48.126 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.174 * * * [progress]: [2/2] Setting up program.
0.177 * [progress]: [Phase 2 of 3] Improving.
0.177 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.177 * * [simplify]: Extracting # 0 : cost  0
0.177 * * [simplify]: Extracting # 1 : cost  0
0.177 * * [simplify]: Extracting # 2 : cost  0
0.177 * * [simplify]: Extracting # 3 : cost  0
0.177 * * [simplify]: Extracting # 4 : cost  0
0.178 * * [simplify]: Extracting # 5 : cost  0
0.178 * * [simplify]: Extracting # 6 : cost  0
0.178 * * [simplify]: Extracting # 7 : cost  0
0.178 * * [simplify]: iteration  0 :  13  enodes  (cost  16 )
0.181 * * [simplify]: Extracting # 0 : cost  0
0.181 * * [simplify]: Extracting # 1 : cost  0
0.181 * * [simplify]: Extracting # 2 : cost  0
0.181 * * [simplify]: Extracting # 3 : cost  0
0.181 * * [simplify]: Extracting # 4 : cost  0
0.181 * * [simplify]: Extracting # 5 : cost  0
0.181 * * [simplify]: iteration  1 :  29  enodes  (cost  16 )
0.191 * * [simplify]: Extracting # 0 : cost  0
0.191 * * [simplify]: Extracting # 1 : cost  0
0.192 * * [simplify]: Extracting # 2 : cost  0
0.192 * * [simplify]: Extracting # 3 : cost  0
0.192 * * [simplify]: Extracting # 4 : cost  0
0.192 * * [simplify]: iteration  2 :  59  enodes  (cost  16 )
0.217 * * [simplify]: Extracting # 0 : cost  0
0.217 * * [simplify]: Extracting # 1 : cost  0
0.218 * * [simplify]: Extracting # 2 : cost  0
0.218 * * [simplify]: Extracting # 3 : cost  0
0.218 * * [simplify]: Extracting # 4 : cost  0
0.218 * * [simplify]: iteration  3 :  119  enodes  (cost  16 )
0.279 * * [simplify]: Extracting # 0 : cost  0
0.280 * * [simplify]: Extracting # 1 : cost  0
0.280 * * [simplify]: Extracting # 2 : cost  0
0.281 * * [simplify]: Extracting # 3 : cost  0
0.691 * * [simplify]: Extracting # 4 : cost  0
0.692 * * [simplify]: iteration  4 :  313  enodes  (cost  16 )
0.931 * * [simplify]: Extracting # 0 : cost  0
0.933 * * [simplify]: Extracting # 1 : cost  0
0.935 * * [simplify]: Extracting # 2 : cost  0
0.936 * * [simplify]: Extracting # 3 : cost  0
0.937 * * [simplify]: Extracting # 4 : cost  0
0.939 * * [simplify]: iteration  5 :  853  enodes  (cost  16 )
2.417 * * [simplify]: Extracting # 0 : cost  0
2.420 * * [simplify]: Extracting # 1 : cost  0
2.423 * * [simplify]: Extracting # 2 : cost  0
2.429 * * [simplify]: Extracting # 3 : cost  0
2.432 * * [simplify]: Extracting # 4 : cost  0
2.434 * * [simplify]: iteration  6 :  3196  enodes  (cost  16 )
4.188 * * [simplify]: Extracting # 0 : cost  0
4.199 * * [simplify]: Extracting # 1 : cost  0
4.208 * * [simplify]: Extracting # 2 : cost  0
4.217 * * [simplify]: Extracting # 3 : cost  0
4.232 * * [simplify]: Extracting # 4 : cost  0
4.242 * * [simplify]: iteration done:  5001  enodes  (cost  16 )
4.242 * [simplify]: Simplified to:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.242 * * [progress]: iteration 1 / 4
4.242 * * * [progress]: picking best candidate
4.247 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
4.247 * * * [progress]: localizing error
4.275 * * * [progress]: generating rewritten candidates
4.275 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
4.312 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
4.338 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
4.352 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
4.415 * * * [progress]: generating series expansions
4.415 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
4.416 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
4.416 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
4.417 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
4.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
4.417 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
4.417 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
4.417 * [taylor]: Taking taylor expansion of 0.5 in k
4.417 * [backup-simplify]: Simplify 0.5 into 0.5
4.417 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
4.417 * [taylor]: Taking taylor expansion of 1.0 in k
4.417 * [backup-simplify]: Simplify 1.0 into 1.0
4.417 * [taylor]: Taking taylor expansion of k in k
4.417 * [backup-simplify]: Simplify 0 into 0
4.417 * [backup-simplify]: Simplify 1 into 1
4.417 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
4.417 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
4.417 * [taylor]: Taking taylor expansion of 2.0 in k
4.417 * [backup-simplify]: Simplify 2.0 into 2.0
4.417 * [taylor]: Taking taylor expansion of (* n PI) in k
4.417 * [taylor]: Taking taylor expansion of n in k
4.417 * [backup-simplify]: Simplify n into n
4.417 * [taylor]: Taking taylor expansion of PI in k
4.417 * [backup-simplify]: Simplify PI into PI
4.417 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.417 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
4.417 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
4.418 * [backup-simplify]: Simplify (- 0) into 0
4.419 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
4.419 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
4.419 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
4.419 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
4.420 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
4.420 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
4.420 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
4.420 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
4.420 * [taylor]: Taking taylor expansion of 0.5 in n
4.420 * [backup-simplify]: Simplify 0.5 into 0.5
4.420 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
4.420 * [taylor]: Taking taylor expansion of 1.0 in n
4.420 * [backup-simplify]: Simplify 1.0 into 1.0
4.420 * [taylor]: Taking taylor expansion of k in n
4.420 * [backup-simplify]: Simplify k into k
4.420 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.420 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.420 * [taylor]: Taking taylor expansion of 2.0 in n
4.420 * [backup-simplify]: Simplify 2.0 into 2.0
4.420 * [taylor]: Taking taylor expansion of (* n PI) in n
4.420 * [taylor]: Taking taylor expansion of n in n
4.420 * [backup-simplify]: Simplify 0 into 0
4.420 * [backup-simplify]: Simplify 1 into 1
4.420 * [taylor]: Taking taylor expansion of PI in n
4.420 * [backup-simplify]: Simplify PI into PI
4.421 * [backup-simplify]: Simplify (* 0 PI) into 0
4.421 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.423 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.425 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.426 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.426 * [backup-simplify]: Simplify (- k) into (- k)
4.426 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
4.426 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
4.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.429 * [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))))
4.431 * [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)))))
4.431 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
4.431 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
4.431 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
4.431 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
4.431 * [taylor]: Taking taylor expansion of 0.5 in n
4.431 * [backup-simplify]: Simplify 0.5 into 0.5
4.431 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
4.431 * [taylor]: Taking taylor expansion of 1.0 in n
4.431 * [backup-simplify]: Simplify 1.0 into 1.0
4.431 * [taylor]: Taking taylor expansion of k in n
4.431 * [backup-simplify]: Simplify k into k
4.431 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.431 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.431 * [taylor]: Taking taylor expansion of 2.0 in n
4.431 * [backup-simplify]: Simplify 2.0 into 2.0
4.431 * [taylor]: Taking taylor expansion of (* n PI) in n
4.431 * [taylor]: Taking taylor expansion of n in n
4.431 * [backup-simplify]: Simplify 0 into 0
4.431 * [backup-simplify]: Simplify 1 into 1
4.431 * [taylor]: Taking taylor expansion of PI in n
4.431 * [backup-simplify]: Simplify PI into PI
4.432 * [backup-simplify]: Simplify (* 0 PI) into 0
4.432 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.434 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.441 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.442 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.442 * [backup-simplify]: Simplify (- k) into (- k)
4.443 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
4.443 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
4.444 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.446 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
4.447 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
4.447 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
4.447 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
4.447 * [taylor]: Taking taylor expansion of 0.5 in k
4.447 * [backup-simplify]: Simplify 0.5 into 0.5
4.447 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
4.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
4.448 * [taylor]: Taking taylor expansion of 1.0 in k
4.448 * [backup-simplify]: Simplify 1.0 into 1.0
4.448 * [taylor]: Taking taylor expansion of k in k
4.448 * [backup-simplify]: Simplify 0 into 0
4.448 * [backup-simplify]: Simplify 1 into 1
4.448 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
4.448 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
4.448 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
4.448 * [taylor]: Taking taylor expansion of 2.0 in k
4.448 * [backup-simplify]: Simplify 2.0 into 2.0
4.448 * [taylor]: Taking taylor expansion of PI in k
4.448 * [backup-simplify]: Simplify PI into PI
4.448 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.450 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.450 * [taylor]: Taking taylor expansion of (log n) in k
4.450 * [taylor]: Taking taylor expansion of n in k
4.450 * [backup-simplify]: Simplify n into n
4.450 * [backup-simplify]: Simplify (log n) into (log n)
4.450 * [backup-simplify]: Simplify (- 0) into 0
4.451 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
4.452 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
4.453 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
4.454 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
4.455 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
4.457 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
4.458 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
4.459 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
4.461 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
4.462 * [backup-simplify]: Simplify (- 0) into 0
4.462 * [backup-simplify]: Simplify (+ 0 0) into 0
4.462 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
4.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.466 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
4.468 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.468 * [taylor]: Taking taylor expansion of 0 in k
4.468 * [backup-simplify]: Simplify 0 into 0
4.468 * [backup-simplify]: Simplify 0 into 0
4.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
4.471 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
4.471 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
4.472 * [backup-simplify]: Simplify (+ 0 0) into 0
4.472 * [backup-simplify]: Simplify (- 1) into -1
4.472 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.473 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
4.475 * [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))))
4.477 * [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))))))
4.479 * [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))))))
4.479 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
4.480 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
4.482 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
4.482 * [backup-simplify]: Simplify (- 0) into 0
4.483 * [backup-simplify]: Simplify (+ 0 0) into 0
4.483 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
4.484 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.485 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
4.486 * [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
4.486 * [taylor]: Taking taylor expansion of 0 in k
4.486 * [backup-simplify]: Simplify 0 into 0
4.486 * [backup-simplify]: Simplify 0 into 0
4.487 * [backup-simplify]: Simplify 0 into 0
4.487 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.489 * [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
4.490 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
4.491 * [backup-simplify]: Simplify (+ 0 0) into 0
4.491 * [backup-simplify]: Simplify (- 0) into 0
4.491 * [backup-simplify]: Simplify (+ 0 0) into 0
4.492 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
4.494 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
4.496 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
4.500 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
4.512 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
4.513 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
4.513 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
4.513 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
4.513 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
4.513 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
4.513 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
4.513 * [taylor]: Taking taylor expansion of 0.5 in k
4.513 * [backup-simplify]: Simplify 0.5 into 0.5
4.513 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
4.513 * [taylor]: Taking taylor expansion of 1.0 in k
4.513 * [backup-simplify]: Simplify 1.0 into 1.0
4.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.513 * [taylor]: Taking taylor expansion of k in k
4.513 * [backup-simplify]: Simplify 0 into 0
4.513 * [backup-simplify]: Simplify 1 into 1
4.513 * [backup-simplify]: Simplify (/ 1 1) into 1
4.513 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
4.514 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
4.514 * [taylor]: Taking taylor expansion of 2.0 in k
4.514 * [backup-simplify]: Simplify 2.0 into 2.0
4.514 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.514 * [taylor]: Taking taylor expansion of PI in k
4.514 * [backup-simplify]: Simplify PI into PI
4.514 * [taylor]: Taking taylor expansion of n in k
4.514 * [backup-simplify]: Simplify n into n
4.514 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.514 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
4.514 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
4.514 * [backup-simplify]: Simplify (- 1) into -1
4.515 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.515 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
4.516 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
4.516 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
4.516 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
4.516 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
4.516 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
4.516 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
4.516 * [taylor]: Taking taylor expansion of 0.5 in n
4.516 * [backup-simplify]: Simplify 0.5 into 0.5
4.516 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
4.516 * [taylor]: Taking taylor expansion of 1.0 in n
4.516 * [backup-simplify]: Simplify 1.0 into 1.0
4.516 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.516 * [taylor]: Taking taylor expansion of k in n
4.516 * [backup-simplify]: Simplify k into k
4.516 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.516 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
4.516 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
4.516 * [taylor]: Taking taylor expansion of 2.0 in n
4.517 * [backup-simplify]: Simplify 2.0 into 2.0
4.517 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.517 * [taylor]: Taking taylor expansion of PI in n
4.517 * [backup-simplify]: Simplify PI into PI
4.517 * [taylor]: Taking taylor expansion of n in n
4.517 * [backup-simplify]: Simplify 0 into 0
4.517 * [backup-simplify]: Simplify 1 into 1
4.517 * [backup-simplify]: Simplify (/ PI 1) into PI
4.518 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.519 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.519 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.519 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
4.519 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
4.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.522 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
4.523 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
4.523 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
4.523 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
4.523 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
4.523 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
4.523 * [taylor]: Taking taylor expansion of 0.5 in n
4.523 * [backup-simplify]: Simplify 0.5 into 0.5
4.523 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
4.523 * [taylor]: Taking taylor expansion of 1.0 in n
4.524 * [backup-simplify]: Simplify 1.0 into 1.0
4.524 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.524 * [taylor]: Taking taylor expansion of k in n
4.524 * [backup-simplify]: Simplify k into k
4.524 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.524 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
4.524 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
4.524 * [taylor]: Taking taylor expansion of 2.0 in n
4.524 * [backup-simplify]: Simplify 2.0 into 2.0
4.524 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.524 * [taylor]: Taking taylor expansion of PI in n
4.524 * [backup-simplify]: Simplify PI into PI
4.524 * [taylor]: Taking taylor expansion of n in n
4.524 * [backup-simplify]: Simplify 0 into 0
4.524 * [backup-simplify]: Simplify 1 into 1
4.525 * [backup-simplify]: Simplify (/ PI 1) into PI
4.525 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.526 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.527 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.527 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
4.527 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
4.528 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.530 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
4.531 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
4.531 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
4.531 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
4.531 * [taylor]: Taking taylor expansion of 0.5 in k
4.531 * [backup-simplify]: Simplify 0.5 into 0.5
4.531 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
4.531 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
4.531 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
4.531 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
4.531 * [taylor]: Taking taylor expansion of 2.0 in k
4.531 * [backup-simplify]: Simplify 2.0 into 2.0
4.531 * [taylor]: Taking taylor expansion of PI in k
4.531 * [backup-simplify]: Simplify PI into PI
4.532 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.533 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.533 * [taylor]: Taking taylor expansion of (log n) in k
4.533 * [taylor]: Taking taylor expansion of n in k
4.533 * [backup-simplify]: Simplify n into n
4.533 * [backup-simplify]: Simplify (log n) into (log n)
4.533 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
4.533 * [taylor]: Taking taylor expansion of 1.0 in k
4.533 * [backup-simplify]: Simplify 1.0 into 1.0
4.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.533 * [taylor]: Taking taylor expansion of k in k
4.533 * [backup-simplify]: Simplify 0 into 0
4.533 * [backup-simplify]: Simplify 1 into 1
4.534 * [backup-simplify]: Simplify (/ 1 1) into 1
4.534 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.535 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
4.535 * [backup-simplify]: Simplify (- 1) into -1
4.536 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.537 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
4.538 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
4.539 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
4.541 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
4.542 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.543 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
4.545 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
4.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.545 * [backup-simplify]: Simplify (- 0) into 0
4.546 * [backup-simplify]: Simplify (+ 0 0) into 0
4.546 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
4.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.549 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
4.551 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.551 * [taylor]: Taking taylor expansion of 0 in k
4.551 * [backup-simplify]: Simplify 0 into 0
4.551 * [backup-simplify]: Simplify 0 into 0
4.551 * [backup-simplify]: Simplify 0 into 0
4.553 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.554 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.558 * [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
4.558 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.559 * [backup-simplify]: Simplify (- 0) into 0
4.559 * [backup-simplify]: Simplify (+ 0 0) into 0
4.560 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
4.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.563 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
4.566 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.566 * [taylor]: Taking taylor expansion of 0 in k
4.566 * [backup-simplify]: Simplify 0 into 0
4.566 * [backup-simplify]: Simplify 0 into 0
4.566 * [backup-simplify]: Simplify 0 into 0
4.566 * [backup-simplify]: Simplify 0 into 0
4.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.569 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.575 * [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
4.576 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.576 * [backup-simplify]: Simplify (- 0) into 0
4.577 * [backup-simplify]: Simplify (+ 0 0) into 0
4.584 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
4.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
4.587 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
4.591 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
4.591 * [taylor]: Taking taylor expansion of 0 in k
4.591 * [backup-simplify]: Simplify 0 into 0
4.591 * [backup-simplify]: Simplify 0 into 0
4.592 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
4.593 * [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)))
4.593 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
4.593 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
4.593 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
4.593 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
4.593 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
4.593 * [taylor]: Taking taylor expansion of 0.5 in k
4.593 * [backup-simplify]: Simplify 0.5 into 0.5
4.593 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
4.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.593 * [taylor]: Taking taylor expansion of k in k
4.593 * [backup-simplify]: Simplify 0 into 0
4.593 * [backup-simplify]: Simplify 1 into 1
4.594 * [backup-simplify]: Simplify (/ 1 1) into 1
4.594 * [taylor]: Taking taylor expansion of 1.0 in k
4.594 * [backup-simplify]: Simplify 1.0 into 1.0
4.594 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
4.594 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
4.594 * [taylor]: Taking taylor expansion of -2.0 in k
4.594 * [backup-simplify]: Simplify -2.0 into -2.0
4.594 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.594 * [taylor]: Taking taylor expansion of PI in k
4.594 * [backup-simplify]: Simplify PI into PI
4.594 * [taylor]: Taking taylor expansion of n in k
4.594 * [backup-simplify]: Simplify n into n
4.594 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.594 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
4.595 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
4.595 * [backup-simplify]: Simplify (+ 1 0) into 1
4.595 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
4.595 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
4.596 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
4.596 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
4.596 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
4.596 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
4.596 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
4.596 * [taylor]: Taking taylor expansion of 0.5 in n
4.596 * [backup-simplify]: Simplify 0.5 into 0.5
4.596 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
4.596 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.596 * [taylor]: Taking taylor expansion of k in n
4.596 * [backup-simplify]: Simplify k into k
4.596 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.596 * [taylor]: Taking taylor expansion of 1.0 in n
4.596 * [backup-simplify]: Simplify 1.0 into 1.0
4.596 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
4.596 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
4.596 * [taylor]: Taking taylor expansion of -2.0 in n
4.596 * [backup-simplify]: Simplify -2.0 into -2.0
4.596 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.596 * [taylor]: Taking taylor expansion of PI in n
4.596 * [backup-simplify]: Simplify PI into PI
4.596 * [taylor]: Taking taylor expansion of n in n
4.596 * [backup-simplify]: Simplify 0 into 0
4.596 * [backup-simplify]: Simplify 1 into 1
4.596 * [backup-simplify]: Simplify (/ PI 1) into PI
4.597 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.597 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
4.598 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
4.598 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
4.599 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.599 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
4.600 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
4.600 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
4.600 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
4.600 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
4.600 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
4.600 * [taylor]: Taking taylor expansion of 0.5 in n
4.600 * [backup-simplify]: Simplify 0.5 into 0.5
4.600 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
4.600 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.600 * [taylor]: Taking taylor expansion of k in n
4.600 * [backup-simplify]: Simplify k into k
4.600 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.600 * [taylor]: Taking taylor expansion of 1.0 in n
4.600 * [backup-simplify]: Simplify 1.0 into 1.0
4.600 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
4.600 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
4.601 * [taylor]: Taking taylor expansion of -2.0 in n
4.601 * [backup-simplify]: Simplify -2.0 into -2.0
4.601 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.601 * [taylor]: Taking taylor expansion of PI in n
4.601 * [backup-simplify]: Simplify PI into PI
4.601 * [taylor]: Taking taylor expansion of n in n
4.601 * [backup-simplify]: Simplify 0 into 0
4.601 * [backup-simplify]: Simplify 1 into 1
4.601 * [backup-simplify]: Simplify (/ PI 1) into PI
4.601 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.602 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
4.602 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
4.602 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
4.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.604 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
4.605 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
4.605 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
4.605 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
4.605 * [taylor]: Taking taylor expansion of 0.5 in k
4.605 * [backup-simplify]: Simplify 0.5 into 0.5
4.606 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
4.606 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
4.606 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.606 * [taylor]: Taking taylor expansion of k in k
4.606 * [backup-simplify]: Simplify 0 into 0
4.606 * [backup-simplify]: Simplify 1 into 1
4.606 * [backup-simplify]: Simplify (/ 1 1) into 1
4.606 * [taylor]: Taking taylor expansion of 1.0 in k
4.606 * [backup-simplify]: Simplify 1.0 into 1.0
4.606 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
4.606 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
4.606 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
4.606 * [taylor]: Taking taylor expansion of -2.0 in k
4.606 * [backup-simplify]: Simplify -2.0 into -2.0
4.606 * [taylor]: Taking taylor expansion of PI in k
4.606 * [backup-simplify]: Simplify PI into PI
4.607 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.607 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
4.607 * [taylor]: Taking taylor expansion of (log n) in k
4.607 * [taylor]: Taking taylor expansion of n in k
4.607 * [backup-simplify]: Simplify n into n
4.608 * [backup-simplify]: Simplify (log n) into (log n)
4.608 * [backup-simplify]: Simplify (+ 1 0) into 1
4.608 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.609 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
4.609 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
4.610 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
4.611 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
4.612 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
4.612 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.613 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
4.614 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
4.614 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.614 * [backup-simplify]: Simplify (+ 0 0) into 0
4.615 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
4.616 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.616 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
4.618 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.618 * [taylor]: Taking taylor expansion of 0 in k
4.618 * [backup-simplify]: Simplify 0 into 0
4.618 * [backup-simplify]: Simplify 0 into 0
4.618 * [backup-simplify]: Simplify 0 into 0
4.618 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.619 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.621 * [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
4.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.621 * [backup-simplify]: Simplify (+ 0 0) into 0
4.622 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
4.623 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.624 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
4.625 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.625 * [taylor]: Taking taylor expansion of 0 in k
4.625 * [backup-simplify]: Simplify 0 into 0
4.626 * [backup-simplify]: Simplify 0 into 0
4.626 * [backup-simplify]: Simplify 0 into 0
4.626 * [backup-simplify]: Simplify 0 into 0
4.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.627 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.630 * [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
4.630 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.631 * [backup-simplify]: Simplify (+ 0 0) into 0
4.632 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
4.634 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
4.636 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
4.639 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
4.639 * [taylor]: Taking taylor expansion of 0 in k
4.639 * [backup-simplify]: Simplify 0 into 0
4.639 * [backup-simplify]: Simplify 0 into 0
4.641 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
4.641 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
4.642 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
4.642 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
4.642 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.642 * [taylor]: Taking taylor expansion of 2.0 in n
4.642 * [backup-simplify]: Simplify 2.0 into 2.0
4.642 * [taylor]: Taking taylor expansion of (* n PI) in n
4.642 * [taylor]: Taking taylor expansion of n in n
4.642 * [backup-simplify]: Simplify 0 into 0
4.642 * [backup-simplify]: Simplify 1 into 1
4.642 * [taylor]: Taking taylor expansion of PI in n
4.642 * [backup-simplify]: Simplify PI into PI
4.642 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.642 * [taylor]: Taking taylor expansion of 2.0 in n
4.642 * [backup-simplify]: Simplify 2.0 into 2.0
4.642 * [taylor]: Taking taylor expansion of (* n PI) in n
4.642 * [taylor]: Taking taylor expansion of n in n
4.642 * [backup-simplify]: Simplify 0 into 0
4.642 * [backup-simplify]: Simplify 1 into 1
4.642 * [taylor]: Taking taylor expansion of PI in n
4.642 * [backup-simplify]: Simplify PI into PI
4.643 * [backup-simplify]: Simplify (* 0 PI) into 0
4.643 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.643 * [backup-simplify]: Simplify 0 into 0
4.645 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.647 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.647 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.648 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
4.649 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
4.649 * [backup-simplify]: Simplify 0 into 0
4.651 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
4.652 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
4.652 * [backup-simplify]: Simplify 0 into 0
4.654 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.655 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
4.655 * [backup-simplify]: Simplify 0 into 0
4.657 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
4.658 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
4.658 * [backup-simplify]: Simplify 0 into 0
4.660 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
4.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
4.662 * [backup-simplify]: Simplify 0 into 0
4.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
4.666 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
4.666 * [backup-simplify]: Simplify 0 into 0
4.667 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
4.668 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
4.668 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
4.668 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
4.668 * [taylor]: Taking taylor expansion of 2.0 in n
4.668 * [backup-simplify]: Simplify 2.0 into 2.0
4.668 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.668 * [taylor]: Taking taylor expansion of PI in n
4.668 * [backup-simplify]: Simplify PI into PI
4.668 * [taylor]: Taking taylor expansion of n in n
4.668 * [backup-simplify]: Simplify 0 into 0
4.668 * [backup-simplify]: Simplify 1 into 1
4.669 * [backup-simplify]: Simplify (/ PI 1) into PI
4.669 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
4.669 * [taylor]: Taking taylor expansion of 2.0 in n
4.669 * [backup-simplify]: Simplify 2.0 into 2.0
4.669 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.669 * [taylor]: Taking taylor expansion of PI in n
4.669 * [backup-simplify]: Simplify PI into PI
4.669 * [taylor]: Taking taylor expansion of n in n
4.669 * [backup-simplify]: Simplify 0 into 0
4.669 * [backup-simplify]: Simplify 1 into 1
4.669 * [backup-simplify]: Simplify (/ PI 1) into PI
4.670 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.671 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
4.672 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.672 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
4.672 * [backup-simplify]: Simplify 0 into 0
4.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.675 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.675 * [backup-simplify]: Simplify 0 into 0
4.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.677 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.677 * [backup-simplify]: Simplify 0 into 0
4.679 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.680 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.680 * [backup-simplify]: Simplify 0 into 0
4.682 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.683 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
4.683 * [backup-simplify]: Simplify 0 into 0
4.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.686 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
4.687 * [backup-simplify]: Simplify 0 into 0
4.687 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
4.688 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
4.688 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
4.688 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
4.688 * [taylor]: Taking taylor expansion of -2.0 in n
4.688 * [backup-simplify]: Simplify -2.0 into -2.0
4.688 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.688 * [taylor]: Taking taylor expansion of PI in n
4.688 * [backup-simplify]: Simplify PI into PI
4.688 * [taylor]: Taking taylor expansion of n in n
4.688 * [backup-simplify]: Simplify 0 into 0
4.689 * [backup-simplify]: Simplify 1 into 1
4.689 * [backup-simplify]: Simplify (/ PI 1) into PI
4.689 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
4.689 * [taylor]: Taking taylor expansion of -2.0 in n
4.689 * [backup-simplify]: Simplify -2.0 into -2.0
4.689 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.689 * [taylor]: Taking taylor expansion of PI in n
4.689 * [backup-simplify]: Simplify PI into PI
4.689 * [taylor]: Taking taylor expansion of n in n
4.689 * [backup-simplify]: Simplify 0 into 0
4.689 * [backup-simplify]: Simplify 1 into 1
4.690 * [backup-simplify]: Simplify (/ PI 1) into PI
4.690 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.691 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
4.691 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.692 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
4.692 * [backup-simplify]: Simplify 0 into 0
4.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.693 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
4.693 * [backup-simplify]: Simplify 0 into 0
4.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.694 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.694 * [backup-simplify]: Simplify 0 into 0
4.695 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.696 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.696 * [backup-simplify]: Simplify 0 into 0
