (/ PI 1) into PI
13.323 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.323 * [taylor]: Taking taylor expansion of -2.0 in n
13.323 * [backup-simplify]: Simplify -2.0 into -2.0
13.323 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.323 * [taylor]: Taking taylor expansion of PI in n
13.323 * [backup-simplify]: Simplify PI into PI
13.324 * [taylor]: Taking taylor expansion of n in n
13.324 * [backup-simplify]: Simplify 0 into 0
13.324 * [backup-simplify]: Simplify 1 into 1
13.324 * [backup-simplify]: Simplify (/ PI 1) into PI
13.325 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.325 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.326 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.327 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.327 * [backup-simplify]: Simplify 0 into 0
13.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.329 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.329 * [backup-simplify]: Simplify 0 into 0
13.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.332 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.332 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.334 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.334 * [backup-simplify]: Simplify 0 into 0
13.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.335 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.335 * [backup-simplify]: Simplify 0 into 0
13.336 * [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
13.337 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.337 * [backup-simplify]: Simplify 0 into 0
13.337 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
13.338 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
13.338 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.338 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
13.338 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.338 * [taylor]: Taking taylor expansion of 2.0 in n
13.338 * [backup-simplify]: Simplify 2.0 into 2.0
13.338 * [taylor]: Taking taylor expansion of (* n PI) in n
13.338 * [taylor]: Taking taylor expansion of n in n
13.338 * [backup-simplify]: Simplify 0 into 0
13.338 * [backup-simplify]: Simplify 1 into 1
13.338 * [taylor]: Taking taylor expansion of PI in n
13.338 * [backup-simplify]: Simplify PI into PI
13.338 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.338 * [taylor]: Taking taylor expansion of 2.0 in n
13.338 * [backup-simplify]: Simplify 2.0 into 2.0
13.338 * [taylor]: Taking taylor expansion of (* n PI) in n
13.338 * [taylor]: Taking taylor expansion of n in n
13.338 * [backup-simplify]: Simplify 0 into 0
13.338 * [backup-simplify]: Simplify 1 into 1
13.338 * [taylor]: Taking taylor expansion of PI in n
13.338 * [backup-simplify]: Simplify PI into PI
13.339 * [backup-simplify]: Simplify (* 0 PI) into 0
13.339 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.339 * [backup-simplify]: Simplify 0 into 0
13.340 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.341 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.341 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.342 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.342 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.342 * [backup-simplify]: Simplify 0 into 0
13.343 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.344 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.344 * [backup-simplify]: Simplify 0 into 0
13.345 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.345 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.345 * [backup-simplify]: Simplify 0 into 0
13.346 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.347 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.347 * [backup-simplify]: Simplify 0 into 0
13.350 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.352 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.352 * [backup-simplify]: Simplify 0 into 0
13.353 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.354 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.354 * [backup-simplify]: Simplify 0 into 0
13.354 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.355 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
13.355 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
13.355 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.355 * [taylor]: Taking taylor expansion of 2.0 in n
13.355 * [backup-simplify]: Simplify 2.0 into 2.0
13.355 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.355 * [taylor]: Taking taylor expansion of PI in n
13.355 * [backup-simplify]: Simplify PI into PI
13.355 * [taylor]: Taking taylor expansion of n in n
13.355 * [backup-simplify]: Simplify 0 into 0
13.355 * [backup-simplify]: Simplify 1 into 1
13.355 * [backup-simplify]: Simplify (/ PI 1) into PI
13.355 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.355 * [taylor]: Taking taylor expansion of 2.0 in n
13.355 * [backup-simplify]: Simplify 2.0 into 2.0
13.355 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.355 * [taylor]: Taking taylor expansion of PI in n
13.355 * [backup-simplify]: Simplify PI into PI
13.355 * [taylor]: Taking taylor expansion of n in n
13.355 * [backup-simplify]: Simplify 0 into 0
13.355 * [backup-simplify]: Simplify 1 into 1
13.356 * [backup-simplify]: Simplify (/ PI 1) into PI
13.356 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.356 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.357 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.357 * [backup-simplify]: Simplify 0 into 0
13.358 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.358 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.358 * [backup-simplify]: Simplify 0 into 0
13.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.360 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.360 * [backup-simplify]: Simplify 0 into 0
13.360 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.361 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.361 * [backup-simplify]: Simplify 0 into 0
13.362 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.363 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.363 * [backup-simplify]: Simplify 0 into 0
13.364 * [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
13.365 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.365 * [backup-simplify]: Simplify 0 into 0
13.366 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
13.366 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
13.366 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
13.366 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.366 * [taylor]: Taking taylor expansion of -2.0 in n
13.366 * [backup-simplify]: Simplify -2.0 into -2.0
13.366 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.366 * [taylor]: Taking taylor expansion of PI in n
13.366 * [backup-simplify]: Simplify PI into PI
13.367 * [taylor]: Taking taylor expansion of n in n
13.367 * [backup-simplify]: Simplify 0 into 0
13.367 * [backup-simplify]: Simplify 1 into 1
13.367 * [backup-simplify]: Simplify (/ PI 1) into PI
13.367 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.367 * [taylor]: Taking taylor expansion of -2.0 in n
13.367 * [backup-simplify]: Simplify -2.0 into -2.0
13.367 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.367 * [taylor]: Taking taylor expansion of PI in n
13.367 * [backup-simplify]: Simplify PI into PI
13.367 * [taylor]: Taking taylor expansion of n in n
13.367 * [backup-simplify]: Simplify 0 into 0
13.367 * [backup-simplify]: Simplify 1 into 1
13.368 * [backup-simplify]: Simplify (/ PI 1) into PI
13.368 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.369 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.370 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.371 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.371 * [backup-simplify]: Simplify 0 into 0
13.372 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.373 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.373 * [backup-simplify]: Simplify 0 into 0
13.375 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.376 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.376 * [backup-simplify]: Simplify 0 into 0
13.377 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.378 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.378 * [backup-simplify]: Simplify 0 into 0
13.380 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.381 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.381 * [backup-simplify]: Simplify 0 into 0
13.382 * [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
13.384 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.384 * [backup-simplify]: Simplify 0 into 0
13.385 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
13.385 * * * * [progress]: [ 3 / 4 ] generating series at (2)
13.387 * [backup-simplify]: Simplify (* (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)))) into (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k)))
13.387 * [approximate]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in (n k) around 0
13.387 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in k
13.387 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k
13.387 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.387 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.387 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.387 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.387 * [taylor]: Taking taylor expansion of 0.5 in k
13.387 * [backup-simplify]: Simplify 0.5 into 0.5
13.387 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.387 * [taylor]: Taking taylor expansion of 1.0 in k
13.387 * [backup-simplify]: Simplify 1.0 into 1.0
13.387 * [taylor]: Taking taylor expansion of k in k
13.387 * [backup-simplify]: Simplify 0 into 0
13.387 * [backup-simplify]: Simplify 1 into 1
13.387 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.387 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.387 * [taylor]: Taking taylor expansion of 2.0 in k
13.387 * [backup-simplify]: Simplify 2.0 into 2.0
13.387 * [taylor]: Taking taylor expansion of (* n PI) in k
13.387 * [taylor]: Taking taylor expansion of n in k
13.387 * [backup-simplify]: Simplify n into n
13.387 * [taylor]: Taking taylor expansion of PI in k
13.387 * [backup-simplify]: Simplify PI into PI
13.387 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.388 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.388 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.388 * [backup-simplify]: Simplify (- 0) into 0
13.388 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.389 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.389 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.389 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.389 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
13.389 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
13.389 * [taylor]: Taking taylor expansion of 1.0 in k
13.389 * [backup-simplify]: Simplify 1.0 into 1.0
13.390 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.390 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.391 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.391 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.391 * [taylor]: Taking taylor expansion of k in k
13.391 * [backup-simplify]: Simplify 0 into 0
13.391 * [backup-simplify]: Simplify 1 into 1
13.391 * [backup-simplify]: Simplify (/ 1 1) into 1
13.391 * [backup-simplify]: Simplify (sqrt 0) into 0
13.393 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.393 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
13.393 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
13.393 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.393 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.393 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.393 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.393 * [taylor]: Taking taylor expansion of 0.5 in n
13.393 * [backup-simplify]: Simplify 0.5 into 0.5
13.393 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.393 * [taylor]: Taking taylor expansion of 1.0 in n
13.393 * [backup-simplify]: Simplify 1.0 into 1.0
13.393 * [taylor]: Taking taylor expansion of k in n
13.393 * [backup-simplify]: Simplify k into k
13.393 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.393 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.394 * [taylor]: Taking taylor expansion of 2.0 in n
13.394 * [backup-simplify]: Simplify 2.0 into 2.0
13.394 * [taylor]: Taking taylor expansion of (* n PI) in n
13.394 * [taylor]: Taking taylor expansion of n in n
13.394 * [backup-simplify]: Simplify 0 into 0
13.394 * [backup-simplify]: Simplify 1 into 1
13.394 * [taylor]: Taking taylor expansion of PI in n
13.394 * [backup-simplify]: Simplify PI into PI
13.394 * [backup-simplify]: Simplify (* 0 PI) into 0
13.395 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.396 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.398 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.399 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.399 * [backup-simplify]: Simplify (- k) into (- k)
13.399 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.399 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.401 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.401 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
13.402 * [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)))))
13.402 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
13.402 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
13.402 * [taylor]: Taking taylor expansion of 1.0 in n
13.402 * [backup-simplify]: Simplify 1.0 into 1.0
13.402 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.403 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.403 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.403 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.403 * [taylor]: Taking taylor expansion of k in n
13.403 * [backup-simplify]: Simplify k into k
13.403 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.403 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.403 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.403 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.403 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
13.403 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
13.403 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.403 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.403 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.403 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.403 * [taylor]: Taking taylor expansion of 0.5 in n
13.403 * [backup-simplify]: Simplify 0.5 into 0.5
13.403 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.403 * [taylor]: Taking taylor expansion of 1.0 in n
13.403 * [backup-simplify]: Simplify 1.0 into 1.0
13.403 * [taylor]: Taking taylor expansion of k in n
13.403 * [backup-simplify]: Simplify k into k
13.403 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.403 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.403 * [taylor]: Taking taylor expansion of 2.0 in n
13.403 * [backup-simplify]: Simplify 2.0 into 2.0
13.403 * [taylor]: Taking taylor expansion of (* n PI) in n
13.403 * [taylor]: Taking taylor expansion of n in n
13.403 * [backup-simplify]: Simplify 0 into 0
13.403 * [backup-simplify]: Simplify 1 into 1
13.403 * [taylor]: Taking taylor expansion of PI in n
13.403 * [backup-simplify]: Simplify PI into PI
13.404 * [backup-simplify]: Simplify (* 0 PI) into 0
13.404 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.405 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.406 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.407 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.407 * [backup-simplify]: Simplify (- k) into (- k)
13.407 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.407 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.408 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.408 * [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))))
13.409 * [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)))))
13.409 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
13.409 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
13.409 * [taylor]: Taking taylor expansion of 1.0 in n
13.409 * [backup-simplify]: Simplify 1.0 into 1.0
13.409 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.410 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.410 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.410 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.410 * [taylor]: Taking taylor expansion of k in n
13.410 * [backup-simplify]: Simplify k into k
13.410 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.410 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.410 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.411 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.413 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
13.414 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k)))
13.414 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) in k
13.414 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
13.414 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
13.414 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
13.414 * [taylor]: Taking taylor expansion of 1.0 in k
13.414 * [backup-simplify]: Simplify 1.0 into 1.0
13.414 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.415 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.415 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.415 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.415 * [taylor]: Taking taylor expansion of 0.5 in k
13.415 * [backup-simplify]: Simplify 0.5 into 0.5
13.415 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.415 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.415 * [taylor]: Taking taylor expansion of 1.0 in k
13.415 * [backup-simplify]: Simplify 1.0 into 1.0
13.415 * [taylor]: Taking taylor expansion of k in k
13.415 * [backup-simplify]: Simplify 0 into 0
13.415 * [backup-simplify]: Simplify 1 into 1
13.415 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.415 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.415 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.415 * [taylor]: Taking taylor expansion of 2.0 in k
13.415 * [backup-simplify]: Simplify 2.0 into 2.0
13.415 * [taylor]: Taking taylor expansion of PI in k
13.415 * [backup-simplify]: Simplify PI into PI
13.415 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.416 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.416 * [taylor]: Taking taylor expansion of (log n) in k