4.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.698 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
4.698 * [backup-simplify]: Simplify 0 into 0
4.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.699 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
4.699 * [backup-simplify]: Simplify 0 into 0
4.700 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
4.700 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
4.700 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
4.700 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
4.700 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
4.700 * [taylor]: Taking taylor expansion of 1.0 in k
4.700 * [backup-simplify]: Simplify 1.0 into 1.0
4.700 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.700 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.700 * [taylor]: Taking taylor expansion of k in k
4.700 * [backup-simplify]: Simplify 0 into 0
4.700 * [backup-simplify]: Simplify 1 into 1
4.700 * [backup-simplify]: Simplify (/ 1 1) into 1
4.701 * [backup-simplify]: Simplify (sqrt 0) into 0
4.702 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.702 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
4.702 * [taylor]: Taking taylor expansion of 1.0 in k
4.702 * [backup-simplify]: Simplify 1.0 into 1.0
4.702 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.702 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.702 * [taylor]: Taking taylor expansion of k in k
4.702 * [backup-simplify]: Simplify 0 into 0
4.702 * [backup-simplify]: Simplify 1 into 1
4.702 * [backup-simplify]: Simplify (/ 1 1) into 1
4.702 * [backup-simplify]: Simplify (sqrt 0) into 0
4.703 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.703 * [backup-simplify]: Simplify (* 1.0 0) into 0
4.703 * [backup-simplify]: Simplify 0 into 0
4.704 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
4.704 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.705 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
4.710 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.712 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
4.712 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.713 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.715 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.716 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
4.716 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.717 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
4.718 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
4.718 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
4.718 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
4.718 * [taylor]: Taking taylor expansion of 1.0 in k
4.718 * [backup-simplify]: Simplify 1.0 into 1.0
4.718 * [taylor]: Taking taylor expansion of (sqrt k) in k
4.718 * [taylor]: Taking taylor expansion of k in k
4.718 * [backup-simplify]: Simplify 0 into 0
4.718 * [backup-simplify]: Simplify 1 into 1
4.718 * [backup-simplify]: Simplify (sqrt 0) into 0
4.719 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.719 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
4.719 * [taylor]: Taking taylor expansion of 1.0 in k
4.719 * [backup-simplify]: Simplify 1.0 into 1.0
4.719 * [taylor]: Taking taylor expansion of (sqrt k) in k
4.719 * [taylor]: Taking taylor expansion of k in k
4.719 * [backup-simplify]: Simplify 0 into 0
4.719 * [backup-simplify]: Simplify 1 into 1
4.719 * [backup-simplify]: Simplify (sqrt 0) into 0
4.721 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.721 * [backup-simplify]: Simplify (* 1.0 0) into 0
4.721 * [backup-simplify]: Simplify 0 into 0
4.723 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
4.723 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.726 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.728 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
4.729 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.733 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.735 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
4.735 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.736 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
4.736 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
4.736 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
4.736 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
4.736 * [taylor]: Taking taylor expansion of 1.0 in k
4.736 * [backup-simplify]: Simplify 1.0 into 1.0
4.736 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.736 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.736 * [taylor]: Taking taylor expansion of -1 in k
4.736 * [backup-simplify]: Simplify -1 into -1
4.736 * [taylor]: Taking taylor expansion of k in k
4.737 * [backup-simplify]: Simplify 0 into 0
4.737 * [backup-simplify]: Simplify 1 into 1
4.737 * [backup-simplify]: Simplify (/ -1 1) into -1
4.737 * [backup-simplify]: Simplify (sqrt 0) into 0
4.738 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.738 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
4.738 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
4.738 * [taylor]: Taking taylor expansion of 1.0 in k
4.738 * [backup-simplify]: Simplify 1.0 into 1.0
4.738 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.738 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.738 * [taylor]: Taking taylor expansion of -1 in k
4.738 * [backup-simplify]: Simplify -1 into -1
4.738 * [taylor]: Taking taylor expansion of k in k
4.738 * [backup-simplify]: Simplify 0 into 0
4.738 * [backup-simplify]: Simplify 1 into 1
4.739 * [backup-simplify]: Simplify (/ -1 1) into -1
4.739 * [backup-simplify]: Simplify (sqrt 0) into 0
4.740 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.740 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
4.740 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
4.742 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.744 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
4.744 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.747 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.749 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
4.750 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.750 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
4.750 * * * * [progress]: [ 4 / 4 ] generating series at (2)
4.751 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))))
4.751 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0
4.751 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
4.751 * [taylor]: Taking taylor expansion of 1.0 in n
4.751 * [backup-simplify]: Simplify 1.0 into 1.0
4.751 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
4.751 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
4.751 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.751 * [taylor]: Taking taylor expansion of k in n
4.751 * [backup-simplify]: Simplify k into k
4.751 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.751 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
4.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.751 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
4.751 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
4.752 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
4.752 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
4.752 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
4.752 * [taylor]: Taking taylor expansion of 0.5 in n
4.752 * [backup-simplify]: Simplify 0.5 into 0.5
4.752 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
4.752 * [taylor]: Taking taylor expansion of 1.0 in n
4.752 * [backup-simplify]: Simplify 1.0 into 1.0
4.752 * [taylor]: Taking taylor expansion of k in n
4.752 * [backup-simplify]: Simplify k into k
4.752 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.752 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.752 * [taylor]: Taking taylor expansion of 2.0 in n
4.752 * [backup-simplify]: Simplify 2.0 into 2.0
4.752 * [taylor]: Taking taylor expansion of (* n PI) in n
4.752 * [taylor]: Taking taylor expansion of n in n
4.752 * [backup-simplify]: Simplify 0 into 0
4.752 * [backup-simplify]: Simplify 1 into 1
4.752 * [taylor]: Taking taylor expansion of PI in n
4.752 * [backup-simplify]: Simplify PI into PI
4.752 * [backup-simplify]: Simplify (* 0 PI) into 0
4.752 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.753 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.754 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.755 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.755 * [backup-simplify]: Simplify (- k) into (- k)
4.755 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
4.755 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
4.756 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.757 * [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))))
4.757 * [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)))))
4.757 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
4.757 * [taylor]: Taking taylor expansion of 1.0 in k
4.757 * [backup-simplify]: Simplify 1.0 into 1.0
4.757 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
4.758 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.758 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.758 * [taylor]: Taking taylor expansion of k in k
4.758 * [backup-simplify]: Simplify 0 into 0
4.758 * [backup-simplify]: Simplify 1 into 1
4.758 * [backup-simplify]: Simplify (/ 1 1) into 1
4.758 * [backup-simplify]: Simplify (sqrt 0) into 0
4.759 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.759 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
4.759 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
4.759 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
4.759 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
4.759 * [taylor]: Taking taylor expansion of 0.5 in k
4.759 * [backup-simplify]: Simplify 0.5 into 0.5
4.759 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
4.759 * [taylor]: Taking taylor expansion of 1.0 in k
4.759 * [backup-simplify]: Simplify 1.0 into 1.0
4.759 * [taylor]: Taking taylor expansion of k in k
4.759 * [backup-simplify]: Simplify 0 into 0
4.759 * [backup-simplify]: Simplify 1 into 1
4.759 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
4.759 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
4.759 * [taylor]: Taking taylor expansion of 2.0 in k
4.759 * [backup-simplify]: Simplify 2.0 into 2.0
4.759 * [taylor]: Taking taylor expansion of (* n PI) in k
4.759 * [taylor]: Taking taylor expansion of n in k
4.759 * [backup-simplify]: Simplify n into n
4.759 * [taylor]: Taking taylor expansion of PI in k
4.759 * [backup-simplify]: Simplify PI into PI
4.759 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.759 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
4.759 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
4.760 * [backup-simplify]: Simplify (- 0) into 0
4.760 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
4.760 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
4.760 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
4.760 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
4.760 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
4.760 * [taylor]: Taking taylor expansion of 1.0 in k
4.760 * [backup-simplify]: Simplify 1.0 into 1.0
4.761 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
4.761 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.761 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.761 * [taylor]: Taking taylor expansion of k in k
4.761 * [backup-simplify]: Simplify 0 into 0
4.761 * [backup-simplify]: Simplify 1 into 1
4.761 * [backup-simplify]: Simplify (/ 1 1) into 1
4.761 * [backup-simplify]: Simplify (sqrt 0) into 0
4.762 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.762 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
4.762 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
4.762 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
4.762 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
4.762 * [taylor]: Taking taylor expansion of 0.5 in k
4.762 * [backup-simplify]: Simplify 0.5 into 0.5
4.762 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
4.762 * [taylor]: Taking taylor expansion of 1.0 in k
4.762 * [backup-simplify]: Simplify 1.0 into 1.0
4.762 * [taylor]: Taking taylor expansion of k in k
4.762 * [backup-simplify]: Simplify 0 into 0
4.762 * [backup-simplify]: Simplify 1 into 1
4.762 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
4.762 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
4.762 * [taylor]: Taking taylor expansion of 2.0 in k
4.762 * [backup-simplify]: Simplify 2.0 into 2.0
4.762 * [taylor]: Taking taylor expansion of (* n PI) in k
4.762 * [taylor]: Taking taylor expansion of n in k
4.762 * [backup-simplify]: Simplify n into n
4.762 * [taylor]: Taking taylor expansion of PI in k
4.762 * [backup-simplify]: Simplify PI into PI
4.762 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.762 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
4.762 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
4.763 * [backup-simplify]: Simplify (- 0) into 0
4.763 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
4.763 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
4.764 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
4.764 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
4.764 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
4.765 * [backup-simplify]: Simplify (* 1.0 0) into 0
4.765 * [taylor]: Taking taylor expansion of 0 in n
4.765 * [backup-simplify]: Simplify 0 into 0
4.765 * [backup-simplify]: Simplify 0 into 0
4.765 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
4.766 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
4.767 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
4.767 * [backup-simplify]: Simplify (- 1) into -1
4.767 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.769 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
4.770 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
4.770 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
4.772 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
4.774 * [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)))
4.774 * [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
4.774 * [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
4.774 * [taylor]: Taking taylor expansion of +nan.0 in n
4.774 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.775 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
4.775 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
4.775 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
4.775 * [taylor]: Taking taylor expansion of 0.5 in n
4.775 * [backup-simplify]: Simplify 0.5 into 0.5
4.775 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
4.775 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
4.775 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
4.775 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
4.775 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
4.775 * [taylor]: Taking taylor expansion of 1.0 in n
4.775 * [backup-simplify]: Simplify 1.0 into 1.0
4.775 * [taylor]: Taking taylor expansion of (log PI) in n
4.775 * [taylor]: Taking taylor expansion of PI in n
4.775 * [backup-simplify]: Simplify PI into PI
4.775 * [backup-simplify]: Simplify (log PI) into (log PI)
4.776 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
4.778 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
4.778 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
4.778 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
4.778 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
4.778 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
4.778 * [taylor]: Taking taylor expansion of 1.0 in n
4.778 * [backup-simplify]: Simplify 1.0 into 1.0
4.778 * [taylor]: Taking taylor expansion of (log n) in n
4.778 * [taylor]: Taking taylor expansion of n in n
4.778 * [backup-simplify]: Simplify 0 into 0
4.778 * [backup-simplify]: Simplify 1 into 1
4.779 * [backup-simplify]: Simplify (log 1) into 0
4.779 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.779 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
4.779 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
4.779 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
4.779 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
4.779 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
4.779 * [taylor]: Taking taylor expansion of 1.0 in n
4.779 * [backup-simplify]: Simplify 1.0 into 1.0
4.779 * [taylor]: Taking taylor expansion of (log 2.0) in n
4.779 * [taylor]: Taking taylor expansion of 2.0 in n
4.779 * [backup-simplify]: Simplify 2.0 into 2.0
4.780 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
4.780 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
4.781 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
4.782 * [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)
4.782 * [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)
4.783 * [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))
4.784 * [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)))
4.785 * [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)
4.786 * [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))
4.787 * [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)))
4.788 * [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)))
4.788 * [backup-simplify]: Simplify 0 into 0
4.788 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
4.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
4.790 * [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
4.790 * [backup-simplify]: Simplify (- 0) into 0
4.790 * [backup-simplify]: Simplify (+ 0 0) into 0
4.791 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
4.791 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
4.792 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
4.793 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
4.794 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.797 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))
4.800 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))
4.800 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n
4.800 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n
4.800 * [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
4.800 * [taylor]: Taking taylor expansion of +nan.0 in n
4.800 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.800 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
4.800 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
4.800 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
4.800 * [taylor]: Taking taylor expansion of 0.5 in n
4.800 * [backup-simplify]: Simplify 0.5 into 0.5
4.800 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
4.800 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
4.800 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
4.800 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
4.800 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
4.800 * [taylor]: Taking taylor expansion of 1.0 in n
4.800 * [backup-simplify]: Simplify 1.0 into 1.0
4.800 * [taylor]: Taking taylor expansion of (log PI) in n
4.800 * [taylor]: Taking taylor expansion of PI in n
4.800 * [backup-simplify]: Simplify PI into PI
4.801 * [backup-simplify]: Simplify (log PI) into (log PI)
4.801 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
4.802 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
4.802 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
4.802 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
4.802 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
4.802 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
4.802 * [taylor]: Taking taylor expansion of 1.0 in n
4.802 * [backup-simplify]: Simplify 1.0 into 1.0
4.802 * [taylor]: Taking taylor expansion of (log n) in n
4.802 * [taylor]: Taking taylor expansion of n in n
4.802 * [backup-simplify]: Simplify 0 into 0
4.802 * [backup-simplify]: Simplify 1 into 1
4.803 * [backup-simplify]: Simplify (log 1) into 0
4.803 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.803 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
4.803 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
4.803 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
4.803 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
4.803 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
4.803 * [taylor]: Taking taylor expansion of 1.0 in n
4.803 * [backup-simplify]: Simplify 1.0 into 1.0
4.803 * [taylor]: Taking taylor expansion of (log 2.0) in n
4.803 * [taylor]: Taking taylor expansion of 2.0 in n
4.803 * [backup-simplify]: Simplify 2.0 into 2.0
4.804 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
4.804 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
4.805 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
4.805 * [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)
4.806 * [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)
4.807 * [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))
4.808 * [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)))
4.809 * [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)
4.809 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n
4.809 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
4.809 * [taylor]: Taking taylor expansion of +nan.0 in n
4.809 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.809 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
4.809 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
4.809 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
4.809 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
4.809 * [taylor]: Taking taylor expansion of 0.5 in n
4.809 * [backup-simplify]: Simplify 0.5 into 0.5
4.809 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
4.809 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
4.809 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
4.809 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
4.809 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
4.809 * [taylor]: Taking taylor expansion of 1.0 in n
4.809 * [backup-simplify]: Simplify 1.0 into 1.0
4.809 * [taylor]: Taking taylor expansion of (log 2.0) in n
4.809 * [taylor]: Taking taylor expansion of 2.0 in n
4.809 * [backup-simplify]: Simplify 2.0 into 2.0
4.810 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
4.810 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
4.811 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
4.811 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
4.811 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
4.811 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
4.812 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
4.812 * [taylor]: Taking taylor expansion of 1.0 in n
4.812 * [backup-simplify]: Simplify 1.0 into 1.0
4.812 * [taylor]: Taking taylor expansion of (log PI) in n
4.812 * [taylor]: Taking taylor expansion of PI in n
4.812 * [backup-simplify]: Simplify PI into PI
4.812 * [backup-simplify]: Simplify (log PI) into (log PI)
4.813 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
4.815 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
4.815 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
4.815 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
4.815 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
4.815 * [taylor]: Taking taylor expansion of 1.0 in n
4.815 * [backup-simplify]: Simplify 1.0 into 1.0
4.815 * [taylor]: Taking taylor expansion of (log n) in n
4.815 * [taylor]: Taking taylor expansion of n in n
4.815 * [backup-simplify]: Simplify 0 into 0
4.815 * [backup-simplify]: Simplify 1 into 1
4.816 * [backup-simplify]: Simplify (log 1) into 0
4.816 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.816 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
4.817 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
4.817 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
4.824 * [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)
4.825 * [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))
4.827 * [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)))
4.829 * [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)
4.829 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.829 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.829 * [taylor]: Taking taylor expansion of 2.0 in n
4.829 * [backup-simplify]: Simplify 2.0 into 2.0
4.829 * [taylor]: Taking taylor expansion of (* n PI) in n
4.829 * [taylor]: Taking taylor expansion of n in n
4.829 * [backup-simplify]: Simplify 0 into 0
4.829 * [backup-simplify]: Simplify 1 into 1
4.829 * [taylor]: Taking taylor expansion of PI in n
4.829 * [backup-simplify]: Simplify PI into PI
4.830 * [backup-simplify]: Simplify (* 0 PI) into 0
4.830 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.832 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.834 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.835 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.837 * [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))
4.838 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.841 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
4.843 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
4.846 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))
4.852 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
4.858 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
4.865 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
4.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
4.868 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
4.870 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
4.871 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
4.871 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.871 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
4.872 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
4.873 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
4.874 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
4.874 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
4.875 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
4.876 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
4.877 * [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
4.878 * [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
4.880 * [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
4.881 * [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
4.881 * [backup-simplify]: Simplify (- 0) into 0
4.881 * [backup-simplify]: Simplify 0 into 0
4.881 * [backup-simplify]: Simplify 0 into 0
4.882 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.883 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
4.885 * [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
4.885 * [backup-simplify]: Simplify (- 0) into 0
4.885 * [backup-simplify]: Simplify (+ 0 0) into 0
4.886 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
4.887 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
4.888 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
4.888 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.891 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.894 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
4.902 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
4.902 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n
4.902 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n
4.902 * [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
4.902 * [taylor]: Taking taylor expansion of +nan.0 in n
4.903 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.903 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
4.903 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
4.903 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
4.903 * [taylor]: Taking taylor expansion of 0.5 in n
4.903 * [backup-simplify]: Simplify 0.5 into 0.5
4.903 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
4.903 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
4.903 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
4.903 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
4.903 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
4.903 * [taylor]: Taking taylor expansion of 1.0 in n
4.903 * [backup-simplify]: Simplify 1.0 into 1.0
4.903 * [taylor]: Taking taylor expansion of (log 2.0) in n
4.903 * [taylor]: Taking taylor expansion of 2.0 in n
4.903 * [backup-simplify]: Simplify 2.0 into 2.0
4.904 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
4.904 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
4.906 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
4.906 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
4.906 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
4.906 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
4.906 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
4.906 * [taylor]: Taking taylor expansion of 1.0 in n
4.906 * [backup-simplify]: Simplify 1.0 into 1.0
4.906 * [taylor]: Taking taylor expansion of (log n) in n
4.906 * [taylor]: Taking taylor expansion of n in n
4.906 * [backup-simplify]: Simplify 0 into 0
4.906 * [backup-simplify]: Simplify 1 into 1
4.907 * [backup-simplify]: Simplify (log 1) into 0
4.908 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.908 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
4.908 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
4.908 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
4.908 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
4.908 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
4.908 * [taylor]: Taking taylor expansion of 1.0 in n
4.908 * [backup-simplify]: Simplify 1.0 into 1.0
4.908 * [taylor]: Taking taylor expansion of (log PI) in n
4.908 * [taylor]: Taking taylor expansion of PI in n
4.908 * [backup-simplify]: Simplify PI into PI
4.909 * [backup-simplify]: Simplify (log PI) into (log PI)
4.910 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
4.911 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
4.912 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
4.913 * [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)
4.915 * [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))
4.916 * [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)))
4.918 * [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)
4.918 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n
4.918 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n
4.918 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
4.918 * [taylor]: Taking taylor expansion of +nan.0 in n
4.918 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.918 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
4.918 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
4.918 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
4.918 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
4.918 * [taylor]: Taking taylor expansion of 0.5 in n
4.918 * [backup-simplify]: Simplify 0.5 into 0.5
4.918 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
4.918 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
4.918 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
4.918 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
4.919 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
4.919 * [taylor]: Taking taylor expansion of 1.0 in n
4.919 * [backup-simplify]: Simplify 1.0 into 1.0
4.919 * [taylor]: Taking taylor expansion of (log 2.0) in n
4.919 * [taylor]: Taking taylor expansion of 2.0 in n
4.919 * [backup-simplify]: Simplify 2.0 into 2.0
4.919 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
4.920 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
4.922 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
4.922 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
4.922 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
4.922 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
4.922 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
4.922 * [taylor]: Taking taylor expansion of 1.0 in n
4.922 * [backup-simplify]: Simplify 1.0 into 1.0
4.922 * [taylor]: Taking taylor expansion of (log PI) in n
4.922 * [taylor]: Taking taylor expansion of PI in n
4.922 * [backup-simplify]: Simplify PI into PI
4.923 * [backup-simplify]: Simplify (log PI) into (log PI)
4.924 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
4.926 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
4.926 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
4.926 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
4.926 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
4.926 * [taylor]: Taking taylor expansion of 1.0 in n
4.926 * [backup-simplify]: Simplify 1.0 into 1.0
4.926 * [taylor]: Taking taylor expansion of (log n) in n
4.926 * [taylor]: Taking taylor expansion of n in n
4.926 * [backup-simplify]: Simplify 0 into 0
4.926 * [backup-simplify]: Simplify 1 into 1
4.926 * [backup-simplify]: Simplify (log 1) into 0
4.927 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.927 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
4.927 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
4.928 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
4.929 * [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)
4.930 * [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))
4.931 * [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)))
4.933 * [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)
4.933 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.933 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.933 * [taylor]: Taking taylor expansion of 2.0 in n
4.933 * [backup-simplify]: Simplify 2.0 into 2.0
4.933 * [taylor]: Taking taylor expansion of (* n PI) in n
4.933 * [taylor]: Taking taylor expansion of n in n
4.933 * [backup-simplify]: Simplify 0 into 0
4.933 * [backup-simplify]: Simplify 1 into 1
4.933 * [taylor]: Taking taylor expansion of PI in n
4.934 * [backup-simplify]: Simplify PI into PI
4.934 * [backup-simplify]: Simplify (* 0 PI) into 0
4.934 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.936 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.938 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.939 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.939 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n
4.939 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
4.939 * [taylor]: Taking taylor expansion of +nan.0 in n
4.939 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.939 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
4.939 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
4.939 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
4.939 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
4.939 * [taylor]: Taking taylor expansion of 0.5 in n
4.939 * [backup-simplify]: Simplify 0.5 into 0.5
4.939 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
4.939 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
4.939 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
4.939 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
4.939 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
4.939 * [taylor]: Taking taylor expansion of 1.0 in n
4.939 * [backup-simplify]: Simplify 1.0 into 1.0
4.940 * [taylor]: Taking taylor expansion of (log 2.0) in n
4.940 * [taylor]: Taking taylor expansion of 2.0 in n
4.940 * [backup-simplify]: Simplify 2.0 into 2.0
4.940 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
4.941 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
4.943 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
4.943 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
4.943 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
4.943 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
4.943 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
4.943 * [taylor]: Taking taylor expansion of 1.0 in n
4.943 * [backup-simplify]: Simplify 1.0 into 1.0
4.943 * [taylor]: Taking taylor expansion of (log PI) in n
4.943 * [taylor]: Taking taylor expansion of PI in n
4.943 * [backup-simplify]: Simplify PI into PI
4.943 * [backup-simplify]: Simplify (log PI) into (log PI)
4.944 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
4.946 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
4.946 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
4.946 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
4.946 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
4.946 * [taylor]: Taking taylor expansion of 1.0 in n
4.946 * [backup-simplify]: Simplify 1.0 into 1.0
4.946 * [taylor]: Taking taylor expansion of (log n) in n
4.946 * [taylor]: Taking taylor expansion of n in n
4.946 * [backup-simplify]: Simplify 0 into 0
4.946 * [backup-simplify]: Simplify 1 into 1
4.947 * [backup-simplify]: Simplify (log 1) into 0
4.947 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
4.947 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
4.948 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
4.948 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
4.950 * [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)
4.951 * [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))
4.953 * [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)))
4.954 * [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)
4.955 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
4.955 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
4.955 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
4.955 * [taylor]: Taking taylor expansion of 2.0 in n
4.955 * [backup-simplify]: Simplify 2.0 into 2.0
4.955 * [taylor]: Taking taylor expansion of (* n PI) in n
4.955 * [taylor]: Taking taylor expansion of n in n
4.955 * [backup-simplify]: Simplify 0 into 0
4.955 * [backup-simplify]: Simplify 1 into 1
4.955 * [taylor]: Taking taylor expansion of PI in n
4.955 * [backup-simplify]: Simplify PI into PI
4.955 * [backup-simplify]: Simplify (* 0 PI) into 0
4.955 * [backup-simplify]: Simplify (* 2.0 0) into 0
4.956 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.958 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
4.958 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
4.963 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.964 * [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))
4.965 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.967 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
4.968 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
4.969 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.970 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
4.971 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
4.973 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
4.975 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
4.977 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
4.984 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))
4.994 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))
5.010 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
5.020 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
5.030 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
5.046 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
5.046 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
5.046 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0
5.046 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
5.046 * [taylor]: Taking taylor expansion of 1.0 in n
5.046 * [backup-simplify]: Simplify 1.0 into 1.0
5.046 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
5.046 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.046 * [taylor]: Taking taylor expansion of k in n
5.046 * [backup-simplify]: Simplify k into k
5.047 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.047 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.047 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.047 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.047 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.047 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.047 * [taylor]: Taking taylor expansion of 0.5 in n
5.047 * [backup-simplify]: Simplify 0.5 into 0.5
5.047 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.047 * [taylor]: Taking taylor expansion of 1.0 in n
5.047 * [backup-simplify]: Simplify 1.0 into 1.0
5.047 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.047 * [taylor]: Taking taylor expansion of k in n
5.047 * [backup-simplify]: Simplify k into k
5.047 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.047 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.047 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.047 * [taylor]: Taking taylor expansion of 2.0 in n
5.047 * [backup-simplify]: Simplify 2.0 into 2.0
5.047 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.047 * [taylor]: Taking taylor expansion of PI in n
5.047 * [backup-simplify]: Simplify PI into PI
5.047 * [taylor]: Taking taylor expansion of n in n
5.047 * [backup-simplify]: Simplify 0 into 0
5.047 * [backup-simplify]: Simplify 1 into 1
5.047 * [backup-simplify]: Simplify (/ PI 1) into PI
5.048 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.048 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.048 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.048 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.049 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.049 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.050 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.051 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.051 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
5.051 * [taylor]: Taking taylor expansion of 1.0 in k
5.051 * [backup-simplify]: Simplify 1.0 into 1.0
5.051 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
5.051 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.051 * [taylor]: Taking taylor expansion of k in k
5.051 * [backup-simplify]: Simplify 0 into 0
5.051 * [backup-simplify]: Simplify 1 into 1
5.051 * [backup-simplify]: Simplify (sqrt 0) into 0
5.052 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.052 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
5.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
5.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
5.052 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
5.052 * [taylor]: Taking taylor expansion of 0.5 in k
5.052 * [backup-simplify]: Simplify 0.5 into 0.5
5.053 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.053 * [taylor]: Taking taylor expansion of 1.0 in k
5.053 * [backup-simplify]: Simplify 1.0 into 1.0
5.053 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.053 * [taylor]: Taking taylor expansion of k in k
5.053 * [backup-simplify]: Simplify 0 into 0
5.053 * [backup-simplify]: Simplify 1 into 1
5.053 * [backup-simplify]: Simplify (/ 1 1) into 1
5.053 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
5.053 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
5.053 * [taylor]: Taking taylor expansion of 2.0 in k
5.053 * [backup-simplify]: Simplify 2.0 into 2.0
5.053 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.053 * [taylor]: Taking taylor expansion of PI in k
5.053 * [backup-simplify]: Simplify PI into PI
5.053 * [taylor]: Taking taylor expansion of n in k
5.053 * [backup-simplify]: Simplify n into n
5.053 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.053 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
5.053 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
5.053 * [backup-simplify]: Simplify (- 1) into -1
5.054 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.054 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
5.054 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
5.054 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
5.054 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
5.054 * [taylor]: Taking taylor expansion of 1.0 in k
5.054 * [backup-simplify]: Simplify 1.0 into 1.0
5.054 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
5.054 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.054 * [taylor]: Taking taylor expansion of k in k
5.054 * [backup-simplify]: Simplify 0 into 0
5.054 * [backup-simplify]: Simplify 1 into 1
5.055 * [backup-simplify]: Simplify (sqrt 0) into 0
5.055 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.055 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
5.055 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
5.055 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
5.056 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
5.056 * [taylor]: Taking taylor expansion of 0.5 in k
5.056 * [backup-simplify]: Simplify 0.5 into 0.5
5.056 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.056 * [taylor]: Taking taylor expansion of 1.0 in k
5.056 * [backup-simplify]: Simplify 1.0 into 1.0
5.056 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.056 * [taylor]: Taking taylor expansion of k in k
5.056 * [backup-simplify]: Simplify 0 into 0
5.056 * [backup-simplify]: Simplify 1 into 1
5.056 * [backup-simplify]: Simplify (/ 1 1) into 1
5.056 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
5.056 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
5.056 * [taylor]: Taking taylor expansion of 2.0 in k
5.056 * [backup-simplify]: Simplify 2.0 into 2.0
5.056 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.056 * [taylor]: Taking taylor expansion of PI in k
5.056 * [backup-simplify]: Simplify PI into PI
5.056 * [taylor]: Taking taylor expansion of n in k
5.056 * [backup-simplify]: Simplify n into n
5.056 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.056 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
5.056 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
5.056 * [backup-simplify]: Simplify (- 1) into -1
5.057 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.057 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
5.057 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
5.057 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
5.057 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
5.058 * [backup-simplify]: Simplify (* 1.0 0) into 0
5.058 * [taylor]: Taking taylor expansion of 0 in n
5.058 * [backup-simplify]: Simplify 0 into 0
5.058 * [backup-simplify]: Simplify 0 into 0
5.058 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
5.059 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
5.059 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
5.059 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
5.059 * [taylor]: Taking taylor expansion of +nan.0 in n
5.059 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.059 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
5.059 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
5.059 * [taylor]: Taking taylor expansion of 0.5 in n
5.059 * [backup-simplify]: Simplify 0.5 into 0.5
5.059 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
5.059 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.059 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.059 * [taylor]: Taking taylor expansion of 2.0 in n
5.059 * [backup-simplify]: Simplify 2.0 into 2.0
5.059 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.059 * [taylor]: Taking taylor expansion of PI in n
5.060 * [backup-simplify]: Simplify PI into PI
5.060 * [taylor]: Taking taylor expansion of n in n
5.060 * [backup-simplify]: Simplify 0 into 0
5.060 * [backup-simplify]: Simplify 1 into 1
5.065 * [backup-simplify]: Simplify (/ PI 1) into PI
5.066 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.067 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.067 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.067 * [taylor]: Taking taylor expansion of 1.0 in n
5.067 * [backup-simplify]: Simplify 1.0 into 1.0
5.067 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.067 * [taylor]: Taking taylor expansion of k in n
5.067 * [backup-simplify]: Simplify k into k
5.067 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.069 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.069 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.069 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.071 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
5.072 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.073 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.074 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
5.076 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
5.077 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
5.077 * [backup-simplify]: Simplify 0 into 0
5.080 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
5.083 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
5.083 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
5.083 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
5.083 * [taylor]: Taking taylor expansion of +nan.0 in n
5.083 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.083 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
5.083 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
5.083 * [taylor]: Taking taylor expansion of 0.5 in n
5.083 * [backup-simplify]: Simplify 0.5 into 0.5
5.083 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
5.083 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.083 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.083 * [taylor]: Taking taylor expansion of 2.0 in n
5.083 * [backup-simplify]: Simplify 2.0 into 2.0
5.083 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.083 * [taylor]: Taking taylor expansion of PI in n
5.083 * [backup-simplify]: Simplify PI into PI
5.083 * [taylor]: Taking taylor expansion of n in n
5.083 * [backup-simplify]: Simplify 0 into 0
5.083 * [backup-simplify]: Simplify 1 into 1
5.084 * [backup-simplify]: Simplify (/ PI 1) into PI
5.084 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.085 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.086 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.086 * [taylor]: Taking taylor expansion of 1.0 in n
5.086 * [backup-simplify]: Simplify 1.0 into 1.0
5.086 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.086 * [taylor]: Taking taylor expansion of k in n
5.086 * [backup-simplify]: Simplify k into k
5.086 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.087 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.087 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.087 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.089 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
5.090 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.091 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.092 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
5.093 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
5.094 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
5.095 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.095 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.095 * [backup-simplify]: Simplify (- 0) into 0
5.095 * [backup-simplify]: Simplify (+ 0 0) into 0
5.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.096 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.097 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.098 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
5.099 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
5.100 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.101 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
5.102 * [backup-simplify]: Simplify (- 0) into 0
5.102 * [backup-simplify]: Simplify 0 into 0
5.102 * [backup-simplify]: Simplify 0 into 0
5.104 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.105 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
5.106 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
5.106 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
5.106 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
5.106 * [taylor]: Taking taylor expansion of +nan.0 in n
5.106 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.106 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
5.106 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
5.106 * [taylor]: Taking taylor expansion of 0.5 in n
5.106 * [backup-simplify]: Simplify 0.5 into 0.5
5.106 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
5.106 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.106 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.106 * [taylor]: Taking taylor expansion of 2.0 in n
5.106 * [backup-simplify]: Simplify 2.0 into 2.0
5.106 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.106 * [taylor]: Taking taylor expansion of PI in n
5.106 * [backup-simplify]: Simplify PI into PI
5.106 * [taylor]: Taking taylor expansion of n in n
5.106 * [backup-simplify]: Simplify 0 into 0
5.106 * [backup-simplify]: Simplify 1 into 1
5.107 * [backup-simplify]: Simplify (/ PI 1) into PI
5.107 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.108 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.108 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.108 * [taylor]: Taking taylor expansion of 1.0 in n
5.108 * [backup-simplify]: Simplify 1.0 into 1.0
5.108 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.108 * [taylor]: Taking taylor expansion of k in n
5.108 * [backup-simplify]: Simplify k into k
5.108 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.109 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.109 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.109 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.110 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
5.111 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.112 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.113 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
5.113 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
5.114 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
5.117 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
5.118 * [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))))
5.118 * [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
5.118 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
5.118 * [taylor]: Taking taylor expansion of 1.0 in n
5.118 * [backup-simplify]: Simplify 1.0 into 1.0
5.118 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
5.118 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
5.118 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
5.118 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
5.118 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
5.118 * [taylor]: Taking taylor expansion of 0.5 in n
5.118 * [backup-simplify]: Simplify 0.5 into 0.5
5.118 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.118 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.118 * [taylor]: Taking taylor expansion of k in n
5.118 * [backup-simplify]: Simplify k into k
5.118 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.118 * [taylor]: Taking taylor expansion of 1.0 in n
5.118 * [backup-simplify]: Simplify 1.0 into 1.0
5.118 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.118 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.118 * [taylor]: Taking taylor expansion of -2.0 in n
5.118 * [backup-simplify]: Simplify -2.0 into -2.0
5.118 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.118 * [taylor]: Taking taylor expansion of PI in n
5.118 * [backup-simplify]: Simplify PI into PI
5.118 * [taylor]: Taking taylor expansion of n in n
5.118 * [backup-simplify]: Simplify 0 into 0
5.118 * [backup-simplify]: Simplify 1 into 1
5.119 * [backup-simplify]: Simplify (/ PI 1) into PI
5.119 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.121 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.121 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.121 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
5.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.124 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
5.125 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.125 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.125 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.125 * [taylor]: Taking taylor expansion of -1 in n
5.125 * [backup-simplify]: Simplify -1 into -1
5.125 * [taylor]: Taking taylor expansion of k in n
5.125 * [backup-simplify]: Simplify k into k
5.125 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.125 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.126 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.126 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.128 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))
5.128 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
5.128 * [taylor]: Taking taylor expansion of 1.0 in k
5.128 * [backup-simplify]: Simplify 1.0 into 1.0
5.128 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
5.128 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
5.128 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
5.128 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
5.128 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
5.128 * [taylor]: Taking taylor expansion of 0.5 in k
5.128 * [backup-simplify]: Simplify 0.5 into 0.5
5.128 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.129 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.129 * [taylor]: Taking taylor expansion of k in k
5.129 * [backup-simplify]: Simplify 0 into 0
5.129 * [backup-simplify]: Simplify 1 into 1
5.129 * [backup-simplify]: Simplify (/ 1 1) into 1
5.129 * [taylor]: Taking taylor expansion of 1.0 in k
5.129 * [backup-simplify]: Simplify 1.0 into 1.0
5.129 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
5.129 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
5.129 * [taylor]: Taking taylor expansion of -2.0 in k
5.129 * [backup-simplify]: Simplify -2.0 into -2.0
5.129 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.129 * [taylor]: Taking taylor expansion of PI in k
5.129 * [backup-simplify]: Simplify PI into PI
5.129 * [taylor]: Taking taylor expansion of n in k
5.130 * [backup-simplify]: Simplify n into n
5.130 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.130 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
5.130 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
5.130 * [backup-simplify]: Simplify (+ 1 0) into 1
5.131 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
5.131 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
5.131 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
5.132 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.132 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.132 * [taylor]: Taking taylor expansion of -1 in k
5.132 * [backup-simplify]: Simplify -1 into -1
5.132 * [taylor]: Taking taylor expansion of k in k
5.132 * [backup-simplify]: Simplify 0 into 0
5.132 * [backup-simplify]: Simplify 1 into 1
5.132 * [backup-simplify]: Simplify (/ -1 1) into -1
5.133 * [backup-simplify]: Simplify (sqrt 0) into 0
5.134 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.134 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
5.134 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
5.134 * [taylor]: Taking taylor expansion of 1.0 in k
5.135 * [backup-simplify]: Simplify 1.0 into 1.0
5.135 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
5.135 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
5.135 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
5.135 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
5.135 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
5.135 * [taylor]: Taking taylor expansion of 0.5 in k
5.135 * [backup-simplify]: Simplify 0.5 into 0.5
5.135 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.135 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.135 * [taylor]: Taking taylor expansion of k in k
5.135 * [backup-simplify]: Simplify 0 into 0
5.135 * [backup-simplify]: Simplify 1 into 1
5.135 * [backup-simplify]: Simplify (/ 1 1) into 1
5.135 * [taylor]: Taking taylor expansion of 1.0 in k
5.135 * [backup-simplify]: Simplify 1.0 into 1.0
5.135 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
5.135 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
5.136 * [taylor]: Taking taylor expansion of -2.0 in k
5.136 * [backup-simplify]: Simplify -2.0 into -2.0
5.136 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.136 * [taylor]: Taking taylor expansion of PI in k
5.136 * [backup-simplify]: Simplify PI into PI
5.136 * [taylor]: Taking taylor expansion of n in k
5.136 * [backup-simplify]: Simplify n into n
5.136 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.136 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
5.136 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
5.136 * [backup-simplify]: Simplify (+ 1 0) into 1
5.137 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
5.137 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
5.137 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
5.137 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.137 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.137 * [taylor]: Taking taylor expansion of -1 in k
5.137 * [backup-simplify]: Simplify -1 into -1
5.138 * [taylor]: Taking taylor expansion of k in k
5.138 * [backup-simplify]: Simplify 0 into 0
5.138 * [backup-simplify]: Simplify 1 into 1
5.138 * [backup-simplify]: Simplify (/ -1 1) into -1
5.138 * [backup-simplify]: Simplify (sqrt 0) into 0
5.140 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.140 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
5.141 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
5.141 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
5.141 * [taylor]: Taking taylor expansion of +nan.0 in n
5.141 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.141 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
5.141 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
5.141 * [taylor]: Taking taylor expansion of 0.5 in n
5.141 * [backup-simplify]: Simplify 0.5 into 0.5
5.141 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
5.141 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.141 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.141 * [taylor]: Taking taylor expansion of k in n
5.141 * [backup-simplify]: Simplify k into k
5.141 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.141 * [taylor]: Taking taylor expansion of 1.0 in n
5.141 * [backup-simplify]: Simplify 1.0 into 1.0
5.141 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.141 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.141 * [taylor]: Taking taylor expansion of -2.0 in n
5.141 * [backup-simplify]: Simplify -2.0 into -2.0
5.141 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.141 * [taylor]: Taking taylor expansion of PI in n
5.141 * [backup-simplify]: Simplify PI into PI
5.141 * [taylor]: Taking taylor expansion of n in n
5.141 * [backup-simplify]: Simplify 0 into 0
5.141 * [backup-simplify]: Simplify 1 into 1
5.142 * [backup-simplify]: Simplify (/ PI 1) into PI
5.143 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.144 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.144 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.145 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.146 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
5.148 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
5.149 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.150 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
5.152 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
5.153 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.156 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.157 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
5.158 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
5.158 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
5.158 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
5.158 * [taylor]: Taking taylor expansion of +nan.0 in n
5.158 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.158 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
5.158 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
5.158 * [taylor]: Taking taylor expansion of 0.5 in n
5.158 * [backup-simplify]: Simplify 0.5 into 0.5
5.158 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
5.158 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.158 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.158 * [taylor]: Taking taylor expansion of k in n
5.158 * [backup-simplify]: Simplify k into k
5.159 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.159 * [taylor]: Taking taylor expansion of 1.0 in n
5.159 * [backup-simplify]: Simplify 1.0 into 1.0
5.159 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.159 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.159 * [taylor]: Taking taylor expansion of -2.0 in n
5.159 * [backup-simplify]: Simplify -2.0 into -2.0
5.159 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.159 * [taylor]: Taking taylor expansion of PI in n
5.159 * [backup-simplify]: Simplify PI into PI
5.159 * [taylor]: Taking taylor expansion of n in n
5.159 * [backup-simplify]: Simplify 0 into 0
5.159 * [backup-simplify]: Simplify 1 into 1
5.159 * [backup-simplify]: Simplify (/ PI 1) into PI
5.160 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.161 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.161 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.164 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
5.165 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
5.167 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.168 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
5.169 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
5.171 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
5.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.173 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
5.175 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
5.175 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.175 * [backup-simplify]: Simplify (+ 0 0) into 0
5.177 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.178 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
5.180 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
5.182 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.184 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
5.184 * [backup-simplify]: Simplify 0 into 0
5.185 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.189 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.192 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
5.193 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
5.193 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
5.193 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
5.193 * [taylor]: Taking taylor expansion of +nan.0 in n
5.193 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.193 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
5.193 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
5.193 * [taylor]: Taking taylor expansion of 0.5 in n
5.193 * [backup-simplify]: Simplify 0.5 into 0.5
5.193 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
5.193 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.193 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.193 * [taylor]: Taking taylor expansion of k in n
5.193 * [backup-simplify]: Simplify k into k
5.193 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.193 * [taylor]: Taking taylor expansion of 1.0 in n
5.193 * [backup-simplify]: Simplify 1.0 into 1.0
5.193 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.193 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.194 * [taylor]: Taking taylor expansion of -2.0 in n
5.194 * [backup-simplify]: Simplify -2.0 into -2.0
5.194 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.194 * [taylor]: Taking taylor expansion of PI in n
5.194 * [backup-simplify]: Simplify PI into PI
5.194 * [taylor]: Taking taylor expansion of n in n
5.194 * [backup-simplify]: Simplify 0 into 0
5.194 * [backup-simplify]: Simplify 1 into 1
5.194 * [backup-simplify]: Simplify (/ PI 1) into PI
5.195 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.196 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.196 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.198 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.199 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
5.201 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
5.202 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.203 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
5.205 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
5.206 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
5.217 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
5.217 * * * [progress]: simplifying candidates
5.222 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) 1)
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
5.232 * * [simplify]: Extracting # 0 : cost  0
5.233 * * [simplify]: Extracting # 1 : cost  0
5.234 * * [simplify]: Extracting # 2 : cost  0
5.234 * * [simplify]: Extracting # 3 : cost  0
5.235 * * [simplify]: Extracting # 4 : cost  0
5.236 * * [simplify]: Extracting # 5 : cost  0
5.237 * * [simplify]: Extracting # 6 : cost  0
5.238 * * [simplify]: Extracting # 7 : cost  0
5.239 * * [simplify]: Extracting # 8 : cost  0
5.240 * * [simplify]: Extracting # 9 : cost  0
5.241 * * [simplify]: Extracting # 10 : cost  0
5.243 * * [simplify]: Extracting # 11 : cost  0
5.244 * * [simplify]: Extracting # 12 : cost  0
5.245 * * [simplify]: Extracting # 13 : cost  0
5.246 * * [simplify]: Extracting # 14 : cost  0
5.247 * * [simplify]: Extracting # 15 : cost  0
5.248 * * [simplify]: Extracting # 16 : cost  0
5.249 * * [simplify]: Extracting # 17 : cost  0
5.250 * * [simplify]: Extracting # 18 : cost  0
5.252 * * [simplify]: Extracting # 19 : cost  0
5.253 * * [simplify]: Extracting # 20 : cost  0
5.254 * * [simplify]: Extracting # 21 : cost  0
5.255 * * [simplify]: Extracting # 22 : cost  0
5.257 * * [simplify]: Extracting # 23 : cost  0
5.258 * * [simplify]: Extracting # 24 : cost  0
5.259 * * [simplify]: Extracting # 25 : cost  0
5.260 * * [simplify]: Extracting # 26 : cost  0
5.261 * * [simplify]: Extracting # 27 : cost  0
5.262 * * [simplify]: Extracting # 28 : cost  0
5.264 * * [simplify]: Extracting # 29 : cost  0
5.265 * * [simplify]: Extracting # 30 : cost  0
5.266 * * [simplify]: Extracting # 31 : cost  0
5.267 * * [simplify]: Extracting # 32 : cost  0
5.268 * * [simplify]: iteration  0 :  369  enodes  (cost  2880 )
5.416 * * [simplify]: Extracting # 0 : cost  0
5.418 * * [simplify]: Extracting # 1 : cost  0
5.419 * * [simplify]: Extracting # 2 : cost  0
5.420 * * [simplify]: Extracting # 3 : cost  0
5.428 * * [simplify]: Extracting # 4 : cost  0
5.430 * * [simplify]: Extracting # 5 : cost  0
5.433 * * [simplify]: Extracting # 6 : cost  0
5.436 * * [simplify]: iteration  1 :  961  enodes  (cost  2712 )
6.054 * * [simplify]: Extracting # 0 : cost  0
6.058 * * [simplify]: Extracting # 1 : cost  0
6.062 * * [simplify]: Extracting # 2 : cost  0
6.066 * * [simplify]: Extracting # 3 : cost  0
6.072 * * [simplify]: Extracting # 4 : cost  0
6.079 * * [simplify]: Extracting # 5 : cost  0
6.083 * * [simplify]: iteration  2 :  3137  enodes  (cost  2550 )
7.407 * * [simplify]: Extracting # 0 : cost  0
7.420 * * [simplify]: Extracting # 1 : cost  0
7.444 * * [simplify]: Extracting # 2 : cost  0
7.457 * * [simplify]: Extracting # 3 : cost  0
7.468 * * [simplify]: Extracting # 4 : cost  0
7.480 * * [simplify]: iteration done:  5000  enodes  (cost  2540 )
7.483 * [simplify]: Simplified to:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 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))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* PI n) 2.0)
  (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)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* PI n) 2.0)
  (* (* PI n) 2.0)
  (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 (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* PI n) 2.0)
  (* (* PI n) 2.0)
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (pow (* (* 2.0 PI) n) 3)
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (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)
  (* PI n)
  (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)))
  (/ (pow 1.0 3) (* k (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (pow (/ 1.0 (sqrt k)) 3)
  (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)) (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 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (* (/ 1.0 (sqrt k)) (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))))
  (log (* (/ 1.0 (sqrt k)) (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))))
  (log (* (/ 1.0 (sqrt k)) (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))))
  (log (* (/ 1.0 (sqrt k)) (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))))
  (log (* (/ 1.0 (sqrt k)) (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))))
  (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))))
  (* (/ (pow 1.0 3) k) (/ (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt k)))
  (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3)
  (* (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))))
  (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3)
  (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))
  (* (/ 1.0 (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)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (* (/ 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)))
  (fma 0.5 (* (- k) (fma (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5) (* (log n) (pow (* (* 2.0 PI) n) 0.5)))) (fma (* 0.125 (pow k 2)) (fma (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2))) (fma 0.25 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (* 2.0 PI) n) 0.5)) (pow (* (* 2.0 PI) n) 0.5))))
  (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k))
  (pow (exp (* 0.5 (- 1.0 k))) (- (log (* -2.0 PI)) (log (/ -1 n))))
  (* (* PI n) 2.0)
  (* (* PI n) 2.0)
  (* (* PI n) 2.0)
  (fma k (- +nan.0) (fma +nan.0 (pow k 2) (- +nan.0)))
  (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (/ (- +nan.0) (pow k 2)))
  (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0))
  (fma (- (* +nan.0 (* (pow k 2) (pow (log (* 2.0 PI)) 2)))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (fma (pow k 2) (* (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) +nan.0) (fma (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (- +nan.0) (fma (pow k 2) (* (* (log n) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) +nan.0) (fma (- +nan.0) (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (fma (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)) +nan.0 (fma (- (* (* k (log n)) (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 n 1.0) (pow PI 1.0))) 0.5) +nan.0 (- (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
  (fma +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 2))) (- (* +nan.0 (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3)))))
  (fma +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (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))))
7.485 * * * [progress]: adding candidates to table
8.226 * * [progress]: iteration 2 / 4
8.227 * * * [progress]: picking best candidate
8.269 * * * * [pick]: Picked  #<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))))>
8.270 * * * [progress]: localizing error
8.301 * * * [progress]: generating rewritten candidates
8.301 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
8.342 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2)
8.369 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
8.403 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1)
8.462 * * * [progress]: generating series expansions
8.463 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
8.464 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k)))
8.464 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0
8.464 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k
8.464 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
8.464 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
8.464 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k
8.464 * [taylor]: Taking taylor expansion of 0.25 in k
8.464 * [backup-simplify]: Simplify 0.25 into 0.25
8.464 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.464 * [taylor]: Taking taylor expansion of 1.0 in k
8.464 * [backup-simplify]: Simplify 1.0 into 1.0
8.464 * [taylor]: Taking taylor expansion of k in k
8.464 * [backup-simplify]: Simplify 0 into 0
8.464 * [backup-simplify]: Simplify 1 into 1
8.464 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