13.416 * [taylor]: Taking taylor expansion of n in k
13.416 * [backup-simplify]: Simplify n into n
13.416 * [backup-simplify]: Simplify (log n) into (log n)
13.416 * [backup-simplify]: Simplify (- 0) into 0
13.417 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.417 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.418 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.419 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.419 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.419 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.419 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.420 * [taylor]: Taking taylor expansion of k in k
13.420 * [backup-simplify]: Simplify 0 into 0
13.420 * [backup-simplify]: Simplify 1 into 1
13.420 * [backup-simplify]: Simplify (/ 1 1) into 1
13.420 * [backup-simplify]: Simplify (sqrt 0) into 0
13.421 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.422 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.423 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))
13.424 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) 0) into 0
13.424 * [backup-simplify]: Simplify 0 into 0
13.425 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
13.425 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.426 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.427 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.427 * [backup-simplify]: Simplify (- 0) into 0
13.428 * [backup-simplify]: Simplify (+ 0 0) into 0
13.428 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.429 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.430 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.432 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.434 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0
13.436 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
13.436 * [taylor]: Taking taylor expansion of 0 in k
13.436 * [backup-simplify]: Simplify 0 into 0
13.437 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.439 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.440 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.440 * [backup-simplify]: Simplify (+ 0 0) into 0
13.441 * [backup-simplify]: Simplify (- 1) into -1
13.441 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.443 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.445 * [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))))
13.448 * [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))))))
13.449 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
13.454 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))
13.463 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
13.465 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
13.465 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.466 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
13.467 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
13.468 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
13.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.479 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.480 * [backup-simplify]: Simplify (- 0) into 0
13.480 * [backup-simplify]: Simplify (+ 0 0) into 0
13.481 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.482 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.484 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.486 * [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
13.489 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2)))) into 0
13.491 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
13.491 * [taylor]: Taking taylor expansion of 0 in k
13.491 * [backup-simplify]: Simplify 0 into 0
13.491 * [backup-simplify]: Simplify 0 into 0
13.492 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.495 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.496 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.500 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.502 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.502 * [backup-simplify]: Simplify (+ 0 0) into 0
13.502 * [backup-simplify]: Simplify (- 0) into 0
13.503 * [backup-simplify]: Simplify (+ 0 0) into 0
13.505 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.508 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.512 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
13.513 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
13.514 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
13.525 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))
13.538 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) 0))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.543 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.543 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.543 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
13.544 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
13.545 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
13.546 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.546 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.550 * [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
13.550 * [backup-simplify]: Simplify (- 0) into 0
13.550 * [backup-simplify]: Simplify (+ 0 0) into 0
13.551 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
13.552 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.553 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.554 * [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
13.556 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2))))) into 0
13.558 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
13.558 * [taylor]: Taking taylor expansion of 0 in k
13.558 * [backup-simplify]: Simplify 0 into 0
13.558 * [backup-simplify]: Simplify 0 into 0
13.558 * [backup-simplify]: Simplify 0 into 0
13.559 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.561 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.563 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.569 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.572 * [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
13.572 * [backup-simplify]: Simplify (+ 0 0) into 0
13.573 * [backup-simplify]: Simplify (- 0) into 0
13.573 * [backup-simplify]: Simplify (+ 0 0) into 0
13.574 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.576 * [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
13.580 * [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 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.581 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
13.582 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
13.596 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.623 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (+ (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) +nan.0) (* (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 0)))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
13.640 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
13.660 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
13.661 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k))
13.662 * [approximate]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in (n k) around 0
13.662 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in k
13.662 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
13.662 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
13.662 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
13.662 * [taylor]: Taking taylor expansion of 1.0 in k
13.662 * [backup-simplify]: Simplify 1.0 into 1.0
13.662 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.663 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.663 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.663 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.663 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.663 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.663 * [taylor]: Taking taylor expansion of 0.5 in k
13.663 * [backup-simplify]: Simplify 0.5 into 0.5
13.663 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.663 * [taylor]: Taking taylor expansion of 1.0 in k
13.663 * [backup-simplify]: Simplify 1.0 into 1.0
13.663 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.663 * [taylor]: Taking taylor expansion of k in k
13.663 * [backup-simplify]: Simplify 0 into 0
13.663 * [backup-simplify]: Simplify 1 into 1
13.664 * [backup-simplify]: Simplify (/ 1 1) into 1
13.664 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.664 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.664 * [taylor]: Taking taylor expansion of 2.0 in k
13.664 * [backup-simplify]: Simplify 2.0 into 2.0
13.664 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.664 * [taylor]: Taking taylor expansion of PI in k
13.664 * [backup-simplify]: Simplify PI into PI
13.664 * [taylor]: Taking taylor expansion of n in k
13.664 * [backup-simplify]: Simplify n into n
13.664 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.664 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.664 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.665 * [backup-simplify]: Simplify (- 1) into -1
13.665 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.666 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.666 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.666 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
13.666 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.666 * [taylor]: Taking taylor expansion of k in k
13.666 * [backup-simplify]: Simplify 0 into 0
13.666 * [backup-simplify]: Simplify 1 into 1
13.666 * [backup-simplify]: Simplify (sqrt 0) into 0
13.668 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.668 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
13.668 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.668 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
13.668 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
13.668 * [taylor]: Taking taylor expansion of 1.0 in n
13.668 * [backup-simplify]: Simplify 1.0 into 1.0
13.669 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.669 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.669 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.669 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.669 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.670 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.670 * [taylor]: Taking taylor expansion of 0.5 in n
13.670 * [backup-simplify]: Simplify 0.5 into 0.5
13.670 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.670 * [taylor]: Taking taylor expansion of 1.0 in n
13.670 * [backup-simplify]: Simplify 1.0 into 1.0
13.670 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.670 * [taylor]: Taking taylor expansion of k in n
13.670 * [backup-simplify]: Simplify k into k
13.670 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.670 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.670 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.670 * [taylor]: Taking taylor expansion of 2.0 in n
13.670 * [backup-simplify]: Simplify 2.0 into 2.0
13.670 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.670 * [taylor]: Taking taylor expansion of PI in n
13.670 * [backup-simplify]: Simplify PI into PI
13.670 * [taylor]: Taking taylor expansion of n in n
13.670 * [backup-simplify]: Simplify 0 into 0
13.670 * [backup-simplify]: Simplify 1 into 1
13.671 * [backup-simplify]: Simplify (/ PI 1) into PI
13.671 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.672 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.672 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.672 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.673 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.674 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.675 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
13.677 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
13.677 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.677 * [taylor]: Taking taylor expansion of k in n
13.677 * [backup-simplify]: Simplify k into k
13.677 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.677 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.677 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
13.677 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.677 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
13.677 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
13.677 * [taylor]: Taking taylor expansion of 1.0 in n
13.677 * [backup-simplify]: Simplify 1.0 into 1.0
13.678 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.678 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.678 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.678 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.678 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.678 * [taylor]: Taking taylor expansion of 0.5 in n
13.678 * [backup-simplify]: Simplify 0.5 into 0.5
13.679 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.679 * [taylor]: Taking taylor expansion of 1.0 in n
13.679 * [backup-simplify]: Simplify 1.0 into 1.0
13.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.679 * [taylor]: Taking taylor expansion of k in n
13.679 * [backup-simplify]: Simplify k into k
13.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.679 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.679 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.679 * [taylor]: Taking taylor expansion of 2.0 in n
13.679 * [backup-simplify]: Simplify 2.0 into 2.0
13.679 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.679 * [taylor]: Taking taylor expansion of PI in n
13.679 * [backup-simplify]: Simplify PI into PI
13.679 * [taylor]: Taking taylor expansion of n in n
13.679 * [backup-simplify]: Simplify 0 into 0
13.679 * [backup-simplify]: Simplify 1 into 1
13.680 * [backup-simplify]: Simplify (/ PI 1) into PI
13.680 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.681 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.681 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.681 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.681 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.683 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.685 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
13.686 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
13.686 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.686 * [taylor]: Taking taylor expansion of k in n
13.686 * [backup-simplify]: Simplify k into k
13.686 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.686 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.688 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.690 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
13.692 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k))
13.692 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) in k
13.693 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) in k
13.693 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
13.693 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
13.693 * [taylor]: Taking taylor expansion of 1.0 in k
13.693 * [backup-simplify]: Simplify 1.0 into 1.0
13.693 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.694 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.694 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
13.694 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
13.694 * [taylor]: Taking taylor expansion of 0.5 in k
13.694 * [backup-simplify]: Simplify 0.5 into 0.5
13.694 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
13.694 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.694 * [taylor]: Taking taylor expansion of 1.0 in k
13.694 * [backup-simplify]: Simplify 1.0 into 1.0
13.694 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.694 * [taylor]: Taking taylor expansion of k in k
13.694 * [backup-simplify]: Simplify 0 into 0
13.694 * [backup-simplify]: Simplify 1 into 1
13.695 * [backup-simplify]: Simplify (/ 1 1) into 1
13.695 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.695 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.695 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.695 * [taylor]: Taking taylor expansion of 2.0 in k
13.695 * [backup-simplify]: Simplify 2.0 into 2.0
13.695 * [taylor]: Taking taylor expansion of PI in k
13.695 * [backup-simplify]: Simplify PI into PI
13.695 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.700 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.700 * [taylor]: Taking taylor expansion of (log n) in k
13.700 * [taylor]: Taking taylor expansion of n in k
13.700 * [backup-simplify]: Simplify n into n
13.700 * [backup-simplify]: Simplify (log n) into (log n)
13.701 * [backup-simplify]: Simplify (- 1) into -1
13.701 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.702 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.703 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.704 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.705 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.706 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
13.706 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.706 * [taylor]: Taking taylor expansion of k in k
13.706 * [backup-simplify]: Simplify 0 into 0
13.706 * [backup-simplify]: Simplify 1 into 1
13.707 * [backup-simplify]: Simplify (sqrt 0) into 0
13.708 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.710 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.712 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
13.714 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) into 0
13.714 * [backup-simplify]: Simplify 0 into 0
13.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.718 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.718 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.719 * [backup-simplify]: Simplify (- 0) into 0
13.719 * [backup-simplify]: Simplify (+ 0 0) into 0
13.720 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.722 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.725 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.725 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
13.727 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
13.730 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt k))) into 0
13.730 * [taylor]: Taking taylor expansion of 0 in k
13.730 * [backup-simplify]: Simplify 0 into 0
13.730 * [backup-simplify]: Simplify 0 into 0
13.731 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
13.733 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
13.736 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
13.738 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
13.739 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
13.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.743 * [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
13.743 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.743 * [backup-simplify]: Simplify (- 0) into 0
13.744 * [backup-simplify]: Simplify (+ 0 0) into 0
13.744 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.746 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.748 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.748 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
13.749 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
13.750 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
13.752 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
13.752 * [taylor]: Taking taylor expansion of 0 in k
13.752 * [backup-simplify]: Simplify 0 into 0
13.752 * [backup-simplify]: Simplify 0 into 0
13.752 * [backup-simplify]: Simplify 0 into 0
13.754 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.755 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
13.755 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
13.757 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
13.758 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
13.760 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
13.760 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
13.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.762 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.765 * [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
13.765 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.765 * [backup-simplify]: Simplify (- 0) into 0
13.766 * [backup-simplify]: Simplify (+ 0 0) into 0
13.767 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.767 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.769 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.770 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 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
13.771 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
13.772 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
13.773 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
13.775 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
13.775 * [taylor]: Taking taylor expansion of 0 in k
13.775 * [backup-simplify]: Simplify 0 into 0
13.775 * [backup-simplify]: Simplify 0 into 0
13.775 * [backup-simplify]: Simplify 0 into 0
13.775 * [backup-simplify]: Simplify 0 into 0
13.778 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.778 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
13.779 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
13.781 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
13.783 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
13.784 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
13.789 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
13.790 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))))) into (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
13.791 * [approximate]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in (n k) around 0
13.791 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
13.791 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
13.791 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
13.791 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
13.791 * [taylor]: Taking taylor expansion of 1.0 in k
13.791 * [backup-simplify]: Simplify 1.0 into 1.0
13.791 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.791 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.791 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.791 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.791 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.791 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.791 * [taylor]: Taking taylor expansion of 0.5 in k
13.791 * [backup-simplify]: Simplify 0.5 into 0.5
13.791 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.792 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.792 * [taylor]: Taking taylor expansion of k in k
13.792 * [backup-simplify]: Simplify 0 into 0
13.792 * [backup-simplify]: Simplify 1 into 1
13.792 * [backup-simplify]: Simplify (/ 1 1) into 1
13.792 * [taylor]: Taking taylor expansion of 1.0 in k
13.792 * [backup-simplify]: Simplify 1.0 into 1.0
13.792 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.792 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.792 * [taylor]: Taking taylor expansion of -2.0 in k
13.792 * [backup-simplify]: Simplify -2.0 into -2.0
13.792 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.792 * [taylor]: Taking taylor expansion of PI in k
13.792 * [backup-simplify]: Simplify PI into PI
13.792 * [taylor]: Taking taylor expansion of n in k
13.792 * [backup-simplify]: Simplify n into n
13.792 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.792 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.792 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.792 * [backup-simplify]: Simplify (+ 1 0) into 1
13.793 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.793 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.793 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
13.793 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.793 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.793 * [taylor]: Taking taylor expansion of -1 in k
13.793 * [backup-simplify]: Simplify -1 into -1
13.793 * [taylor]: Taking taylor expansion of k in k
13.793 * [backup-simplify]: Simplify 0 into 0
13.793 * [backup-simplify]: Simplify 1 into 1
13.793 * [backup-simplify]: Simplify (/ -1 1) into -1
13.794 * [backup-simplify]: Simplify (sqrt 0) into 0
13.795 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.795 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.796 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
13.797 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
13.797 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
13.797 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
13.797 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
13.797 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
13.797 * [taylor]: Taking taylor expansion of 1.0 in n
13.797 * [backup-simplify]: Simplify 1.0 into 1.0
13.797 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.798 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.798 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.798 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.798 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.798 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.798 * [taylor]: Taking taylor expansion of 0.5 in n
13.798 * [backup-simplify]: Simplify 0.5 into 0.5
13.798 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.798 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.798 * [taylor]: Taking taylor expansion of k in n
13.798 * [backup-simplify]: Simplify k into k
13.798 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.798 * [taylor]: Taking taylor expansion of 1.0 in n
13.798 * [backup-simplify]: Simplify 1.0 into 1.0
13.798 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.798 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.798 * [taylor]: Taking taylor expansion of -2.0 in n
13.798 * [backup-simplify]: Simplify -2.0 into -2.0
13.798 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.798 * [taylor]: Taking taylor expansion of PI in n
13.798 * [backup-simplify]: Simplify PI into PI
13.798 * [taylor]: Taking taylor expansion of n in n
13.798 * [backup-simplify]: Simplify 0 into 0
13.798 * [backup-simplify]: Simplify 1 into 1
13.798 * [backup-simplify]: Simplify (/ PI 1) into PI
13.799 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.799 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.800 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.800 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.800 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.801 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
13.802 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
13.802 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.802 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.802 * [taylor]: Taking taylor expansion of -1 in n
13.802 * [backup-simplify]: Simplify -1 into -1
13.802 * [taylor]: Taking taylor expansion of k in n
13.802 * [backup-simplify]: Simplify k into k
13.802 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.802 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.802 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.802 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.803 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.807 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
13.809 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
13.809 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
13.809 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
13.809 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
13.809 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
13.809 * [taylor]: Taking taylor expansion of 1.0 in n
13.809 * [backup-simplify]: Simplify 1.0 into 1.0
13.809 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.809 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.809 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.809 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.809 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.809 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.809 * [taylor]: Taking taylor expansion of 0.5 in n
13.809 * [backup-simplify]: Simplify 0.5 into 0.5
13.810 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.810 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.810 * [taylor]: Taking taylor expansion of k in n
13.810 * [backup-simplify]: Simplify k into k
13.810 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.810 * [taylor]: Taking taylor expansion of 1.0 in n
13.810 * [backup-simplify]: Simplify 1.0 into 1.0
13.810 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.810 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.810 * [taylor]: Taking taylor expansion of -2.0 in n
13.810 * [backup-simplify]: Simplify -2.0 into -2.0
13.810 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.810 * [taylor]: Taking taylor expansion of PI in n
13.810 * [backup-simplify]: Simplify PI into PI
13.810 * [taylor]: Taking taylor expansion of n in n
13.810 * [backup-simplify]: Simplify 0 into 0
13.810 * [backup-simplify]: Simplify 1 into 1
13.810 * [backup-simplify]: Simplify (/ PI 1) into PI
13.810 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.811 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.811 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.811 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.812 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.813 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
13.814 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
13.814 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.814 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.814 * [taylor]: Taking taylor expansion of -1 in n
13.814 * [backup-simplify]: Simplify -1 into -1
13.814 * [taylor]: Taking taylor expansion of k in n
13.814 * [backup-simplify]: Simplify k into k
13.814 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.814 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.814 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.814 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.815 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.816 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
13.817 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
13.818 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) in k
13.818 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) in k
13.818 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
13.818 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
13.818 * [taylor]: Taking taylor expansion of 1.0 in k
13.818 * [backup-simplify]: Simplify 1.0 into 1.0
13.818 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
13.818 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
13.818 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
13.818 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
13.818 * [taylor]: Taking taylor expansion of 0.5 in k
13.818 * [backup-simplify]: Simplify 0.5 into 0.5
13.818 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
13.819 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
13.819 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
13.819 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
13.819 * [taylor]: Taking taylor expansion of -2.0 in k
13.819 * [backup-simplify]: Simplify -2.0 into -2.0
13.819 * [taylor]: Taking taylor expansion of PI in k
13.819 * [backup-simplify]: Simplify PI into PI
13.819 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.820 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.820 * [taylor]: Taking taylor expansion of (log n) in k
13.820 * [taylor]: Taking taylor expansion of n in k
13.820 * [backup-simplify]: Simplify n into n
13.820 * [backup-simplify]: Simplify (log n) into (log n)
13.820 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.820 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.820 * [taylor]: Taking taylor expansion of k in k
13.820 * [backup-simplify]: Simplify 0 into 0
13.820 * [backup-simplify]: Simplify 1 into 1
13.820 * [backup-simplify]: Simplify (/ 1 1) into 1
13.820 * [taylor]: Taking taylor expansion of 1.0 in k
13.820 * [backup-simplify]: Simplify 1.0 into 1.0
13.820 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.821 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
13.821 * [backup-simplify]: Simplify (+ 1 0) into 1
13.822 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
13.822 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
13.823 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
13.823 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.823 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.823 * [taylor]: Taking taylor expansion of -1 in k
13.823 * [backup-simplify]: Simplify -1 into -1
13.823 * [taylor]: Taking taylor expansion of k in k
13.823 * [backup-simplify]: Simplify 0 into 0
13.823 * [backup-simplify]: Simplify 1 into 1
13.824 * [backup-simplify]: Simplify (/ -1 1) into -1
13.824 * [backup-simplify]: Simplify (sqrt 0) into 0
13.825 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.825 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
13.827 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
13.828 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.829 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
13.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.831 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.832 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
13.832 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.832 * [backup-simplify]: Simplify (+ 0 0) into 0
13.832 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
13.833 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.834 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
13.835 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.836 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
13.837 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
13.838 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
13.838 * [taylor]: Taking taylor expansion of 0 in k
13.838 * [backup-simplify]: Simplify 0 into 0
13.838 * [backup-simplify]: Simplify 0 into 0
13.839 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
13.840 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
13.841 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.842 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.845 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
13.846 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
13.847 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.847 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.849 * [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
13.849 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.850 * [backup-simplify]: Simplify (+ 0 0) into 0
13.850 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
13.851 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.852 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
13.854 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.855 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
13.855 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
13.857 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
13.857 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.857 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
13.859 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
13.859 * [taylor]: Taking taylor expansion of 0 in k
13.859 * [backup-simplify]: Simplify 0 into 0
13.859 * [backup-simplify]: Simplify 0 into 0
13.859 * [backup-simplify]: Simplify 0 into 0
13.860 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
13.860 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
13.862 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
13.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.865 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.868 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
13.870 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
13.875 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
13.875 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
13.876 * [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))))
13.876 * [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
13.876 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
13.876 * [taylor]: Taking taylor expansion of 1.0 in k
13.876 * [backup-simplify]: Simplify 1.0 into 1.0
13.876 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
13.876 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.876 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.876 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.876 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.876 * [taylor]: Taking taylor expansion of 0.5 in k
13.876 * [backup-simplify]: Simplify 0.5 into 0.5
13.876 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.876 * [taylor]: Taking taylor expansion of 1.0 in k
13.876 * [backup-simplify]: Simplify 1.0 into 1.0
13.876 * [taylor]: Taking taylor expansion of k in k
13.876 * [backup-simplify]: Simplify 0 into 0
13.876 * [backup-simplify]: Simplify 1 into 1