8.464 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
8.464 * [taylor]: Taking taylor expansion of 2.0 in k
8.464 * [backup-simplify]: Simplify 2.0 into 2.0
8.464 * [taylor]: Taking taylor expansion of (* n PI) in k
8.464 * [taylor]: Taking taylor expansion of n in k
8.465 * [backup-simplify]: Simplify n into n
8.465 * [taylor]: Taking taylor expansion of PI in k
8.465 * [backup-simplify]: Simplify PI into PI
8.465 * [backup-simplify]: Simplify (* n PI) into (* n PI)
8.465 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
8.465 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
8.465 * [backup-simplify]: Simplify (- 0) into 0
8.466 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.466 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25
8.467 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI))))
8.467 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25)
8.467 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n
8.467 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.467 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.467 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n
8.467 * [taylor]: Taking taylor expansion of 0.25 in n
8.467 * [backup-simplify]: Simplify 0.25 into 0.25
8.467 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.467 * [taylor]: Taking taylor expansion of 1.0 in n
8.467 * [backup-simplify]: Simplify 1.0 into 1.0
8.467 * [taylor]: Taking taylor expansion of k in n
8.467 * [backup-simplify]: Simplify k into k
8.467 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.467 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.467 * [taylor]: Taking taylor expansion of 2.0 in n
8.467 * [backup-simplify]: Simplify 2.0 into 2.0
8.467 * [taylor]: Taking taylor expansion of (* n PI) in n
8.467 * [taylor]: Taking taylor expansion of n in n
8.467 * [backup-simplify]: Simplify 0 into 0
8.467 * [backup-simplify]: Simplify 1 into 1
8.467 * [taylor]: Taking taylor expansion of PI in n
8.467 * [backup-simplify]: Simplify PI into PI
8.468 * [backup-simplify]: Simplify (* 0 PI) into 0
8.469 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.470 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.472 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.473 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.473 * [backup-simplify]: Simplify (- k) into (- k)
8.473 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.473 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k))
8.475 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.476 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
8.478 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.478 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n
8.478 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.478 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.478 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n
8.478 * [taylor]: Taking taylor expansion of 0.25 in n
8.478 * [backup-simplify]: Simplify 0.25 into 0.25
8.478 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.478 * [taylor]: Taking taylor expansion of 1.0 in n
8.478 * [backup-simplify]: Simplify 1.0 into 1.0
8.478 * [taylor]: Taking taylor expansion of k in n
8.478 * [backup-simplify]: Simplify k into k
8.478 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.478 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.478 * [taylor]: Taking taylor expansion of 2.0 in n
8.478 * [backup-simplify]: Simplify 2.0 into 2.0
8.478 * [taylor]: Taking taylor expansion of (* n PI) in n
8.478 * [taylor]: Taking taylor expansion of n in n
8.478 * [backup-simplify]: Simplify 0 into 0
8.478 * [backup-simplify]: Simplify 1 into 1
8.478 * [taylor]: Taking taylor expansion of PI in n
8.478 * [backup-simplify]: Simplify PI into PI
8.479 * [backup-simplify]: Simplify (* 0 PI) into 0
8.479 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.480 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.481 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.482 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.482 * [backup-simplify]: Simplify (- k) into (- k)
8.482 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.482 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k))
8.483 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.484 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
8.484 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.484 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
8.485 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
8.485 * [taylor]: Taking taylor expansion of 0.25 in k
8.485 * [backup-simplify]: Simplify 0.25 into 0.25
8.485 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
8.485 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.485 * [taylor]: Taking taylor expansion of 1.0 in k
8.485 * [backup-simplify]: Simplify 1.0 into 1.0
8.485 * [taylor]: Taking taylor expansion of k in k
8.485 * [backup-simplify]: Simplify 0 into 0
8.485 * [backup-simplify]: Simplify 1 into 1
8.485 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
8.485 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.485 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.485 * [taylor]: Taking taylor expansion of 2.0 in k
8.485 * [backup-simplify]: Simplify 2.0 into 2.0
8.485 * [taylor]: Taking taylor expansion of PI in k
8.485 * [backup-simplify]: Simplify PI into PI
8.485 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.486 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.486 * [taylor]: Taking taylor expansion of (log n) in k
8.486 * [taylor]: Taking taylor expansion of n in k
8.486 * [backup-simplify]: Simplify n into n
8.486 * [backup-simplify]: Simplify (log n) into (log n)
8.486 * [backup-simplify]: Simplify (- 0) into 0
8.486 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.487 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
8.488 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
8.489 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n)))
8.489 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))
8.490 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))
8.491 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.491 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.492 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.493 * [backup-simplify]: Simplify (- 0) into 0
8.493 * [backup-simplify]: Simplify (+ 0 0) into 0
8.493 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0
8.494 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.495 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
8.496 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.496 * [taylor]: Taking taylor expansion of 0 in k
8.496 * [backup-simplify]: Simplify 0 into 0
8.496 * [backup-simplify]: Simplify 0 into 0
8.496 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.498 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.498 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
8.498 * [backup-simplify]: Simplify (+ 0 0) into 0
8.499 * [backup-simplify]: Simplify (- 1) into -1
8.499 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.504 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
8.505 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))))
8.508 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))
8.511 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))
8.512 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.514 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.518 * [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
8.518 * [backup-simplify]: Simplify (- 0) into 0
8.519 * [backup-simplify]: Simplify (+ 0 0) into 0
8.520 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
8.521 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.523 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.526 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.526 * [taylor]: Taking taylor expansion of 0 in k
8.526 * [backup-simplify]: Simplify 0 into 0
8.526 * [backup-simplify]: Simplify 0 into 0
8.526 * [backup-simplify]: Simplify 0 into 0
8.527 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.531 * [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
8.533 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
8.534 * [backup-simplify]: Simplify (+ 0 0) into 0
8.534 * [backup-simplify]: Simplify (- 0) into 0
8.534 * [backup-simplify]: Simplify (+ 0 0) into 0
8.536 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.540 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
8.544 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))
8.550 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))
8.561 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
8.562 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k))))
8.562 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0
8.562 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k
8.562 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
8.562 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
8.562 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k
8.562 * [taylor]: Taking taylor expansion of 0.25 in k
8.562 * [backup-simplify]: Simplify 0.25 into 0.25
8.562 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.562 * [taylor]: Taking taylor expansion of 1.0 in k
8.562 * [backup-simplify]: Simplify 1.0 into 1.0
8.562 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.563 * [taylor]: Taking taylor expansion of k in k
8.563 * [backup-simplify]: Simplify 0 into 0
8.563 * [backup-simplify]: Simplify 1 into 1
8.563 * [backup-simplify]: Simplify (/ 1 1) into 1
8.563 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
8.563 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
8.563 * [taylor]: Taking taylor expansion of 2.0 in k
8.563 * [backup-simplify]: Simplify 2.0 into 2.0
8.563 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.563 * [taylor]: Taking taylor expansion of PI in k
8.563 * [backup-simplify]: Simplify PI into PI
8.563 * [taylor]: Taking taylor expansion of n in k
8.563 * [backup-simplify]: Simplify n into n
8.563 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.563 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
8.563 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
8.563 * [backup-simplify]: Simplify (- 1) into -1
8.564 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.564 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25
8.564 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n))))
8.564 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
8.564 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n
8.564 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.564 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.564 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n
8.564 * [taylor]: Taking taylor expansion of 0.25 in n
8.564 * [backup-simplify]: Simplify 0.25 into 0.25
8.564 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.564 * [taylor]: Taking taylor expansion of 1.0 in n
8.564 * [backup-simplify]: Simplify 1.0 into 1.0
8.564 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.564 * [taylor]: Taking taylor expansion of k in n
8.564 * [backup-simplify]: Simplify k into k
8.564 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.564 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.565 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.565 * [taylor]: Taking taylor expansion of 2.0 in n
8.565 * [backup-simplify]: Simplify 2.0 into 2.0
8.565 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.565 * [taylor]: Taking taylor expansion of PI in n
8.565 * [backup-simplify]: Simplify PI into PI
8.565 * [taylor]: Taking taylor expansion of n in n
8.565 * [backup-simplify]: Simplify 0 into 0
8.565 * [backup-simplify]: Simplify 1 into 1
8.565 * [backup-simplify]: Simplify (/ PI 1) into PI
8.565 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.566 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.566 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.566 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.566 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k)))
8.567 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.568 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
8.568 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.569 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n
8.569 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.569 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.569 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n
8.569 * [taylor]: Taking taylor expansion of 0.25 in n
8.569 * [backup-simplify]: Simplify 0.25 into 0.25
8.569 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.569 * [taylor]: Taking taylor expansion of 1.0 in n
8.569 * [backup-simplify]: Simplify 1.0 into 1.0
8.569 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.569 * [taylor]: Taking taylor expansion of k in n
8.569 * [backup-simplify]: Simplify k into k
8.569 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.569 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.569 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.569 * [taylor]: Taking taylor expansion of 2.0 in n
8.569 * [backup-simplify]: Simplify 2.0 into 2.0
8.569 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.569 * [taylor]: Taking taylor expansion of PI in n
8.569 * [backup-simplify]: Simplify PI into PI
8.569 * [taylor]: Taking taylor expansion of n in n
8.569 * [backup-simplify]: Simplify 0 into 0
8.569 * [backup-simplify]: Simplify 1 into 1
8.569 * [backup-simplify]: Simplify (/ PI 1) into PI
8.570 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.570 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.570 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.570 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.570 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k)))
8.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.572 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
8.573 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.573 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
8.573 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
8.573 * [taylor]: Taking taylor expansion of 0.25 in k
8.573 * [backup-simplify]: Simplify 0.25 into 0.25
8.573 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
8.573 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
8.573 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.573 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.573 * [taylor]: Taking taylor expansion of 2.0 in k
8.573 * [backup-simplify]: Simplify 2.0 into 2.0
8.573 * [taylor]: Taking taylor expansion of PI in k
8.573 * [backup-simplify]: Simplify PI into PI
8.573 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.574 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.574 * [taylor]: Taking taylor expansion of (log n) in k
8.574 * [taylor]: Taking taylor expansion of n in k
8.574 * [backup-simplify]: Simplify n into n
8.574 * [backup-simplify]: Simplify (log n) into (log n)
8.574 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.574 * [taylor]: Taking taylor expansion of 1.0 in k
8.574 * [backup-simplify]: Simplify 1.0 into 1.0
8.574 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.574 * [taylor]: Taking taylor expansion of k in k
8.574 * [backup-simplify]: Simplify 0 into 0
8.574 * [backup-simplify]: Simplify 1 into 1
8.574 * [backup-simplify]: Simplify (/ 1 1) into 1
8.575 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.575 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
8.575 * [backup-simplify]: Simplify (- 1) into -1
8.576 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.576 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
8.577 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n)))
8.578 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.578 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.579 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.580 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.581 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.581 * [backup-simplify]: Simplify (- 0) into 0
8.581 * [backup-simplify]: Simplify (+ 0 0) into 0
8.581 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0
8.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.583 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
8.584 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.584 * [taylor]: Taking taylor expansion of 0 in k
8.584 * [backup-simplify]: Simplify 0 into 0
8.584 * [backup-simplify]: Simplify 0 into 0
8.584 * [backup-simplify]: Simplify 0 into 0
8.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.586 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.588 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
8.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.588 * [backup-simplify]: Simplify (- 0) into 0
8.588 * [backup-simplify]: Simplify (+ 0 0) into 0
8.589 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
8.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.591 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
8.592 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.592 * [taylor]: Taking taylor expansion of 0 in k
8.592 * [backup-simplify]: Simplify 0 into 0
8.592 * [backup-simplify]: Simplify 0 into 0
8.592 * [backup-simplify]: Simplify 0 into 0
8.592 * [backup-simplify]: Simplify 0 into 0
8.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.594 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.599 * [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
8.600 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.600 * [backup-simplify]: Simplify (- 0) into 0
8.601 * [backup-simplify]: Simplify (+ 0 0) into 0
8.602 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
8.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.605 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
8.609 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
8.609 * [taylor]: Taking taylor expansion of 0 in k
8.609 * [backup-simplify]: Simplify 0 into 0
8.609 * [backup-simplify]: Simplify 0 into 0
8.610 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
8.611 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0)))
8.611 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0
8.611 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k
8.611 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
8.611 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
8.611 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k
8.611 * [taylor]: Taking taylor expansion of 0.25 in k
8.612 * [backup-simplify]: Simplify 0.25 into 0.25
8.612 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
8.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.612 * [taylor]: Taking taylor expansion of k in k
8.612 * [backup-simplify]: Simplify 0 into 0
8.612 * [backup-simplify]: Simplify 1 into 1
8.612 * [backup-simplify]: Simplify (/ 1 1) into 1
8.612 * [taylor]: Taking taylor expansion of 1.0 in k
8.612 * [backup-simplify]: Simplify 1.0 into 1.0
8.612 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
8.612 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
8.612 * [taylor]: Taking taylor expansion of -2.0 in k
8.612 * [backup-simplify]: Simplify -2.0 into -2.0
8.612 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.612 * [taylor]: Taking taylor expansion of PI in k
8.612 * [backup-simplify]: Simplify PI into PI
8.612 * [taylor]: Taking taylor expansion of n in k
8.612 * [backup-simplify]: Simplify n into n
8.613 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.613 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
8.613 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
8.613 * [backup-simplify]: Simplify (+ 1 0) into 1
8.614 * [backup-simplify]: Simplify (* 0.25 1) into 0.25
8.614 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n))))
8.614 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
8.614 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n
8.614 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
8.614 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
8.614 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n
8.614 * [taylor]: Taking taylor expansion of 0.25 in n
8.614 * [backup-simplify]: Simplify 0.25 into 0.25
8.614 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
8.614 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.614 * [taylor]: Taking taylor expansion of k in n
8.614 * [backup-simplify]: Simplify k into k
8.615 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.615 * [taylor]: Taking taylor expansion of 1.0 in n
8.615 * [backup-simplify]: Simplify 1.0 into 1.0
8.615 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
8.615 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.615 * [taylor]: Taking taylor expansion of -2.0 in n
8.615 * [backup-simplify]: Simplify -2.0 into -2.0
8.615 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.615 * [taylor]: Taking taylor expansion of PI in n
8.615 * [backup-simplify]: Simplify PI into PI
8.615 * [taylor]: Taking taylor expansion of n in n
8.615 * [backup-simplify]: Simplify 0 into 0
8.615 * [backup-simplify]: Simplify 1 into 1
8.615 * [backup-simplify]: Simplify (/ PI 1) into PI
8.616 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.617 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.617 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
8.617 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0))
8.619 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.620 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
8.621 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.621 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n
8.621 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
8.621 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
8.621 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n
8.622 * [taylor]: Taking taylor expansion of 0.25 in n
8.622 * [backup-simplify]: Simplify 0.25 into 0.25
8.622 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
8.622 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.622 * [taylor]: Taking taylor expansion of k in n
8.622 * [backup-simplify]: Simplify k into k
8.622 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.622 * [taylor]: Taking taylor expansion of 1.0 in n
8.622 * [backup-simplify]: Simplify 1.0 into 1.0
8.622 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
8.622 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.622 * [taylor]: Taking taylor expansion of -2.0 in n
8.622 * [backup-simplify]: Simplify -2.0 into -2.0
8.622 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.622 * [taylor]: Taking taylor expansion of PI in n
8.622 * [backup-simplify]: Simplify PI into PI
8.622 * [taylor]: Taking taylor expansion of n in n
8.622 * [backup-simplify]: Simplify 0 into 0
8.622 * [backup-simplify]: Simplify 1 into 1
8.623 * [backup-simplify]: Simplify (/ PI 1) into PI
8.623 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.624 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.624 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
8.624 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0))
8.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.625 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
8.626 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.626 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
8.626 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
8.626 * [taylor]: Taking taylor expansion of 0.25 in k
8.626 * [backup-simplify]: Simplify 0.25 into 0.25
8.626 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
8.626 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
8.626 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.626 * [taylor]: Taking taylor expansion of k in k
8.626 * [backup-simplify]: Simplify 0 into 0
8.626 * [backup-simplify]: Simplify 1 into 1
8.627 * [backup-simplify]: Simplify (/ 1 1) into 1
8.627 * [taylor]: Taking taylor expansion of 1.0 in k
8.627 * [backup-simplify]: Simplify 1.0 into 1.0
8.627 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
8.627 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
8.627 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
8.627 * [taylor]: Taking taylor expansion of -2.0 in k
8.627 * [backup-simplify]: Simplify -2.0 into -2.0
8.627 * [taylor]: Taking taylor expansion of PI in k
8.627 * [backup-simplify]: Simplify PI into PI
8.627 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.628 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.628 * [taylor]: Taking taylor expansion of (log n) in k
8.628 * [taylor]: Taking taylor expansion of n in k
8.628 * [backup-simplify]: Simplify n into n
8.628 * [backup-simplify]: Simplify (log n) into (log n)
8.628 * [backup-simplify]: Simplify (+ 1 0) into 1
8.628 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.629 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
8.633 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
8.633 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n)))
8.634 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.635 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.636 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.636 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
8.637 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
8.637 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.637 * [backup-simplify]: Simplify (+ 0 0) into 0
8.638 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0
8.639 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.639 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
8.641 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.641 * [taylor]: Taking taylor expansion of 0 in k
8.641 * [backup-simplify]: Simplify 0 into 0
8.641 * [backup-simplify]: Simplify 0 into 0
8.641 * [backup-simplify]: Simplify 0 into 0
8.641 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.642 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.644 * [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
8.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.644 * [backup-simplify]: Simplify (+ 0 0) into 0
8.645 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
8.646 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.646 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
8.649 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.649 * [taylor]: Taking taylor expansion of 0 in k
8.649 * [backup-simplify]: Simplify 0 into 0
8.649 * [backup-simplify]: Simplify 0 into 0
8.649 * [backup-simplify]: Simplify 0 into 0
8.649 * [backup-simplify]: Simplify 0 into 0
8.651 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.652 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.659 * [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
8.659 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.660 * [backup-simplify]: Simplify (+ 0 0) into 0
8.661 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
8.663 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.665 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
8.668 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
8.668 * [taylor]: Taking taylor expansion of 0 in k
8.668 * [backup-simplify]: Simplify 0 into 0
8.668 * [backup-simplify]: Simplify 0 into 0
8.670 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
8.670 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2)
8.671 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k)))
8.671 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0
8.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k
8.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
8.671 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
8.671 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k
8.671 * [taylor]: Taking taylor expansion of 0.25 in k
8.671 * [backup-simplify]: Simplify 0.25 into 0.25
8.671 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.671 * [taylor]: Taking taylor expansion of 1.0 in k
8.671 * [backup-simplify]: Simplify 1.0 into 1.0
8.671 * [taylor]: Taking taylor expansion of k in k
8.671 * [backup-simplify]: Simplify 0 into 0
8.671 * [backup-simplify]: Simplify 1 into 1
8.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
8.671 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
8.671 * [taylor]: Taking taylor expansion of 2.0 in k
8.671 * [backup-simplify]: Simplify 2.0 into 2.0
8.671 * [taylor]: Taking taylor expansion of (* n PI) in k
8.671 * [taylor]: Taking taylor expansion of n in k
8.671 * [backup-simplify]: Simplify n into n
8.671 * [taylor]: Taking taylor expansion of PI in k
8.671 * [backup-simplify]: Simplify PI into PI
8.671 * [backup-simplify]: Simplify (* n PI) into (* n PI)
8.671 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
8.672 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
8.672 * [backup-simplify]: Simplify (- 0) into 0
8.672 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.673 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25
8.673 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI))))
8.673 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25)
8.673 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n
8.673 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.673 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.673 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n
8.673 * [taylor]: Taking taylor expansion of 0.25 in n
8.673 * [backup-simplify]: Simplify 0.25 into 0.25
8.673 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.674 * [taylor]: Taking taylor expansion of 1.0 in n
8.674 * [backup-simplify]: Simplify 1.0 into 1.0
8.674 * [taylor]: Taking taylor expansion of k in n
8.674 * [backup-simplify]: Simplify k into k
8.674 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.674 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.674 * [taylor]: Taking taylor expansion of 2.0 in n
8.674 * [backup-simplify]: Simplify 2.0 into 2.0
8.674 * [taylor]: Taking taylor expansion of (* n PI) in n
8.674 * [taylor]: Taking taylor expansion of n in n
8.674 * [backup-simplify]: Simplify 0 into 0
8.674 * [backup-simplify]: Simplify 1 into 1
8.674 * [taylor]: Taking taylor expansion of PI in n
8.674 * [backup-simplify]: Simplify PI into PI
8.674 * [backup-simplify]: Simplify (* 0 PI) into 0
8.675 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.676 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.678 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.679 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.679 * [backup-simplify]: Simplify (- k) into (- k)
8.679 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.679 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k))
8.681 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.682 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
8.683 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.683 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n
8.684 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
8.684 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
8.684 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n
8.684 * [taylor]: Taking taylor expansion of 0.25 in n
8.684 * [backup-simplify]: Simplify 0.25 into 0.25
8.684 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
8.684 * [taylor]: Taking taylor expansion of 1.0 in n
8.684 * [backup-simplify]: Simplify 1.0 into 1.0
8.684 * [taylor]: Taking taylor expansion of k in n
8.684 * [backup-simplify]: Simplify k into k
8.684 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
8.684 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.684 * [taylor]: Taking taylor expansion of 2.0 in n
8.684 * [backup-simplify]: Simplify 2.0 into 2.0
8.684 * [taylor]: Taking taylor expansion of (* n PI) in n
8.684 * [taylor]: Taking taylor expansion of n in n
8.684 * [backup-simplify]: Simplify 0 into 0
8.684 * [backup-simplify]: Simplify 1 into 1
8.684 * [taylor]: Taking taylor expansion of PI in n
8.684 * [backup-simplify]: Simplify PI into PI
8.685 * [backup-simplify]: Simplify (* 0 PI) into 0
8.685 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.687 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.688 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.688 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.688 * [backup-simplify]: Simplify (- k) into (- k)
8.688 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
8.689 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k))
8.689 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.690 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
8.691 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
8.691 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
8.691 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
8.691 * [taylor]: Taking taylor expansion of 0.25 in k
8.691 * [backup-simplify]: Simplify 0.25 into 0.25
8.691 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
8.691 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
8.691 * [taylor]: Taking taylor expansion of 1.0 in k
8.691 * [backup-simplify]: Simplify 1.0 into 1.0
8.691 * [taylor]: Taking taylor expansion of k in k
8.691 * [backup-simplify]: Simplify 0 into 0
8.691 * [backup-simplify]: Simplify 1 into 1
8.691 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
8.691 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.691 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.691 * [taylor]: Taking taylor expansion of 2.0 in k
8.691 * [backup-simplify]: Simplify 2.0 into 2.0
8.691 * [taylor]: Taking taylor expansion of PI in k
8.691 * [backup-simplify]: Simplify PI into PI
8.692 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.692 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.692 * [taylor]: Taking taylor expansion of (log n) in k
8.692 * [taylor]: Taking taylor expansion of n in k
8.692 * [backup-simplify]: Simplify n into n
8.692 * [backup-simplify]: Simplify (log n) into (log n)
8.693 * [backup-simplify]: Simplify (- 0) into 0
8.693 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
8.693 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
8.694 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
8.695 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n)))
8.696 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))
8.696 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))
8.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.697 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.698 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.699 * [backup-simplify]: Simplify (- 0) into 0
8.699 * [backup-simplify]: Simplify (+ 0 0) into 0
8.699 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0
8.700 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.701 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
8.702 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.702 * [taylor]: Taking taylor expansion of 0 in k
8.702 * [backup-simplify]: Simplify 0 into 0
8.702 * [backup-simplify]: Simplify 0 into 0
8.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.704 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.704 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
8.704 * [backup-simplify]: Simplify (+ 0 0) into 0
8.705 * [backup-simplify]: Simplify (- 1) into -1
8.705 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.706 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
8.708 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))))
8.712 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))
8.715 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))
8.716 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.721 * [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
8.722 * [backup-simplify]: Simplify (- 0) into 0
8.722 * [backup-simplify]: Simplify (+ 0 0) into 0
8.723 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
8.725 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
8.726 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.729 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.729 * [taylor]: Taking taylor expansion of 0 in k
8.729 * [backup-simplify]: Simplify 0 into 0
8.729 * [backup-simplify]: Simplify 0 into 0
8.729 * [backup-simplify]: Simplify 0 into 0
8.730 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.734 * [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
8.736 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
8.737 * [backup-simplify]: Simplify (+ 0 0) into 0
8.737 * [backup-simplify]: Simplify (- 0) into 0
8.737 * [backup-simplify]: Simplify (+ 0 0) into 0
8.739 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
8.742 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
8.747 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))
8.753 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))
8.766 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
8.767 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k))))
8.767 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0
8.767 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k
8.767 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
8.767 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
8.767 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k
8.767 * [taylor]: Taking taylor expansion of 0.25 in k
8.767 * [backup-simplify]: Simplify 0.25 into 0.25
8.767 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.767 * [taylor]: Taking taylor expansion of 1.0 in k
8.767 * [backup-simplify]: Simplify 1.0 into 1.0
8.767 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.767 * [taylor]: Taking taylor expansion of k in k
8.767 * [backup-simplify]: Simplify 0 into 0
8.767 * [backup-simplify]: Simplify 1 into 1
8.768 * [backup-simplify]: Simplify (/ 1 1) into 1
8.768 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
8.768 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
8.768 * [taylor]: Taking taylor expansion of 2.0 in k
8.768 * [backup-simplify]: Simplify 2.0 into 2.0
8.768 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.768 * [taylor]: Taking taylor expansion of PI in k
8.768 * [backup-simplify]: Simplify PI into PI
8.768 * [taylor]: Taking taylor expansion of n in k
8.768 * [backup-simplify]: Simplify n into n
8.768 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.768 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