13.876 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.876 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.876 * [taylor]: Taking taylor expansion of 2.0 in k
13.876 * [backup-simplify]: Simplify 2.0 into 2.0
13.876 * [taylor]: Taking taylor expansion of (* n PI) in k
13.876 * [taylor]: Taking taylor expansion of n in k
13.876 * [backup-simplify]: Simplify n into n
13.876 * [taylor]: Taking taylor expansion of PI in k
13.876 * [backup-simplify]: Simplify PI into PI
13.876 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.876 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.876 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.876 * [backup-simplify]: Simplify (- 0) into 0
13.877 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.877 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.877 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.877 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.877 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.878 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.878 * [taylor]: Taking taylor expansion of k in k
13.878 * [backup-simplify]: Simplify 0 into 0
13.878 * [backup-simplify]: Simplify 1 into 1
13.878 * [backup-simplify]: Simplify (/ 1 1) into 1
13.878 * [backup-simplify]: Simplify (sqrt 0) into 0
13.879 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.879 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.879 * [taylor]: Taking taylor expansion of 1.0 in n
13.879 * [backup-simplify]: Simplify 1.0 into 1.0
13.879 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.879 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.879 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.879 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.879 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.879 * [taylor]: Taking taylor expansion of 0.5 in n
13.879 * [backup-simplify]: Simplify 0.5 into 0.5
13.879 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.879 * [taylor]: Taking taylor expansion of 1.0 in n
13.879 * [backup-simplify]: Simplify 1.0 into 1.0
13.879 * [taylor]: Taking taylor expansion of k in n
13.879 * [backup-simplify]: Simplify k into k
13.879 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.879 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.879 * [taylor]: Taking taylor expansion of 2.0 in n
13.879 * [backup-simplify]: Simplify 2.0 into 2.0
13.879 * [taylor]: Taking taylor expansion of (* n PI) in n
13.879 * [taylor]: Taking taylor expansion of n in n
13.879 * [backup-simplify]: Simplify 0 into 0
13.879 * [backup-simplify]: Simplify 1 into 1
13.879 * [taylor]: Taking taylor expansion of PI in n
13.879 * [backup-simplify]: Simplify PI into PI
13.880 * [backup-simplify]: Simplify (* 0 PI) into 0
13.880 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.881 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.882 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.883 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.883 * [backup-simplify]: Simplify (- k) into (- k)
13.883 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.883 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.884 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.884 * [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))))
13.885 * [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)))))
13.885 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.885 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.885 * [taylor]: Taking taylor expansion of k in n
13.885 * [backup-simplify]: Simplify k into k
13.885 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.885 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.886 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.886 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.886 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.886 * [taylor]: Taking taylor expansion of 1.0 in n
13.886 * [backup-simplify]: Simplify 1.0 into 1.0
13.886 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.886 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.886 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.886 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.886 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.886 * [taylor]: Taking taylor expansion of 0.5 in n
13.886 * [backup-simplify]: Simplify 0.5 into 0.5
13.886 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.886 * [taylor]: Taking taylor expansion of 1.0 in n
13.886 * [backup-simplify]: Simplify 1.0 into 1.0
13.886 * [taylor]: Taking taylor expansion of k in n
13.886 * [backup-simplify]: Simplify k into k
13.886 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.886 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.886 * [taylor]: Taking taylor expansion of 2.0 in n
13.886 * [backup-simplify]: Simplify 2.0 into 2.0
13.886 * [taylor]: Taking taylor expansion of (* n PI) in n
13.886 * [taylor]: Taking taylor expansion of n in n
13.886 * [backup-simplify]: Simplify 0 into 0
13.886 * [backup-simplify]: Simplify 1 into 1
13.886 * [taylor]: Taking taylor expansion of PI in n
13.886 * [backup-simplify]: Simplify PI into PI
13.886 * [backup-simplify]: Simplify (* 0 PI) into 0
13.887 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.888 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.889 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.889 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.889 * [backup-simplify]: Simplify (- k) into (- k)
13.889 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.889 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 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 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
13.892 * [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)))))
13.892 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.892 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.892 * [taylor]: Taking taylor expansion of k in n
13.892 * [backup-simplify]: Simplify k into k
13.892 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.892 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.892 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.892 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.893 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
13.894 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
13.894 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
13.894 * [taylor]: Taking taylor expansion of 1.0 in k
13.894 * [backup-simplify]: Simplify 1.0 into 1.0
13.894 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
13.894 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.894 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.894 * [taylor]: Taking taylor expansion of 0.5 in k
13.894 * [backup-simplify]: Simplify 0.5 into 0.5
13.894 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.894 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.894 * [taylor]: Taking taylor expansion of 1.0 in k
13.894 * [backup-simplify]: Simplify 1.0 into 1.0
13.894 * [taylor]: Taking taylor expansion of k in k
13.894 * [backup-simplify]: Simplify 0 into 0
13.894 * [backup-simplify]: Simplify 1 into 1
13.894 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.894 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.894 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.894 * [taylor]: Taking taylor expansion of 2.0 in k
13.894 * [backup-simplify]: Simplify 2.0 into 2.0
13.894 * [taylor]: Taking taylor expansion of PI in k
13.894 * [backup-simplify]: Simplify PI into PI
13.895 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.895 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.895 * [taylor]: Taking taylor expansion of (log n) in k
13.895 * [taylor]: Taking taylor expansion of n in k
13.896 * [backup-simplify]: Simplify n into n
13.896 * [backup-simplify]: Simplify (log n) into (log n)
13.896 * [backup-simplify]: Simplify (- 0) into 0
13.899 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.899 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.900 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.901 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.902 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.902 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.902 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.902 * [taylor]: Taking taylor expansion of k in k
13.902 * [backup-simplify]: Simplify 0 into 0
13.902 * [backup-simplify]: Simplify 1 into 1
13.902 * [backup-simplify]: Simplify (/ 1 1) into 1
13.902 * [backup-simplify]: Simplify (sqrt 0) into 0
13.903 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.904 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
13.904 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.904 * [backup-simplify]: Simplify 0 into 0
13.905 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.905 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.907 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.907 * [backup-simplify]: Simplify (- 0) into 0
13.907 * [backup-simplify]: Simplify (+ 0 0) into 0
13.907 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.908 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.909 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.910 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.911 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
13.912 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
13.912 * [taylor]: Taking taylor expansion of 0 in k
13.912 * [backup-simplify]: Simplify 0 into 0
13.913 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.914 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.914 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.914 * [backup-simplify]: Simplify (+ 0 0) into 0
13.915 * [backup-simplify]: Simplify (- 1) into -1
13.915 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.916 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.917 * [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))))
13.919 * [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))))))
13.922 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (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)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.923 * [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))))))
13.924 * [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))))))
13.924 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.924 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
13.925 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.926 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.928 * [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
13.928 * [backup-simplify]: Simplify (- 0) into 0
13.928 * [backup-simplify]: Simplify (+ 0 0) into 0
13.929 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.930 * [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 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.932 * [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
13.933 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
13.934 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
13.934 * [taylor]: Taking taylor expansion of 0 in k
13.934 * [backup-simplify]: Simplify 0 into 0
13.935 * [backup-simplify]: Simplify 0 into 0
13.935 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.937 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.937 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.939 * [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
13.940 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.941 * [backup-simplify]: Simplify (+ 0 0) into 0
13.941 * [backup-simplify]: Simplify (- 0) into 0
13.941 * [backup-simplify]: Simplify (+ 0 0) into 0
13.942 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.944 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.947 * [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 n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
13.953 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (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)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.957 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 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)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.960 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
13.960 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.960 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
13.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.965 * [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
13.966 * [backup-simplify]: Simplify (- 0) into 0
13.966 * [backup-simplify]: Simplify (+ 0 0) into 0
13.967 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
13.968 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.969 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.971 * [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
13.972 * [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
13.973 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
13.973 * [taylor]: Taking taylor expansion of 0 in k
13.973 * [backup-simplify]: Simplify 0 into 0
13.974 * [backup-simplify]: Simplify 0 into 0
13.974 * [backup-simplify]: Simplify 0 into 0
13.974 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.977 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.984 * [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
13.987 * [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
13.987 * [backup-simplify]: Simplify (+ 0 0) into 0
13.988 * [backup-simplify]: Simplify (- 0) into 0
13.992 * [backup-simplify]: Simplify (+ 0 0) into 0
13.994 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.998 * [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
14.006 * [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 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
14.025 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (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)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
14.046 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 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)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +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)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
14.060 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +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)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (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)))) (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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
14.082 * [backup-simplify]: Simplify (+ (* (- (+ (* +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))))) (- (+ (* +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 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +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)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (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)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
14.083 * [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 (- 1.0 (/ 1 k)))) (sqrt k)))
14.083 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
14.083 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
14.083 * [taylor]: Taking taylor expansion of 1.0 in k
14.083 * [backup-simplify]: Simplify 1.0 into 1.0
14.083 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
14.083 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
14.083 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
14.083 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
14.083 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
14.083 * [taylor]: Taking taylor expansion of 0.5 in k
14.083 * [backup-simplify]: Simplify 0.5 into 0.5
14.083 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
14.083 * [taylor]: Taking taylor expansion of 1.0 in k
14.083 * [backup-simplify]: Simplify 1.0 into 1.0
14.084 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.084 * [taylor]: Taking taylor expansion of k in k
14.084 * [backup-simplify]: Simplify 0 into 0
14.084 * [backup-simplify]: Simplify 1 into 1
14.084 * [backup-simplify]: Simplify (/ 1 1) into 1
14.084 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
14.084 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
14.084 * [taylor]: Taking taylor expansion of 2.0 in k
14.084 * [backup-simplify]: Simplify 2.0 into 2.0
14.084 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.084 * [taylor]: Taking taylor expansion of PI in k
14.084 * [backup-simplify]: Simplify PI into PI
14.084 * [taylor]: Taking taylor expansion of n in k
14.084 * [backup-simplify]: Simplify n into n
14.084 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.084 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
14.085 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
14.085 * [backup-simplify]: Simplify (- 1) into -1
14.085 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.086 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
14.086 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
14.086 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
14.086 * [taylor]: Taking taylor expansion of (sqrt k) in k
14.086 * [taylor]: Taking taylor expansion of k in k
14.086 * [backup-simplify]: Simplify 0 into 0
14.086 * [backup-simplify]: Simplify 1 into 1
14.087 * [backup-simplify]: Simplify (sqrt 0) into 0
14.088 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.088 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
14.088 * [taylor]: Taking taylor expansion of 1.0 in n
14.088 * [backup-simplify]: Simplify 1.0 into 1.0
14.088 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
14.088 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
14.088 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
14.088 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
14.088 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
14.089 * [taylor]: Taking taylor expansion of 0.5 in n
14.089 * [backup-simplify]: Simplify 0.5 into 0.5
14.089 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
14.089 * [taylor]: Taking taylor expansion of 1.0 in n
14.089 * [backup-simplify]: Simplify 1.0 into 1.0
14.089 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.089 * [taylor]: Taking taylor expansion of k in n
14.089 * [backup-simplify]: Simplify k into k
14.089 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.089 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
14.089 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
14.089 * [taylor]: Taking taylor expansion of 2.0 in n
14.089 * [backup-simplify]: Simplify 2.0 into 2.0
14.089 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.089 * [taylor]: Taking taylor expansion of PI in n
14.089 * [backup-simplify]: Simplify PI into PI
14.089 * [taylor]: Taking taylor expansion of n in n
14.089 * [backup-simplify]: Simplify 0 into 0
14.089 * [backup-simplify]: Simplify 1 into 1
14.090 * [backup-simplify]: Simplify (/ PI 1) into PI
14.090 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.091 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.091 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.091 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
14.091 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
14.093 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.093 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
14.094 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
14.094 * [taylor]: Taking taylor expansion of (sqrt k) in n
14.094 * [taylor]: Taking taylor expansion of k in n
14.094 * [backup-simplify]: Simplify k into k
14.094 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
14.094 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
14.094 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
14.094 * [taylor]: Taking taylor expansion of 1.0 in n
14.094 * [backup-simplify]: Simplify 1.0 into 1.0
14.094 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
14.094 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
14.094 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
14.094 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
14.094 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
14.094 * [taylor]: Taking taylor expansion of 0.5 in n
14.094 * [backup-simplify]: Simplify 0.5 into 0.5
14.095 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
14.095 * [taylor]: Taking taylor expansion of 1.0 in n
14.095 * [backup-simplify]: Simplify 1.0 into 1.0
14.095 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.095 * [taylor]: Taking taylor expansion of k in n
14.095 * [backup-simplify]: Simplify k into k
14.095 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.095 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
14.095 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
14.095 * [taylor]: Taking taylor expansion of 2.0 in n
14.095 * [backup-simplify]: Simplify 2.0 into 2.0
14.095 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.095 * [taylor]: Taking taylor expansion of PI in n
14.095 * [backup-simplify]: Simplify PI into PI
14.095 * [taylor]: Taking taylor expansion of n in n
14.095 * [backup-simplify]: Simplify 0 into 0
14.095 * [backup-simplify]: Simplify 1 into 1
14.095 * [backup-simplify]: Simplify (/ PI 1) into PI
14.095 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.096 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.096 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.096 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
14.096 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
14.097 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.098 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
14.099 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
14.099 * [taylor]: Taking taylor expansion of (sqrt k) in n
14.099 * [taylor]: Taking taylor expansion of k in n
14.099 * [backup-simplify]: Simplify k into k
14.099 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
14.099 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
14.100 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
14.100 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
14.100 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
14.101 * [taylor]: Taking taylor expansion of 1.0 in k
14.101 * [backup-simplify]: Simplify 1.0 into 1.0
14.101 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
14.101 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
14.101 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
14.101 * [taylor]: Taking taylor expansion of 0.5 in k
14.101 * [backup-simplify]: Simplify 0.5 into 0.5
14.101 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
14.101 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
14.101 * [taylor]: Taking taylor expansion of 1.0 in k
14.101 * [backup-simplify]: Simplify 1.0 into 1.0
14.101 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.101 * [taylor]: Taking taylor expansion of k in k
14.101 * [backup-simplify]: Simplify 0 into 0
14.101 * [backup-simplify]: Simplify 1 into 1
14.101 * [backup-simplify]: Simplify (/ 1 1) into 1
14.101 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
14.101 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
14.101 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
14.101 * [taylor]: Taking taylor expansion of 2.0 in k
14.101 * [backup-simplify]: Simplify 2.0 into 2.0
14.101 * [taylor]: Taking taylor expansion of PI in k
14.101 * [backup-simplify]: Simplify PI into PI
14.101 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.102 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.102 * [taylor]: Taking taylor expansion of (log n) in k
14.102 * [taylor]: Taking taylor expansion of n in k
14.102 * [backup-simplify]: Simplify n into n
14.102 * [backup-simplify]: Simplify (log n) into (log n)
14.102 * [backup-simplify]: Simplify (- 1) into -1
14.103 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.103 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.103 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
14.104 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
14.105 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
14.105 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
14.106 * [taylor]: Taking taylor expansion of (sqrt k) in k
14.106 * [taylor]: Taking taylor expansion of k in k
14.106 * [backup-simplify]: Simplify 0 into 0
14.106 * [backup-simplify]: Simplify 1 into 1
14.106 * [backup-simplify]: Simplify (sqrt 0) into 0
14.107 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.107 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
14.108 * [backup-simplify]: Simplify (* 1.0 0) into 0
14.108 * [backup-simplify]: Simplify 0 into 0
14.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.109 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
14.110 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
14.110 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.110 * [backup-simplify]: Simplify (- 0) into 0
14.111 * [backup-simplify]: Simplify (+ 0 0) into 0
14.111 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
14.112 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.112 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
14.114 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.114 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
14.115 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
14.116 * [taylor]: Taking taylor expansion of 0 in k
14.116 * [backup-simplify]: Simplify 0 into 0
14.116 * [backup-simplify]: Simplify 0 into 0
14.117 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.118 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.119 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.119 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
14.122 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.123 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.126 * [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
14.126 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.127 * [backup-simplify]: Simplify (- 0) into 0
14.127 * [backup-simplify]: Simplify (+ 0 0) into 0
14.128 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
14.130 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.131 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
14.134 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.136 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
14.138 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
14.138 * [taylor]: Taking taylor expansion of 0 in k
14.138 * [backup-simplify]: Simplify 0 into 0
14.138 * [backup-simplify]: Simplify 0 into 0
14.138 * [backup-simplify]: Simplify 0 into 0
14.141 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.143 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.146 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.147 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.148 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
14.150 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.151 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.157 * [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
14.157 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.158 * [backup-simplify]: Simplify (- 0) into 0
14.158 * [backup-simplify]: Simplify (+ 0 0) into 0
14.159 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
14.161 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.162 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
14.165 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 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
14.168 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
14.170 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
14.170 * [taylor]: Taking taylor expansion of 0 in k
14.170 * [backup-simplify]: Simplify 0 into 0
14.170 * [backup-simplify]: Simplify 0 into 0
14.170 * [backup-simplify]: Simplify 0 into 0
14.170 * [backup-simplify]: Simplify 0 into 0
14.174 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.177 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.181 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.182 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
14.187 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +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)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
14.188 * [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))))
14.188 * [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
14.188 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
14.188 * [taylor]: Taking taylor expansion of 1.0 in k
14.188 * [backup-simplify]: Simplify 1.0 into 1.0
14.188 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
14.188 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
14.188 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
14.188 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
14.188 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
14.188 * [taylor]: Taking taylor expansion of 0.5 in k
14.188 * [backup-simplify]: Simplify 0.5 into 0.5
14.188 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
14.188 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.188 * [taylor]: Taking taylor expansion of k in k
14.188 * [backup-simplify]: Simplify 0 into 0
14.188 * [backup-simplify]: Simplify 1 into 1
14.189 * [backup-simplify]: Simplify (/ 1 1) into 1
14.189 * [taylor]: Taking taylor expansion of 1.0 in k
14.189 * [backup-simplify]: Simplify 1.0 into 1.0
14.189 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
14.189 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
14.189 * [taylor]: Taking taylor expansion of -2.0 in k
14.189 * [backup-simplify]: Simplify -2.0 into -2.0
14.189 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.189 * [taylor]: Taking taylor expansion of PI in k
14.189 * [backup-simplify]: Simplify PI into PI
14.189 * [taylor]: Taking taylor expansion of n in k
14.189 * [backup-simplify]: Simplify n into n
14.189 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.189 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
14.189 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
14.190 * [backup-simplify]: Simplify (+ 1 0) into 1
14.190 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
14.191 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
14.191 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
14.191 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.191 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.191 * [taylor]: Taking taylor expansion of -1 in k
14.191 * [backup-simplify]: Simplify -1 into -1
14.191 * [taylor]: Taking taylor expansion of k in k
14.191 * [backup-simplify]: Simplify 0 into 0
14.191 * [backup-simplify]: Simplify 1 into 1
14.191 * [backup-simplify]: Simplify (/ -1 1) into -1
14.192 * [backup-simplify]: Simplify (sqrt 0) into 0
14.193 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.193 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
14.194 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
14.194 * [taylor]: Taking taylor expansion of 1.0 in n
14.194 * [backup-simplify]: Simplify 1.0 into 1.0
14.194 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
14.194 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
14.194 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
14.194 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
14.194 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
14.194 * [taylor]: Taking taylor expansion of 0.5 in n
14.194 * [backup-simplify]: Simplify 0.5 into 0.5
14.194 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
14.194 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.194 * [taylor]: Taking taylor expansion of k in n
14.194 * [backup-simplify]: Simplify k into k
14.194 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.194 * [taylor]: Taking taylor expansion of 1.0 in n
14.194 * [backup-simplify]: Simplify 1.0 into 1.0
14.194 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
14.194 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
14.194 * [taylor]: Taking taylor expansion of -2.0 in n
14.194 * [backup-simplify]: Simplify -2.0 into -2.0
14.194 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.194 * [taylor]: Taking taylor expansion of PI in n
14.194 * [backup-simplify]: Simplify PI into PI
14.194 * [taylor]: Taking taylor expansion of n in n
14.194 * [backup-simplify]: Simplify 0 into 0
14.194 * [backup-simplify]: Simplify 1 into 1
14.195 * [backup-simplify]: Simplify (/ PI 1) into PI
14.195 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.196 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.196 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
14.197 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
14.198 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.199 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
14.201 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
14.201 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
14.201 * [taylor]: Taking taylor expansion of (/ -1 k) in n
14.201 * [taylor]: Taking taylor expansion of -1 in n
14.201 * [backup-simplify]: Simplify -1 into -1
14.201 * [taylor]: Taking taylor expansion of k in n
14.201 * [backup-simplify]: Simplify k into k
14.201 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
14.201 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
14.201 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
14.201 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
14.203 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
14.203 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
14.203 * [taylor]: Taking taylor expansion of 1.0 in n
14.203 * [backup-simplify]: Simplify 1.0 into 1.0
14.203 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
14.203 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
14.203 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
14.203 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
14.203 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
14.203 * [taylor]: Taking taylor expansion of 0.5 in n
14.203 * [backup-simplify]: Simplify 0.5 into 0.5
14.203 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
14.203 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.203 * [taylor]: Taking taylor expansion of k in n
14.203 * [backup-simplify]: Simplify k into k
14.203 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.203 * [taylor]: Taking taylor expansion of 1.0 in n
14.203 * [backup-simplify]: Simplify 1.0 into 1.0
14.203 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
14.203 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
14.203 * [taylor]: Taking taylor expansion of -2.0 in n
14.203 * [backup-simplify]: Simplify -2.0 into -2.0
14.203 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.203 * [taylor]: Taking taylor expansion of PI in n
14.203 * [backup-simplify]: Simplify PI into PI
14.203 * [taylor]: Taking taylor expansion of n in n
14.203 * [backup-simplify]: Simplify 0 into 0
14.203 * [backup-simplify]: Simplify 1 into 1
14.204 * [backup-simplify]: Simplify (/ PI 1) into PI
14.204 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.206 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.206 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
14.206 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
14.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.208 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
14.210 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
14.210 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
14.210 * [taylor]: Taking taylor expansion of (/ -1 k) in n
14.210 * [taylor]: Taking taylor expansion of -1 in n
14.210 * [backup-simplify]: Simplify -1 into -1
14.210 * [taylor]: Taking taylor expansion of k in n
14.210 * [backup-simplify]: Simplify k into k
14.210 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
14.210 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
14.210 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
14.210 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
14.212 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
14.213 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
14.213 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
14.213 * [taylor]: Taking taylor expansion of 1.0 in k
14.213 * [backup-simplify]: Simplify 1.0 into 1.0
14.213 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
14.213 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
14.213 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
14.213 * [taylor]: Taking taylor expansion of 0.5 in k
14.213 * [backup-simplify]: Simplify 0.5 into 0.5
14.213 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
14.214 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
14.214 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
14.214 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
14.214 * [taylor]: Taking taylor expansion of -2.0 in k
14.214 * [backup-simplify]: Simplify -2.0 into -2.0
14.214 * [taylor]: Taking taylor expansion of PI in k
14.214 * [backup-simplify]: Simplify PI into PI