8.768 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
8.768 * [backup-simplify]: Simplify (- 1) into -1
8.768 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.769 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25
8.769 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n))))
8.769 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
8.769 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n
8.769 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.769 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.769 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n
8.769 * [taylor]: Taking taylor expansion of 0.25 in n
8.769 * [backup-simplify]: Simplify 0.25 into 0.25
8.769 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.769 * [taylor]: Taking taylor expansion of 1.0 in n
8.769 * [backup-simplify]: Simplify 1.0 into 1.0
8.769 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.769 * [taylor]: Taking taylor expansion of k in n
8.769 * [backup-simplify]: Simplify k into k
8.769 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.769 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.769 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.769 * [taylor]: Taking taylor expansion of 2.0 in n
8.769 * [backup-simplify]: Simplify 2.0 into 2.0
8.769 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.769 * [taylor]: Taking taylor expansion of PI in n
8.769 * [backup-simplify]: Simplify PI into PI
8.769 * [taylor]: Taking taylor expansion of n in n
8.769 * [backup-simplify]: Simplify 0 into 0
8.769 * [backup-simplify]: Simplify 1 into 1
8.770 * [backup-simplify]: Simplify (/ PI 1) into PI
8.770 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.771 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.771 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.771 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.771 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k)))
8.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.772 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
8.773 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.773 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n
8.773 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
8.773 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
8.773 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n
8.773 * [taylor]: Taking taylor expansion of 0.25 in n
8.773 * [backup-simplify]: Simplify 0.25 into 0.25
8.773 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
8.773 * [taylor]: Taking taylor expansion of 1.0 in n
8.773 * [backup-simplify]: Simplify 1.0 into 1.0
8.773 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.773 * [taylor]: Taking taylor expansion of k in n
8.773 * [backup-simplify]: Simplify k into k
8.774 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.774 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
8.774 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.774 * [taylor]: Taking taylor expansion of 2.0 in n
8.774 * [backup-simplify]: Simplify 2.0 into 2.0
8.774 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.774 * [taylor]: Taking taylor expansion of PI in n
8.774 * [backup-simplify]: Simplify PI into PI
8.774 * [taylor]: Taking taylor expansion of n in n
8.774 * [backup-simplify]: Simplify 0 into 0
8.774 * [backup-simplify]: Simplify 1 into 1
8.774 * [backup-simplify]: Simplify (/ PI 1) into PI
8.774 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.775 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.775 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.775 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
8.775 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k)))
8.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.777 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
8.777 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.778 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
8.778 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
8.778 * [taylor]: Taking taylor expansion of 0.25 in k
8.778 * [backup-simplify]: Simplify 0.25 into 0.25
8.778 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
8.778 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
8.778 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
8.778 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
8.778 * [taylor]: Taking taylor expansion of 2.0 in k
8.778 * [backup-simplify]: Simplify 2.0 into 2.0
8.778 * [taylor]: Taking taylor expansion of PI in k
8.778 * [backup-simplify]: Simplify PI into PI
8.778 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.779 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
8.779 * [taylor]: Taking taylor expansion of (log n) in k
8.779 * [taylor]: Taking taylor expansion of n in k
8.779 * [backup-simplify]: Simplify n into n
8.779 * [backup-simplify]: Simplify (log n) into (log n)
8.779 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
8.779 * [taylor]: Taking taylor expansion of 1.0 in k
8.779 * [backup-simplify]: Simplify 1.0 into 1.0
8.779 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.779 * [taylor]: Taking taylor expansion of k in k
8.779 * [backup-simplify]: Simplify 0 into 0
8.779 * [backup-simplify]: Simplify 1 into 1
8.779 * [backup-simplify]: Simplify (/ 1 1) into 1
8.779 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.780 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
8.780 * [backup-simplify]: Simplify (- 1) into -1
8.780 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.781 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
8.782 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n)))
8.782 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.783 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
8.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.784 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.785 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
8.785 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.786 * [backup-simplify]: Simplify (- 0) into 0
8.786 * [backup-simplify]: Simplify (+ 0 0) into 0
8.786 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0
8.787 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.788 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
8.789 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.789 * [taylor]: Taking taylor expansion of 0 in k
8.789 * [backup-simplify]: Simplify 0 into 0
8.789 * [backup-simplify]: Simplify 0 into 0
8.789 * [backup-simplify]: Simplify 0 into 0
8.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.794 * [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
8.794 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.795 * [backup-simplify]: Simplify (- 0) into 0
8.795 * [backup-simplify]: Simplify (+ 0 0) into 0
8.796 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
8.797 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.799 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
8.802 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.802 * [taylor]: Taking taylor expansion of 0 in k
8.802 * [backup-simplify]: Simplify 0 into 0
8.802 * [backup-simplify]: Simplify 0 into 0
8.802 * [backup-simplify]: Simplify 0 into 0
8.802 * [backup-simplify]: Simplify 0 into 0
8.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.812 * [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
8.812 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.813 * [backup-simplify]: Simplify (- 0) into 0
8.813 * [backup-simplify]: Simplify (+ 0 0) into 0
8.815 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
8.816 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
8.818 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
8.821 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
8.821 * [taylor]: Taking taylor expansion of 0 in k
8.821 * [backup-simplify]: Simplify 0 into 0
8.821 * [backup-simplify]: Simplify 0 into 0
8.823 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
8.824 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0)))
8.824 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0
8.824 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k
8.824 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
8.824 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
8.824 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k
8.824 * [taylor]: Taking taylor expansion of 0.25 in k
8.824 * [backup-simplify]: Simplify 0.25 into 0.25
8.824 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
8.824 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.824 * [taylor]: Taking taylor expansion of k in k
8.824 * [backup-simplify]: Simplify 0 into 0
8.824 * [backup-simplify]: Simplify 1 into 1
8.824 * [backup-simplify]: Simplify (/ 1 1) into 1
8.824 * [taylor]: Taking taylor expansion of 1.0 in k
8.825 * [backup-simplify]: Simplify 1.0 into 1.0
8.825 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
8.825 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
8.825 * [taylor]: Taking taylor expansion of -2.0 in k
8.825 * [backup-simplify]: Simplify -2.0 into -2.0
8.825 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.825 * [taylor]: Taking taylor expansion of PI in k
8.825 * [backup-simplify]: Simplify PI into PI
8.825 * [taylor]: Taking taylor expansion of n in k
8.825 * [backup-simplify]: Simplify n into n
8.825 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.825 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
8.825 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
8.826 * [backup-simplify]: Simplify (+ 1 0) into 1
8.826 * [backup-simplify]: Simplify (* 0.25 1) into 0.25
8.826 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n))))
8.826 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
8.826 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n
8.826 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
8.827 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
8.827 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n
8.827 * [taylor]: Taking taylor expansion of 0.25 in n
8.827 * [backup-simplify]: Simplify 0.25 into 0.25
8.827 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
8.827 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.827 * [taylor]: Taking taylor expansion of k in n
8.827 * [backup-simplify]: Simplify k into k
8.827 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.827 * [taylor]: Taking taylor expansion of 1.0 in n
8.827 * [backup-simplify]: Simplify 1.0 into 1.0
8.827 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
8.827 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.827 * [taylor]: Taking taylor expansion of -2.0 in n
8.827 * [backup-simplify]: Simplify -2.0 into -2.0
8.827 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.827 * [taylor]: Taking taylor expansion of PI in n
8.827 * [backup-simplify]: Simplify PI into PI
8.827 * [taylor]: Taking taylor expansion of n in n
8.827 * [backup-simplify]: Simplify 0 into 0
8.827 * [backup-simplify]: Simplify 1 into 1
8.828 * [backup-simplify]: Simplify (/ PI 1) into PI
8.828 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.830 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.830 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
8.830 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0))
8.831 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.833 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
8.834 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.834 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n
8.834 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
8.834 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
8.834 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n
8.834 * [taylor]: Taking taylor expansion of 0.25 in n
8.834 * [backup-simplify]: Simplify 0.25 into 0.25
8.834 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
8.834 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.835 * [taylor]: Taking taylor expansion of k in n
8.835 * [backup-simplify]: Simplify k into k
8.835 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.835 * [taylor]: Taking taylor expansion of 1.0 in n
8.835 * [backup-simplify]: Simplify 1.0 into 1.0
8.835 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
8.835 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.835 * [taylor]: Taking taylor expansion of -2.0 in n
8.835 * [backup-simplify]: Simplify -2.0 into -2.0
8.835 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.835 * [taylor]: Taking taylor expansion of PI in n
8.835 * [backup-simplify]: Simplify PI into PI
8.835 * [taylor]: Taking taylor expansion of n in n
8.835 * [backup-simplify]: Simplify 0 into 0
8.835 * [backup-simplify]: Simplify 1 into 1
8.836 * [backup-simplify]: Simplify (/ PI 1) into PI
8.836 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.837 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.837 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
8.837 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0))
8.839 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.840 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
8.841 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.842 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
8.842 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
8.842 * [taylor]: Taking taylor expansion of 0.25 in k
8.842 * [backup-simplify]: Simplify 0.25 into 0.25
8.842 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
8.842 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
8.842 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.842 * [taylor]: Taking taylor expansion of k in k
8.842 * [backup-simplify]: Simplify 0 into 0
8.842 * [backup-simplify]: Simplify 1 into 1
8.842 * [backup-simplify]: Simplify (/ 1 1) into 1
8.842 * [taylor]: Taking taylor expansion of 1.0 in k
8.842 * [backup-simplify]: Simplify 1.0 into 1.0
8.842 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
8.842 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
8.842 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
8.842 * [taylor]: Taking taylor expansion of -2.0 in k
8.843 * [backup-simplify]: Simplify -2.0 into -2.0
8.843 * [taylor]: Taking taylor expansion of PI in k
8.843 * [backup-simplify]: Simplify PI into PI
8.843 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.844 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
8.844 * [taylor]: Taking taylor expansion of (log n) in k
8.844 * [taylor]: Taking taylor expansion of n in k
8.844 * [backup-simplify]: Simplify n into n
8.844 * [backup-simplify]: Simplify (log n) into (log n)
8.845 * [backup-simplify]: Simplify (+ 1 0) into 1
8.845 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.846 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
8.847 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
8.848 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n)))
8.850 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.851 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
8.852 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.853 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
8.855 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
8.855 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.855 * [backup-simplify]: Simplify (+ 0 0) into 0
8.856 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0
8.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.859 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
8.861 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.861 * [taylor]: Taking taylor expansion of 0 in k
8.861 * [backup-simplify]: Simplify 0 into 0
8.861 * [backup-simplify]: Simplify 0 into 0
8.861 * [backup-simplify]: Simplify 0 into 0
8.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.863 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.867 * [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
8.867 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.868 * [backup-simplify]: Simplify (+ 0 0) into 0
8.869 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
8.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.872 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
8.875 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.875 * [taylor]: Taking taylor expansion of 0 in k
8.875 * [backup-simplify]: Simplify 0 into 0
8.875 * [backup-simplify]: Simplify 0 into 0
8.875 * [backup-simplify]: Simplify 0 into 0
8.875 * [backup-simplify]: Simplify 0 into 0
8.876 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.878 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.882 * [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
8.882 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.882 * [backup-simplify]: Simplify (+ 0 0) into 0
8.883 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
8.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
8.885 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
8.887 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
8.887 * [taylor]: Taking taylor expansion of 0 in k
8.887 * [backup-simplify]: Simplify 0 into 0
8.887 * [backup-simplify]: Simplify 0 into 0
8.888 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
8.888 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
8.888 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
8.888 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
8.888 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.888 * [taylor]: Taking taylor expansion of 2.0 in n
8.888 * [backup-simplify]: Simplify 2.0 into 2.0
8.888 * [taylor]: Taking taylor expansion of (* n PI) in n
8.888 * [taylor]: Taking taylor expansion of n in n
8.888 * [backup-simplify]: Simplify 0 into 0
8.888 * [backup-simplify]: Simplify 1 into 1
8.888 * [taylor]: Taking taylor expansion of PI in n
8.888 * [backup-simplify]: Simplify PI into PI
8.888 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.888 * [taylor]: Taking taylor expansion of 2.0 in n
8.888 * [backup-simplify]: Simplify 2.0 into 2.0
8.888 * [taylor]: Taking taylor expansion of (* n PI) in n
8.888 * [taylor]: Taking taylor expansion of n in n
8.888 * [backup-simplify]: Simplify 0 into 0
8.888 * [backup-simplify]: Simplify 1 into 1
8.888 * [taylor]: Taking taylor expansion of PI in n
8.888 * [backup-simplify]: Simplify PI into PI
8.889 * [backup-simplify]: Simplify (* 0 PI) into 0
8.889 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.889 * [backup-simplify]: Simplify 0 into 0
8.890 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.891 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.892 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.892 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.896 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.896 * [backup-simplify]: Simplify 0 into 0
8.897 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.898 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.898 * [backup-simplify]: Simplify 0 into 0
8.898 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.899 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.899 * [backup-simplify]: Simplify 0 into 0
8.900 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.901 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
8.901 * [backup-simplify]: Simplify 0 into 0
8.902 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.903 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
8.903 * [backup-simplify]: Simplify 0 into 0
8.904 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
8.905 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
8.905 * [backup-simplify]: Simplify 0 into 0
8.906 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
8.906 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
8.906 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
8.906 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.906 * [taylor]: Taking taylor expansion of 2.0 in n
8.906 * [backup-simplify]: Simplify 2.0 into 2.0
8.906 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.906 * [taylor]: Taking taylor expansion of PI in n
8.906 * [backup-simplify]: Simplify PI into PI
8.906 * [taylor]: Taking taylor expansion of n in n
8.906 * [backup-simplify]: Simplify 0 into 0
8.906 * [backup-simplify]: Simplify 1 into 1
8.907 * [backup-simplify]: Simplify (/ PI 1) into PI
8.907 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.907 * [taylor]: Taking taylor expansion of 2.0 in n
8.907 * [backup-simplify]: Simplify 2.0 into 2.0
8.907 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.907 * [taylor]: Taking taylor expansion of PI in n
8.907 * [backup-simplify]: Simplify PI into PI
8.907 * [taylor]: Taking taylor expansion of n in n
8.907 * [backup-simplify]: Simplify 0 into 0
8.907 * [backup-simplify]: Simplify 1 into 1
8.907 * [backup-simplify]: Simplify (/ PI 1) into PI
8.908 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.909 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.910 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.910 * [backup-simplify]: Simplify 0 into 0
8.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.913 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.913 * [backup-simplify]: Simplify 0 into 0
8.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.915 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.915 * [backup-simplify]: Simplify 0 into 0
8.916 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.916 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.916 * [backup-simplify]: Simplify 0 into 0
8.917 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.918 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.918 * [backup-simplify]: Simplify 0 into 0
8.919 * [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
8.919 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.919 * [backup-simplify]: Simplify 0 into 0
8.920 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
8.920 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
8.920 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
8.920 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.920 * [taylor]: Taking taylor expansion of -2.0 in n
8.920 * [backup-simplify]: Simplify -2.0 into -2.0
8.920 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.920 * [taylor]: Taking taylor expansion of PI in n
8.920 * [backup-simplify]: Simplify PI into PI
8.920 * [taylor]: Taking taylor expansion of n in n
8.920 * [backup-simplify]: Simplify 0 into 0
8.920 * [backup-simplify]: Simplify 1 into 1
8.921 * [backup-simplify]: Simplify (/ PI 1) into PI
8.921 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.921 * [taylor]: Taking taylor expansion of -2.0 in n
8.921 * [backup-simplify]: Simplify -2.0 into -2.0
8.921 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.921 * [taylor]: Taking taylor expansion of PI in n
8.921 * [backup-simplify]: Simplify PI into PI
8.921 * [taylor]: Taking taylor expansion of n in n
8.921 * [backup-simplify]: Simplify 0 into 0
8.921 * [backup-simplify]: Simplify 1 into 1
8.921 * [backup-simplify]: Simplify (/ PI 1) into PI
8.922 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.922 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.922 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.923 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
8.923 * [backup-simplify]: Simplify 0 into 0
8.923 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.924 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.924 * [backup-simplify]: Simplify 0 into 0
8.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.925 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.925 * [backup-simplify]: Simplify 0 into 0
8.926 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.927 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.927 * [backup-simplify]: Simplify 0 into 0
8.928 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.929 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.929 * [backup-simplify]: Simplify 0 into 0
8.929 * [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
8.930 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.930 * [backup-simplify]: Simplify 0 into 0
8.931 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
8.931 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1)
8.931 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
8.931 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
8.931 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.931 * [taylor]: Taking taylor expansion of 2.0 in n
8.931 * [backup-simplify]: Simplify 2.0 into 2.0
8.931 * [taylor]: Taking taylor expansion of (* n PI) in n
8.931 * [taylor]: Taking taylor expansion of n in n
8.932 * [backup-simplify]: Simplify 0 into 0
8.932 * [backup-simplify]: Simplify 1 into 1
8.932 * [taylor]: Taking taylor expansion of PI in n
8.932 * [backup-simplify]: Simplify PI into PI
8.932 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
8.932 * [taylor]: Taking taylor expansion of 2.0 in n
8.932 * [backup-simplify]: Simplify 2.0 into 2.0
8.932 * [taylor]: Taking taylor expansion of (* n PI) in n
8.932 * [taylor]: Taking taylor expansion of n in n
8.932 * [backup-simplify]: Simplify 0 into 0
8.932 * [backup-simplify]: Simplify 1 into 1
8.932 * [taylor]: Taking taylor expansion of PI in n
8.932 * [backup-simplify]: Simplify PI into PI
8.932 * [backup-simplify]: Simplify (* 0 PI) into 0
8.932 * [backup-simplify]: Simplify (* 2.0 0) into 0
8.932 * [backup-simplify]: Simplify 0 into 0
8.933 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.934 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
8.935 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.935 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.936 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
8.936 * [backup-simplify]: Simplify 0 into 0
8.936 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.937 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.937 * [backup-simplify]: Simplify 0 into 0
8.938 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.939 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.939 * [backup-simplify]: Simplify 0 into 0
8.940 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.940 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
8.940 * [backup-simplify]: Simplify 0 into 0
8.941 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.942 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
8.942 * [backup-simplify]: Simplify 0 into 0
8.944 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
8.946 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
8.946 * [backup-simplify]: Simplify 0 into 0
8.947 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
8.948 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
8.948 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
8.948 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.948 * [taylor]: Taking taylor expansion of 2.0 in n
8.948 * [backup-simplify]: Simplify 2.0 into 2.0
8.948 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.948 * [taylor]: Taking taylor expansion of PI in n
8.948 * [backup-simplify]: Simplify PI into PI
8.948 * [taylor]: Taking taylor expansion of n in n
8.948 * [backup-simplify]: Simplify 0 into 0
8.948 * [backup-simplify]: Simplify 1 into 1
8.948 * [backup-simplify]: Simplify (/ PI 1) into PI
8.949 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
8.949 * [taylor]: Taking taylor expansion of 2.0 in n
8.949 * [backup-simplify]: Simplify 2.0 into 2.0
8.949 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.949 * [taylor]: Taking taylor expansion of PI in n
8.949 * [backup-simplify]: Simplify PI into PI
8.949 * [taylor]: Taking taylor expansion of n in n
8.949 * [backup-simplify]: Simplify 0 into 0
8.949 * [backup-simplify]: Simplify 1 into 1
8.949 * [backup-simplify]: Simplify (/ PI 1) into PI
8.950 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.950 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
8.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.952 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
8.952 * [backup-simplify]: Simplify 0 into 0
8.953 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.954 * [backup-simplify]: Simplify 0 into 0
8.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.956 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.956 * [backup-simplify]: Simplify 0 into 0
8.957 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.959 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.959 * [backup-simplify]: Simplify 0 into 0
8.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.962 * [backup-simplify]: Simplify 0 into 0
8.963 * [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
8.964 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.964 * [backup-simplify]: Simplify 0 into 0
8.965 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
8.966 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
8.966 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
8.966 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.966 * [taylor]: Taking taylor expansion of -2.0 in n
8.966 * [backup-simplify]: Simplify -2.0 into -2.0
8.966 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.966 * [taylor]: Taking taylor expansion of PI in n
8.966 * [backup-simplify]: Simplify PI into PI
8.966 * [taylor]: Taking taylor expansion of n in n
8.966 * [backup-simplify]: Simplify 0 into 0
8.966 * [backup-simplify]: Simplify 1 into 1
8.966 * [backup-simplify]: Simplify (/ PI 1) into PI
8.966 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
8.966 * [taylor]: Taking taylor expansion of -2.0 in n
8.966 * [backup-simplify]: Simplify -2.0 into -2.0
8.966 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.966 * [taylor]: Taking taylor expansion of PI in n
8.967 * [backup-simplify]: Simplify PI into PI
8.967 * [taylor]: Taking taylor expansion of n in n
8.967 * [backup-simplify]: Simplify 0 into 0
8.967 * [backup-simplify]: Simplify 1 into 1
8.967 * [backup-simplify]: Simplify (/ PI 1) into PI
8.968 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.968 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
8.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.970 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
8.970 * [backup-simplify]: Simplify 0 into 0
8.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.972 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
8.972 * [backup-simplify]: Simplify 0 into 0
8.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.974 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.974 * [backup-simplify]: Simplify 0 into 0
8.975 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.976 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.976 * [backup-simplify]: Simplify 0 into 0
8.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.977 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.977 * [backup-simplify]: Simplify 0 into 0
8.978 * [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
8.979 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.979 * [backup-simplify]: Simplify 0 into 0
8.979 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
8.979 * * * [progress]: simplifying candidates
8.983 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* 1 (/ (/ (- 1.0 k) 2.0) 2))
  (* 1 (/ (/ (- 1.0 k) 2.0) 2))
  (* 1 (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
  (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))
  (pow n (/ (/ (- 1.0 k) 2.0) 2))
  (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
  (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* 1 (/ (/ (- 1.0 k) 2.0) 2))
  (* 1 (/ (/ (- 1.0 k) 2.0) 2))
  (* 1 (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
  (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))
  (pow n (/ (/ (- 1.0 k) 2.0) 2))
  (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
  (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)
  (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
8.987 * * [simplify]: Extracting # 0 : cost  0
8.987 * * [simplify]: Extracting # 1 : cost  0
8.987 * * [simplify]: Extracting # 2 : cost  0
8.988 * * [simplify]: Extracting # 3 : cost  0
8.988 * * [simplify]: Extracting # 4 : cost  0
8.988 * * [simplify]: Extracting # 5 : cost  0
8.988 * * [simplify]: Extracting # 6 : cost  0
8.989 * * [simplify]: Extracting # 7 : cost  0
8.989 * * [simplify]: Extracting # 8 : cost  0
8.989 * * [simplify]: Extracting # 9 : cost  0
8.990 * * [simplify]: Extracting # 10 : cost  0
8.990 * * [simplify]: Extracting # 11 : cost  0
8.990 * * [simplify]: Extracting # 12 : cost  0
8.991 * * [simplify]: Extracting # 13 : cost  0
8.991 * * [simplify]: iteration  0 :  245  enodes  (cost  3332 )
9.090 * * [simplify]: Extracting # 0 : cost  0
9.092 * * [simplify]: Extracting # 1 : cost  0
9.099 * * [simplify]: Extracting # 2 : cost  0
9.100 * * [simplify]: Extracting # 3 : cost  0
9.101 * * [simplify]: Extracting # 4 : cost  0
9.102 * * [simplify]: Extracting # 5 : cost  0
9.103 * * [simplify]: iteration  1 :  682  enodes  (cost  3090 )
9.530 * * [simplify]: Extracting # 0 : cost  0
9.540 * * [simplify]: Extracting # 1 : cost  0
9.545 * * [simplify]: Extracting # 2 : cost  0
9.551 * * [simplify]: Extracting # 3 : cost  0
9.556 * * [simplify]: Extracting # 4 : cost  0
9.560 * * [simplify]: Extracting # 5 : cost  0
9.563 * * [simplify]: iteration  2 :  2126  enodes  (cost  2974 )
10.466 * * [simplify]: Extracting # 0 : cost  0
10.490 * * [simplify]: Extracting # 1 : cost  0
10.502 * * [simplify]: Extracting # 2 : cost  0
10.515 * * [simplify]: Extracting # 3 : cost  0
10.523 * * [simplify]: Extracting # 4 : cost  0
10.530 * * [simplify]: iteration done:  5000  enodes  (cost  2930 )
10.531 * [simplify]: Simplified to:
  (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (/ (/ (- 1.0 k) 2) 2.0)
  (/ (/ (- 1.0 k) 2) 2.0)
  (/ (/ (- 1.0 k) 2) 2.0)
  (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (* n (* 2.0 PI))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (* n (* 2.0 PI))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (* n (* 2.0 PI))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (* n (* 2.0 PI))
  (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))
  (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))
  (pow n (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3)
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))
  (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (/ (/ (- 1.0 k) 2) 2.0)
  (/ (/ (- 1.0 k) 2) 2.0)
  (/ (/ (- 1.0 k) 2) 2.0)
  (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (* n (* 2.0 PI))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (* n (* 2.0 PI))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2)))
  (* n (* 2.0 PI))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2)))
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (* n (* 2.0 PI))
  (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))
  (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2))
  (pow n (/ (/ (- 1.0 k) 2.0) 2))
  (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2))
  (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) 3)
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* n (* 2.0 PI))
  (* n (* 2.0 PI))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (pow (* (* 2.0 PI) n) 3)
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (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)
  (* PI n)
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* n (* 2.0 PI))
  (* n (* 2.0 PI))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (pow (* (* 2.0 PI) n) 3)
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (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)
  (* PI n)
  (- (+ (fma (* (* 0.0625 (pow k 2)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25))) (log n) (pow (* (* 2.0 PI) n) 0.25)) (* (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (+ (pow (log n) 2) (pow (log (* 2.0 PI)) 2)))) (* (* (* 0.25 k) (pow (* (* 2.0 PI) n) 0.25)) (log (* (* 2.0 PI) n))))
  (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k))
  (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (- (+ (fma (* (* 0.0625 (pow k 2)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.25))) (log n) (pow (* (* 2.0 PI) n) 0.25)) (* (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (+ (pow (log n) 2) (pow (log (* 2.0 PI)) 2)))) (* (* (* 0.25 k) (pow (* (* 2.0 PI) n) 0.25)) (log (* (* 2.0 PI) n))))
  (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k))
  (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 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))
10.533 * * * [progress]: adding candidates to table
11.644 * * [progress]: iteration 3 / 4
11.644 * * * [progress]: picking best candidate
11.688 * * * * [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)))))>
11.688 * * * [progress]: localizing error
11.708 * * * [progress]: generating rewritten candidates
11.708 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
11.744 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
11.763 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
11.769 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
11.780 * * * [progress]: generating series expansions
11.780 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
11.780 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
11.781 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
11.781 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
11.781 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
11.781 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
11.781 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
11.781 * [taylor]: Taking taylor expansion of 0.5 in k
11.781 * [backup-simplify]: Simplify 0.5 into 0.5
11.781 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.781 * [taylor]: Taking taylor expansion of 1.0 in k
11.781 * [backup-simplify]: Simplify 1.0 into 1.0
11.781 * [taylor]: Taking taylor expansion of k in k
11.781 * [backup-simplify]: Simplify 0 into 0
11.781 * [backup-simplify]: Simplify 1 into 1
11.781 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
11.781 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
11.781 * [taylor]: Taking taylor expansion of 2.0 in k
11.781 * [backup-simplify]: Simplify 2.0 into 2.0
11.781 * [taylor]: Taking taylor expansion of (* n PI) in k
11.781 * [taylor]: Taking taylor expansion of n in k
11.781 * [backup-simplify]: Simplify n into n
11.781 * [taylor]: Taking taylor expansion of PI in k
11.781 * [backup-simplify]: Simplify PI into PI
11.781 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.781 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
11.781 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
11.781 * [backup-simplify]: Simplify (- 0) into 0
11.782 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.782 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
11.782 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
11.782 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
11.782 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.782 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.782 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.782 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.782 * [taylor]: Taking taylor expansion of 0.5 in n
11.782 * [backup-simplify]: Simplify 0.5 into 0.5
11.782 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.782 * [taylor]: Taking taylor expansion of 1.0 in n
11.782 * [backup-simplify]: Simplify 1.0 into 1.0
11.782 * [taylor]: Taking taylor expansion of k in n
11.782 * [backup-simplify]: Simplify k into k
11.782 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.782 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.782 * [taylor]: Taking taylor expansion of 2.0 in n
11.782 * [backup-simplify]: Simplify 2.0 into 2.0
11.782 * [taylor]: Taking taylor expansion of (* n PI) in n
11.782 * [taylor]: Taking taylor expansion of n in n
11.782 * [backup-simplify]: Simplify 0 into 0
11.782 * [backup-simplify]: Simplify 1 into 1
11.782 * [taylor]: Taking taylor expansion of PI in n
11.782 * [backup-simplify]: Simplify PI into PI
11.783 * [backup-simplify]: Simplify (* 0 PI) into 0
11.783 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.784 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.785 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.786 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.786 * [backup-simplify]: Simplify (- k) into (- k)
11.786 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.786 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.787 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.787 * [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))))
11.788 * [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)))))
11.788 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.788 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.788 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.788 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.788 * [taylor]: Taking taylor expansion of 0.5 in n
11.788 * [backup-simplify]: Simplify 0.5 into 0.5
11.788 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.788 * [taylor]: Taking taylor expansion of 1.0 in n
11.788 * [backup-simplify]: Simplify 1.0 into 1.0
11.788 * [taylor]: Taking taylor expansion of k in n
11.788 * [backup-simplify]: Simplify k into k
11.788 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.788 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.788 * [taylor]: Taking taylor expansion of 2.0 in n
11.788 * [backup-simplify]: Simplify 2.0 into 2.0
11.788 * [taylor]: Taking taylor expansion of (* n PI) in n
11.788 * [taylor]: Taking taylor expansion of n in n
11.788 * [backup-simplify]: Simplify 0 into 0
11.788 * [backup-simplify]: Simplify 1 into 1
11.788 * [taylor]: Taking taylor expansion of PI in n
11.788 * [backup-simplify]: Simplify PI into PI
11.789 * [backup-simplify]: Simplify (* 0 PI) into 0
11.789 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.790 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.791 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.791 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.791 * [backup-simplify]: Simplify (- k) into (- k)
11.791 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.792 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.792 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.793 * [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))))
11.794 * [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)))))
11.794 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
11.794 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
11.794 * [taylor]: Taking taylor expansion of 0.5 in k
11.794 * [backup-simplify]: Simplify 0.5 into 0.5
11.794 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
11.794 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.794 * [taylor]: Taking taylor expansion of 1.0 in k
11.794 * [backup-simplify]: Simplify 1.0 into 1.0
11.794 * [taylor]: Taking taylor expansion of k in k
11.794 * [backup-simplify]: Simplify 0 into 0
11.794 * [backup-simplify]: Simplify 1 into 1
11.794 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
11.794 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
11.794 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
11.794 * [taylor]: Taking taylor expansion of 2.0 in k
11.794 * [backup-simplify]: Simplify 2.0 into 2.0
11.794 * [taylor]: Taking taylor expansion of PI in k
11.794 * [backup-simplify]: Simplify PI into PI
11.795 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.795 * [taylor]: Taking taylor expansion of (log n) in k
11.795 * [taylor]: Taking taylor expansion of n in k
11.795 * [backup-simplify]: Simplify n into n
11.795 * [backup-simplify]: Simplify (log n) into (log n)
11.796 * [backup-simplify]: Simplify (- 0) into 0
11.796 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.796 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
11.797 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
11.798 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
11.799 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
11.799 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
11.800 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.801 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.802 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.802 * [backup-simplify]: Simplify (- 0) into 0
11.802 * [backup-simplify]: Simplify (+ 0 0) into 0
11.803 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
11.804 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.805 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
11.806 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.806 * [taylor]: Taking taylor expansion of 0 in k
11.806 * [backup-simplify]: Simplify 0 into 0
11.806 * [backup-simplify]: Simplify 0 into 0
11.807 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.808 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.808 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.809 * [backup-simplify]: Simplify (+ 0 0) into 0
11.809 * [backup-simplify]: Simplify (- 1) into -1
11.809 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.810 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
11.811 * [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))))
11.813 * [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))))))
11.815 * [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))))))
11.821 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.822 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.824 * [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
11.824 * [backup-simplify]: Simplify (- 0) into 0
11.824 * [backup-simplify]: Simplify (+ 0 0) into 0
11.825 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
11.826 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.827 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
11.828 * [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
11.828 * [taylor]: Taking taylor expansion of 0 in k
11.828 * [backup-simplify]: Simplify 0 into 0
11.828 * [backup-simplify]: Simplify 0 into 0
11.828 * [backup-simplify]: Simplify 0 into 0
11.829 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.831 * [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
11.833 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.834 * [backup-simplify]: Simplify (+ 0 0) into 0
11.834 * [backup-simplify]: Simplify (- 0) into 0
11.835 * [backup-simplify]: Simplify (+ 0 0) into 0
11.837 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
11.839 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.843 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
11.850 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
11.858 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
11.858 * [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))))
11.858 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
11.858 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
11.858 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
11.858 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
11.858 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
11.858 * [taylor]: Taking taylor expansion of 0.5 in k
11.858 * [backup-simplify]: Simplify 0.5 into 0.5
11.858 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
11.858 * [taylor]: Taking taylor expansion of 1.0 in k
11.858 * [backup-simplify]: Simplify 1.0 into 1.0
11.858 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.858 * [taylor]: Taking taylor expansion of k in k
11.859 * [backup-simplify]: Simplify 0 into 0
11.859 * [backup-simplify]: Simplify 1 into 1
11.859 * [backup-simplify]: Simplify (/ 1 1) into 1
11.859 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
11.859 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
11.859 * [taylor]: Taking taylor expansion of 2.0 in k
11.859 * [backup-simplify]: Simplify 2.0 into 2.0
11.859 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.859 * [taylor]: Taking taylor expansion of PI in k
11.859 * [backup-simplify]: Simplify PI into PI
11.859 * [taylor]: Taking taylor expansion of n in k
11.859 * [backup-simplify]: Simplify n into n
11.859 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.859 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
11.859 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
11.859 * [backup-simplify]: Simplify (- 1) into -1
11.860 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.860 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
11.860 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
11.860 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
11.860 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
11.860 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
11.860 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
11.860 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
11.860 * [taylor]: Taking taylor expansion of 0.5 in n
11.860 * [backup-simplify]: Simplify 0.5 into 0.5
11.860 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
11.860 * [taylor]: Taking taylor expansion of 1.0 in n
11.860 * [backup-simplify]: Simplify 1.0 into 1.0
11.860 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.860 * [taylor]: Taking taylor expansion of k in n
11.860 * [backup-simplify]: Simplify k into k
11.860 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.860 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
11.860 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.860 * [taylor]: Taking taylor expansion of 2.0 in n
11.860 * [backup-simplify]: Simplify 2.0 into 2.0
11.860 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.860 * [taylor]: Taking taylor expansion of PI in n
11.860 * [backup-simplify]: Simplify PI into PI
11.860 * [taylor]: Taking taylor expansion of n in n
11.861 * [backup-simplify]: Simplify 0 into 0
11.861 * [backup-simplify]: Simplify 1 into 1
11.861 * [backup-simplify]: Simplify (/ PI 1) into PI
11.861 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.862 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.862 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.862 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
11.862 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
11.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.864 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
11.864 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
11.864 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
11.864 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
11.864 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
11.864 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
11.865 * [taylor]: Taking taylor expansion of 0.5 in n
11.865 * [backup-simplify]: Simplify 0.5 into 0.5
11.865 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
11.865 * [taylor]: Taking taylor expansion of 1.0 in n
11.865 * [backup-simplify]: Simplify 1.0 into 1.0
11.865 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.865 * [taylor]: Taking taylor expansion of k in n
11.865 * [backup-simplify]: Simplify k into k
11.865 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.865 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
11.865 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.865 * [taylor]: Taking taylor expansion of 2.0 in n
11.865 * [backup-simplify]: Simplify 2.0 into 2.0
11.865 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.865 * [taylor]: Taking taylor expansion of PI in n
11.865 * [backup-simplify]: Simplify PI into PI
11.865 * [taylor]: Taking taylor expansion of n in n
11.865 * [backup-simplify]: Simplify 0 into 0
11.865 * [backup-simplify]: Simplify 1 into 1
11.865 * [backup-simplify]: Simplify (/ PI 1) into PI
11.865 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.866 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.866 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.866 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
11.866 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
11.867 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.868 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
11.869 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
11.869 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
11.869 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
11.869 * [taylor]: Taking taylor expansion of 0.5 in k
11.869 * [backup-simplify]: Simplify 0.5 into 0.5
11.869 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
11.869 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
11.869 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
11.869 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
11.869 * [taylor]: Taking taylor expansion of 2.0 in k
11.869 * [backup-simplify]: Simplify 2.0 into 2.0
11.869 * [taylor]: Taking taylor expansion of PI in k
11.869 * [backup-simplify]: Simplify PI into PI
11.869 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.870 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.870 * [taylor]: Taking taylor expansion of (log n) in k
11.870 * [taylor]: Taking taylor expansion of n in k
11.870 * [backup-simplify]: Simplify n into n
11.870 * [backup-simplify]: Simplify (log n) into (log n)
11.870 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
11.870 * [taylor]: Taking taylor expansion of 1.0 in k
11.870 * [backup-simplify]: Simplify 1.0 into 1.0
11.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.870 * [taylor]: Taking taylor expansion of k in k
11.870 * [backup-simplify]: Simplify 0 into 0
11.870 * [backup-simplify]: Simplify 1 into 1
11.870 * [backup-simplify]: Simplify (/ 1 1) into 1
11.870 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.871 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
11.871 * [backup-simplify]: Simplify (- 1) into -1
11.872 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.872 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
11.873 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
11.874 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
11.874 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
11.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.875 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.877 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.877 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.877 * [backup-simplify]: Simplify (- 0) into 0
11.877 * [backup-simplify]: Simplify (+ 0 0) into 0
11.877 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
11.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.879 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
11.880 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.880 * [taylor]: Taking taylor expansion of 0 in k
11.880 * [backup-simplify]: Simplify 0 into 0
11.880 * [backup-simplify]: Simplify 0 into 0
11.880 * [backup-simplify]: Simplify 0 into 0
11.881 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.882 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.884 * [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
11.885 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.885 * [backup-simplify]: Simplify (- 0) into 0
11.885 * [backup-simplify]: Simplify (+ 0 0) into 0
11.886 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
11.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.890 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
11.892 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.892 * [taylor]: Taking taylor expansion of 0 in k
11.892 * [backup-simplify]: Simplify 0 into 0
11.892 * [backup-simplify]: Simplify 0 into 0
11.892 * [backup-simplify]: Simplify 0 into 0
11.892 * [backup-simplify]: Simplify 0 into 0
11.893 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.895 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.901 * [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
11.902 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.902 * [backup-simplify]: Simplify (- 0) into 0
11.903 * [backup-simplify]: Simplify (+ 0 0) into 0
11.904 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
11.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
11.907 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
11.910 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.911 * [taylor]: Taking taylor expansion of 0 in k
11.911 * [backup-simplify]: Simplify 0 into 0
11.911 * [backup-simplify]: Simplify 0 into 0
11.912 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
11.913 * [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)))
11.913 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
11.913 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
11.913 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
11.913 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
11.913 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
11.913 * [taylor]: Taking taylor expansion of 0.5 in k
11.913 * [backup-simplify]: Simplify 0.5 into 0.5
11.913 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
11.913 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.913 * [taylor]: Taking taylor expansion of k in k
11.913 * [backup-simplify]: Simplify 0 into 0
11.913 * [backup-simplify]: Simplify 1 into 1
11.914 * [backup-simplify]: Simplify (/ 1 1) into 1
11.914 * [taylor]: Taking taylor expansion of 1.0 in k
11.914 * [backup-simplify]: Simplify 1.0 into 1.0
11.914 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
11.914 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
11.914 * [taylor]: Taking taylor expansion of -2.0 in k
11.914 * [backup-simplify]: Simplify -2.0 into -2.0
11.914 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.914 * [taylor]: Taking taylor expansion of PI in k
11.914 * [backup-simplify]: Simplify PI into PI
11.914 * [taylor]: Taking taylor expansion of n in k
11.914 * [backup-simplify]: Simplify n into n
11.914 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.914 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
11.914 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
11.915 * [backup-simplify]: Simplify (+ 1 0) into 1
11.915 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
11.915 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
11.916 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
11.916 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
11.916 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
11.916 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
11.916 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
11.916 * [taylor]: Taking taylor expansion of 0.5 in n
11.916 * [backup-simplify]: Simplify 0.5 into 0.5
11.916 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
11.916 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.916 * [taylor]: Taking taylor expansion of k in n
11.916 * [backup-simplify]: Simplify k into k
11.916 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.916 * [taylor]: Taking taylor expansion of 1.0 in n
11.916 * [backup-simplify]: Simplify 1.0 into 1.0
11.916 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
11.916 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.916 * [taylor]: Taking taylor expansion of -2.0 in n
11.916 * [backup-simplify]: Simplify -2.0 into -2.0
11.916 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.916 * [taylor]: Taking taylor expansion of PI in n
11.916 * [backup-simplify]: Simplify PI into PI
11.916 * [taylor]: Taking taylor expansion of n in n
11.916 * [backup-simplify]: Simplify 0 into 0
11.916 * [backup-simplify]: Simplify 1 into 1
11.917 * [backup-simplify]: Simplify (/ PI 1) into PI
11.917 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.919 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
11.919 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
11.919 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
11.920 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.920 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
11.921 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
11.921 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
11.921 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
11.921 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
11.921 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
11.921 * [taylor]: Taking taylor expansion of 0.5 in n
11.921 * [backup-simplify]: Simplify 0.5 into 0.5
11.921 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
11.921 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.921 * [taylor]: Taking taylor expansion of k in n
11.921 * [backup-simplify]: Simplify k into k
11.921 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.921 * [taylor]: Taking taylor expansion of 1.0 in n
11.921 * [backup-simplify]: Simplify 1.0 into 1.0
11.921 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
11.921 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.921 * [taylor]: Taking taylor expansion of -2.0 in n
11.922 * [backup-simplify]: Simplify -2.0 into -2.0
11.922 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.922 * [taylor]: Taking taylor expansion of PI in n
11.922 * [backup-simplify]: Simplify PI into PI
11.922 * [taylor]: Taking taylor expansion of n in n
11.922 * [backup-simplify]: Simplify 0 into 0
11.922 * [backup-simplify]: Simplify 1 into 1
11.922 * [backup-simplify]: Simplify (/ PI 1) into PI
11.922 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.923 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
11.923 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
11.923 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
11.924 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.925 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
11.925 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
11.925 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
11.925 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
11.925 * [taylor]: Taking taylor expansion of 0.5 in k
11.925 * [backup-simplify]: Simplify 0.5 into 0.5
11.925 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
11.925 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
11.926 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.926 * [taylor]: Taking taylor expansion of k in k
11.926 * [backup-simplify]: Simplify 0 into 0
11.926 * [backup-simplify]: Simplify 1 into 1
11.926 * [backup-simplify]: Simplify (/ 1 1) into 1
11.926 * [taylor]: Taking taylor expansion of 1.0 in k
11.926 * [backup-simplify]: Simplify 1.0 into 1.0
11.926 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
11.926 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
11.926 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
11.926 * [taylor]: Taking taylor expansion of -2.0 in k
11.926 * [backup-simplify]: Simplify -2.0 into -2.0
11.926 * [taylor]: Taking taylor expansion of PI in k
11.926 * [backup-simplify]: Simplify PI into PI
11.926 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.927 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
11.927 * [taylor]: Taking taylor expansion of (log n) in k
11.927 * [taylor]: Taking taylor expansion of n in k
11.927 * [backup-simplify]: Simplify n into n
11.927 * [backup-simplify]: Simplify (log n) into (log n)
11.927 * [backup-simplify]: Simplify (+ 1 0) into 1
11.927 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.928 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
11.929 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
11.929 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
11.930 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
11.931 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
11.931 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.932 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.933 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
11.933 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.933 * [backup-simplify]: Simplify (+ 0 0) into 0
11.934 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
11.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.941 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
11.942 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.942 * [taylor]: Taking taylor expansion of 0 in k
11.942 * [backup-simplify]: Simplify 0 into 0
11.943 * [backup-simplify]: Simplify 0 into 0
11.943 * [backup-simplify]: Simplify 0 into 0
11.944 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.945 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.949 * [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
11.949 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.950 * [backup-simplify]: Simplify (+ 0 0) into 0
11.950 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
11.952 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.954 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
11.956 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.956 * [taylor]: Taking taylor expansion of 0 in k
11.957 * [backup-simplify]: Simplify 0 into 0
11.957 * [backup-simplify]: Simplify 0 into 0
11.957 * [backup-simplify]: Simplify 0 into 0
11.957 * [backup-simplify]: Simplify 0 into 0
11.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.959 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.964 * [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
11.965 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.965 * [backup-simplify]: Simplify (+ 0 0) into 0
11.966 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
11.967 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
11.968 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
11.970 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.970 * [taylor]: Taking taylor expansion of 0 in k
11.970 * [backup-simplify]: Simplify 0 into 0
11.970 * [backup-simplify]: Simplify 0 into 0
11.970 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
11.971 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
11.971 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.971 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
11.971 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.971 * [taylor]: Taking taylor expansion of 2.0 in n
11.971 * [backup-simplify]: Simplify 2.0 into 2.0
11.971 * [taylor]: Taking taylor expansion of (* n PI) in n
11.971 * [taylor]: Taking taylor expansion of n in n
11.971 * [backup-simplify]: Simplify 0 into 0
11.971 * [backup-simplify]: Simplify 1 into 1
11.971 * [taylor]: Taking taylor expansion of PI in n
11.971 * [backup-simplify]: Simplify PI into PI
11.971 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.971 * [taylor]: Taking taylor expansion of 2.0 in n
11.971 * [backup-simplify]: Simplify 2.0 into 2.0
11.971 * [taylor]: Taking taylor expansion of (* n PI) in n
11.971 * [taylor]: Taking taylor expansion of n in n
11.971 * [backup-simplify]: Simplify 0 into 0
11.971 * [backup-simplify]: Simplify 1 into 1
11.971 * [taylor]: Taking taylor expansion of PI in n
11.971 * [backup-simplify]: Simplify PI into PI
11.972 * [backup-simplify]: Simplify (* 0 PI) into 0
11.972 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.972 * [backup-simplify]: Simplify 0 into 0
11.973 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.974 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.974 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.975 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.975 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.975 * [backup-simplify]: Simplify 0 into 0
11.976 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.977 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.977 * [backup-simplify]: Simplify 0 into 0
11.977 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.978 * [backup-simplify]: Simplify 0 into 0
11.979 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.980 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
11.980 * [backup-simplify]: Simplify 0 into 0
11.981 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.982 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
11.982 * [backup-simplify]: Simplify 0 into 0
11.983 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
11.984 * [backup-simplify]: Simplify 0 into 0
11.985 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.985 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
11.985 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
11.985 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.985 * [taylor]: Taking taylor expansion of 2.0 in n
11.985 * [backup-simplify]: Simplify 2.0 into 2.0
11.985 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.985 * [taylor]: Taking taylor expansion of PI in n
11.985 * [backup-simplify]: Simplify PI into PI
11.985 * [taylor]: Taking taylor expansion of n in n
11.985 * [backup-simplify]: Simplify 0 into 0
11.985 * [backup-simplify]: Simplify 1 into 1
11.986 * [backup-simplify]: Simplify (/ PI 1) into PI
11.986 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.986 * [taylor]: Taking taylor expansion of 2.0 in n
11.986 * [backup-simplify]: Simplify 2.0 into 2.0
11.986 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.986 * [taylor]: Taking taylor expansion of PI in n
11.986 * [backup-simplify]: Simplify PI into PI
11.986 * [taylor]: Taking taylor expansion of n in n
11.986 * [backup-simplify]: Simplify 0 into 0
11.986 * [backup-simplify]: Simplify 1 into 1
11.986 * [backup-simplify]: Simplify (/ PI 1) into PI
11.986 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.987 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.987 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.988 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.988 * [backup-simplify]: Simplify 0 into 0
11.988 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.989 * [backup-simplify]: Simplify 0 into 0
11.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.990 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.990 * [backup-simplify]: Simplify 0 into 0
11.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.992 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.992 * [backup-simplify]: Simplify 0 into 0
11.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.993 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.993 * [backup-simplify]: Simplify 0 into 0
11.994 * [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
11.995 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.995 * [backup-simplify]: Simplify 0 into 0
11.995 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
11.996 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
11.996 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
11.996 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.996 * [taylor]: Taking taylor expansion of -2.0 in n
11.996 * [backup-simplify]: Simplify -2.0 into -2.0
11.996 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.996 * [taylor]: Taking taylor expansion of PI in n
11.996 * [backup-simplify]: Simplify PI into PI
11.996 * [taylor]: Taking taylor expansion of n in n
11.996 * [backup-simplify]: Simplify 0 into 0
11.996 * [backup-simplify]: Simplify 1 into 1
11.996 * [backup-simplify]: Simplify (/ PI 1) into PI
11.996 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.996 * [taylor]: Taking taylor expansion of -2.0 in n
11.996 * [backup-simplify]: Simplify -2.0 into -2.0
11.996 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.996 * [taylor]: Taking taylor expansion of PI in n
11.996 * [backup-simplify]: Simplify PI into PI
11.996 * [taylor]: Taking taylor expansion of n in n
11.996 * [backup-simplify]: Simplify 0 into 0
11.996 * [backup-simplify]: Simplify 1 into 1
11.997 * [backup-simplify]: Simplify (/ PI 1) into PI
11.997 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.997 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.998 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.998 * [backup-simplify]: Simplify 0 into 0
11.999 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.000 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.000 * [backup-simplify]: Simplify 0 into 0
12.001 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.003 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.003 * [backup-simplify]: Simplify 0 into 0
12.004 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.005 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.005 * [backup-simplify]: Simplify 0 into 0
12.006 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.008 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.008 * [backup-simplify]: Simplify 0 into 0
12.009 * [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
12.011 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.011 * [backup-simplify]: Simplify 0 into 0
12.012 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
12.012 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
12.012 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
12.012 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
12.012 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
12.012 * [taylor]: Taking taylor expansion of 1.0 in k
12.012 * [backup-simplify]: Simplify 1.0 into 1.0
12.012 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.012 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.012 * [taylor]: Taking taylor expansion of k in k
12.012 * [backup-simplify]: Simplify 0 into 0
12.012 * [backup-simplify]: Simplify 1 into 1
12.013 * [backup-simplify]: Simplify (/ 1 1) into 1
12.013 * [backup-simplify]: Simplify (sqrt 0) into 0
12.014 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.014 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
12.014 * [taylor]: Taking taylor expansion of 1.0 in k
12.015 * [backup-simplify]: Simplify 1.0 into 1.0
12.015 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.015 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.015 * [taylor]: Taking taylor expansion of k in k
12.015 * [backup-simplify]: Simplify 0 into 0
12.015 * [backup-simplify]: Simplify 1 into 1
12.015 * [backup-simplify]: Simplify (/ 1 1) into 1
12.015 * [backup-simplify]: Simplify (sqrt 0) into 0
12.017 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.017 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.017 * [backup-simplify]: Simplify 0 into 0
12.019 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
12.019 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.020 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.022 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.023 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
12.023 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.024 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.026 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.027 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
12.027 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.028 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
12.028 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
12.028 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
12.028 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
12.028 * [taylor]: Taking taylor expansion of 1.0 in k
12.028 * [backup-simplify]: Simplify 1.0 into 1.0
12.028 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.028 * [taylor]: Taking taylor expansion of k in k
12.028 * [backup-simplify]: Simplify 0 into 0
12.028 * [backup-simplify]: Simplify 1 into 1
12.029 * [backup-simplify]: Simplify (sqrt 0) into 0
12.029 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.029 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
12.029 * [taylor]: Taking taylor expansion of 1.0 in k
12.029 * [backup-simplify]: Simplify 1.0 into 1.0
12.029 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.030 * [taylor]: Taking taylor expansion of k in k
12.030 * [backup-simplify]: Simplify 0 into 0
12.030 * [backup-simplify]: Simplify 1 into 1
12.030 * [backup-simplify]: Simplify (sqrt 0) into 0
12.031 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.031 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.031 * [backup-simplify]: Simplify 0 into 0
12.032 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
12.032 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.034 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.035 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
12.035 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.037 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.039 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
12.039 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.040 * [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))))))))
12.040 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