14.214 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.215 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.215 * [taylor]: Taking taylor expansion of (log n) in k
14.215 * [taylor]: Taking taylor expansion of n in k
14.216 * [backup-simplify]: Simplify n into n
14.216 * [backup-simplify]: Simplify (log n) into (log n)
14.216 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
14.216 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.216 * [taylor]: Taking taylor expansion of k in k
14.216 * [backup-simplify]: Simplify 0 into 0
14.216 * [backup-simplify]: Simplify 1 into 1
14.216 * [backup-simplify]: Simplify (/ 1 1) into 1
14.216 * [taylor]: Taking taylor expansion of 1.0 in k
14.216 * [backup-simplify]: Simplify 1.0 into 1.0
14.216 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.218 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
14.218 * [backup-simplify]: Simplify (+ 1 0) into 1
14.219 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
14.220 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
14.221 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
14.221 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.221 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.221 * [taylor]: Taking taylor expansion of -1 in k
14.221 * [backup-simplify]: Simplify -1 into -1
14.221 * [taylor]: Taking taylor expansion of k in k
14.221 * [backup-simplify]: Simplify 0 into 0
14.221 * [backup-simplify]: Simplify 1 into 1
14.222 * [backup-simplify]: Simplify (/ -1 1) into -1
14.222 * [backup-simplify]: Simplify (sqrt 0) into 0
14.223 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.224 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
14.224 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
14.225 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
14.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.226 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
14.228 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
14.228 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.228 * [backup-simplify]: Simplify (+ 0 0) into 0
14.229 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
14.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.230 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
14.231 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
14.232 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
14.233 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
14.233 * [taylor]: Taking taylor expansion of 0 in k
14.234 * [backup-simplify]: Simplify 0 into 0
14.234 * [backup-simplify]: Simplify 0 into 0
14.234 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.236 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.237 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
14.239 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
14.240 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
14.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.241 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.243 * [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
14.243 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.243 * [backup-simplify]: Simplify (+ 0 0) into 0
14.244 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
14.245 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.246 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
14.247 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.248 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.248 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
14.249 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
14.253 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
14.253 * [taylor]: Taking taylor expansion of 0 in k
14.253 * [backup-simplify]: Simplify 0 into 0
14.254 * [backup-simplify]: Simplify 0 into 0
14.254 * [backup-simplify]: Simplify 0 into 0
14.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.257 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.259 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
14.261 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
14.262 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
14.265 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +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))))))))
14.265 * * * [progress]: simplifying candidates
14.268 * [simplify]: Simplifying:
  (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 (* (* 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 (/ (* 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)))))
  (log1p (* (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)))))
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (+ 1 1)
  (+ (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (log (* (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)))))
  (exp (* (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)))))
  (* (* (* (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)))) (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))) (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)))))
  (* (cbrt (* (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))))) (cbrt (* (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))))))
  (cbrt (* (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)))))
  (* (* (* (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)))) (* (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))))) (* (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (* (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)))))
  (sqrt (* (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)))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (* (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (* (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))))) (sqrt (* (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))))))
  (* (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1.0 (* (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)))))
  (* (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1.0 (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)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (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 (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (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 (/ 1.0 (sqrt 1))) (sqrt (/ 1.0 (sqrt 1))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (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 (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (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 (/ 1.0 1)) (sqrt (/ 1.0 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)) (sqrt k))))
  (* (sqrt 1) (sqrt 1))
  (* (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))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* 1 1)
  (* (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))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* 2 1/2)
  (* 2 1)
  (* 2 (/ 1 2))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (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))) (sqrt (* (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))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (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))) (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt 1))
  (* (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 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (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)
  (* (cbrt (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))))
  (* (sqrt (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))))
  (* (sqrt (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))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* 1.0 (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 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* 1.0 (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 (/ (* 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))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (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))))
  (* (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))))
  (* (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 (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (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)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (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)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log 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)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +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))))))))
14.273 * * [simplify]: iteration 0: 346 enodes
14.438 * * [simplify]: iteration 1: 941 enodes
14.785 * * [simplify]: iteration 2: 3199 enodes
15.790 * * [simplify]: iteration complete: 5004 enodes
15.790 * * [simplify]: Extracting #0: cost 66 inf + 0
15.791 * * [simplify]: Extracting #1: cost 487 inf + 3
15.794 * * [simplify]: Extracting #2: cost 907 inf + 4244
15.806 * * [simplify]: Extracting #3: cost 1017 inf + 25722
15.828 * * [simplify]: Extracting #4: cost 857 inf + 105078
15.928 * * [simplify]: Extracting #5: cost 466 inf + 327144
16.086 * * [simplify]: Extracting #6: cost 179 inf + 491059
16.337 * * [simplify]: Extracting #7: cost 84 inf + 574021
16.618 * * [simplify]: Extracting #8: cost 22 inf + 599355
16.922 * * [simplify]: Extracting #9: cost 0 inf + 609671
17.207 * * [simplify]: Extracting #10: cost 0 inf + 609411
17.523 * * [simplify]: Extracting #11: cost 0 inf + 609301
17.842 * * [simplify]: Extracting #12: cost 0 inf + 609286
18.064 * [simplify]: Simplified to:
  (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))
  (* 2.0 PI)
  (* n PI)
  (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))
  (* 2.0 PI)
  (* 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)))))
  1
  1
  2
  1
  1
  (* (/ 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)))))
  2
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (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)))))
  (* (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)))))
  (* (/ 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)))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)
  (sqrt k)
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))))
  (* (cbrt (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))) (cbrt (sqrt (/ 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)))))
  (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)))))
  (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 (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 (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 (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
  (/ 1.0 (/ (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 (sqrt k))
  (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)))))
  (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
  (/ 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)))))
  (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)))))
  (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)))))
  (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
  2
  1
  (* (* (cbrt (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))) (cbrt (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))))))
  (* (fabs (cbrt (/ 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))))) (sqrt (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))))) (sqrt (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (sqrt (/ 1.0 (fabs (cbrt k)))))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt 1.0) (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))))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt 1.0) (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)))))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (sqrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (sqrt (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)))))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (cbrt (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))))) (sqrt (cbrt (/ 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 (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (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))))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))) (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))))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ 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 (sqrt k))) (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))))) (sqrt (sqrt (/ 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 (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)))
  (* (sqrt (/ 1.0 (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (sqrt (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)))
  (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)))))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (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)))
  (/ (* (/ 1.0 (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)))
  (* (/ 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)))
  (* (pow (* 2.0 (* n PI)) (/ k 2.0)) (sqrt k))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (- (fma (* (* 1.0 +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (log n) k) (fma (* (* (* 1.0 +nan.0) k) (exp (* (log (* 2.0 (* n PI))) 0.5))) (log (* 2.0 PI)) (- (- (fma (log (* 2.0 PI)) (* (* (* 1.0 +nan.0) (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5))) (- (fma +nan.0 (* (log (* 2.0 PI)) (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) 1.0) (* (* k k) (log n)))) (fma (- +nan.0) (* 1.0 (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (* (log (* 2.0 PI)) (log (* 2.0 PI)))))) (fma (* (* 1.0 +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (* k k) (log n)) (* (* 1.0 +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5)))))) (* (* (* 1.0 +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (* k k) (* (log n) (log n)))))) (* (* (* 1.0 +nan.0) (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5))))))) (* (* (* 1.0 +nan.0) k) (exp (* (log (* 2.0 (* n PI))) 0.5)))))
  (- (- (fma (/ +nan.0 k) (* (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) (* k k)) 1.0) (* (* (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) (* k k)) 1.0) +nan.0)) (/ (* (* +nan.0 1.0) (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5))) k)))
  (- (fma (/ (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) (/ k 1.0)) +nan.0 (- (* (* +nan.0 (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5))) (- 1.0)) (/ (* (* +nan.0 (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5))) (- 1.0)) (* k k)))))
  (- (fma (* (log n) (* (* k k) (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* (log (* 2.0 PI)) +nan.0) (+ (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (fma (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) +nan.0) (* (* k k) (exp (* (log (* 2.0 (* n PI))) 0.5))) (fma (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* k k) (fma +nan.0 (* (* (* k k) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (log n) (log n))) (fma (* (log n) (* (* k k) (exp (* (log (* 2.0 (* n PI))) 0.5)))) (- +nan.0) (fma (* (* k k) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (log (* 2.0 PI)) +nan.0) (fma (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (+ (- +nan.0) (* (log (* 2.0 PI)) +nan.0)) (* (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (log n) k)))))))))))
  (fma +nan.0 (- (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) (* k k))) (- (* +nan.0 (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) k)) (* (/ +nan.0 (* k k)) (/ (exp (* (* (- 1.0 k) (log (* 2.0 (* n PI)))) 0.5)) k))))
  (fma (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) (- +nan.0) (fma +nan.0 (/ (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) k) (* (/ (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) k) (/ (- +nan.0) k))))
18.083 * * * [progress]: adding candidates to table
19.263 * * [progress]: iteration 4 / 4
19.263 * * * [progress]: picking best candidate
19.302 * * * * [pick]: Picked  #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
19.303 * * * [progress]: localizing error
19.341 * * * [progress]: generating rewritten candidates
19.341 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
19.403 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1)
19.409 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1)
19.418 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
19.464 * * * [progress]: generating series expansions
19.464 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
19.465 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) into (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k)))
19.465 * [approximate]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in (k) around 0
19.465 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in k
19.465 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
19.465 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
19.465 * [taylor]: Taking taylor expansion of 1.0 in k
19.465 * [backup-simplify]: Simplify 1.0 into 1.0
19.466 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
19.466 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
19.466 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.466 * [taylor]: Taking taylor expansion of k in k
19.466 * [backup-simplify]: Simplify 0 into 0
19.466 * [backup-simplify]: Simplify 1 into 1
19.467 * [backup-simplify]: Simplify (/ 1 1) into 1
19.467 * [backup-simplify]: Simplify (sqrt 0) into 0
19.469 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.469 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt (/ 1 k))) in k
19.469 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
19.469 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
19.469 * [taylor]: Taking taylor expansion of 1.0 in k
19.469 * [backup-simplify]: Simplify 1.0 into 1.0
19.469 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
19.470 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
19.470 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.470 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.470 * [taylor]: Taking taylor expansion of k in k
19.470 * [backup-simplify]: Simplify 0 into 0
19.470 * [backup-simplify]: Simplify 1 into 1
19.470 * [backup-simplify]: Simplify (/ 1 1) into 1
19.471 * [backup-simplify]: Simplify (sqrt 0) into 0
19.472 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.473 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
19.474 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) 0) into 0
19.474 * [backup-simplify]: Simplify 0 into 0
19.475 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
19.478 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.481 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.482 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
19.485 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.486 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
19.487 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
19.491 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.493 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.494 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.496 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.497 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
19.498 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
19.504 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.506 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.511 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow k 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) k) (- (* +nan.0 (pow (sqrt 1.0) 2))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) k)))))))
19.511 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 k)))) (sqrt (/ 1.0 (sqrt (/ 1 k))))) into (* (pow (sqrt 1.0) 2) (sqrt k))
19.511 * [approximate]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in (k) around 0
19.511 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in k
19.511 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
19.511 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
19.511 * [taylor]: Taking taylor expansion of 1.0 in k
19.511 * [backup-simplify]: Simplify 1.0 into 1.0
19.511 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
19.512 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
19.512 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.512 * [taylor]: Taking taylor expansion of k in k
19.512 * [backup-simplify]: Simplify 0 into 0
19.512 * [backup-simplify]: Simplify 1 into 1
19.512 * [backup-simplify]: Simplify (sqrt 0) into 0
19.513 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.513 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (sqrt k)) in k
19.513 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
19.513 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
19.513 * [taylor]: Taking taylor expansion of 1.0 in k
19.513 * [backup-simplify]: Simplify 1.0 into 1.0
19.513 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
19.514 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
19.514 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.514 * [taylor]: Taking taylor expansion of k in k
19.514 * [backup-simplify]: Simplify 0 into 0
19.514 * [backup-simplify]: Simplify 1 into 1
19.514 * [backup-simplify]: Simplify (sqrt 0) into 0
19.515 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.516 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
19.516 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) 0) into 0
19.516 * [backup-simplify]: Simplify 0 into 0
19.517 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
19.519 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.520 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.522 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.523 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
19.523 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
19.526 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.528 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.531 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.532 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
19.532 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
19.535 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.536 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.542 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 3)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 k) 2)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 k)))) into (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
19.542 * [backup-simplify]: Simplify (* (sqrt (/ 1.0 (sqrt (/ 1 (- k))))) (sqrt (/ 1.0 (sqrt (/ 1 (- k)))))) into (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k)))
19.542 * [approximate]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in (k) around 0
19.542 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k
19.542 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
19.542 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
19.542 * [taylor]: Taking taylor expansion of 1.0 in k
19.542 * [backup-simplify]: Simplify 1.0 into 1.0
19.543 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
19.543 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
19.543 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.543 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.543 * [taylor]: Taking taylor expansion of -1 in k
19.543 * [backup-simplify]: Simplify -1 into -1
19.543 * [taylor]: Taking taylor expansion of k in k
19.544 * [backup-simplify]: Simplify 0 into 0
19.544 * [backup-simplify]: Simplify 1 into 1
19.544 * [backup-simplify]: Simplify (/ -1 1) into -1
19.545 * [backup-simplify]: Simplify (sqrt 0) into 0
19.546 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.547 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
19.549 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2))
19.549 * [taylor]: Taking taylor expansion of (/ (pow (sqrt 1.0) 2) (sqrt (/ -1 k))) in k
19.549 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
19.549 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
19.549 * [taylor]: Taking taylor expansion of 1.0 in k
19.549 * [backup-simplify]: Simplify 1.0 into 1.0
19.550 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
19.550 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
19.550 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.550 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.550 * [taylor]: Taking taylor expansion of -1 in k
19.550 * [backup-simplify]: Simplify -1 into -1
19.551 * [taylor]: Taking taylor expansion of k in k
19.551 * [backup-simplify]: Simplify 0 into 0
19.551 * [backup-simplify]: Simplify 1 into 1
19.551 * [backup-simplify]: Simplify (/ -1 1) into -1
19.551 * [backup-simplify]: Simplify (sqrt 0) into 0
19.553 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.554 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
19.556 * [backup-simplify]: Simplify (/ (pow (sqrt 1.0) 2) +nan.0) into (* +nan.0 (pow (sqrt 1.0) 2))
19.557 * [backup-simplify]: Simplify (* +nan.0 (pow (sqrt 1.0) 2)) into (* +nan.0 (pow (sqrt 1.0) 2))
19.558 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
19.559 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
19.562 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.568 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.571 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.572 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
19.573 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
19.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.578 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.589 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (pow (sqrt 1.0) 2)) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.591 * [backup-simplify]: Simplify (- (* +nan.0 (pow (sqrt 1.0) 2))) into (- (* +nan.0 (pow (sqrt 1.0) 2)))
19.598 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (pow (sqrt 1.0) 2))) (/ 1 (- k))) (* +nan.0 (pow (sqrt 1.0) 2)))) into (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
19.599 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1)
19.599 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
19.599 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
19.599 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
19.599 * [taylor]: Taking taylor expansion of 1.0 in k
19.599 * [backup-simplify]: Simplify 1.0 into 1.0
19.599 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.599 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.599 * [taylor]: Taking taylor expansion of k in k
19.599 * [backup-simplify]: Simplify 0 into 0
19.599 * [backup-simplify]: Simplify 1 into 1
19.599 * [backup-simplify]: Simplify (/ 1 1) into 1
19.600 * [backup-simplify]: Simplify (sqrt 0) into 0
19.601 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.601 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
19.601 * [taylor]: Taking taylor expansion of 1.0 in k
19.601 * [backup-simplify]: Simplify 1.0 into 1.0
19.601 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.601 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.601 * [taylor]: Taking taylor expansion of k in k
19.601 * [backup-simplify]: Simplify 0 into 0
19.601 * [backup-simplify]: Simplify 1 into 1
19.602 * [backup-simplify]: Simplify (/ 1 1) into 1
19.602 * [backup-simplify]: Simplify (sqrt 0) into 0
19.603 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.604 * [backup-simplify]: Simplify (* 1.0 0) into 0
19.604 * [backup-simplify]: Simplify 0 into 0
19.606 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
19.606 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.607 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
19.610 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.612 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
19.613 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.614 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.618 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.622 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
19.623 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.624 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
19.625 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
19.625 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
19.625 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
19.625 * [taylor]: Taking taylor expansion of 1.0 in k
19.625 * [backup-simplify]: Simplify 1.0 into 1.0
19.625 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.625 * [taylor]: Taking taylor expansion of k in k
19.625 * [backup-simplify]: Simplify 0 into 0
19.625 * [backup-simplify]: Simplify 1 into 1
19.625 * [backup-simplify]: Simplify (sqrt 0) into 0
19.627 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.627 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
19.627 * [taylor]: Taking taylor expansion of 1.0 in k
19.627 * [backup-simplify]: Simplify 1.0 into 1.0
19.627 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.627 * [taylor]: Taking taylor expansion of k in k
19.627 * [backup-simplify]: Simplify 0 into 0
19.627 * [backup-simplify]: Simplify 1 into 1
19.627 * [backup-simplify]: Simplify (sqrt 0) into 0
19.629 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.629 * [backup-simplify]: Simplify (* 1.0 0) into 0
19.629 * [backup-simplify]: Simplify 0 into 0
19.631 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
19.631 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.634 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.636 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
19.637 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.641 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.643 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
19.643 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.645 * [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))))))))
19.645 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
19.645 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
19.645 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
19.645 * [taylor]: Taking taylor expansion of 1.0 in k
19.645 * [backup-simplify]: Simplify 1.0 into 1.0
19.645 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.645 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.645 * [taylor]: Taking taylor expansion of -1 in k
19.645 * [backup-simplify]: Simplify -1 into -1
19.645 * [taylor]: Taking taylor expansion of k in k
19.645 * [backup-simplify]: Simplify 0 into 0
19.645 * [backup-simplify]: Simplify 1 into 1
19.645 * [backup-simplify]: Simplify (/ -1 1) into -1
19.645 * [backup-simplify]: Simplify (sqrt 0) into 0
19.646 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.646 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
19.647 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
19.647 * [taylor]: Taking taylor expansion of 1.0 in k
19.647 * [backup-simplify]: Simplify 1.0 into 1.0
19.647 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.647 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.647 * [taylor]: Taking taylor expansion of -1 in k
19.647 * [backup-simplify]: Simplify -1 into -1
19.647 * [taylor]: Taking taylor expansion of k in k
19.647 * [backup-simplify]: Simplify 0 into 0
19.647 * [backup-simplify]: Simplify 1 into 1
19.647 * [backup-simplify]: Simplify (/ -1 1) into -1
19.647 * [backup-simplify]: Simplify (sqrt 0) into 0
19.648 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.648 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
19.648 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
19.651 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.652 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
19.653 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.653 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.656 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.658 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
19.659 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.659 * [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)))))
19.659 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1)
19.659 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
19.659 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
19.659 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
19.659 * [taylor]: Taking taylor expansion of 1.0 in k
19.659 * [backup-simplify]: Simplify 1.0 into 1.0
19.659 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.660 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.660 * [taylor]: Taking taylor expansion of k in k
19.660 * [backup-simplify]: Simplify 0 into 0
19.660 * [backup-simplify]: Simplify 1 into 1
19.660 * [backup-simplify]: Simplify (/ 1 1) into 1
19.660 * [backup-simplify]: Simplify (sqrt 0) into 0
19.661 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.661 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
19.661 * [taylor]: Taking taylor expansion of 1.0 in k
19.661 * [backup-simplify]: Simplify 1.0 into 1.0
19.661 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.661 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.661 * [taylor]: Taking taylor expansion of k in k
19.661 * [backup-simplify]: Simplify 0 into 0
19.661 * [backup-simplify]: Simplify 1 into 1
19.661 * [backup-simplify]: Simplify (/ 1 1) into 1
19.662 * [backup-simplify]: Simplify (sqrt 0) into 0
19.662 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.663 * [backup-simplify]: Simplify (* 1.0 0) into 0
19.663 * [backup-simplify]: Simplify 0 into 0
19.664 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
19.664 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.664 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
19.666 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.667 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
19.668 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.668 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.670 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.672 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
19.672 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.673 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
19.673 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
19.673 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
19.673 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
19.673 * [taylor]: Taking taylor expansion of 1.0 in k
19.673 * [backup-simplify]: Simplify 1.0 into 1.0
19.673 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.673 * [taylor]: Taking taylor expansion of k in k
19.673 * [backup-simplify]: Simplify 0 into 0
19.673 * [backup-simplify]: Simplify 1 into 1
19.673 * [backup-simplify]: Simplify (sqrt 0) into 0
19.674 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.674 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
19.674 * [taylor]: Taking taylor expansion of 1.0 in k
19.674 * [backup-simplify]: Simplify 1.0 into 1.0
19.674 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.674 * [taylor]: Taking taylor expansion of k in k
19.674 * [backup-simplify]: Simplify 0 into 0
19.674 * [backup-simplify]: Simplify 1 into 1
19.674 * [backup-simplify]: Simplify (sqrt 0) into 0
19.675 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.675 * [backup-simplify]: Simplify (* 1.0 0) into 0
19.676 * [backup-simplify]: Simplify 0 into 0
19.676 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
19.677 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.680 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.682 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
19.682 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.687 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.689 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
19.690 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.692 * [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))))))))
19.692 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
19.692 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
19.692 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
19.692 * [taylor]: Taking taylor expansion of 1.0 in k
19.692 * [backup-simplify]: Simplify 1.0 into 1.0
19.692 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.692 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.693 * [taylor]: Taking taylor expansion of -1 in k
19.693 * [backup-simplify]: Simplify -1 into -1
19.693 * [taylor]: Taking taylor expansion of k in k
19.693 * [backup-simplify]: Simplify 0 into 0
19.693 * [backup-simplify]: Simplify 1 into 1
19.693 * [backup-simplify]: Simplify (/ -1 1) into -1
19.694 * [backup-simplify]: Simplify (sqrt 0) into 0
19.695 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.696 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
19.696 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
19.696 * [taylor]: Taking taylor expansion of 1.0 in k
19.696 * [backup-simplify]: Simplify 1.0 into 1.0
19.696 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.696 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.696 * [taylor]: Taking taylor expansion of -1 in k