12.040 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
12.040 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
12.040 * [taylor]: Taking taylor expansion of 1.0 in k
12.040 * [backup-simplify]: Simplify 1.0 into 1.0
12.040 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.040 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.040 * [taylor]: Taking taylor expansion of -1 in k
12.040 * [backup-simplify]: Simplify -1 into -1
12.040 * [taylor]: Taking taylor expansion of k in k
12.040 * [backup-simplify]: Simplify 0 into 0
12.040 * [backup-simplify]: Simplify 1 into 1
12.041 * [backup-simplify]: Simplify (/ -1 1) into -1
12.041 * [backup-simplify]: Simplify (sqrt 0) into 0
12.042 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.042 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
12.042 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
12.042 * [taylor]: Taking taylor expansion of 1.0 in k
12.042 * [backup-simplify]: Simplify 1.0 into 1.0
12.042 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.042 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.042 * [taylor]: Taking taylor expansion of -1 in k
12.042 * [backup-simplify]: Simplify -1 into -1
12.042 * [taylor]: Taking taylor expansion of k in k
12.042 * [backup-simplify]: Simplify 0 into 0
12.042 * [backup-simplify]: Simplify 1 into 1
12.043 * [backup-simplify]: Simplify (/ -1 1) into -1
12.043 * [backup-simplify]: Simplify (sqrt 0) into 0
12.044 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.044 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
12.044 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.053 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.056 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
12.056 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.060 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.062 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
12.063 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.063 * [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)))))
12.063 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
12.064 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
12.064 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
12.064 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
12.064 * [taylor]: Taking taylor expansion of 1.0 in k
12.064 * [backup-simplify]: Simplify 1.0 into 1.0
12.064 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.064 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.064 * [taylor]: Taking taylor expansion of k in k
12.064 * [backup-simplify]: Simplify 0 into 0
12.064 * [backup-simplify]: Simplify 1 into 1
12.064 * [backup-simplify]: Simplify (/ 1 1) into 1
12.064 * [backup-simplify]: Simplify (sqrt 0) into 0
12.065 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.065 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
12.065 * [taylor]: Taking taylor expansion of 1.0 in k
12.065 * [backup-simplify]: Simplify 1.0 into 1.0
12.065 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.065 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.065 * [taylor]: Taking taylor expansion of k in k
12.065 * [backup-simplify]: Simplify 0 into 0
12.065 * [backup-simplify]: Simplify 1 into 1
12.065 * [backup-simplify]: Simplify (/ 1 1) into 1
12.066 * [backup-simplify]: Simplify (sqrt 0) into 0
12.066 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.067 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.067 * [backup-simplify]: Simplify 0 into 0
12.067 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
12.068 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.068 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.070 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.071 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
12.071 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.072 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.074 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.076 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
12.076 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.077 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
12.077 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
12.077 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
12.077 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
12.077 * [taylor]: Taking taylor expansion of 1.0 in k
12.077 * [backup-simplify]: Simplify 1.0 into 1.0
12.077 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.077 * [taylor]: Taking taylor expansion of k in k
12.077 * [backup-simplify]: Simplify 0 into 0
12.077 * [backup-simplify]: Simplify 1 into 1
12.077 * [backup-simplify]: Simplify (sqrt 0) into 0
12.078 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.078 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
12.078 * [taylor]: Taking taylor expansion of 1.0 in k
12.078 * [backup-simplify]: Simplify 1.0 into 1.0
12.078 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.078 * [taylor]: Taking taylor expansion of k in k
12.078 * [backup-simplify]: Simplify 0 into 0
12.078 * [backup-simplify]: Simplify 1 into 1
12.079 * [backup-simplify]: Simplify (sqrt 0) into 0
12.079 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.080 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.080 * [backup-simplify]: Simplify 0 into 0
12.081 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
12.081 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.083 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.084 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
12.084 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.086 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.088 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
12.088 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.090 * [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))))))))
12.090 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
12.090 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
12.090 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
12.090 * [taylor]: Taking taylor expansion of 1.0 in k
12.090 * [backup-simplify]: Simplify 1.0 into 1.0
12.090 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.090 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.091 * [taylor]: Taking taylor expansion of -1 in k
12.091 * [backup-simplify]: Simplify -1 into -1
12.091 * [taylor]: Taking taylor expansion of k in k
12.091 * [backup-simplify]: Simplify 0 into 0
12.091 * [backup-simplify]: Simplify 1 into 1
12.091 * [backup-simplify]: Simplify (/ -1 1) into -1
12.091 * [backup-simplify]: Simplify (sqrt 0) into 0
12.093 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.093 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
12.093 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
12.093 * [taylor]: Taking taylor expansion of 1.0 in k
12.093 * [backup-simplify]: Simplify 1.0 into 1.0
12.093 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.093 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.093 * [taylor]: Taking taylor expansion of -1 in k
12.093 * [backup-simplify]: Simplify -1 into -1
12.093 * [taylor]: Taking taylor expansion of k in k
12.093 * [backup-simplify]: Simplify 0 into 0
12.094 * [backup-simplify]: Simplify 1 into 1
12.094 * [backup-simplify]: Simplify (/ -1 1) into -1
12.094 * [backup-simplify]: Simplify (sqrt 0) into 0
12.096 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.096 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
12.096 * [backup-simplify]: Simplify +nan.0 into +nan.0
12.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.100 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.103 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
12.103 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.108 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.113 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
12.113 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
12.114 * [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)))))
12.114 * * * [progress]: simplifying candidates
12.117 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (expm1 (/ 1.0 (sqrt k)))
  (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)
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
12.119 * * [simplify]: Extracting # 0 : cost  0
12.119 * * [simplify]: Extracting # 1 : cost  0
12.120 * * [simplify]: Extracting # 2 : cost  0
12.120 * * [simplify]: Extracting # 3 : cost  0
12.120 * * [simplify]: Extracting # 4 : cost  0
12.120 * * [simplify]: Extracting # 5 : cost  0
12.121 * * [simplify]: Extracting # 6 : cost  0
12.121 * * [simplify]: Extracting # 7 : cost  0
12.121 * * [simplify]: Extracting # 8 : cost  0
12.122 * * [simplify]: Extracting # 9 : cost  0
12.122 * * [simplify]: Extracting # 10 : cost  0
12.122 * * [simplify]: Extracting # 11 : cost  0
12.122 * * [simplify]: Extracting # 12 : cost  0
12.123 * * [simplify]: Extracting # 13 : cost  0
12.123 * * [simplify]: iteration  0 :  240  enodes  (cost  1698 )
12.195 * * [simplify]: Extracting # 0 : cost  0
12.197 * * [simplify]: Extracting # 1 : cost  0
12.198 * * [simplify]: Extracting # 2 : cost  0
12.200 * * [simplify]: Extracting # 3 : cost  0
12.201 * * [simplify]: Extracting # 4 : cost  0
12.202 * * [simplify]: Extracting # 5 : cost  0
12.204 * * [simplify]: Extracting # 6 : cost  0
12.205 * * [simplify]: Extracting # 7 : cost  0
12.207 * * [simplify]: iteration  1 :  571  enodes  (cost  1560 )
12.514 * * [simplify]: Extracting # 0 : cost  0
12.516 * * [simplify]: Extracting # 1 : cost  0
12.519 * * [simplify]: Extracting # 2 : cost  0
12.521 * * [simplify]: Extracting # 3 : cost  0
12.524 * * [simplify]: Extracting # 4 : cost  0
12.529 * * [simplify]: Extracting # 5 : cost  0
12.534 * * [simplify]: iteration  2 :  1753  enodes  (cost  1456 )
13.345 * * [simplify]: Extracting # 0 : cost  0
13.351 * * [simplify]: Extracting # 1 : cost  0
13.358 * * [simplify]: Extracting # 2 : cost  0
13.376 * * [simplify]: Extracting # 3 : cost  0
13.388 * * [simplify]: Extracting # 4 : cost  0
13.395 * * [simplify]: Extracting # 5 : cost  0
13.402 * * [simplify]: iteration done:  5000  enodes  (cost  1434 )
13.403 * [simplify]: Simplified to:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 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))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* PI (* 2.0 n))
  (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)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (log (* (* 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (pow (* (* 2.0 PI) n) 3)
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (pow (* (* 2.0 PI) n) 3)
  (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)
  (* n PI)
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (/ (pow 1.0 3) (sqrt k)) k)
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (pow (/ 1.0 (sqrt k)) 3)
  (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)) (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 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (/ (pow 1.0 3) (sqrt k)) k)
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (pow (/ 1.0 (sqrt k)) 3)
  (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)) (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)
  (fma (* 0.125 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.5) (+ (pow (log (* 2.0 PI)) 2) (pow (log n) 2))) (- (fma (* 0.25 (pow k 2)) (* (log n) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5))) (pow (* (* 2.0 PI) n) 0.5)) (* (* 0.5 k) (* (pow (* (* 2.0 PI) n) 0.5) (log (* (* 2.0 PI) n))))))
  (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (- (+ (* +nan.0 (- k (* k k))) +nan.0))
  (+ (- (/ (/ +nan.0 k) k)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))
  (+ (- (/ +nan.0 k) +nan.0) (- (/ (/ +nan.0 k) k)))
  (- (+ (* +nan.0 (- k (* k k))) +nan.0))
  (+ (- (/ (/ +nan.0 k) k)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))
  (+ (- (/ +nan.0 k) +nan.0) (- (/ (/ +nan.0 k) k)))
13.404 * * * [progress]: adding candidates to table
14.177 * * [progress]: iteration 4 / 4
14.178 * * * [progress]: picking best candidate
14.201 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>
14.202 * * * [progress]: localizing error
14.250 * * * [progress]: generating rewritten candidates
14.251 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
14.279 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
14.313 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1 1)
14.324 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2 1)
14.408 * * * [progress]: generating series expansions
14.408 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
14.409 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
14.409 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
14.410 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
14.410 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
14.410 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
14.410 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
14.410 * [taylor]: Taking taylor expansion of 0.5 in k
14.410 * [backup-simplify]: Simplify 0.5 into 0.5
14.410 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
14.410 * [taylor]: Taking taylor expansion of 1.0 in k
14.410 * [backup-simplify]: Simplify 1.0 into 1.0
14.410 * [taylor]: Taking taylor expansion of k in k
14.410 * [backup-simplify]: Simplify 0 into 0
14.410 * [backup-simplify]: Simplify 1 into 1
14.410 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
14.410 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
14.410 * [taylor]: Taking taylor expansion of 2.0 in k
14.410 * [backup-simplify]: Simplify 2.0 into 2.0
14.410 * [taylor]: Taking taylor expansion of (* n PI) in k
14.410 * [taylor]: Taking taylor expansion of n in k
14.410 * [backup-simplify]: Simplify n into n
14.410 * [taylor]: Taking taylor expansion of PI in k
14.410 * [backup-simplify]: Simplify PI into PI
14.410 * [backup-simplify]: Simplify (* n PI) into (* n PI)
14.410 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
14.410 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
14.410 * [backup-simplify]: Simplify (- 0) into 0
14.411 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
14.411 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
14.411 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
14.411 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
14.411 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
14.411 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
14.411 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
14.411 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
14.411 * [taylor]: Taking taylor expansion of 0.5 in n
14.411 * [backup-simplify]: Simplify 0.5 into 0.5
14.411 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
14.411 * [taylor]: Taking taylor expansion of 1.0 in n
14.411 * [backup-simplify]: Simplify 1.0 into 1.0
14.411 * [taylor]: Taking taylor expansion of k in n
14.411 * [backup-simplify]: Simplify k into k
14.411 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
14.411 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
14.411 * [taylor]: Taking taylor expansion of 2.0 in n
14.411 * [backup-simplify]: Simplify 2.0 into 2.0
14.411 * [taylor]: Taking taylor expansion of (* n PI) in n
14.411 * [taylor]: Taking taylor expansion of n in n
14.411 * [backup-simplify]: Simplify 0 into 0
14.411 * [backup-simplify]: Simplify 1 into 1
14.412 * [taylor]: Taking taylor expansion of PI in n
14.412 * [backup-simplify]: Simplify PI into PI
14.412 * [backup-simplify]: Simplify (* 0 PI) into 0
14.412 * [backup-simplify]: Simplify (* 2.0 0) into 0
14.413 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
14.414 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
14.415 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.415 * [backup-simplify]: Simplify (- k) into (- k)
14.415 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
14.415 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
14.416 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
14.417 * [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))))
14.418 * [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)))))
14.418 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
14.418 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
14.418 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
14.418 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
14.418 * [taylor]: Taking taylor expansion of 0.5 in n
14.418 * [backup-simplify]: Simplify 0.5 into 0.5
14.418 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
14.418 * [taylor]: Taking taylor expansion of 1.0 in n
14.418 * [backup-simplify]: Simplify 1.0 into 1.0
14.418 * [taylor]: Taking taylor expansion of k in n
14.418 * [backup-simplify]: Simplify k into k
14.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
14.418 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
14.418 * [taylor]: Taking taylor expansion of 2.0 in n
14.418 * [backup-simplify]: Simplify 2.0 into 2.0
14.418 * [taylor]: Taking taylor expansion of (* n PI) in n
14.418 * [taylor]: Taking taylor expansion of n in n
14.418 * [backup-simplify]: Simplify 0 into 0
14.418 * [backup-simplify]: Simplify 1 into 1
14.418 * [taylor]: Taking taylor expansion of PI in n
14.418 * [backup-simplify]: Simplify PI into PI
14.418 * [backup-simplify]: Simplify (* 0 PI) into 0
14.426 * [backup-simplify]: Simplify (* 2.0 0) into 0
14.427 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
14.428 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
14.428 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.429 * [backup-simplify]: Simplify (- k) into (- k)
14.429 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
14.429 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
14.430 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
14.430 * [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))))
14.431 * [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)))))
14.431 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
14.432 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
14.432 * [taylor]: Taking taylor expansion of 0.5 in k
14.432 * [backup-simplify]: Simplify 0.5 into 0.5
14.432 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
14.432 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
14.432 * [taylor]: Taking taylor expansion of 1.0 in k
14.432 * [backup-simplify]: Simplify 1.0 into 1.0
14.432 * [taylor]: Taking taylor expansion of k in k
14.432 * [backup-simplify]: Simplify 0 into 0
14.432 * [backup-simplify]: Simplify 1 into 1
14.432 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
14.432 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
14.432 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
14.432 * [taylor]: Taking taylor expansion of 2.0 in k
14.432 * [backup-simplify]: Simplify 2.0 into 2.0
14.432 * [taylor]: Taking taylor expansion of PI in k
14.432 * [backup-simplify]: Simplify PI into PI
14.433 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.434 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.434 * [taylor]: Taking taylor expansion of (log n) in k
14.434 * [taylor]: Taking taylor expansion of n in k
14.434 * [backup-simplify]: Simplify n into n
14.434 * [backup-simplify]: Simplify (log n) into (log n)
14.434 * [backup-simplify]: Simplify (- 0) into 0
14.435 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
14.436 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
14.437 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
14.438 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
14.439 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
14.441 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
14.442 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
14.443 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
14.445 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
14.446 * [backup-simplify]: Simplify (- 0) into 0
14.446 * [backup-simplify]: Simplify (+ 0 0) into 0
14.446 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
14.448 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
14.449 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
14.451 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.451 * [taylor]: Taking taylor expansion of 0 in k
14.451 * [backup-simplify]: Simplify 0 into 0
14.451 * [backup-simplify]: Simplify 0 into 0
14.452 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
14.454 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
14.455 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
14.455 * [backup-simplify]: Simplify (+ 0 0) into 0
14.456 * [backup-simplify]: Simplify (- 1) into -1
14.456 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.458 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
14.460 * [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))))
14.465 * [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))))))
14.468 * [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))))))
14.470 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
14.471 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
14.474 * [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
14.475 * [backup-simplify]: Simplify (- 0) into 0
14.475 * [backup-simplify]: Simplify (+ 0 0) into 0
14.476 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
14.477 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
14.479 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
14.481 * [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
14.482 * [taylor]: Taking taylor expansion of 0 in k
14.482 * [backup-simplify]: Simplify 0 into 0
14.482 * [backup-simplify]: Simplify 0 into 0
14.482 * [backup-simplify]: Simplify 0 into 0
14.483 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.485 * [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
14.486 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
14.486 * [backup-simplify]: Simplify (+ 0 0) into 0
14.486 * [backup-simplify]: Simplify (- 0) into 0
14.486 * [backup-simplify]: Simplify (+ 0 0) into 0
14.488 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
14.489 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
14.492 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
14.495 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
14.501 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
14.501 * [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))))
14.501 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
14.501 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
14.501 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
14.501 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
14.501 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
14.501 * [taylor]: Taking taylor expansion of 0.5 in k
14.502 * [backup-simplify]: Simplify 0.5 into 0.5
14.502 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
14.502 * [taylor]: Taking taylor expansion of 1.0 in k
14.502 * [backup-simplify]: Simplify 1.0 into 1.0
14.502 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.502 * [taylor]: Taking taylor expansion of k in k
14.502 * [backup-simplify]: Simplify 0 into 0
14.502 * [backup-simplify]: Simplify 1 into 1
14.502 * [backup-simplify]: Simplify (/ 1 1) into 1
14.502 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
14.502 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
14.502 * [taylor]: Taking taylor expansion of 2.0 in k
14.502 * [backup-simplify]: Simplify 2.0 into 2.0
14.502 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.502 * [taylor]: Taking taylor expansion of PI in k
14.502 * [backup-simplify]: Simplify PI into PI
14.502 * [taylor]: Taking taylor expansion of n in k
14.502 * [backup-simplify]: Simplify n into n
14.502 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.502 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
14.502 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
14.502 * [backup-simplify]: Simplify (- 1) into -1
14.503 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.503 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
14.503 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
14.503 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
14.503 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
14.503 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
14.503 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
14.503 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
14.503 * [taylor]: Taking taylor expansion of 0.5 in n
14.503 * [backup-simplify]: Simplify 0.5 into 0.5
14.503 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
14.503 * [taylor]: Taking taylor expansion of 1.0 in n
14.503 * [backup-simplify]: Simplify 1.0 into 1.0
14.503 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.503 * [taylor]: Taking taylor expansion of k in n
14.503 * [backup-simplify]: Simplify k into k
14.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.504 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
14.504 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
14.504 * [taylor]: Taking taylor expansion of 2.0 in n
14.504 * [backup-simplify]: Simplify 2.0 into 2.0
14.504 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.504 * [taylor]: Taking taylor expansion of PI in n
14.504 * [backup-simplify]: Simplify PI into PI
14.504 * [taylor]: Taking taylor expansion of n in n
14.504 * [backup-simplify]: Simplify 0 into 0
14.504 * [backup-simplify]: Simplify 1 into 1
14.504 * [backup-simplify]: Simplify (/ PI 1) into PI
14.504 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.505 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.505 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.505 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
14.505 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
14.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.507 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
14.508 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
14.508 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
14.508 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
14.508 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
14.508 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
14.508 * [taylor]: Taking taylor expansion of 0.5 in n
14.508 * [backup-simplify]: Simplify 0.5 into 0.5
14.508 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
14.508 * [taylor]: Taking taylor expansion of 1.0 in n
14.508 * [backup-simplify]: Simplify 1.0 into 1.0
14.508 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.508 * [taylor]: Taking taylor expansion of k in n
14.508 * [backup-simplify]: Simplify k into k
14.508 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.508 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
14.508 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
14.508 * [taylor]: Taking taylor expansion of 2.0 in n
14.508 * [backup-simplify]: Simplify 2.0 into 2.0
14.508 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.508 * [taylor]: Taking taylor expansion of PI in n
14.508 * [backup-simplify]: Simplify PI into PI
14.508 * [taylor]: Taking taylor expansion of n in n
14.508 * [backup-simplify]: Simplify 0 into 0
14.508 * [backup-simplify]: Simplify 1 into 1
14.508 * [backup-simplify]: Simplify (/ PI 1) into PI
14.509 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.509 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.509 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
14.509 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
14.509 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
14.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.511 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
14.512 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
14.512 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
14.512 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
14.512 * [taylor]: Taking taylor expansion of 0.5 in k
14.512 * [backup-simplify]: Simplify 0.5 into 0.5
14.512 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
14.512 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
14.512 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
14.512 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
14.512 * [taylor]: Taking taylor expansion of 2.0 in k
14.512 * [backup-simplify]: Simplify 2.0 into 2.0
14.512 * [taylor]: Taking taylor expansion of PI in k
14.512 * [backup-simplify]: Simplify PI into PI
14.512 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.513 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
14.513 * [taylor]: Taking taylor expansion of (log n) in k
14.513 * [taylor]: Taking taylor expansion of n in k
14.513 * [backup-simplify]: Simplify n into n
14.513 * [backup-simplify]: Simplify (log n) into (log n)
14.513 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
14.513 * [taylor]: Taking taylor expansion of 1.0 in k
14.513 * [backup-simplify]: Simplify 1.0 into 1.0
14.513 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.513 * [taylor]: Taking taylor expansion of k in k
14.513 * [backup-simplify]: Simplify 0 into 0
14.513 * [backup-simplify]: Simplify 1 into 1
14.514 * [backup-simplify]: Simplify (/ 1 1) into 1
14.514 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.514 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
14.515 * [backup-simplify]: Simplify (- 1) into -1
14.515 * [backup-simplify]: Simplify (+ 0 -1) into -1
14.515 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
14.516 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
14.517 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
14.518 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
14.518 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.519 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
14.520 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
14.520 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.520 * [backup-simplify]: Simplify (- 0) into 0
14.520 * [backup-simplify]: Simplify (+ 0 0) into 0
14.521 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
14.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.522 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
14.523 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.523 * [taylor]: Taking taylor expansion of 0 in k
14.523 * [backup-simplify]: Simplify 0 into 0
14.523 * [backup-simplify]: Simplify 0 into 0
14.524 * [backup-simplify]: Simplify 0 into 0
14.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.525 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.527 * [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
14.527 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.527 * [backup-simplify]: Simplify (- 0) into 0
14.527 * [backup-simplify]: Simplify (+ 0 0) into 0
14.528 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
14.529 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.530 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
14.531 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.531 * [taylor]: Taking taylor expansion of 0 in k
14.532 * [backup-simplify]: Simplify 0 into 0
14.532 * [backup-simplify]: Simplify 0 into 0
14.532 * [backup-simplify]: Simplify 0 into 0
14.532 * [backup-simplify]: Simplify 0 into 0
14.532 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.542 * [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
14.542 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.543 * [backup-simplify]: Simplify (- 0) into 0
14.543 * [backup-simplify]: Simplify (+ 0 0) into 0
14.544 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
14.545 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
14.546 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
14.548 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.548 * [taylor]: Taking taylor expansion of 0 in k
14.548 * [backup-simplify]: Simplify 0 into 0
14.548 * [backup-simplify]: Simplify 0 into 0
14.549 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
14.549 * [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)))
14.549 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
14.549 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
14.549 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
14.549 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
14.549 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
14.549 * [taylor]: Taking taylor expansion of 0.5 in k
14.549 * [backup-simplify]: Simplify 0.5 into 0.5
14.549 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
14.549 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.550 * [taylor]: Taking taylor expansion of k in k
14.550 * [backup-simplify]: Simplify 0 into 0
14.550 * [backup-simplify]: Simplify 1 into 1
14.550 * [backup-simplify]: Simplify (/ 1 1) into 1
14.550 * [taylor]: Taking taylor expansion of 1.0 in k
14.550 * [backup-simplify]: Simplify 1.0 into 1.0
14.550 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
14.550 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
14.550 * [taylor]: Taking taylor expansion of -2.0 in k
14.550 * [backup-simplify]: Simplify -2.0 into -2.0
14.550 * [taylor]: Taking taylor expansion of (/ PI n) in k
14.550 * [taylor]: Taking taylor expansion of PI in k
14.550 * [backup-simplify]: Simplify PI into PI
14.550 * [taylor]: Taking taylor expansion of n in k
14.550 * [backup-simplify]: Simplify n into n
14.550 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
14.550 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
14.550 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
14.550 * [backup-simplify]: Simplify (+ 1 0) into 1
14.551 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
14.551 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
14.551 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
14.551 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
14.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
14.551 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
14.551 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
14.551 * [taylor]: Taking taylor expansion of 0.5 in n
14.551 * [backup-simplify]: Simplify 0.5 into 0.5
14.551 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
14.551 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.551 * [taylor]: Taking taylor expansion of k in n
14.551 * [backup-simplify]: Simplify k into k
14.551 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.551 * [taylor]: Taking taylor expansion of 1.0 in n
14.551 * [backup-simplify]: Simplify 1.0 into 1.0
14.551 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
14.551 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
14.551 * [taylor]: Taking taylor expansion of -2.0 in n
14.551 * [backup-simplify]: Simplify -2.0 into -2.0
14.551 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.551 * [taylor]: Taking taylor expansion of PI in n
14.551 * [backup-simplify]: Simplify PI into PI
14.551 * [taylor]: Taking taylor expansion of n in n
14.551 * [backup-simplify]: Simplify 0 into 0
14.551 * [backup-simplify]: Simplify 1 into 1
14.552 * [backup-simplify]: Simplify (/ PI 1) into PI
14.552 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.553 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.553 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
14.553 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
14.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.555 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
14.555 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
14.555 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
14.555 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
14.555 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
14.555 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
14.555 * [taylor]: Taking taylor expansion of 0.5 in n
14.555 * [backup-simplify]: Simplify 0.5 into 0.5
14.555 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
14.556 * [taylor]: Taking taylor expansion of (/ 1 k) in n
14.556 * [taylor]: Taking taylor expansion of k in n
14.556 * [backup-simplify]: Simplify k into k
14.556 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
14.556 * [taylor]: Taking taylor expansion of 1.0 in n
14.556 * [backup-simplify]: Simplify 1.0 into 1.0
14.556 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
14.556 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
14.556 * [taylor]: Taking taylor expansion of -2.0 in n
14.556 * [backup-simplify]: Simplify -2.0 into -2.0
14.556 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.556 * [taylor]: Taking taylor expansion of PI in n
14.556 * [backup-simplify]: Simplify PI into PI
14.556 * [taylor]: Taking taylor expansion of n in n
14.556 * [backup-simplify]: Simplify 0 into 0
14.556 * [backup-simplify]: Simplify 1 into 1
14.556 * [backup-simplify]: Simplify (/ PI 1) into PI
14.556 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.557 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.557 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
14.557 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
14.558 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.559 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
14.560 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
14.560 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
14.560 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
14.560 * [taylor]: Taking taylor expansion of 0.5 in k
14.560 * [backup-simplify]: Simplify 0.5 into 0.5
14.560 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
14.560 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
14.560 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.560 * [taylor]: Taking taylor expansion of k in k
14.560 * [backup-simplify]: Simplify 0 into 0
14.560 * [backup-simplify]: Simplify 1 into 1
14.560 * [backup-simplify]: Simplify (/ 1 1) into 1
14.560 * [taylor]: Taking taylor expansion of 1.0 in k
14.560 * [backup-simplify]: Simplify 1.0 into 1.0
14.560 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
14.561 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
14.561 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
14.561 * [taylor]: Taking taylor expansion of -2.0 in k
14.561 * [backup-simplify]: Simplify -2.0 into -2.0