19.696 * [backup-simplify]: Simplify -1 into -1
19.696 * [taylor]: Taking taylor expansion of k in k
19.696 * [backup-simplify]: Simplify 0 into 0
19.696 * [backup-simplify]: Simplify 1 into 1
19.696 * [backup-simplify]: Simplify (/ -1 1) into -1
19.697 * [backup-simplify]: Simplify (sqrt 0) into 0
19.698 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.699 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
19.699 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
19.703 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.706 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
19.706 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.708 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.711 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.714 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
19.714 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
19.715 * [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)))))
19.715 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
19.715 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
19.715 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
19.715 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.715 * [taylor]: Taking taylor expansion of 2.0 in n
19.716 * [backup-simplify]: Simplify 2.0 into 2.0
19.716 * [taylor]: Taking taylor expansion of (* n PI) in n
19.716 * [taylor]: Taking taylor expansion of n in n
19.716 * [backup-simplify]: Simplify 0 into 0
19.716 * [backup-simplify]: Simplify 1 into 1
19.716 * [taylor]: Taking taylor expansion of PI in n
19.716 * [backup-simplify]: Simplify PI into PI
19.716 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.716 * [taylor]: Taking taylor expansion of 2.0 in n
19.716 * [backup-simplify]: Simplify 2.0 into 2.0
19.716 * [taylor]: Taking taylor expansion of (* n PI) in n
19.716 * [taylor]: Taking taylor expansion of n in n
19.716 * [backup-simplify]: Simplify 0 into 0
19.716 * [backup-simplify]: Simplify 1 into 1
19.716 * [taylor]: Taking taylor expansion of PI in n
19.716 * [backup-simplify]: Simplify PI into PI
19.716 * [backup-simplify]: Simplify (* 0 PI) into 0
19.716 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.716 * [backup-simplify]: Simplify 0 into 0
19.717 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.718 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.719 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.719 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
19.720 * [backup-simplify]: Simplify 0 into 0
19.721 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.721 * [backup-simplify]: Simplify 0 into 0
19.722 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
19.723 * [backup-simplify]: Simplify 0 into 0
19.724 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
19.725 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
19.725 * [backup-simplify]: Simplify 0 into 0
19.726 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
19.727 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
19.727 * [backup-simplify]: Simplify 0 into 0
19.728 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
19.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
19.729 * [backup-simplify]: Simplify 0 into 0
19.729 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
19.730 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
19.730 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
19.730 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.730 * [taylor]: Taking taylor expansion of 2.0 in n
19.730 * [backup-simplify]: Simplify 2.0 into 2.0
19.730 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.730 * [taylor]: Taking taylor expansion of PI in n
19.730 * [backup-simplify]: Simplify PI into PI
19.730 * [taylor]: Taking taylor expansion of n in n
19.730 * [backup-simplify]: Simplify 0 into 0
19.730 * [backup-simplify]: Simplify 1 into 1
19.730 * [backup-simplify]: Simplify (/ PI 1) into PI
19.730 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.730 * [taylor]: Taking taylor expansion of 2.0 in n
19.730 * [backup-simplify]: Simplify 2.0 into 2.0
19.730 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.730 * [taylor]: Taking taylor expansion of PI in n
19.730 * [backup-simplify]: Simplify PI into PI
19.730 * [taylor]: Taking taylor expansion of n in n
19.730 * [backup-simplify]: Simplify 0 into 0
19.730 * [backup-simplify]: Simplify 1 into 1
19.731 * [backup-simplify]: Simplify (/ PI 1) into PI
19.731 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.731 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.735 * [backup-simplify]: Simplify 0 into 0
19.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.736 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.736 * [backup-simplify]: Simplify 0 into 0
19.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.738 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.738 * [backup-simplify]: Simplify 0 into 0
19.739 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.741 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.741 * [backup-simplify]: Simplify 0 into 0
19.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
19.743 * [backup-simplify]: Simplify 0 into 0
19.745 * [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
19.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
19.746 * [backup-simplify]: Simplify 0 into 0
19.747 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
19.748 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
19.748 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
19.748 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.748 * [taylor]: Taking taylor expansion of -2.0 in n
19.748 * [backup-simplify]: Simplify -2.0 into -2.0
19.748 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.748 * [taylor]: Taking taylor expansion of PI in n
19.748 * [backup-simplify]: Simplify PI into PI
19.748 * [taylor]: Taking taylor expansion of n in n
19.748 * [backup-simplify]: Simplify 0 into 0
19.748 * [backup-simplify]: Simplify 1 into 1
19.748 * [backup-simplify]: Simplify (/ PI 1) into PI
19.748 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.748 * [taylor]: Taking taylor expansion of -2.0 in n
19.748 * [backup-simplify]: Simplify -2.0 into -2.0
19.748 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.748 * [taylor]: Taking taylor expansion of PI in n
19.749 * [backup-simplify]: Simplify PI into PI
19.749 * [taylor]: Taking taylor expansion of n in n
19.749 * [backup-simplify]: Simplify 0 into 0
19.749 * [backup-simplify]: Simplify 1 into 1
19.749 * [backup-simplify]: Simplify (/ PI 1) into PI
19.750 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.750 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.752 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
19.752 * [backup-simplify]: Simplify 0 into 0
19.753 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.754 * [backup-simplify]: Simplify 0 into 0
19.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.756 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.756 * [backup-simplify]: Simplify 0 into 0
19.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.758 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.758 * [backup-simplify]: Simplify 0 into 0
19.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.760 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
19.760 * [backup-simplify]: Simplify 0 into 0
19.760 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.761 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
19.761 * [backup-simplify]: Simplify 0 into 0
19.762 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
19.762 * * * [progress]: simplifying candidates
19.766 * [simplify]: Simplifying:
  (expm1 (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (log1p (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (+ 1 1)
  (+ (log (sqrt (/ 1.0 (sqrt k)))) (log (sqrt (/ 1.0 (sqrt k)))))
  (log (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (exp (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k)))))
  (* (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))))
  (cbrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (sqrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt 1.0) (sqrt 1.0))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (* (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))))
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))) (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))))
  (* (sqrt (cbrt (/ 1.0 (sqrt k)))) (sqrt (cbrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt 1))) (sqrt (/ (sqrt 1.0) (sqrt 1))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) 1)) (sqrt (/ (sqrt 1.0) 1)))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k))))
  (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (cbrt (sqrt k)))) (sqrt (/ 1.0 (cbrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt (cbrt k)))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt 1))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ 1 1)) (sqrt (/ 1 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt 1) (sqrt 1))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt 1.0) (sqrt 1.0))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* 1 1)
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* 2 1/2)
  (* 2 1)
  (* 2 (/ 1 2))
  (* (sqrt (/ 1.0 (sqrt k))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 1)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) 1)
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (cbrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (sqrt 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (cbrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (* (sqrt 1.0) (sqrt (/ 1.0 (sqrt k))))
  (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)))
  (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 (* (* 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)
  (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) k)))))))
  (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 3))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
  (- (+ (* +nan.0 (pow (sqrt 1.0) 2)) (- (+ (* +nan.0 (/ (pow (sqrt 1.0) 2) (pow k 2))) (- (* +nan.0 (/ (pow (sqrt 1.0) 2) k)))))))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +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)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +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))
19.769 * * [simplify]: iteration 0: 291 enodes
19.888 * * [simplify]: iteration 1: 595 enodes
20.163 * * [simplify]: iteration 2: 1518 enodes
21.273 * * [simplify]: iteration 3: 4705 enodes
22.480 * * [simplify]: iteration complete: 5000 enodes
22.480 * * [simplify]: Extracting #0: cost 92 inf + 0
22.483 * * [simplify]: Extracting #1: cost 611 inf + 44
22.505 * * [simplify]: Extracting #2: cost 1254 inf + 5782
22.530 * * [simplify]: Extracting #3: cost 665 inf + 93865
22.586 * * [simplify]: Extracting #4: cost 160 inf + 176661
22.659 * * [simplify]: Extracting #5: cost 4 inf + 219388
22.732 * * [simplify]: Extracting #6: cost 0 inf + 220746
22.804 * [simplify]: Simplified to:
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  1
  1
  2
  1
  1
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (/ 1.0 (sqrt k))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  2
  (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)))
  (* (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)))
  (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  1.0
  (sqrt k)
  (* (sqrt (/ 1.0 (sqrt k))) (cbrt (sqrt (/ 1.0 (sqrt k)))))
  (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k)))))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 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) (fabs (cbrt k))) (cbrt 1.0))
  (/ (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 (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (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) (sqrt (sqrt k))))
  (/ (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 (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 (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 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  1
  (/ 1.0 (sqrt k))
  1.0
  (/ 1 (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  1
  2
  1
  (* (sqrt (/ 1.0 (sqrt k))) (* (cbrt (sqrt (/ 1.0 (sqrt k)))) (cbrt (sqrt (/ 1.0 (sqrt k))))))
  (* (fabs (cbrt (/ 1.0 (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (fabs (/ (cbrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (cbrt 1.0) (/ (cbrt 1.0) (sqrt (sqrt k))))))
  (* (fabs (cbrt 1.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (* (cbrt 1.0) (/ (cbrt 1.0) (sqrt (sqrt k))))))
  (* (fabs (cbrt 1.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (fabs (cbrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt 1.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt 1.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))))
  (* (sqrt (/ 1 (fabs (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (sqrt (/ 1.0 (sqrt k)))
  (* (sqrt (/ 1.0 (sqrt k))) (cbrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (cbrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k))))
  (* (sqrt (/ (cbrt 1.0) (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (cbrt 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (cbrt (sqrt k)))))
  (* (sqrt (/ (sqrt 1.0) (sqrt (cbrt k)))) (sqrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ (sqrt 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (cbrt k)))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ 1.0 (sqrt k))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ 1.0 (sqrt k))
  (/ 1.0 (sqrt k))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (sqrt (/ 1.0 (sqrt k)))))
  (/ 1.0 (sqrt k))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt 1.0))
  (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 (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 k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))
  (/ (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))
  (/ (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))
  (/ (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 (sqrt k)))
  (log1p (/ 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)))
  (* (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 (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (fabs (cbrt k))) (cbrt 1.0))
  (/ (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))
  (/ (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))
  (/ (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 (* (* PI 2.0) n))
  (log1p (* (* PI 2.0) n))
  (* (* PI 2.0) n)
  (* (* PI 2.0) n)
  (log (* (* PI 2.0) n))
  (log (* (* PI 2.0) n))
  (log (* (* PI 2.0) n))
  (exp (* (* PI 2.0) n))
  (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI)))
  (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI)))
  (* (cbrt (* (* PI 2.0) n)) (cbrt (* (* PI 2.0) n)))
  (cbrt (* (* PI 2.0) n))
  (* (* (* n (* 2.0 PI)) (* n (* 2.0 PI))) (* n (* 2.0 PI)))
  (sqrt (* (* PI 2.0) n))
  (sqrt (* (* PI 2.0) n))
  (* (cbrt n) (* (* 2.0 PI) (cbrt n)))
  (* (* 2.0 (sqrt n)) PI)
  (* 2.0 PI)
  (* n PI)
  (fma (* k (* k 1.0)) (- +nan.0) (* +nan.0 (- 1.0 (* 1.0 k))))
  (- (fma +nan.0 (- (/ 1.0 (* k k)) (/ (/ 1.0 (* k k)) k)) (* (/ 1.0 k) +nan.0)))
  (- (fma (/ 1.0 k) +nan.0 (* +nan.0 (- 1.0 (/ 1.0 (* k k))))))
  (- (fma (* +nan.0 k) k (- (* +nan.0 k) +nan.0)))
  (- (fma (/ -1 (* k k)) +nan.0 (/ +nan.0 k)) (/ +nan.0 (* (* k k) k)))
  (fma (/ -1 (* k k)) +nan.0 (- (/ +nan.0 k) +nan.0))
  (- (fma (* +nan.0 k) k (- (* +nan.0 k) +nan.0)))
  (- (fma (/ -1 (* k k)) +nan.0 (/ +nan.0 k)) (/ +nan.0 (* (* k k) k)))
  (fma (/ -1 (* k k)) +nan.0 (- (/ +nan.0 k) +nan.0))
  (* (* PI 2.0) n)
  (* (* PI 2.0) n)
  (* (* PI 2.0) n)
22.838 * * * [progress]: adding candidates to table
24.312 * [progress]: [Phase 3 of 3] Extracting.
24.312 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (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)))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 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 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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))))>)
24.314 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
24.314 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (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)))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 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 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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))))>)
24.414 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (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)))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 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 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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))))>)
24.482 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (/ (* 1.0 (pow (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (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)))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 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 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<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))))>)
24.582 * * * [regime]: Found split indices: #<option (#s(si 1 255))>
24.583 * [simplify]: Simplifying:
  (* (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))))
24.583 * * [simplify]: iteration 0: 15 enodes
24.585 * * [simplify]: iteration 1: 18 enodes
24.586 * * [simplify]: iteration complete: 18 enodes
24.586 * * [simplify]: Extracting #0: cost 1 inf + 0
24.586 * * [simplify]: Extracting #1: cost 2 inf + 0
24.586 * * [simplify]: Extracting #2: cost 3 inf + 0
24.586 * * [simplify]: Extracting #3: cost 5 inf + 0
24.586 * * [simplify]: Extracting #4: cost 8 inf + 0
24.586 * * [simplify]: Extracting #5: cost 7 inf + 43
24.586 * * [simplify]: Extracting #6: cost 11 inf + 43
24.586 * * [simplify]: Extracting #7: cost 9 inf + 87
24.586 * * [simplify]: Extracting #8: cost 4 inf + 671
24.587 * * [simplify]: Extracting #9: cost 1 inf + 2116
24.587 * * [simplify]: Extracting #10: cost 0 inf + 2691
24.587 * [simplify]: Simplified to:
  (* (sqrt (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
31.879 * [regime-testing]: Baseline error score: 0.4395176143333959
31.895 * [regime-testing]: Oracle error score: 0.07037439836274606
31.932 * [regime-testing]: End program error score: 0.4395176143333959