14.561 * [taylor]: Taking taylor expansion of PI in k
14.561 * [backup-simplify]: Simplify PI into PI
14.561 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.562 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
14.562 * [taylor]: Taking taylor expansion of (log n) in k
14.562 * [taylor]: Taking taylor expansion of n in k
14.562 * [backup-simplify]: Simplify n into n
14.562 * [backup-simplify]: Simplify (log n) into (log n)
14.562 * [backup-simplify]: Simplify (+ 1 0) into 1
14.562 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
14.563 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
14.564 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
14.565 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
14.565 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
14.566 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
14.567 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.567 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
14.568 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
14.568 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
14.569 * [backup-simplify]: Simplify (+ 0 0) into 0
14.569 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
14.570 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.571 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
14.572 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
14.573 * [taylor]: Taking taylor expansion of 0 in k
14.573 * [backup-simplify]: Simplify 0 into 0
14.573 * [backup-simplify]: Simplify 0 into 0
14.573 * [backup-simplify]: Simplify 0 into 0
14.574 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.575 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.579 * [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
14.579 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.579 * [backup-simplify]: Simplify (+ 0 0) into 0
14.580 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
14.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.584 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
14.586 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.586 * [taylor]: Taking taylor expansion of 0 in k
14.586 * [backup-simplify]: Simplify 0 into 0
14.586 * [backup-simplify]: Simplify 0 into 0
14.586 * [backup-simplify]: Simplify 0 into 0
14.586 * [backup-simplify]: Simplify 0 into 0
14.587 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.589 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.594 * [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
14.595 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
14.595 * [backup-simplify]: Simplify (+ 0 0) into 0
14.596 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
14.598 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
14.600 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
14.602 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.603 * [taylor]: Taking taylor expansion of 0 in k
14.603 * [backup-simplify]: Simplify 0 into 0
14.603 * [backup-simplify]: Simplify 0 into 0
14.604 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
14.604 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
14.604 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k)))
14.604 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
14.604 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
14.604 * [taylor]: Taking taylor expansion of 1.0 in k
14.604 * [backup-simplify]: Simplify 1.0 into 1.0
14.604 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
14.604 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.605 * [taylor]: Taking taylor expansion of k in k
14.605 * [backup-simplify]: Simplify 0 into 0
14.605 * [backup-simplify]: Simplify 1 into 1
14.605 * [backup-simplify]: Simplify (/ 1 1) into 1
14.605 * [backup-simplify]: Simplify (sqrt 0) into 0
14.607 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.607 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
14.607 * [taylor]: Taking taylor expansion of 1.0 in k
14.607 * [backup-simplify]: Simplify 1.0 into 1.0
14.607 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
14.607 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.607 * [taylor]: Taking taylor expansion of k in k
14.607 * [backup-simplify]: Simplify 0 into 0
14.607 * [backup-simplify]: Simplify 1 into 1
14.607 * [backup-simplify]: Simplify (/ 1 1) into 1
14.608 * [backup-simplify]: Simplify (sqrt 0) into 0
14.609 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.609 * [backup-simplify]: Simplify (* 1.0 0) into 0
14.610 * [backup-simplify]: Simplify 0 into 0
14.611 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
14.611 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.612 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
14.615 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.617 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
14.617 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.618 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.622 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.624 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
14.624 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.626 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
14.626 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k))
14.626 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
14.626 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
14.626 * [taylor]: Taking taylor expansion of 1.0 in k
14.626 * [backup-simplify]: Simplify 1.0 into 1.0
14.626 * [taylor]: Taking taylor expansion of (sqrt k) in k
14.626 * [taylor]: Taking taylor expansion of k in k
14.626 * [backup-simplify]: Simplify 0 into 0
14.626 * [backup-simplify]: Simplify 1 into 1
14.627 * [backup-simplify]: Simplify (sqrt 0) into 0
14.628 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.628 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
14.628 * [taylor]: Taking taylor expansion of 1.0 in k
14.628 * [backup-simplify]: Simplify 1.0 into 1.0
14.628 * [taylor]: Taking taylor expansion of (sqrt k) in k
14.628 * [taylor]: Taking taylor expansion of k in k
14.628 * [backup-simplify]: Simplify 0 into 0
14.628 * [backup-simplify]: Simplify 1 into 1
14.628 * [backup-simplify]: Simplify (sqrt 0) into 0
14.629 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
14.629 * [backup-simplify]: Simplify (* 1.0 0) into 0
14.629 * [backup-simplify]: Simplify 0 into 0
14.630 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
14.630 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.632 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.633 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
14.633 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.636 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.637 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
14.637 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.638 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
14.639 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k)))
14.639 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
14.639 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
14.639 * [taylor]: Taking taylor expansion of 1.0 in k
14.639 * [backup-simplify]: Simplify 1.0 into 1.0
14.639 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.639 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.639 * [taylor]: Taking taylor expansion of -1 in k
14.639 * [backup-simplify]: Simplify -1 into -1
14.639 * [taylor]: Taking taylor expansion of k in k
14.639 * [backup-simplify]: Simplify 0 into 0
14.639 * [backup-simplify]: Simplify 1 into 1
14.639 * [backup-simplify]: Simplify (/ -1 1) into -1
14.639 * [backup-simplify]: Simplify (sqrt 0) into 0
14.640 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.641 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
14.641 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
14.641 * [taylor]: Taking taylor expansion of 1.0 in k
14.641 * [backup-simplify]: Simplify 1.0 into 1.0
14.641 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.641 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.641 * [taylor]: Taking taylor expansion of -1 in k
14.641 * [backup-simplify]: Simplify -1 into -1
14.641 * [taylor]: Taking taylor expansion of k in k
14.641 * [backup-simplify]: Simplify 0 into 0
14.641 * [backup-simplify]: Simplify 1 into 1
14.641 * [backup-simplify]: Simplify (/ -1 1) into -1
14.641 * [backup-simplify]: Simplify (sqrt 0) into 0
14.642 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.642 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
14.642 * [backup-simplify]: Simplify +nan.0 into +nan.0
14.643 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.645 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.646 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
14.646 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.649 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.652 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
14.652 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
14.653 * [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)))))
14.653 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1 1)
14.653 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4))
14.653 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0
14.653 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
14.653 * [taylor]: Taking taylor expansion of 1.0 in k
14.653 * [backup-simplify]: Simplify 1.0 into 1.0
14.653 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
14.653 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
14.653 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
14.653 * [taylor]: Taking taylor expansion of 1/4 in k
14.653 * [backup-simplify]: Simplify 1/4 into 1/4
14.653 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
14.653 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.653 * [taylor]: Taking taylor expansion of k in k
14.653 * [backup-simplify]: Simplify 0 into 0
14.653 * [backup-simplify]: Simplify 1 into 1
14.653 * [backup-simplify]: Simplify (/ 1 1) into 1
14.661 * [backup-simplify]: Simplify (log 1) into 0
14.662 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.662 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
14.662 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
14.662 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
14.662 * [taylor]: Taking taylor expansion of 1.0 in k
14.662 * [backup-simplify]: Simplify 1.0 into 1.0
14.662 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
14.662 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
14.662 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
14.662 * [taylor]: Taking taylor expansion of 1/4 in k
14.662 * [backup-simplify]: Simplify 1/4 into 1/4
14.662 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
14.662 * [taylor]: Taking taylor expansion of (/ 1 k) in k
14.662 * [taylor]: Taking taylor expansion of k in k
14.662 * [backup-simplify]: Simplify 0 into 0
14.662 * [backup-simplify]: Simplify 1 into 1
14.663 * [backup-simplify]: Simplify (/ 1 1) into 1
14.663 * [backup-simplify]: Simplify (log 1) into 0
14.664 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.664 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
14.664 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
14.664 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
14.664 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
14.665 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
14.666 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
14.667 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.667 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
14.668 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
14.669 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0
14.669 * [backup-simplify]: Simplify 0 into 0
14.670 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.673 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
14.673 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.674 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
14.676 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.677 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0
14.677 * [backup-simplify]: Simplify 0 into 0
14.678 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.683 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
14.684 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.686 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
14.687 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.689 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0
14.689 * [backup-simplify]: Simplify 0 into 0
14.690 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.698 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
14.699 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.700 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
14.701 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.703 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0
14.703 * [backup-simplify]: Simplify 0 into 0
14.703 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.714 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
14.715 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.716 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
14.719 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.721 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0
14.721 * [backup-simplify]: Simplify 0 into 0
14.722 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.756 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
14.757 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
14.759 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
14.765 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.767 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0
14.767 * [backup-simplify]: Simplify 0 into 0
14.767 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
14.768 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4))
14.768 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0
14.768 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
14.768 * [taylor]: Taking taylor expansion of 1.0 in k
14.768 * [backup-simplify]: Simplify 1.0 into 1.0
14.768 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
14.768 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
14.768 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
14.768 * [taylor]: Taking taylor expansion of 1/4 in k
14.768 * [backup-simplify]: Simplify 1/4 into 1/4
14.768 * [taylor]: Taking taylor expansion of (log k) in k
14.768 * [taylor]: Taking taylor expansion of k in k
14.768 * [backup-simplify]: Simplify 0 into 0
14.768 * [backup-simplify]: Simplify 1 into 1
14.768 * [backup-simplify]: Simplify (log 1) into 0
14.769 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.769 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
14.769 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
14.769 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
14.769 * [taylor]: Taking taylor expansion of 1.0 in k
14.769 * [backup-simplify]: Simplify 1.0 into 1.0
14.769 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
14.769 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
14.769 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
14.769 * [taylor]: Taking taylor expansion of 1/4 in k
14.769 * [backup-simplify]: Simplify 1/4 into 1/4
14.769 * [taylor]: Taking taylor expansion of (log k) in k
14.769 * [taylor]: Taking taylor expansion of k in k
14.769 * [backup-simplify]: Simplify 0 into 0
14.769 * [backup-simplify]: Simplify 1 into 1
14.770 * [backup-simplify]: Simplify (log 1) into 0
14.770 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.770 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
14.770 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
14.770 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
14.771 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
14.772 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
14.772 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.773 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
14.774 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
14.774 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0
14.774 * [backup-simplify]: Simplify 0 into 0
14.777 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
14.778 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.779 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
14.780 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.780 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0
14.780 * [backup-simplify]: Simplify 0 into 0
14.783 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
14.783 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.784 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
14.785 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.786 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0
14.786 * [backup-simplify]: Simplify 0 into 0
14.798 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
14.799 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.800 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
14.801 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.802 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0
14.802 * [backup-simplify]: Simplify 0 into 0
14.818 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
14.819 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.821 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
14.825 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
14.827 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0
14.827 * [backup-simplify]: Simplify 0 into 0
14.850 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
14.850 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
14.852 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
14.855 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
14.856 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0
14.856 * [backup-simplify]: Simplify 0 into 0
14.857 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
14.857 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k)))))
14.857 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0
14.857 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
14.857 * [taylor]: Taking taylor expansion of 1.0 in k
14.857 * [backup-simplify]: Simplify 1.0 into 1.0
14.857 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
14.857 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
14.857 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.857 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.857 * [taylor]: Taking taylor expansion of -1 in k
14.857 * [backup-simplify]: Simplify -1 into -1
14.857 * [taylor]: Taking taylor expansion of k in k
14.857 * [backup-simplify]: Simplify 0 into 0
14.857 * [backup-simplify]: Simplify 1 into 1
14.857 * [backup-simplify]: Simplify (/ -1 1) into -1
14.857 * [backup-simplify]: Simplify (sqrt 0) into 0
14.858 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.859 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
14.859 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
14.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.861 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.862 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
14.863 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
14.864 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
14.864 * [taylor]: Taking taylor expansion of 1.0 in k
14.864 * [backup-simplify]: Simplify 1.0 into 1.0
14.864 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
14.864 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
14.864 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
14.864 * [taylor]: Taking taylor expansion of (/ -1 k) in k
14.864 * [taylor]: Taking taylor expansion of -1 in k
14.864 * [backup-simplify]: Simplify -1 into -1
14.864 * [taylor]: Taking taylor expansion of k in k
14.864 * [backup-simplify]: Simplify 0 into 0
14.864 * [backup-simplify]: Simplify 1 into 1
14.864 * [backup-simplify]: Simplify (/ -1 1) into -1
14.864 * [backup-simplify]: Simplify (sqrt 0) into 0
14.865 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
14.865 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
14.865 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
14.866 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
14.868 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
14.870 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
14.873 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
14.874 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
14.875 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
14.878 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
14.880 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
14.882 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.886 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
14.890 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
14.896 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
14.912 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
14.930 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
14.943 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
14.943 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2 1)
14.944 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
14.944 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
14.944 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
14.944 * [taylor]: Taking taylor expansion of 2.0 in n
14.944 * [backup-simplify]: Simplify 2.0 into 2.0
14.944 * [taylor]: Taking taylor expansion of (* n PI) in n
14.944 * [taylor]: Taking taylor expansion of n in n
14.944 * [backup-simplify]: Simplify 0 into 0
14.944 * [backup-simplify]: Simplify 1 into 1
14.944 * [taylor]: Taking taylor expansion of PI in n
14.944 * [backup-simplify]: Simplify PI into PI
14.944 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
14.944 * [taylor]: Taking taylor expansion of 2.0 in n
14.944 * [backup-simplify]: Simplify 2.0 into 2.0
14.944 * [taylor]: Taking taylor expansion of (* n PI) in n
14.944 * [taylor]: Taking taylor expansion of n in n
14.944 * [backup-simplify]: Simplify 0 into 0
14.944 * [backup-simplify]: Simplify 1 into 1
14.944 * [taylor]: Taking taylor expansion of PI in n
14.944 * [backup-simplify]: Simplify PI into PI
14.945 * [backup-simplify]: Simplify (* 0 PI) into 0
14.945 * [backup-simplify]: Simplify (* 2.0 0) into 0
14.945 * [backup-simplify]: Simplify 0 into 0
14.947 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
14.949 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
14.949 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.950 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
14.952 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
14.952 * [backup-simplify]: Simplify 0 into 0
14.953 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
14.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
14.954 * [backup-simplify]: Simplify 0 into 0
14.956 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
14.957 * [backup-simplify]: Simplify 0 into 0
14.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
14.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
14.960 * [backup-simplify]: Simplify 0 into 0
14.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
14.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
14.963 * [backup-simplify]: Simplify 0 into 0
14.964 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
14.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
14.965 * [backup-simplify]: Simplify 0 into 0
14.965 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
14.966 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
14.966 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
14.966 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
14.966 * [taylor]: Taking taylor expansion of 2.0 in n
14.966 * [backup-simplify]: Simplify 2.0 into 2.0
14.966 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.966 * [taylor]: Taking taylor expansion of PI in n
14.966 * [backup-simplify]: Simplify PI into PI
14.966 * [taylor]: Taking taylor expansion of n in n
14.966 * [backup-simplify]: Simplify 0 into 0
14.966 * [backup-simplify]: Simplify 1 into 1
14.966 * [backup-simplify]: Simplify (/ PI 1) into PI
14.966 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
14.967 * [taylor]: Taking taylor expansion of 2.0 in n
14.967 * [backup-simplify]: Simplify 2.0 into 2.0
14.967 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.967 * [taylor]: Taking taylor expansion of PI in n
14.967 * [backup-simplify]: Simplify PI into PI
14.967 * [taylor]: Taking taylor expansion of n in n
14.967 * [backup-simplify]: Simplify 0 into 0
14.967 * [backup-simplify]: Simplify 1 into 1
14.967 * [backup-simplify]: Simplify (/ PI 1) into PI
14.967 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.968 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
14.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.969 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
14.969 * [backup-simplify]: Simplify 0 into 0
14.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.970 * [backup-simplify]: Simplify 0 into 0
14.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.971 * [backup-simplify]: Simplify 0 into 0
14.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.972 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.972 * [backup-simplify]: Simplify 0 into 0
14.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.974 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
14.974 * [backup-simplify]: Simplify 0 into 0
14.975 * [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
14.976 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
14.976 * [backup-simplify]: Simplify 0 into 0
14.976 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
14.976 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
14.976 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
14.976 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
14.976 * [taylor]: Taking taylor expansion of -2.0 in n
14.976 * [backup-simplify]: Simplify -2.0 into -2.0
14.976 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.976 * [taylor]: Taking taylor expansion of PI in n
14.976 * [backup-simplify]: Simplify PI into PI
14.976 * [taylor]: Taking taylor expansion of n in n
14.976 * [backup-simplify]: Simplify 0 into 0
14.976 * [backup-simplify]: Simplify 1 into 1
14.977 * [backup-simplify]: Simplify (/ PI 1) into PI
14.977 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
14.977 * [taylor]: Taking taylor expansion of -2.0 in n
14.977 * [backup-simplify]: Simplify -2.0 into -2.0
14.977 * [taylor]: Taking taylor expansion of (/ PI n) in n
14.977 * [taylor]: Taking taylor expansion of PI in n
14.977 * [backup-simplify]: Simplify PI into PI
14.977 * [taylor]: Taking taylor expansion of n in n
14.977 * [backup-simplify]: Simplify 0 into 0
14.977 * [backup-simplify]: Simplify 1 into 1
14.977 * [backup-simplify]: Simplify (/ PI 1) into PI
14.978 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.978 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
14.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
14.979 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
14.979 * [backup-simplify]: Simplify 0 into 0
14.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.980 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
14.980 * [backup-simplify]: Simplify 0 into 0
14.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.981 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
14.981 * [backup-simplify]: Simplify 0 into 0
14.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.983 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
14.983 * [backup-simplify]: Simplify 0 into 0
14.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
14.984 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
14.984 * [backup-simplify]: Simplify 0 into 0
14.985 * [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
14.986 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
14.986 * [backup-simplify]: Simplify 0 into 0
14.986 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
14.987 * * * [progress]: simplifying candidates
14.999 * [simplify]: Simplifying:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k))))
  (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k))))
  (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (- (/ 1.0 (sqrt (sqrt k))))
  (- (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1)
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1)
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1)
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1)
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
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  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
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  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) 1)
  (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (expm1 (/ 1.0 (sqrt (sqrt k))))
  (log1p (/ 1.0 (sqrt (sqrt k))))
  (- (log 1.0) (log (sqrt (sqrt k))))
  (log (/ 1.0 (sqrt (sqrt k))))
  (exp (/ 1.0 (sqrt (sqrt k))))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (cbrt (/ 1.0 (sqrt (sqrt k))))
  (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (- 1.0)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt 1)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) 1)
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  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
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  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
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  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
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  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (sqrt (sqrt k)) (cbrt 1.0))
  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (sqrt k)) 1.0)
  (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)
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (* 1.0 (pow (/ 1 k) 1/4))
  (* 1.0 (pow (/ 1 k) 1/4))
  (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
15.023 * * [simplify]: Extracting # 0 : cost  0
15.023 * * [simplify]: Extracting # 1 : cost  0
15.024 * * [simplify]: Extracting # 2 : cost  0
15.025 * * [simplify]: Extracting # 3 : cost  0
15.027 * * [simplify]: Extracting # 4 : cost  0
15.035 * * [simplify]: Extracting # 5 : cost  0
15.036 * * [simplify]: Extracting # 6 : cost  0
15.037 * * [simplify]: Extracting # 7 : cost  0
15.038 * * [simplify]: Extracting # 8 : cost  0
15.039 * * [simplify]: Extracting # 9 : cost  0
15.040 * * [simplify]: Extracting # 10 : cost  0
15.041 * * [simplify]: Extracting # 11 : cost  0
15.042 * * [simplify]: Extracting # 12 : cost  0
15.043 * * [simplify]: Extracting # 13 : cost  0
15.044 * * [simplify]: iteration  0 :  566  enodes  (cost  9021 )
15.300 * * [simplify]: Extracting # 0 : cost  0
15.302 * * [simplify]: Extracting # 1 : cost  0
15.311 * * [simplify]: Extracting # 2 : cost  0
15.315 * * [simplify]: Extracting # 3 : cost  0
15.319 * * [simplify]: Extracting # 4 : cost  0
15.322 * * [simplify]: Extracting # 5 : cost  0
15.327 * * [simplify]: iteration  1 :  1341  enodes  (cost  7684 )
16.004 * * [simplify]: Extracting # 0 : cost  0
16.009 * * [simplify]: Extracting # 1 : cost  0
16.014 * * [simplify]: Extracting # 2 : cost  0
16.021 * * [simplify]: Extracting # 3 : cost  0
16.028 * * [simplify]: Extracting # 4 : cost  0
16.035 * * [simplify]: iteration  2 :  3109  enodes  (cost  7109 )
17.257 * * [simplify]: Extracting # 0 : cost  0
17.269 * * [simplify]: Extracting # 1 : cost  0
17.280 * * [simplify]: Extracting # 2 : cost  0
17.291 * * [simplify]: Extracting # 3 : cost  0
17.302 * * [simplify]: Extracting # 4 : cost  0
17.313 * * [simplify]: iteration done:  5000  enodes  (cost  6936 )
17.320 * [simplify]: Simplified to:
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 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))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 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 (* n PI)) (+ (sqrt 1.0) (sqrt k)))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (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 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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (pow (/ 1.0 (sqrt k)) 3)
  (pow (/ 1.0 (sqrt k)) 3)
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (pow (/ 1.0 (sqrt k)) 3)
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- (/ 1.0 (sqrt (sqrt k))))
  (- (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (fabs (cbrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (fabs (cbrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (pow (cbrt (sqrt (sqrt k))) 3)) (cbrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (fabs (cbrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (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 (fabs (cbrt k)))) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (sqrt (fabs (cbrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (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 (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (pow (sqrt (sqrt (sqrt k))) 3))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (pow (cbrt (sqrt (sqrt k))) 3)))
  (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (* (sqrt (fabs (cbrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
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  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (fabs (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (fabs (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1.0 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1.0 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1.0)
  (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (fabs (cbrt (sqrt k))))
  (/ 1.0 (sqrt (fabs (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1.0
  (/ (sqrt (sqrt k)) (cbrt 1.0))
  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (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 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* (* 2.0 PI) n))
  (pow (* 2.0 (* n PI)) 3)
  (pow (* 2.0 (* n PI)) 3)
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (pow (* 2.0 (* n PI)) 3)
  (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)
  (* n PI)
  (fma (- 0.5) (* k (fma (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5) (* (log n) (pow (* 2.0 (* n PI)) 0.5)))) (fma (* 0.125 (pow k 2)) (fma (pow (log (* 2.0 PI)) 2) (pow (* 2.0 (* n PI)) 0.5) (* (pow (log n) 2) (pow (* 2.0 (* n PI)) 0.5))) (fma (* 0.25 (pow k 2)) (* (log n) (* (log (* 2.0 PI)) (pow (* 2.0 (* n PI)) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))
  (pow (pow (* 2.0 (* n PI)) 0.5) (- 1.0 k))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (fma +nan.0 (- k) (fma +nan.0 (pow k 2) (- +nan.0)))
  (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) (/ +nan.0 (pow k 3))))
  (+ (/ (- +nan.0) (pow k 2)) (- (/ +nan.0 k) +nan.0))
  (* 1.0 (pow (/ 1 k) 1/4))
  (* 1.0 (pow (/ 1 k) 1/4))
  (- (fma (sqrt +nan.0) 1.0 (- (/ +nan.0 (* (sqrt +nan.0) k)) (/ +nan.0 (* (pow (sqrt +nan.0) 3) (pow k 2))))) (/ +nan.0 (* (sqrt +nan.0) (pow k 2))))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
17.336 * * * [progress]: adding candidates to table
18.771 * [progress]: [Phase 3 of 3] Extracting.
18.771 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt 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) (* (/ 1.0 (sqrt k)) (cbrt (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3))))> #<alt (λ (k n) (* (sqrt (* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (cbrt (/ (pow 1.0 3) (* k (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
18.777 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
18.777 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt 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) (* (/ 1.0 (sqrt k)) (cbrt (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3))))> #<alt (λ (k n) (* (sqrt (* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (cbrt (/ (pow 1.0 3) (* k (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
18.830 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt 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) (* (/ 1.0 (sqrt k)) (cbrt (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3))))> #<alt (λ (k n) (* (sqrt (* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (cbrt (/ (pow 1.0 3) (* k (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
18.885 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt 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) (* (/ 1.0 (sqrt k)) (cbrt (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3))))> #<alt (λ (k n) (* (sqrt (* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k)))))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (* (cbrt (/ (pow 1.0 3) (* k (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
18.934 * * * [regime]: Found split indices: #<option (#s(si 6 255))>
18.934 * [simplify]: Simplifying:
  (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
18.934 * * [simplify]: Extracting # 0 : cost  0
18.934 * * [simplify]: Extracting # 1 : cost  0
18.934 * * [simplify]: Extracting # 2 : cost  0
18.934 * * [simplify]: Extracting # 3 : cost  0
18.934 * * [simplify]: Extracting # 4 : cost  0
18.935 * * [simplify]: Extracting # 5 : cost  0
18.935 * * [simplify]: Extracting # 6 : cost  0
18.935 * * [simplify]: Extracting # 7 : cost  0
18.935 * * [simplify]: Extracting # 8 : cost  0
18.935 * * [simplify]: Extracting # 9 : cost  0
18.935 * * [simplify]: iteration  0 :  19  enodes  (cost  28 )
18.937 * * [simplify]: Extracting # 0 : cost  0
18.938 * * [simplify]: iteration  1 :  23  enodes  (cost  28 )
18.939 * * [simplify]: Extracting # 0 : cost  0
18.940 * * [simplify]: iteration done:  23  enodes  (cost  28 )
18.940 * [simplify]: Simplified to:
  (* (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
26.365 * [regime-testing]: Baseline error score: 0.43863222890738507
26.369 * [regime-testing]: Oracle error score: 0.07141700993955376
26.378 * [regime-testing]: End program error score: 0.43863222890738507